9 """Z3 is a high performance theorem prover developed at Microsoft Research.
11 Z3 is used in many applications such as: software/hardware verification and testing,
12 constraint solving, analysis of hybrid systems, security, biology (in silico analysis),
13 and geometrical problems.
16 Please send feedback, comments and/or corrections on the Issue tracker for
17 https://github.com/Z3prover/z3.git. Your comments are very valuable.
38 ... x = BitVec('x', 32)
40 ... # the expression x + y is type incorrect
42 ... except Z3Exception as ex:
43 ... print("failed: %s" % ex)
48 from .z3types
import *
49 from .z3consts
import *
50 from .z3printer
import *
51 from fractions
import Fraction
56 if sys.version_info.major >= 3:
57 from typing
import Iterable
67 if sys.version_info.major < 3:
69 return isinstance(v, (int, long))
72 return isinstance(v, int)
84 major = ctypes.c_uint(0)
85 minor = ctypes.c_uint(0)
86 build = ctypes.c_uint(0)
87 rev = ctypes.c_uint(0)
89 return "%s.%s.%s" % (major.value, minor.value, build.value)
93 major = ctypes.c_uint(0)
94 minor = ctypes.c_uint(0)
95 build = ctypes.c_uint(0)
96 rev = ctypes.c_uint(0)
98 return (major.value, minor.value, build.value, rev.value)
105 def _z3_assert(cond, msg):
107 raise Z3Exception(msg)
110 def _z3_check_cint_overflow(n, name):
111 _z3_assert(ctypes.c_int(n).value == n, name +
" is too large")
115 """Log interaction to a file. This function must be invoked immediately after init(). """
120 """Append user-defined string to interaction log. """
125 """Convert an integer or string into a Z3 symbol."""
132 def _symbol2py(ctx, s):
133 """Convert a Z3 symbol back into a Python object. """
146 if len(args) == 1
and (isinstance(args[0], tuple)
or isinstance(args[0], list)):
148 elif len(args) == 1
and (isinstance(args[0], set)
or isinstance(args[0], AstVector)):
149 return [arg
for arg
in args[0]]
158 def _get_args_ast_list(args):
160 if isinstance(args, (set, AstVector, tuple)):
161 return [arg
for arg
in args]
168 def _to_param_value(val):
169 if isinstance(val, bool):
170 return "true" if val
else "false"
181 """A Context manages all other Z3 objects, global configuration options, etc.
183 Z3Py uses a default global context. For most applications this is sufficient.
184 An application may use multiple Z3 contexts. Objects created in one context
185 cannot be used in another one. However, several objects may be "translated" from
186 one context to another. It is not safe to access Z3 objects from multiple threads.
187 The only exception is the method `interrupt()` that can be used to interrupt() a long
189 The initialization method receives global configuration options for the new context.
194 _z3_assert(len(args) % 2 == 0,
"Argument list must have an even number of elements.")
213 if Z3_del_context
is not None and self.
owner:
219 """Return a reference to the actual C pointer to the Z3 context."""
223 """Interrupt a solver performing a satisfiability test, a tactic processing a goal, or simplify functions.
225 This method can be invoked from a thread different from the one executing the
226 interruptible procedure.
231 """Return the global parameter description set."""
240 """Return a reference to the global Z3 context.
243 >>> x.ctx == main_ctx()
248 >>> x2 = Real('x', c)
255 if _main_ctx
is None:
272 """Set Z3 global (or module) parameters.
274 >>> set_param(precision=10)
277 _z3_assert(len(args) % 2 == 0,
"Argument list must have an even number of elements.")
281 if not set_pp_option(k, v):
296 """Reset all global (or module) parameters.
302 """Alias for 'set_param' for backward compatibility.
308 """Return the value of a Z3 global (or module) parameter
310 >>> get_param('nlsat.reorder')
313 ptr = (ctypes.c_char_p * 1)()
315 r = z3core._to_pystr(ptr[0])
317 raise Z3Exception(
"failed to retrieve value for '%s'" % name)
329 """Superclass for all Z3 objects that have support for pretty printing."""
334 def _repr_html_(self):
335 in_html = in_html_mode()
338 set_html_mode(in_html)
343 """AST are Direct Acyclic Graphs (DAGs) used to represent sorts, declarations and expressions."""
351 if self.ctx.ref()
is not None and self.
ast is not None and Z3_dec_ref
is not None:
356 return _to_ast_ref(self.
ast, self.
ctx)
359 return obj_to_string(self)
362 return obj_to_string(self)
365 return self.
eq(other)
378 elif is_eq(self)
and self.num_args() == 2:
379 return self.arg(0).
eq(self.arg(1))
381 raise Z3Exception(
"Symbolic expressions cannot be cast to concrete Boolean values.")
384 """Return a string representing the AST node in s-expression notation.
387 >>> ((x + 1)*x).sexpr()
393 """Return a pointer to the corresponding C Z3_ast object."""
397 """Return unique identifier for object. It can be used for hash-tables and maps."""
401 """Return a reference to the C context where this AST node is stored."""
402 return self.ctx.ref()
405 """Return `True` if `self` and `other` are structurally identical.
412 >>> n1 = simplify(n1)
413 >>> n2 = simplify(n2)
418 _z3_assert(
is_ast(other),
"Z3 AST expected")
422 """Translate `self` to the context `target`. That is, return a copy of `self` in the context `target`.
428 >>> # Nodes in different contexts can't be mixed.
429 >>> # However, we can translate nodes from one context to another.
430 >>> x.translate(c2) + y
434 _z3_assert(isinstance(target, Context),
"argument must be a Z3 context")
441 """Return a hashcode for the `self`.
443 >>> n1 = simplify(Int('x') + 1)
444 >>> n2 = simplify(2 + Int('x') - 1)
445 >>> n1.hash() == n2.hash()
452 """Return `True` if `a` is an AST node.
456 >>> is_ast(IntVal(10))
460 >>> is_ast(BoolSort())
462 >>> is_ast(Function('f', IntSort(), IntSort()))
469 return isinstance(a, AstRef)
473 """Return `True` if `a` and `b` are structurally identical AST nodes.
483 >>> eq(simplify(x + 1), simplify(1 + x))
491 def _ast_kind(ctx, a):
497 def _ctx_from_ast_arg_list(args, default_ctx=None):
505 _z3_assert(ctx == a.ctx,
"Context mismatch")
511 def _ctx_from_ast_args(*args):
512 return _ctx_from_ast_arg_list(args)
515 def _to_func_decl_array(args):
517 _args = (FuncDecl * sz)()
519 _args[i] = args[i].as_func_decl()
523 def _to_ast_array(args):
527 _args[i] = args[i].as_ast()
531 def _to_ref_array(ref, args):
535 _args[i] = args[i].as_ast()
539 def _to_ast_ref(a, ctx):
540 k = _ast_kind(ctx, a)
542 return _to_sort_ref(a, ctx)
543 elif k == Z3_FUNC_DECL_AST:
544 return _to_func_decl_ref(a, ctx)
546 return _to_expr_ref(a, ctx)
555 def _sort_kind(ctx, s):
560 """A Sort is essentially a type. Every Z3 expression has a sort. A sort is an AST node."""
569 """Return the Z3 internal kind of a sort.
570 This method can be used to test if `self` is one of the Z3 builtin sorts.
573 >>> b.kind() == Z3_BOOL_SORT
575 >>> b.kind() == Z3_INT_SORT
577 >>> A = ArraySort(IntSort(), IntSort())
578 >>> A.kind() == Z3_ARRAY_SORT
580 >>> A.kind() == Z3_INT_SORT
583 return _sort_kind(self.
ctx, self.
ast)
586 """Return `True` if `self` is a subsort of `other`.
588 >>> IntSort().subsort(RealSort())
594 """Try to cast `val` as an element of sort `self`.
596 This method is used in Z3Py to convert Python objects such as integers,
597 floats, longs and strings into Z3 expressions.
600 >>> RealSort().cast(x)
604 _z3_assert(
is_expr(val),
"Z3 expression expected")
605 _z3_assert(self.
eq(val.sort()),
"Sort mismatch")
609 """Return the name (string) of sort `self`.
611 >>> BoolSort().name()
613 >>> ArraySort(IntSort(), IntSort()).name()
619 """Return `True` if `self` and `other` are the same Z3 sort.
622 >>> p.sort() == BoolSort()
624 >>> p.sort() == IntSort()
632 """Return `True` if `self` and `other` are not the same Z3 sort.
635 >>> p.sort() != BoolSort()
637 >>> p.sort() != IntSort()
644 return AstRef.__hash__(self)
648 """Return `True` if `s` is a Z3 sort.
650 >>> is_sort(IntSort())
652 >>> is_sort(Int('x'))
654 >>> is_expr(Int('x'))
657 return isinstance(s, SortRef)
660 def _to_sort_ref(s, ctx):
662 _z3_assert(isinstance(s, Sort),
"Z3 Sort expected")
663 k = _sort_kind(ctx, s)
664 if k == Z3_BOOL_SORT:
666 elif k == Z3_INT_SORT
or k == Z3_REAL_SORT:
668 elif k == Z3_BV_SORT:
670 elif k == Z3_ARRAY_SORT:
672 elif k == Z3_DATATYPE_SORT:
674 elif k == Z3_FINITE_DOMAIN_SORT:
676 elif k == Z3_FLOATING_POINT_SORT:
678 elif k == Z3_ROUNDING_MODE_SORT:
680 elif k == Z3_RE_SORT:
682 elif k == Z3_SEQ_SORT:
684 elif k == Z3_CHAR_SORT:
690 return _to_sort_ref(
Z3_get_sort(ctx.ref(), a), ctx)
694 """Create a new uninterpreted sort named `name`.
696 If `ctx=None`, then the new sort is declared in the global Z3Py context.
698 >>> A = DeclareSort('A')
699 >>> a = Const('a', A)
700 >>> b = Const('b', A)
719 """Function declaration. Every constant and function have an associated declaration.
721 The declaration assigns a name, a sort (i.e., type), and for function
722 the sort (i.e., type) of each of its arguments. Note that, in Z3,
723 a constant is a function with 0 arguments.
736 """Return the name of the function declaration `self`.
738 >>> f = Function('f', IntSort(), IntSort())
741 >>> isinstance(f.name(), str)
747 """Return the number of arguments of a function declaration.
748 If `self` is a constant, then `self.arity()` is 0.
750 >>> f = Function('f', IntSort(), RealSort(), BoolSort())
757 """Return the sort of the argument `i` of a function declaration.
758 This method assumes that `0 <= i < self.arity()`.
760 >>> f = Function('f', IntSort(), RealSort(), BoolSort())
769 """Return the sort of the range of a function declaration.
770 For constants, this is the sort of the constant.
772 >>> f = Function('f', IntSort(), RealSort(), BoolSort())
779 """Return the internal kind of a function declaration.
780 It can be used to identify Z3 built-in functions such as addition, multiplication, etc.
783 >>> d = (x + 1).decl()
784 >>> d.kind() == Z3_OP_ADD
786 >>> d.kind() == Z3_OP_MUL
794 result = [
None for i
in range(n)]
797 if k == Z3_PARAMETER_INT:
799 elif k == Z3_PARAMETER_DOUBLE:
801 elif k == Z3_PARAMETER_RATIONAL:
803 elif k == Z3_PARAMETER_SYMBOL:
805 elif k == Z3_PARAMETER_SORT:
807 elif k == Z3_PARAMETER_AST:
809 elif k == Z3_PARAMETER_FUNC_DECL:
816 """Create a Z3 application expression using the function `self`, and the given arguments.
818 The arguments must be Z3 expressions. This method assumes that
819 the sorts of the elements in `args` match the sorts of the
820 domain. Limited coercion is supported. For example, if
821 args[0] is a Python integer, and the function expects a Z3
822 integer, then the argument is automatically converted into a
825 >>> f = Function('f', IntSort(), RealSort(), BoolSort())
833 args = _get_args(args)
835 _args = (Ast * num)()
840 tmp = self.
domain(i).cast(args[i])
842 _args[i] = tmp.as_ast()
847 """Return `True` if `a` is a Z3 function declaration.
849 >>> f = Function('f', IntSort(), IntSort())
856 return isinstance(a, FuncDeclRef)
860 """Create a new Z3 uninterpreted function with the given sorts.
862 >>> f = Function('f', IntSort(), IntSort())
868 _z3_assert(len(sig) > 0,
"At least two arguments expected")
872 _z3_assert(
is_sort(rng),
"Z3 sort expected")
873 dom = (Sort * arity)()
874 for i
in range(arity):
876 _z3_assert(
is_sort(sig[i]),
"Z3 sort expected")
883 """Create a new fresh Z3 uninterpreted function with the given sorts.
887 _z3_assert(len(sig) > 0,
"At least two arguments expected")
891 _z3_assert(
is_sort(rng),
"Z3 sort expected")
892 dom = (z3.Sort * arity)()
893 for i
in range(arity):
895 _z3_assert(
is_sort(sig[i]),
"Z3 sort expected")
901 def _to_func_decl_ref(a, ctx):
906 """Create a new Z3 recursive with the given sorts."""
909 _z3_assert(len(sig) > 0,
"At least two arguments expected")
913 _z3_assert(
is_sort(rng),
"Z3 sort expected")
914 dom = (Sort * arity)()
915 for i
in range(arity):
917 _z3_assert(
is_sort(sig[i]),
"Z3 sort expected")
924 """Set the body of a recursive function.
925 Recursive definitions can be simplified if they are applied to ground
928 >>> fac = RecFunction('fac', IntSort(ctx), IntSort(ctx))
929 >>> n = Int('n', ctx)
930 >>> RecAddDefinition(fac, n, If(n == 0, 1, n*fac(n-1)))
933 >>> s = Solver(ctx=ctx)
934 >>> s.add(fac(n) < 3)
937 >>> s.model().eval(fac(5))
943 args = _get_args(args)
947 _args[i] = args[i].ast
958 """Constraints, formulas and terms are expressions in Z3.
960 Expressions are ASTs. Every expression has a sort.
961 There are three main kinds of expressions:
962 function applications, quantifiers and bounded variables.
963 A constant is a function application with 0 arguments.
964 For quantifier free problems, all expressions are
965 function applications.
975 """Return the sort of expression `self`.
987 """Shorthand for `self.sort().kind()`.
989 >>> a = Array('a', IntSort(), IntSort())
990 >>> a.sort_kind() == Z3_ARRAY_SORT
992 >>> a.sort_kind() == Z3_INT_SORT
995 return self.
sort().kind()
998 """Return a Z3 expression that represents the constraint `self == other`.
1000 If `other` is `None`, then this method simply returns `False`.
1011 a, b = _coerce_exprs(self, other)
1016 return AstRef.__hash__(self)
1019 """Return a Z3 expression that represents the constraint `self != other`.
1021 If `other` is `None`, then this method simply returns `True`.
1032 a, b = _coerce_exprs(self, other)
1033 _args, sz = _to_ast_array((a, b))
1040 """Return the Z3 function declaration associated with a Z3 application.
1042 >>> f = Function('f', IntSort(), IntSort())
1051 _z3_assert(
is_app(self),
"Z3 application expected")
1055 """Return the number of arguments of a Z3 application.
1059 >>> (a + b).num_args()
1061 >>> f = Function('f', IntSort(), IntSort(), IntSort(), IntSort())
1067 _z3_assert(
is_app(self),
"Z3 application expected")
1071 """Return argument `idx` of the application `self`.
1073 This method assumes that `self` is a function application with at least `idx+1` arguments.
1077 >>> f = Function('f', IntSort(), IntSort(), IntSort(), IntSort())
1087 _z3_assert(
is_app(self),
"Z3 application expected")
1088 _z3_assert(idx < self.
num_args(),
"Invalid argument index")
1092 """Return a list containing the children of the given expression
1096 >>> f = Function('f', IntSort(), IntSort(), IntSort(), IntSort())
1116 """inverse function to the serialize method on ExprRef.
1117 It is made available to make it easier for users to serialize expressions back and forth between
1118 strings. Solvers can be serialized using the 'sexpr()' method.
1122 if len(s.assertions()) != 1:
1123 raise Z3Exception(
"single assertion expected")
1124 fml = s.assertions()[0]
1125 if fml.num_args() != 1:
1126 raise Z3Exception(
"dummy function 'F' expected")
1129 def _to_expr_ref(a, ctx):
1130 if isinstance(a, Pattern):
1134 if k == Z3_QUANTIFIER_AST:
1137 if sk == Z3_BOOL_SORT:
1139 if sk == Z3_INT_SORT:
1140 if k == Z3_NUMERAL_AST:
1143 if sk == Z3_REAL_SORT:
1144 if k == Z3_NUMERAL_AST:
1146 if _is_algebraic(ctx, a):
1149 if sk == Z3_BV_SORT:
1150 if k == Z3_NUMERAL_AST:
1154 if sk == Z3_ARRAY_SORT:
1156 if sk == Z3_DATATYPE_SORT:
1158 if sk == Z3_FLOATING_POINT_SORT:
1159 if k == Z3_APP_AST
and _is_numeral(ctx, a):
1162 return FPRef(a, ctx)
1163 if sk == Z3_FINITE_DOMAIN_SORT:
1164 if k == Z3_NUMERAL_AST:
1168 if sk == Z3_ROUNDING_MODE_SORT:
1170 if sk == Z3_SEQ_SORT:
1172 if sk == Z3_CHAR_SORT:
1174 if sk == Z3_RE_SORT:
1175 return ReRef(a, ctx)
1179 def _coerce_expr_merge(s, a):
1192 _z3_assert(s1.ctx == s.ctx,
"context mismatch")
1193 _z3_assert(
False,
"sort mismatch")
1198 def _coerce_exprs(a, b, ctx=None):
1200 a = _py2expr(a, ctx)
1201 b = _py2expr(b, ctx)
1202 if isinstance(a, str)
and isinstance(b, SeqRef):
1204 if isinstance(b, str)
and isinstance(a, SeqRef):
1206 if isinstance(a, float)
and isinstance(b, ArithRef):
1208 if isinstance(b, float)
and isinstance(a, ArithRef):
1212 s = _coerce_expr_merge(s, a)
1213 s = _coerce_expr_merge(s, b)
1219 def _reduce(func, sequence, initial):
1221 for element
in sequence:
1222 result = func(result, element)
1226 def _coerce_expr_list(alist, ctx=None):
1233 alist = [_py2expr(a, ctx)
for a
in alist]
1234 s = _reduce(_coerce_expr_merge, alist,
None)
1235 return [s.cast(a)
for a
in alist]
1239 """Return `True` if `a` is a Z3 expression.
1246 >>> is_expr(IntSort())
1250 >>> is_expr(IntVal(1))
1253 >>> is_expr(ForAll(x, x >= 0))
1255 >>> is_expr(FPVal(1.0))
1258 return isinstance(a, ExprRef)
1262 """Return `True` if `a` is a Z3 function application.
1264 Note that, constants are function applications with 0 arguments.
1271 >>> is_app(IntSort())
1275 >>> is_app(IntVal(1))
1278 >>> is_app(ForAll(x, x >= 0))
1281 if not isinstance(a, ExprRef):
1283 k = _ast_kind(a.ctx, a)
1284 return k == Z3_NUMERAL_AST
or k == Z3_APP_AST
1288 """Return `True` if `a` is Z3 constant/variable expression.
1297 >>> is_const(IntVal(1))
1300 >>> is_const(ForAll(x, x >= 0))
1303 return is_app(a)
and a.num_args() == 0
1307 """Return `True` if `a` is variable.
1309 Z3 uses de-Bruijn indices for representing bound variables in
1317 >>> f = Function('f', IntSort(), IntSort())
1318 >>> # Z3 replaces x with bound variables when ForAll is executed.
1319 >>> q = ForAll(x, f(x) == x)
1325 >>> is_var(b.arg(1))
1328 return is_expr(a)
and _ast_kind(a.ctx, a) == Z3_VAR_AST
1332 """Return the de-Bruijn index of the Z3 bounded variable `a`.
1340 >>> f = Function('f', IntSort(), IntSort(), IntSort())
1341 >>> # Z3 replaces x and y with bound variables when ForAll is executed.
1342 >>> q = ForAll([x, y], f(x, y) == x + y)
1344 f(Var(1), Var(0)) == Var(1) + Var(0)
1348 >>> v1 = b.arg(0).arg(0)
1349 >>> v2 = b.arg(0).arg(1)
1354 >>> get_var_index(v1)
1356 >>> get_var_index(v2)
1360 _z3_assert(
is_var(a),
"Z3 bound variable expected")
1365 """Return `True` if `a` is an application of the given kind `k`.
1369 >>> is_app_of(n, Z3_OP_ADD)
1371 >>> is_app_of(n, Z3_OP_MUL)
1374 return is_app(a)
and a.decl().kind() == k
1377 def If(a, b, c, ctx=None):
1378 """Create a Z3 if-then-else expression.
1382 >>> max = If(x > y, x, y)
1388 if isinstance(a, Probe)
or isinstance(b, Tactic)
or isinstance(c, Tactic):
1389 return Cond(a, b, c, ctx)
1391 ctx = _get_ctx(_ctx_from_ast_arg_list([a, b, c], ctx))
1394 b, c = _coerce_exprs(b, c, ctx)
1396 _z3_assert(a.ctx == b.ctx,
"Context mismatch")
1397 return _to_expr_ref(
Z3_mk_ite(ctx.ref(), a.as_ast(), b.as_ast(), c.as_ast()), ctx)
1401 """Create a Z3 distinct expression.
1408 >>> Distinct(x, y, z)
1410 >>> simplify(Distinct(x, y, z))
1412 >>> simplify(Distinct(x, y, z), blast_distinct=True)
1413 And(Not(x == y), Not(x == z), Not(y == z))
1415 args = _get_args(args)
1416 ctx = _ctx_from_ast_arg_list(args)
1418 _z3_assert(ctx
is not None,
"At least one of the arguments must be a Z3 expression")
1419 args = _coerce_expr_list(args, ctx)
1420 _args, sz = _to_ast_array(args)
1424 def _mk_bin(f, a, b):
1427 _z3_assert(a.ctx == b.ctx,
"Context mismatch")
1428 args[0] = a.as_ast()
1429 args[1] = b.as_ast()
1430 return f(a.ctx.ref(), 2, args)
1434 """Create a constant of the given sort.
1436 >>> Const('x', IntSort())
1440 _z3_assert(isinstance(sort, SortRef),
"Z3 sort expected")
1446 """Create several constants of the given sort.
1448 `names` is a string containing the names of all constants to be created.
1449 Blank spaces separate the names of different constants.
1451 >>> x, y, z = Consts('x y z', IntSort())
1455 if isinstance(names, str):
1456 names = names.split(
" ")
1457 return [
Const(name, sort)
for name
in names]
1461 """Create a fresh constant of a specified sort"""
1462 ctx = _get_ctx(sort.ctx)
1467 """Create a Z3 free variable. Free variables are used to create quantified formulas.
1468 A free variable with index n is bound when it occurs within the scope of n+1 quantified
1471 >>> Var(0, IntSort())
1473 >>> eq(Var(0, IntSort()), Var(0, BoolSort()))
1477 _z3_assert(
is_sort(s),
"Z3 sort expected")
1478 return _to_expr_ref(
Z3_mk_bound(s.ctx_ref(), idx, s.ast), s.ctx)
1483 Create a real free variable. Free variables are used to create quantified formulas.
1484 They are also used to create polynomials.
1494 Create a list of Real free variables.
1495 The variables have ids: 0, 1, ..., n-1
1497 >>> x0, x1, x2, x3 = RealVarVector(4)
1514 """Try to cast `val` as a Boolean.
1516 >>> x = BoolSort().cast(True)
1526 if isinstance(val, bool):
1530 msg =
"True, False or Z3 Boolean expression expected. Received %s of type %s"
1531 _z3_assert(
is_expr(val), msg % (val, type(val)))
1532 if not self.
eq(val.sort()):
1533 _z3_assert(self.
eq(val.sort()),
"Value cannot be converted into a Z3 Boolean value")
1537 return isinstance(other, ArithSortRef)
1547 """All Boolean expressions are instances of this class."""
1556 """Create the Z3 expression `self * other`.
1558 if isinstance(other, int)
and other == 1:
1559 return If(self, 1, 0)
1560 if isinstance(other, int)
and other == 0:
1562 if isinstance(other, BoolRef):
1563 other =
If(other, 1, 0)
1564 return If(self, other, 0)
1568 """Return `True` if `a` is a Z3 Boolean expression.
1574 >>> is_bool(And(p, q))
1582 return isinstance(a, BoolRef)
1586 """Return `True` if `a` is the Z3 true expression.
1591 >>> is_true(simplify(p == p))
1596 >>> # True is a Python Boolean expression
1604 """Return `True` if `a` is the Z3 false expression.
1611 >>> is_false(BoolVal(False))
1618 """Return `True` if `a` is a Z3 and expression.
1620 >>> p, q = Bools('p q')
1621 >>> is_and(And(p, q))
1623 >>> is_and(Or(p, q))
1630 """Return `True` if `a` is a Z3 or expression.
1632 >>> p, q = Bools('p q')
1635 >>> is_or(And(p, q))
1642 """Return `True` if `a` is a Z3 implication expression.
1644 >>> p, q = Bools('p q')
1645 >>> is_implies(Implies(p, q))
1647 >>> is_implies(And(p, q))
1654 """Return `True` if `a` is a Z3 not expression.
1666 """Return `True` if `a` is a Z3 equality expression.
1668 >>> x, y = Ints('x y')
1676 """Return `True` if `a` is a Z3 distinct expression.
1678 >>> x, y, z = Ints('x y z')
1679 >>> is_distinct(x == y)
1681 >>> is_distinct(Distinct(x, y, z))
1688 """Return the Boolean Z3 sort. If `ctx=None`, then the global context is used.
1692 >>> p = Const('p', BoolSort())
1695 >>> r = Function('r', IntSort(), IntSort(), BoolSort())
1702 return BoolSortRef(Z3_mk_bool_sort(ctx.ref()), ctx)
1705 def BoolVal(val, ctx=None):
1706 """Return the Boolean value `
True`
or `
False`. If `ctx=
None`, then the
global context
is used.
1719 return BoolRef(Z3_mk_true(ctx.ref()), ctx)
1721 return BoolRef(Z3_mk_false(ctx.ref()), ctx)
1724 def Bool(name, ctx=None):
1725 """Return a Boolean constant named `name`. If `ctx=
None`, then the
global context
is used.
1733 return BoolRef(Z3_mk_const(ctx.ref(), to_symbol(name, ctx), BoolSort(ctx).ast), ctx)
1736 def Bools(names, ctx=None):
1737 """Return a tuple of Boolean constants.
1739 `names`
is a single string containing all names separated by blank spaces.
1740 If `ctx=
None`, then the
global context
is used.
1742 >>> p, q, r =
Bools(
'p q r')
1743 >>>
And(p,
Or(q, r))
1747 if isinstance(names, str):
1748 names = names.split(" ")
1749 return [Bool(name, ctx) for name in names]
1752 def BoolVector(prefix, sz, ctx=None):
1753 """Return a list of Boolean constants of size `sz`.
1755 The constants are named using the given prefix.
1756 If `ctx=
None`, then the
global context
is used.
1762 And(p__0, p__1, p__2)
1764 return [Bool("%s__%s" % (prefix, i)) for i in range(sz)]
1767 def FreshBool(prefix="b", ctx=None):
1768 """Return a fresh Boolean constant
in the given context using the given prefix.
1770 If `ctx=
None`, then the
global context
is used.
1778 return BoolRef(Z3_mk_fresh_const(ctx.ref(), prefix, BoolSort(ctx).ast), ctx)
1781 def Implies(a, b, ctx=None):
1782 """Create a Z3 implies expression.
1784 >>> p, q =
Bools(
'p q')
1788 ctx = _get_ctx(_ctx_from_ast_arg_list([a, b], ctx))
1792 return BoolRef(Z3_mk_implies(ctx.ref(), a.as_ast(), b.as_ast()), ctx)
1795 def Xor(a, b, ctx=None):
1796 """Create a Z3 Xor expression.
1798 >>> p, q =
Bools(
'p q')
1804 ctx = _get_ctx(_ctx_from_ast_arg_list([a, b], ctx))
1808 return BoolRef(Z3_mk_xor(ctx.ref(), a.as_ast(), b.as_ast()), ctx)
1811 def Not(a, ctx=None):
1812 """Create a Z3
not expression
or probe.
1820 ctx = _get_ctx(_ctx_from_ast_arg_list([a], ctx))
1822 # Not is also used to build probes
1823 return Probe(Z3_probe_not(ctx.ref(), a.probe), ctx)
1827 return BoolRef(Z3_mk_not(ctx.ref(), a.as_ast()), ctx)
1837 def _has_probe(args):
1838 """Return `
True`
if one of the elements of the given collection
is a Z3 probe.
"""
1846 """Create a Z3
and-expression
or and-probe.
1848 >>> p, q, r =
Bools(
'p q r')
1853 And(p__0, p__1, p__2, p__3, p__4)
1857 last_arg = args[len(args) - 1]
1858 if isinstance(last_arg, Context):
1859 ctx = args[len(args) - 1]
1860 args = args[:len(args) - 1]
1861 elif len(args) == 1 and isinstance(args[0], AstVector):
1863 args = [a for a in args[0]]
1866 args = _get_args(args)
1867 ctx = _get_ctx(_ctx_from_ast_arg_list(args, ctx))
1869 _z3_assert(ctx is not None, "At least one of the arguments must be a Z3 expression or probe")
1870 if _has_probe(args):
1871 return _probe_and(args, ctx)
1873 args = _coerce_expr_list(args, ctx)
1874 _args, sz = _to_ast_array(args)
1875 return BoolRef(Z3_mk_and(ctx.ref(), sz, _args), ctx)
1879 """Create a Z3
or-expression
or or-probe.
1881 >>> p, q, r =
Bools(
'p q r')
1886 Or(p__0, p__1, p__2, p__3, p__4)
1890 last_arg = args[len(args) - 1]
1891 if isinstance(last_arg, Context):
1892 ctx = args[len(args) - 1]
1893 args = args[:len(args) - 1]
1894 elif len(args) == 1 and isinstance(args[0], AstVector):
1896 args = [a for a in args[0]]
1899 args = _get_args(args)
1900 ctx = _get_ctx(_ctx_from_ast_arg_list(args, ctx))
1902 _z3_assert(ctx is not None, "At least one of the arguments must be a Z3 expression or probe")
1903 if _has_probe(args):
1904 return _probe_or(args, ctx)
1906 args = _coerce_expr_list(args, ctx)
1907 _args, sz = _to_ast_array(args)
1908 return BoolRef(Z3_mk_or(ctx.ref(), sz, _args), ctx)
1910 #########################################
1914 #########################################
1917 class PatternRef(ExprRef):
1918 """Patterns are hints
for quantifier instantiation.
1923 return Z3_pattern_to_ast(self.ctx_ref(), self.ast)
1926 return Z3_get_ast_id(self.ctx_ref(), self.as_ast())
1930 """Return `
True`
if `a`
is a Z3 pattern (hint
for quantifier instantiation.
1934 >>> q =
ForAll(x, f(x) == 0, patterns = [ f(x) ])
1937 >>> q.num_patterns()
1944 return isinstance(a, PatternRef)
1947 def MultiPattern(*args):
1948 """Create a Z3 multi-pattern using the given expressions `*args`
1956 >>> q.num_patterns()
1964 _z3_assert(len(args) > 0, "At least one argument expected")
1965 _z3_assert(all([is_expr(a) for a in args]), "Z3 expressions expected")
1967 args, sz = _to_ast_array(args)
1968 return PatternRef(Z3_mk_pattern(ctx.ref(), sz, args), ctx)
1971 def _to_pattern(arg):
1975 return MultiPattern(arg)
1977 #########################################
1981 #########################################
1984 class QuantifierRef(BoolRef):
1985 """Universally
and Existentially quantified formulas.
"""
1991 return Z3_get_ast_id(self.ctx_ref(), self.as_ast())
1994 """Return the Boolean sort
or sort of Lambda.
"""
1995 if self.is_lambda():
1996 return _sort(self.ctx, self.as_ast())
1997 return BoolSort(self.ctx)
1999 def is_forall(self):
2000 """Return `
True`
if `self`
is a universal quantifier.
2004 >>> q =
ForAll(x, f(x) == 0)
2007 >>> q =
Exists(x, f(x) != 0)
2011 return Z3_is_quantifier_forall(self.ctx_ref(), self.ast)
2013 def is_exists(self):
2014 """Return `
True`
if `self`
is an existential quantifier.
2018 >>> q =
ForAll(x, f(x) == 0)
2021 >>> q =
Exists(x, f(x) != 0)
2025 return Z3_is_quantifier_exists(self.ctx_ref(), self.ast)
2027 def is_lambda(self):
2028 """Return `
True`
if `self`
is a
lambda expression.
2035 >>> q =
Exists(x, f(x) != 0)
2039 return Z3_is_lambda(self.ctx_ref(), self.ast)
2041 def __getitem__(self, arg):
2042 """Return the Z3 expression `self[arg]`.
2045 _z3_assert(self.is_lambda(), "quantifier should be a lambda expression")
2046 return _array_select(self, arg)
2049 """Return the weight annotation of `self`.
2053 >>> q =
ForAll(x, f(x) == 0)
2056 >>> q =
ForAll(x, f(x) == 0, weight=10)
2060 return int(Z3_get_quantifier_weight(self.ctx_ref(), self.ast))
2062 def num_patterns(self):
2063 """Return the number of patterns (i.e., quantifier instantiation hints)
in `self`.
2068 >>> q =
ForAll(x, f(x) != g(x), patterns = [ f(x), g(x) ])
2069 >>> q.num_patterns()
2072 return int(Z3_get_quantifier_num_patterns(self.ctx_ref(), self.ast))
2074 def pattern(self, idx):
2075 """Return a pattern (i.e., quantifier instantiation hints)
in `self`.
2080 >>> q =
ForAll(x, f(x) != g(x), patterns = [ f(x), g(x) ])
2081 >>> q.num_patterns()
2089 _z3_assert(idx < self.num_patterns(), "Invalid pattern idx")
2090 return PatternRef(Z3_get_quantifier_pattern_ast(self.ctx_ref(), self.ast, idx), self.ctx)
2092 def num_no_patterns(self):
2093 """Return the number of no-patterns.
"""
2094 return Z3_get_quantifier_num_no_patterns(self.ctx_ref(), self.ast)
2096 def no_pattern(self, idx):
2097 """Return a no-pattern.
"""
2099 _z3_assert(idx < self.num_no_patterns(), "Invalid no-pattern idx")
2100 return _to_expr_ref(Z3_get_quantifier_no_pattern_ast(self.ctx_ref(), self.ast, idx), self.ctx)
2103 """Return the expression being quantified.
2107 >>> q =
ForAll(x, f(x) == 0)
2111 return _to_expr_ref(Z3_get_quantifier_body(self.ctx_ref(), self.ast), self.ctx)
2114 """Return the number of variables bounded by this quantifier.
2119 >>> q =
ForAll([x, y], f(x, y) >= x)
2123 return int(Z3_get_quantifier_num_bound(self.ctx_ref(), self.ast))
2125 def var_name(self, idx):
2126 """Return a string representing a name used when displaying the quantifier.
2131 >>> q =
ForAll([x, y], f(x, y) >= x)
2138 _z3_assert(idx < self.num_vars(), "Invalid variable idx")
2139 return _symbol2py(self.ctx, Z3_get_quantifier_bound_name(self.ctx_ref(), self.ast, idx))
2141 def var_sort(self, idx):
2142 """Return the sort of a bound variable.
2147 >>> q =
ForAll([x, y], f(x, y) >= x)
2154 _z3_assert(idx < self.num_vars(), "Invalid variable idx")
2155 return _to_sort_ref(Z3_get_quantifier_bound_sort(self.ctx_ref(), self.ast, idx), self.ctx)
2158 """Return a list containing a single element self.
body()
2162 >>> q =
ForAll(x, f(x) == 0)
2166 return [self.body()]
2169 def is_quantifier(a):
2170 """Return `
True`
if `a`
is a Z3 quantifier.
2174 >>> q =
ForAll(x, f(x) == 0)
2180 return isinstance(a, QuantifierRef)
2183 def _mk_quantifier(is_forall, vs, body, weight=1, qid="", skid="", patterns=[], no_patterns=[]):
2185 _z3_assert(is_bool(body) or is_app(vs) or (len(vs) > 0 and is_app(vs[0])), "Z3 expression expected")
2186 _z3_assert(is_const(vs) or (len(vs) > 0 and all([is_const(v) for v in vs])), "Invalid bounded variable(s)")
2187 _z3_assert(all([is_pattern(a) or is_expr(a) for a in patterns]), "Z3 patterns expected")
2188 _z3_assert(all([is_expr(p) for p in no_patterns]), "no patterns are Z3 expressions")
2194 if not is_expr(body):
2195 body = BoolVal(body, ctx)
2199 _vs = (Ast * num_vars)()
2200 for i in range(num_vars):
2201 # TODO: Check if is constant
2202 _vs[i] = vs[i].as_ast()
2203 patterns = [_to_pattern(p) for p in patterns]
2204 num_pats = len(patterns)
2205 _pats = (Pattern * num_pats)()
2206 for i in range(num_pats):
2207 _pats[i] = patterns[i].ast
2208 _no_pats, num_no_pats = _to_ast_array(no_patterns)
2209 qid = to_symbol(qid, ctx)
2210 skid = to_symbol(skid, ctx)
2211 return QuantifierRef(Z3_mk_quantifier_const_ex(ctx.ref(), is_forall, weight, qid, skid,
2214 num_no_pats, _no_pats,
2215 body.as_ast()), ctx)
2218 def ForAll(vs, body, weight=1, qid="", skid="", patterns=[], no_patterns=[]):
2219 """Create a Z3 forall formula.
2221 The parameters `weight`, `qid`, `skid`, `patterns`
and `no_patterns` are optional annotations.
2226 >>>
ForAll([x, y], f(x, y) >= x)
2227 ForAll([x, y], f(x, y) >= x)
2228 >>>
ForAll([x, y], f(x, y) >= x, patterns=[ f(x, y) ])
2229 ForAll([x, y], f(x, y) >= x)
2230 >>>
ForAll([x, y], f(x, y) >= x, weight=10)
2231 ForAll([x, y], f(x, y) >= x)
2233 return _mk_quantifier(True, vs, body, weight, qid, skid, patterns, no_patterns)
2236 def Exists(vs, body, weight=1, qid="", skid="", patterns=[], no_patterns=[]):
2237 """Create a Z3 exists formula.
2239 The parameters `weight`, `qif`, `skid`, `patterns`
and `no_patterns` are optional annotations.
2245 >>> q =
Exists([x, y], f(x, y) >= x, skid=
"foo")
2247 Exists([x, y], f(x, y) >= x)
2250 >>> r =
Tactic(
'nnf')(q).as_expr()
2254 return _mk_quantifier(False, vs, body, weight, qid, skid, patterns, no_patterns)
2257 def Lambda(vs, body):
2258 """Create a Z3
lambda expression.
2262 >>> lo, hi, e, i =
Ints(
'lo hi e i')
2263 >>> mem1 =
Lambda([i],
If(
And(lo <= i, i <= hi), e, mem0[i]))
2271 _vs = (Ast * num_vars)()
2272 for i in range(num_vars):
2273 # TODO: Check if is constant
2274 _vs[i] = vs[i].as_ast()
2275 return QuantifierRef(Z3_mk_lambda_const(ctx.ref(), num_vars, _vs, body.as_ast()), ctx)
2277 #########################################
2281 #########################################
2284 class ArithSortRef(SortRef):
2285 """Real
and Integer sorts.
"""
2288 """Return `
True`
if `self`
is of the sort Real.
2299 return self.kind() == Z3_REAL_SORT
2302 """Return `
True`
if `self`
is of the sort Integer.
2313 return self.kind() == Z3_INT_SORT
2318 def subsort(self, other):
2319 """Return `
True`
if `self`
is a subsort of `other`.
"""
2320 return self.is_int() and is_arith_sort(other) and other.is_real()
2322 def cast(self, val):
2323 """Try to cast `val`
as an Integer
or Real.
2338 _z3_assert(self.ctx == val.ctx, "Context mismatch")
2342 if val_s.is_int() and self.is_real():
2344 if val_s.is_bool() and self.is_int():
2345 return If(val, 1, 0)
2346 if val_s.is_bool() and self.is_real():
2347 return ToReal(If(val, 1, 0))
2349 _z3_assert(False, "Z3 Integer/Real expression expected")
2352 return IntVal(val, self.ctx)
2354 return RealVal(val, self.ctx)
2356 msg = "int, long, float, string (numeral), or Z3 Integer/Real expression expected. Got %s"
2357 _z3_assert(False, msg % self)
2360 def is_arith_sort(s):
2361 """Return `
True`
if s
is an arithmetical sort (type).
2369 >>> n =
Int(
'x') + 1
2373 return isinstance(s, ArithSortRef)
2376 class ArithRef(ExprRef):
2377 """Integer
and Real expressions.
"""
2380 """Return the sort (type) of the arithmetical expression `self`.
2387 return ArithSortRef(Z3_get_sort(self.ctx_ref(), self.as_ast()), self.ctx)
2390 """Return `
True`
if `self`
is an integer expression.
2401 return self.sort().is_int()
2404 """Return `
True`
if `self`
is an real expression.
2412 return self.sort().is_real()
2414 def __add__(self, other):
2415 """Create the Z3 expression `self + other`.
2424 a, b = _coerce_exprs(self, other)
2425 return ArithRef(_mk_bin(Z3_mk_add, a, b), self.ctx)
2427 def __radd__(self, other):
2428 """Create the Z3 expression `other + self`.
2434 a, b = _coerce_exprs(self, other)
2435 return ArithRef(_mk_bin(Z3_mk_add, b, a), self.ctx)
2437 def __mul__(self, other):
2438 """Create the Z3 expression `self * other`.
2447 if isinstance(other, BoolRef):
2448 return If(other, self, 0)
2449 a, b = _coerce_exprs(self, other)
2450 return ArithRef(_mk_bin(Z3_mk_mul, a, b), self.ctx)
2452 def __rmul__(self, other):
2453 """Create the Z3 expression `other * self`.
2459 a, b = _coerce_exprs(self, other)
2460 return ArithRef(_mk_bin(Z3_mk_mul, b, a), self.ctx)
2462 def __sub__(self, other):
2463 """Create the Z3 expression `self - other`.
2472 a, b = _coerce_exprs(self, other)
2473 return ArithRef(_mk_bin(Z3_mk_sub, a, b), self.ctx)
2475 def __rsub__(self, other):
2476 """Create the Z3 expression `other - self`.
2482 a, b = _coerce_exprs(self, other)
2483 return ArithRef(_mk_bin(Z3_mk_sub, b, a), self.ctx)
2485 def __pow__(self, other):
2486 """Create the Z3 expression `self**other` (**
is the power operator).
2496 a, b = _coerce_exprs(self, other)
2497 return ArithRef(Z3_mk_power(self.ctx_ref(), a.as_ast(), b.as_ast()), self.ctx)
2499 def __rpow__(self, other):
2500 """Create the Z3 expression `other**self` (**
is the power operator).
2510 a, b = _coerce_exprs(self, other)
2511 return ArithRef(Z3_mk_power(self.ctx_ref(), b.as_ast(), a.as_ast()), self.ctx)
2513 def __div__(self, other):
2514 """Create the Z3 expression `other/self`.
2533 a, b = _coerce_exprs(self, other)
2534 return ArithRef(Z3_mk_div(self.ctx_ref(), a.as_ast(), b.as_ast()), self.ctx)
2536 def __truediv__(self, other):
2537 """Create the Z3 expression `other/self`.
"""
2538 return self.__div__(other)
2540 def __rdiv__(self, other):
2541 """Create the Z3 expression `other/self`.
2554 a, b = _coerce_exprs(self, other)
2555 return ArithRef(Z3_mk_div(self.ctx_ref(), b.as_ast(), a.as_ast()), self.ctx)
2557 def __rtruediv__(self, other):
2558 """Create the Z3 expression `other/self`.
"""
2559 return self.__rdiv__(other)
2561 def __mod__(self, other):
2562 """Create the Z3 expression `other%self`.
2571 a, b = _coerce_exprs(self, other)
2573 _z3_assert(a.is_int(), "Z3 integer expression expected")
2574 return ArithRef(Z3_mk_mod(self.ctx_ref(), a.as_ast(), b.as_ast()), self.ctx)
2576 def __rmod__(self, other):
2577 """Create the Z3 expression `other%self`.
2583 a, b = _coerce_exprs(self, other)
2585 _z3_assert(a.is_int(), "Z3 integer expression expected")
2586 return ArithRef(Z3_mk_mod(self.ctx_ref(), b.as_ast(), a.as_ast()), self.ctx)
2589 """Return an expression representing `-self`.
2597 return ArithRef(Z3_mk_unary_minus(self.ctx_ref(), self.as_ast()), self.ctx)
2608 def __le__(self, other):
2609 """Create the Z3 expression `other <= self`.
2611 >>> x, y =
Ints(
'x y')
2618 a, b = _coerce_exprs(self, other)
2619 return BoolRef(Z3_mk_le(self.ctx_ref(), a.as_ast(), b.as_ast()), self.ctx)
2621 def __lt__(self, other):
2622 """Create the Z3 expression `other < self`.
2624 >>> x, y =
Ints(
'x y')
2631 a, b = _coerce_exprs(self, other)
2632 return BoolRef(Z3_mk_lt(self.ctx_ref(), a.as_ast(), b.as_ast()), self.ctx)
2634 def __gt__(self, other):
2635 """Create the Z3 expression `other > self`.
2637 >>> x, y =
Ints(
'x y')
2644 a, b = _coerce_exprs(self, other)
2645 return BoolRef(Z3_mk_gt(self.ctx_ref(), a.as_ast(), b.as_ast()), self.ctx)
2647 def __ge__(self, other):
2648 """Create the Z3 expression `other >= self`.
2650 >>> x, y =
Ints(
'x y')
2657 a, b = _coerce_exprs(self, other)
2658 return BoolRef(Z3_mk_ge(self.ctx_ref(), a.as_ast(), b.as_ast()), self.ctx)
2662 """Return `
True`
if `a`
is an arithmetical expression.
2679 return isinstance(a, ArithRef)
2683 """Return `
True`
if `a`
is an integer expression.
2698 return is_arith(a) and a.is_int()
2702 """Return `
True`
if `a`
is a real expression.
2717 return is_arith(a) and a.is_real()
2720 def _is_numeral(ctx, a):
2721 return Z3_is_numeral_ast(ctx.ref(), a)
2724 def _is_algebraic(ctx, a):
2725 return Z3_is_algebraic_number(ctx.ref(), a)
2728 def is_int_value(a):
2729 """Return `
True`
if `a`
is an integer value of sort Int.
2737 >>> n =
Int(
'x') + 1
2749 return is_arith(a) and a.is_int() and _is_numeral(a.ctx, a.as_ast())
2752 def is_rational_value(a):
2753 """Return `
True`
if `a`
is rational value of sort Real.
2763 >>> n =
Real(
'x') + 1
2771 return is_arith(a) and a.is_real() and _is_numeral(a.ctx, a.as_ast())
2774 def is_algebraic_value(a):
2775 """Return `
True`
if `a`
is an algebraic value of sort Real.
2785 return is_arith(a) and a.is_real() and _is_algebraic(a.ctx, a.as_ast())
2789 """Return `
True`
if `a`
is an expression of the form b + c.
2791 >>> x, y =
Ints(
'x y')
2797 return is_app_of(a, Z3_OP_ADD)
2801 """Return `
True`
if `a`
is an expression of the form b * c.
2803 >>> x, y =
Ints(
'x y')
2809 return is_app_of(a, Z3_OP_MUL)
2813 """Return `
True`
if `a`
is an expression of the form b - c.
2815 >>> x, y =
Ints(
'x y')
2821 return is_app_of(a, Z3_OP_SUB)
2825 """Return `
True`
if `a`
is an expression of the form b / c.
2827 >>> x, y =
Reals(
'x y')
2832 >>> x, y =
Ints(
'x y')
2838 return is_app_of(a, Z3_OP_DIV)
2842 """Return `
True`
if `a`
is an expression of the form b div c.
2844 >>> x, y =
Ints(
'x y')
2850 return is_app_of(a, Z3_OP_IDIV)
2854 """Return `
True`
if `a`
is an expression of the form b % c.
2856 >>> x, y =
Ints(
'x y')
2862 return is_app_of(a, Z3_OP_MOD)
2866 """Return `
True`
if `a`
is an expression of the form b <= c.
2868 >>> x, y =
Ints(
'x y')
2874 return is_app_of(a, Z3_OP_LE)
2878 """Return `
True`
if `a`
is an expression of the form b < c.
2880 >>> x, y =
Ints(
'x y')
2886 return is_app_of(a, Z3_OP_LT)
2890 """Return `
True`
if `a`
is an expression of the form b >= c.
2892 >>> x, y =
Ints(
'x y')
2898 return is_app_of(a, Z3_OP_GE)
2902 """Return `
True`
if `a`
is an expression of the form b > c.
2904 >>> x, y =
Ints(
'x y')
2910 return is_app_of(a, Z3_OP_GT)
2914 """Return `
True`
if `a`
is an expression of the form
IsInt(b).
2922 return is_app_of(a, Z3_OP_IS_INT)
2926 """Return `
True`
if `a`
is an expression of the form
ToReal(b).
2937 return is_app_of(a, Z3_OP_TO_REAL)
2941 """Return `
True`
if `a`
is an expression of the form
ToInt(b).
2952 return is_app_of(a, Z3_OP_TO_INT)
2955 class IntNumRef(ArithRef):
2956 """Integer values.
"""
2959 """Return a Z3 integer numeral
as a Python long (bignum) numeral.
2968 _z3_assert(self.is_int(), "Integer value expected")
2969 return int(self.as_string())
2971 def as_string(self):
2972 """Return a Z3 integer numeral
as a Python string.
2977 return Z3_get_numeral_string(self.ctx_ref(), self.as_ast())
2979 def as_binary_string(self):
2980 """Return a Z3 integer numeral
as a Python binary string.
2982 >>> v.as_binary_string()
2985 return Z3_get_numeral_binary_string(self.ctx_ref(), self.as_ast())
2988 class RatNumRef(ArithRef):
2989 """Rational values.
"""
2991 def numerator(self):
2992 """ Return the numerator of a Z3 rational numeral.
3004 return IntNumRef(Z3_get_numerator(self.ctx_ref(), self.as_ast()), self.ctx)
3006 def denominator(self):
3007 """ Return the denominator of a Z3 rational numeral.
3015 return IntNumRef(Z3_get_denominator(self.ctx_ref(), self.as_ast()), self.ctx)
3017 def numerator_as_long(self):
3018 """ Return the numerator
as a Python long.
3025 >>> v.numerator_as_long() + 1 == 10000000001
3028 return self.numerator().as_long()
3030 def denominator_as_long(self):
3031 """ Return the denominator
as a Python long.
3036 >>> v.denominator_as_long()
3039 return self.denominator().as_long()
3047 def is_int_value(self):
3048 return self.denominator().is_int() and self.denominator_as_long() == 1
3051 _z3_assert(self.is_int_value(), "Expected integer fraction")
3052 return self.numerator_as_long()
3054 def as_decimal(self, prec):
3055 """ Return a Z3 rational value
as a string
in decimal notation using at most `prec` decimal places.
3064 return Z3_get_numeral_decimal_string(self.ctx_ref(), self.as_ast(), prec)
3066 def as_string(self):
3067 """Return a Z3 rational numeral
as a Python string.
3073 return Z3_get_numeral_string(self.ctx_ref(), self.as_ast())
3075 def as_fraction(self):
3076 """Return a Z3 rational
as a Python Fraction object.
3082 return Fraction(self.numerator_as_long(), self.denominator_as_long())
3085 class AlgebraicNumRef(ArithRef):
3086 """Algebraic irrational values.
"""
3088 def approx(self, precision=10):
3089 """Return a Z3 rational number that approximates the algebraic number `self`.
3090 The result `r`
is such that |r - self| <= 1/10^precision
3094 6838717160008073720548335/4835703278458516698824704
3098 return RatNumRef(Z3_get_algebraic_number_upper(self.ctx_ref(), self.as_ast(), precision), self.ctx)
3100 def as_decimal(self, prec):
3101 """Return a string representation of the algebraic number `self`
in decimal notation
3102 using `prec` decimal places.
3105 >>> x.as_decimal(10)
3107 >>> x.as_decimal(20)
3108 '1.41421356237309504880?'
3110 return Z3_get_numeral_decimal_string(self.ctx_ref(), self.as_ast(), prec)
3113 return AstVector(Z3_algebraic_get_poly(self.ctx_ref(), self.as_ast()), self.ctx)
3116 return Z3_algebraic_get_i(self.ctx_ref(), self.as_ast())
3119 def _py2expr(a, ctx=None):
3120 if isinstance(a, bool):
3121 return BoolVal(a, ctx)
3123 return IntVal(a, ctx)
3124 if isinstance(a, float):
3125 return RealVal(a, ctx)
3126 if isinstance(a, str):
3127 return StringVal(a, ctx)
3131 _z3_assert(False, "Python bool, int, long or float expected")
3134 def IntSort(ctx=None):
3135 """Return the integer sort
in the given context. If `ctx=
None`, then the
global context
is used.
3148 return ArithSortRef(Z3_mk_int_sort(ctx.ref()), ctx)
3151 def RealSort(ctx=None):
3152 """Return the real sort
in the given context. If `ctx=
None`, then the
global context
is used.
3165 return ArithSortRef(Z3_mk_real_sort(ctx.ref()), ctx)
3168 def _to_int_str(val):
3169 if isinstance(val, float):
3170 return str(int(val))
3171 elif isinstance(val, bool):
3180 def IntVal(val, ctx=None):
3181 """Return a Z3 integer value. If `ctx=
None`, then the
global context
is used.
3189 return IntNumRef(Z3_mk_numeral(ctx.ref(), _to_int_str(val), IntSort(ctx).ast), ctx)
3192 def RealVal(val, ctx=None):
3193 """Return a Z3 real value.
3195 `val` may be a Python int, long, float
or string representing a number
in decimal
or rational notation.
3196 If `ctx=
None`, then the
global context
is used.
3208 return RatNumRef(Z3_mk_numeral(ctx.ref(), str(val), RealSort(ctx).ast), ctx)
3211 def RatVal(a, b, ctx=None):
3212 """Return a Z3 rational a/b.
3214 If `ctx=
None`, then the
global context
is used.
3222 _z3_assert(_is_int(a) or isinstance(a, str), "First argument cannot be converted into an integer")
3223 _z3_assert(_is_int(b) or isinstance(b, str), "Second argument cannot be converted into an integer")
3224 return simplify(RealVal(a, ctx) / RealVal(b, ctx))
3227 def Q(a, b, ctx=None):
3228 """Return a Z3 rational a/b.
3230 If `ctx=
None`, then the
global context
is used.
3237 return simplify(RatVal(a, b, ctx=ctx))
3240 def Int(name, ctx=None):
3241 """Return an integer constant named `name`. If `ctx=
None`, then the
global context
is used.
3250 return ArithRef(Z3_mk_const(ctx.ref(), to_symbol(name, ctx), IntSort(ctx).ast), ctx)
3253 def Ints(names, ctx=None):
3254 """Return a tuple of Integer constants.
3256 >>> x, y, z =
Ints(
'x y z')
3261 if isinstance(names, str):
3262 names = names.split(" ")
3263 return [Int(name, ctx) for name in names]
3266 def IntVector(prefix, sz, ctx=None):
3267 """Return a list of integer constants of size `sz`.
3276 return [Int("%s__%s" % (prefix, i), ctx) for i in range(sz)]
3279 def FreshInt(prefix="x", ctx=None):
3280 """Return a fresh integer constant
in the given context using the given prefix.
3290 return ArithRef(Z3_mk_fresh_const(ctx.ref(), prefix, IntSort(ctx).ast), ctx)
3293 def Real(name, ctx=None):
3294 """Return a real constant named `name`. If `ctx=
None`, then the
global context
is used.
3303 return ArithRef(Z3_mk_const(ctx.ref(), to_symbol(name, ctx), RealSort(ctx).ast), ctx)
3306 def Reals(names, ctx=None):
3307 """Return a tuple of real constants.
3309 >>> x, y, z =
Reals(
'x y z')
3312 >>>
Sum(x, y, z).sort()
3316 if isinstance(names, str):
3317 names = names.split(" ")
3318 return [Real(name, ctx) for name in names]
3321 def RealVector(prefix, sz, ctx=None):
3322 """Return a list of real constants of size `sz`.
3333 return [Real("%s__%s" % (prefix, i), ctx) for i in range(sz)]
3336 def FreshReal(prefix="b", ctx=None):
3337 """Return a fresh real constant
in the given context using the given prefix.
3347 return ArithRef(Z3_mk_fresh_const(ctx.ref(), prefix, RealSort(ctx).ast), ctx)
3351 """ Return the Z3 expression
ToReal(a).
3363 _z3_assert(a.is_int(), "Z3 integer expression expected.")
3365 return ArithRef(Z3_mk_int2real(ctx.ref(), a.as_ast()), ctx)
3369 """ Return the Z3 expression
ToInt(a).
3381 _z3_assert(a.is_real(), "Z3 real expression expected.")
3383 return ArithRef(Z3_mk_real2int(ctx.ref(), a.as_ast()), ctx)
3387 """ Return the Z3 predicate
IsInt(a).
3390 >>>
IsInt(x +
"1/2")
3394 >>>
solve(
IsInt(x +
"1/2"), x > 0, x < 1, x !=
"1/2")
3398 _z3_assert(a.is_real(), "Z3 real expression expected.")
3400 return BoolRef(Z3_mk_is_int(ctx.ref(), a.as_ast()), ctx)
3403 def Sqrt(a, ctx=None):
3404 """ Return a Z3 expression which represents the square root of a.
3416 def Cbrt(a, ctx=None):
3417 """ Return a Z3 expression which represents the cubic root of a.
3428 #########################################
3432 #########################################
3435 class BitVecSortRef(SortRef):
3436 """Bit-vector sort.
"""
3439 """Return the size (number of bits) of the bit-vector sort `self`.
3445 return int(Z3_get_bv_sort_size(self.ctx_ref(), self.ast))
3447 def subsort(self, other):
3448 return is_bv_sort(other) and self.size() < other.size()
3450 def cast(self, val):
3451 """Try to cast `val`
as a Bit-Vector.
3456 >>> b.cast(10).
sexpr()
3461 _z3_assert(self.ctx == val.ctx, "Context mismatch")
3462 # Idea: use sign_extend if sort of val is a bitvector of smaller size
3465 return BitVecVal(val, self)
3469 """Return
True if `s`
is a Z3 bit-vector sort.
3476 return isinstance(s, BitVecSortRef)
3479 class BitVecRef(ExprRef):
3480 """Bit-vector expressions.
"""
3483 """Return the sort of the bit-vector expression `self`.
3491 return BitVecSortRef(Z3_get_sort(self.ctx_ref(), self.as_ast()), self.ctx)
3494 """Return the number of bits of the bit-vector expression `self`.
3502 return self.sort().size()
3504 def __add__(self, other):
3505 """Create the Z3 expression `self + other`.
3514 a, b = _coerce_exprs(self, other)
3515 return BitVecRef(Z3_mk_bvadd(self.ctx_ref(), a.as_ast(), b.as_ast()), self.ctx)
3517 def __radd__(self, other):
3518 """Create the Z3 expression `other + self`.
3524 a, b = _coerce_exprs(self, other)
3525 return BitVecRef(Z3_mk_bvadd(self.ctx_ref(), b.as_ast(), a.as_ast()), self.ctx)
3527 def __mul__(self, other):
3528 """Create the Z3 expression `self * other`.
3537 a, b = _coerce_exprs(self, other)
3538 return BitVecRef(Z3_mk_bvmul(self.ctx_ref(), a.as_ast(), b.as_ast()), self.ctx)
3540 def __rmul__(self, other):
3541 """Create the Z3 expression `other * self`.
3547 a, b = _coerce_exprs(self, other)
3548 return BitVecRef(Z3_mk_bvmul(self.ctx_ref(), b.as_ast(), a.as_ast()), self.ctx)
3550 def __sub__(self, other):
3551 """Create the Z3 expression `self - other`.
3560 a, b = _coerce_exprs(self, other)
3561 return BitVecRef(Z3_mk_bvsub(self.ctx_ref(), a.as_ast(), b.as_ast()), self.ctx)
3563 def __rsub__(self, other):
3564 """Create the Z3 expression `other - self`.
3570 a, b = _coerce_exprs(self, other)
3571 return BitVecRef(Z3_mk_bvsub(self.ctx_ref(), b.as_ast(), a.as_ast()), self.ctx)
3573 def __or__(self, other):
3574 """Create the Z3 expression bitwise-
or `self | other`.
3583 a, b = _coerce_exprs(self, other)
3584 return BitVecRef(Z3_mk_bvor(self.ctx_ref(), a.as_ast(), b.as_ast()), self.ctx)
3586 def __ror__(self, other):
3587 """Create the Z3 expression bitwise-
or `other | self`.
3593 a, b = _coerce_exprs(self, other)
3594 return BitVecRef(Z3_mk_bvor(self.ctx_ref(), b.as_ast(), a.as_ast()), self.ctx)
3596 def __and__(self, other):
3597 """Create the Z3 expression bitwise-
and `self & other`.
3606 a, b = _coerce_exprs(self, other)
3607 return BitVecRef(Z3_mk_bvand(self.ctx_ref(), a.as_ast(), b.as_ast()), self.ctx)
3609 def __rand__(self, other):
3610 """Create the Z3 expression bitwise-
or `other & self`.
3616 a, b = _coerce_exprs(self, other)
3617 return BitVecRef(Z3_mk_bvand(self.ctx_ref(), b.as_ast(), a.as_ast()), self.ctx)
3619 def __xor__(self, other):
3620 """Create the Z3 expression bitwise-xor `self ^ other`.
3629 a, b = _coerce_exprs(self, other)
3630 return BitVecRef(Z3_mk_bvxor(self.ctx_ref(), a.as_ast(), b.as_ast()), self.ctx)
3632 def __rxor__(self, other):
3633 """Create the Z3 expression bitwise-xor `other ^ self`.
3639 a, b = _coerce_exprs(self, other)
3640 return BitVecRef(Z3_mk_bvxor(self.ctx_ref(), b.as_ast(), a.as_ast()), self.ctx)
3652 """Return an expression representing `-self`.
3660 return BitVecRef(Z3_mk_bvneg(self.ctx_ref(), self.as_ast()), self.ctx)
3662 def __invert__(self):
3663 """Create the Z3 expression bitwise-
not `~self`.
3671 return BitVecRef(Z3_mk_bvnot(self.ctx_ref(), self.as_ast()), self.ctx)
3673 def __div__(self, other):
3674 """Create the Z3 expression (signed) division `self / other`.
3676 Use the function
UDiv()
for unsigned division.
3689 a, b = _coerce_exprs(self, other)
3690 return BitVecRef(Z3_mk_bvsdiv(self.ctx_ref(), a.as_ast(), b.as_ast()), self.ctx)
3692 def __truediv__(self, other):
3693 """Create the Z3 expression (signed) division `self / other`.
"""
3694 return self.__div__(other)
3696 def __rdiv__(self, other):
3697 """Create the Z3 expression (signed) division `other / self`.
3699 Use the function
UDiv()
for unsigned division.
3704 >>> (10 / x).
sexpr()
3705 '(bvsdiv #x0000000a x)'
3707 '(bvudiv #x0000000a x)'
3709 a, b = _coerce_exprs(self, other)
3710 return BitVecRef(Z3_mk_bvsdiv(self.ctx_ref(), b.as_ast(), a.as_ast()), self.ctx)
3712 def __rtruediv__(self, other):
3713 """Create the Z3 expression (signed) division `other / self`.
"""
3714 return self.__rdiv__(other)
3716 def __mod__(self, other):
3717 """Create the Z3 expression (signed) mod `self % other`.
3719 Use the function
URem()
for unsigned remainder,
and SRem()
for signed remainder.
3734 a, b = _coerce_exprs(self, other)
3735 return BitVecRef(Z3_mk_bvsmod(self.ctx_ref(), a.as_ast(), b.as_ast()), self.ctx)
3737 def __rmod__(self, other):
3738 """Create the Z3 expression (signed) mod `other % self`.
3740 Use the function
URem()
for unsigned remainder,
and SRem()
for signed remainder.
3745 >>> (10 % x).
sexpr()
3746 '(bvsmod #x0000000a x)'
3748 '(bvurem #x0000000a x)'
3750 '(bvsrem #x0000000a x)'
3752 a, b = _coerce_exprs(self, other)
3753 return BitVecRef(Z3_mk_bvsmod(self.ctx_ref(), b.as_ast(), a.as_ast()), self.ctx)
3755 def __le__(self, other):
3756 """Create the Z3 expression (signed) `other <= self`.
3758 Use the function
ULE()
for unsigned less than
or equal to.
3763 >>> (x <= y).
sexpr()
3768 a, b = _coerce_exprs(self, other)
3769 return BoolRef(Z3_mk_bvsle(self.ctx_ref(), a.as_ast(), b.as_ast()), self.ctx)
3771 def __lt__(self, other):
3772 """Create the Z3 expression (signed) `other < self`.
3774 Use the function
ULT()
for unsigned less than.
3784 a, b = _coerce_exprs(self, other)
3785 return BoolRef(Z3_mk_bvslt(self.ctx_ref(), a.as_ast(), b.as_ast()), self.ctx)
3787 def __gt__(self, other):
3788 """Create the Z3 expression (signed) `other > self`.
3790 Use the function
UGT()
for unsigned greater than.
3800 a, b = _coerce_exprs(self, other)
3801 return BoolRef(Z3_mk_bvsgt(self.ctx_ref(), a.as_ast(), b.as_ast()), self.ctx)
3803 def __ge__(self, other):
3804 """Create the Z3 expression (signed) `other >= self`.
3806 Use the function
UGE()
for unsigned greater than
or equal to.
3811 >>> (x >= y).
sexpr()
3816 a, b = _coerce_exprs(self, other)
3817 return BoolRef(Z3_mk_bvsge(self.ctx_ref(), a.as_ast(), b.as_ast()), self.ctx)
3819 def __rshift__(self, other):
3820 """Create the Z3 expression (arithmetical) right shift `self >> other`
3822 Use the function
LShR()
for the right logical shift
3827 >>> (x >> y).
sexpr()
3846 a, b = _coerce_exprs(self, other)
3847 return BitVecRef(Z3_mk_bvashr(self.ctx_ref(), a.as_ast(), b.as_ast()), self.ctx)
3849 def __lshift__(self, other):
3850 """Create the Z3 expression left shift `self << other`
3855 >>> (x << y).
sexpr()
3860 a, b = _coerce_exprs(self, other)
3861 return BitVecRef(Z3_mk_bvshl(self.ctx_ref(), a.as_ast(), b.as_ast()), self.ctx)
3863 def __rrshift__(self, other):
3864 """Create the Z3 expression (arithmetical) right shift `other` >> `self`.
3866 Use the function
LShR()
for the right logical shift
3871 >>> (10 >> x).
sexpr()
3872 '(bvashr #x0000000a x)'
3874 a, b = _coerce_exprs(self, other)
3875 return BitVecRef(Z3_mk_bvashr(self.ctx_ref(), b.as_ast(), a.as_ast()), self.ctx)
3877 def __rlshift__(self, other):
3878 """Create the Z3 expression left shift `other << self`.
3880 Use the function
LShR()
for the right logical shift
3885 >>> (10 << x).
sexpr()
3886 '(bvshl #x0000000a x)'
3888 a, b = _coerce_exprs(self, other)
3889 return BitVecRef(Z3_mk_bvshl(self.ctx_ref(), b.as_ast(), a.as_ast()), self.ctx)
3892 class BitVecNumRef(BitVecRef):
3893 """Bit-vector values.
"""
3896 """Return a Z3 bit-vector numeral
as a Python long (bignum) numeral.
3901 >>> print(
"0x%.8x" % v.as_long())
3904 return int(self.as_string())
3906 def as_signed_long(self):
3907 """Return a Z3 bit-vector numeral
as a Python long (bignum) numeral.
3908 The most significant bit
is assumed to be the sign.
3922 val = self.as_long()
3923 if val >= 2**(sz - 1):
3925 if val < -2**(sz - 1):
3929 def as_string(self):
3930 return Z3_get_numeral_string(self.ctx_ref(), self.as_ast())
3932 def as_binary_string(self):
3933 return Z3_get_numeral_binary_string(self.ctx_ref(), self.as_ast())
3937 """Return `
True`
if `a`
is a Z3 bit-vector expression.
3947 return isinstance(a, BitVecRef)
3951 """Return `
True`
if `a`
is a Z3 bit-vector numeral value.
3962 return is_bv(a) and _is_numeral(a.ctx, a.as_ast())
3965 def BV2Int(a, is_signed=False):
3966 """Return the Z3 expression
BV2Int(a).
3974 >>> x >
BV2Int(b, is_signed=
False)
3976 >>> x >
BV2Int(b, is_signed=
True)
3982 _z3_assert(is_bv(a), "First argument must be a Z3 bit-vector expression")
3984 # investigate problem with bv2int
3985 return ArithRef(Z3_mk_bv2int(ctx.ref(), a.as_ast(), is_signed), ctx)
3988 def Int2BV(a, num_bits):
3989 """Return the z3 expression
Int2BV(a, num_bits).
3990 It
is a bit-vector of width num_bits
and represents the
3991 modulo of a by 2^num_bits
3994 return BitVecRef(Z3_mk_int2bv(ctx.ref(), num_bits, a.as_ast()), ctx)
3997 def BitVecSort(sz, ctx=None):
3998 """Return a Z3 bit-vector sort of the given size. If `ctx=
None`, then the
global context
is used.
4004 >>> x =
Const(
'x', Byte)
4009 return BitVecSortRef(Z3_mk_bv_sort(ctx.ref(), sz), ctx)
4012 def BitVecVal(val, bv, ctx=None):
4013 """Return a bit-vector value with the given number of bits. If `ctx=
None`, then the
global context
is used.
4018 >>> print(
"0x%.8x" % v.as_long())
4023 return BitVecNumRef(Z3_mk_numeral(ctx.ref(), _to_int_str(val), bv.ast), ctx)
4026 return BitVecNumRef(Z3_mk_numeral(ctx.ref(), _to_int_str(val), BitVecSort(bv, ctx).ast), ctx)
4029 def BitVec(name, bv, ctx=None):
4030 """Return a bit-vector constant named `name`. `bv` may be the number of bits of a bit-vector sort.
4031 If `ctx=
None`, then the
global context
is used.
4041 >>> x2 =
BitVec(
'x', word)
4045 if isinstance(bv, BitVecSortRef):
4049 bv = BitVecSort(bv, ctx)
4050 return BitVecRef(Z3_mk_const(ctx.ref(), to_symbol(name, ctx), bv.ast), ctx)
4053 def BitVecs(names, bv, ctx=None):
4054 """Return a tuple of bit-vector constants of size bv.
4056 >>> x, y, z =
BitVecs(
'x y z', 16)
4069 if isinstance(names, str):
4070 names = names.split(" ")
4071 return [BitVec(name, bv, ctx) for name in names]
4075 """Create a Z3 bit-vector concatenation expression.
4085 args = _get_args(args)
4088 _z3_assert(sz >= 2, "At least two arguments expected.")
4095 if is_seq(args[0]) or isinstance(args[0], str):
4096 args = [_coerce_seq(s, ctx) for s in args]
4098 _z3_assert(all([is_seq(a) for a in args]), "All arguments must be sequence expressions.")
4101 v[i] = args[i].as_ast()
4102 return SeqRef(Z3_mk_seq_concat(ctx.ref(), sz, v), ctx)
4106 _z3_assert(all([is_re(a) for a in args]), "All arguments must be regular expressions.")
4109 v[i] = args[i].as_ast()
4110 return ReRef(Z3_mk_re_concat(ctx.ref(), sz, v), ctx)
4113 _z3_assert(all([is_bv(a) for a in args]), "All arguments must be Z3 bit-vector expressions.")
4115 for i in range(sz - 1):
4116 r = BitVecRef(Z3_mk_concat(ctx.ref(), r.as_ast(), args[i + 1].as_ast()), ctx)
4120 def Extract(high, low, a):
4121 """Create a Z3 bit-vector extraction expression.
4122 Extract
is overloaded to also work on sequence extraction.
4123 The functions SubString
and SubSeq are redirected to Extract.
4124 For this case, the arguments are reinterpreted
as:
4125 high -
is a sequence (string)
4127 a -
is the length to be extracted
4137 if isinstance(high, str):
4138 high = StringVal(high)
4141 offset, length = _coerce_exprs(low, a, s.ctx)
4142 return SeqRef(Z3_mk_seq_extract(s.ctx_ref(), s.as_ast(), offset.as_ast(), length.as_ast()), s.ctx)
4144 _z3_assert(low <= high, "First argument must be greater than or equal to second argument")
4145 _z3_assert(_is_int(high) and high >= 0 and _is_int(low) and low >= 0,
4146 "First and second arguments must be non negative integers")
4147 _z3_assert(is_bv(a), "Third argument must be a Z3 bit-vector expression")
4148 return BitVecRef(Z3_mk_extract(a.ctx_ref(), high, low, a.as_ast()), a.ctx)
4151 def _check_bv_args(a, b):
4153 _z3_assert(is_bv(a) or is_bv(b), "First or second argument must be a Z3 bit-vector expression")
4157 """Create the Z3 expression (unsigned) `other <= self`.
4159 Use the operator <=
for signed less than
or equal to.
4164 >>> (x <= y).sexpr()
4166 >>>
ULE(x, y).sexpr()
4169 _check_bv_args(a, b)
4170 a, b = _coerce_exprs(a, b)
4171 return BoolRef(Z3_mk_bvule(a.ctx_ref(), a.as_ast(), b.as_ast()), a.ctx)
4175 """Create the Z3 expression (unsigned) `other < self`.
4177 Use the operator <
for signed less than.
4184 >>>
ULT(x, y).sexpr()
4187 _check_bv_args(a, b)
4188 a, b = _coerce_exprs(a, b)
4189 return BoolRef(Z3_mk_bvult(a.ctx_ref(), a.as_ast(), b.as_ast()), a.ctx)
4193 """Create the Z3 expression (unsigned) `other >= self`.
4195 Use the operator >=
for signed greater than
or equal to.
4200 >>> (x >= y).sexpr()
4202 >>>
UGE(x, y).sexpr()
4205 _check_bv_args(a, b)
4206 a, b = _coerce_exprs(a, b)
4207 return BoolRef(Z3_mk_bvuge(a.ctx_ref(), a.as_ast(), b.as_ast()), a.ctx)
4211 """Create the Z3 expression (unsigned) `other > self`.
4213 Use the operator >
for signed greater than.
4220 >>>
UGT(x, y).sexpr()
4223 _check_bv_args(a, b)
4224 a, b = _coerce_exprs(a, b)
4225 return BoolRef(Z3_mk_bvugt(a.ctx_ref(), a.as_ast(), b.as_ast()), a.ctx)
4229 """Create the Z3 expression (unsigned) division `self / other`.
4231 Use the operator /
for signed division.
4237 >>>
UDiv(x, y).sort()
4241 >>>
UDiv(x, y).sexpr()
4244 _check_bv_args(a, b)
4245 a, b = _coerce_exprs(a, b)
4246 return BitVecRef(Z3_mk_bvudiv(a.ctx_ref(), a.as_ast(), b.as_ast()), a.ctx)
4250 """Create the Z3 expression (unsigned) remainder `self % other`.
4252 Use the operator %
for signed modulus,
and SRem()
for signed remainder.
4258 >>>
URem(x, y).sort()
4262 >>>
URem(x, y).sexpr()
4265 _check_bv_args(a, b)
4266 a, b = _coerce_exprs(a, b)
4267 return BitVecRef(Z3_mk_bvurem(a.ctx_ref(), a.as_ast(), b.as_ast()), a.ctx)
4271 """Create the Z3 expression signed remainder.
4273 Use the operator %
for signed modulus,
and URem()
for unsigned remainder.
4279 >>>
SRem(x, y).sort()
4283 >>>
SRem(x, y).sexpr()
4286 _check_bv_args(a, b)
4287 a, b = _coerce_exprs(a, b)
4288 return BitVecRef(Z3_mk_bvsrem(a.ctx_ref(), a.as_ast(), b.as_ast()), a.ctx)
4292 """Create the Z3 expression logical right shift.
4294 Use the operator >>
for the arithmetical right shift.
4299 >>> (x >> y).sexpr()
4301 >>>
LShR(x, y).sexpr()
4318 _check_bv_args(a, b)
4319 a, b = _coerce_exprs(a, b)
4320 return BitVecRef(Z3_mk_bvlshr(a.ctx_ref(), a.as_ast(), b.as_ast()), a.ctx)
4323 def RotateLeft(a, b):
4324 """Return an expression representing `a` rotated to the left `b` times.
4334 _check_bv_args(a, b)
4335 a, b = _coerce_exprs(a, b)
4336 return BitVecRef(Z3_mk_ext_rotate_left(a.ctx_ref(), a.as_ast(), b.as_ast()), a.ctx)
4339 def RotateRight(a, b):
4340 """Return an expression representing `a` rotated to the right `b` times.
4350 _check_bv_args(a, b)
4351 a, b = _coerce_exprs(a, b)
4352 return BitVecRef(Z3_mk_ext_rotate_right(a.ctx_ref(), a.as_ast(), b.as_ast()), a.ctx)
4356 """Return a bit-vector expression with `n` extra sign-bits.
4376 >>> print(
"%.x" % v.as_long())
4380 _z3_assert(_is_int(n), "First argument must be an integer")
4381 _z3_assert(is_bv(a), "Second argument must be a Z3 bit-vector expression")
4382 return BitVecRef(Z3_mk_sign_ext(a.ctx_ref(), n, a.as_ast()), a.ctx)
4386 """Return a bit-vector expression with `n` extra zero-bits.
4408 _z3_assert(_is_int(n), "First argument must be an integer")
4409 _z3_assert(is_bv(a), "Second argument must be a Z3 bit-vector expression")
4410 return BitVecRef(Z3_mk_zero_ext(a.ctx_ref(), n, a.as_ast()), a.ctx)
4413 def RepeatBitVec(n, a):
4414 """Return an expression representing `n` copies of `a`.
4423 >>> print(
"%.x" % v0.as_long())
4428 >>> print(
"%.x" % v.as_long())
4432 _z3_assert(_is_int(n), "First argument must be an integer")
4433 _z3_assert(is_bv(a), "Second argument must be a Z3 bit-vector expression")
4434 return BitVecRef(Z3_mk_repeat(a.ctx_ref(), n, a.as_ast()), a.ctx)
4438 """Return the reduction-
and expression of `a`.
"""
4440 _z3_assert(is_bv(a), "First argument must be a Z3 bit-vector expression")
4441 return BitVecRef(Z3_mk_bvredand(a.ctx_ref(), a.as_ast()), a.ctx)
4445 """Return the reduction-
or expression of `a`.
"""
4447 _z3_assert(is_bv(a), "First argument must be a Z3 bit-vector expression")
4448 return BitVecRef(Z3_mk_bvredor(a.ctx_ref(), a.as_ast()), a.ctx)
4451 def BVAddNoOverflow(a, b, signed):
4452 """A predicate the determines that bit-vector addition does
not overflow
"""
4453 _check_bv_args(a, b)
4454 a, b = _coerce_exprs(a, b)
4455 return BoolRef(Z3_mk_bvadd_no_overflow(a.ctx_ref(), a.as_ast(), b.as_ast(), signed), a.ctx)
4458 def BVAddNoUnderflow(a, b):
4459 """A predicate the determines that signed bit-vector addition does
not underflow
"""
4460 _check_bv_args(a, b)
4461 a, b = _coerce_exprs(a, b)
4462 return BoolRef(Z3_mk_bvadd_no_underflow(a.ctx_ref(), a.as_ast(), b.as_ast()), a.ctx)
4465 def BVSubNoOverflow(a, b):
4466 """A predicate the determines that bit-vector subtraction does
not overflow
"""
4467 _check_bv_args(a, b)
4468 a, b = _coerce_exprs(a, b)
4469 return BoolRef(Z3_mk_bvsub_no_overflow(a.ctx_ref(), a.as_ast(), b.as_ast()), a.ctx)
4472 def BVSubNoUnderflow(a, b, signed):
4473 """A predicate the determines that bit-vector subtraction does
not underflow
"""
4474 _check_bv_args(a, b)
4475 a, b = _coerce_exprs(a, b)
4476 return BoolRef(Z3_mk_bvsub_no_underflow(a.ctx_ref(), a.as_ast(), b.as_ast(), signed), a.ctx)
4479 def BVSDivNoOverflow(a, b):
4480 """A predicate the determines that bit-vector signed division does
not overflow
"""
4481 _check_bv_args(a, b)
4482 a, b = _coerce_exprs(a, b)
4483 return BoolRef(Z3_mk_bvsdiv_no_overflow(a.ctx_ref(), a.as_ast(), b.as_ast()), a.ctx)
4486 def BVSNegNoOverflow(a):
4487 """A predicate the determines that bit-vector unary negation does
not overflow
"""
4489 _z3_assert(is_bv(a), "First argument must be a Z3 bit-vector expression")
4490 return BoolRef(Z3_mk_bvneg_no_overflow(a.ctx_ref(), a.as_ast()), a.ctx)
4493 def BVMulNoOverflow(a, b, signed):
4494 """A predicate the determines that bit-vector multiplication does
not overflow
"""
4495 _check_bv_args(a, b)
4496 a, b = _coerce_exprs(a, b)
4497 return BoolRef(Z3_mk_bvmul_no_overflow(a.ctx_ref(), a.as_ast(), b.as_ast(), signed), a.ctx)
4500 def BVMulNoUnderflow(a, b):
4501 """A predicate the determines that bit-vector signed multiplication does
not underflow
"""
4502 _check_bv_args(a, b)
4503 a, b = _coerce_exprs(a, b)
4504 return BoolRef(Z3_mk_bvmul_no_underflow(a.ctx_ref(), a.as_ast(), b.as_ast()), a.ctx)
4507 #########################################
4511 #########################################
4513 class ArraySortRef(SortRef):
4517 """Return the domain of the array sort `self`.
4523 return _to_sort_ref(Z3_get_array_sort_domain(self.ctx_ref(), self.ast), self.ctx)
4525 def domain_n(self, i):
4526 """Return the domain of the array sort `self`.
4528 return _to_sort_ref(Z3_get_array_sort_domain_n(self.ctx_ref(), self.ast, i), self.ctx)
4531 """Return the range of the array sort `self`.
4537 return _to_sort_ref(Z3_get_array_sort_range(self.ctx_ref(), self.ast), self.ctx)
4540 class ArrayRef(ExprRef):
4541 """Array expressions.
"""
4544 """Return the array sort of the array expression `self`.
4550 return ArraySortRef(Z3_get_sort(self.ctx_ref(), self.as_ast()), self.ctx)
4559 return self.sort().domain()
4561 def domain_n(self, i):
4563 return self.sort().domain_n(i)
4572 return self.sort().range()
4574 def __getitem__(self, arg):
4575 """Return the Z3 expression `self[arg]`.
4584 return _array_select(self, arg)
4587 return _to_expr_ref(Z3_mk_array_default(self.ctx_ref(), self.as_ast()), self.ctx)
4590 def _array_select(ar, arg):
4591 if isinstance(arg, tuple):
4592 args = [ar.sort().domain_n(i).cast(arg[i]) for i in range(len(arg))]
4593 _args, sz = _to_ast_array(args)
4594 return _to_expr_ref(Z3_mk_select_n(ar.ctx_ref(), ar.as_ast(), sz, _args), ar.ctx)
4595 arg = ar.sort().domain().cast(arg)
4596 return _to_expr_ref(Z3_mk_select(ar.ctx_ref(), ar.as_ast(), arg.as_ast()), ar.ctx)
4599 def is_array_sort(a):
4600 return Z3_get_sort_kind(a.ctx.ref(), Z3_get_sort(a.ctx.ref(), a.ast)) == Z3_ARRAY_SORT
4604 """Return `
True`
if `a`
is a Z3 array expression.
4614 return isinstance(a, ArrayRef)
4617 def is_const_array(a):
4618 """Return `
True`
if `a`
is a Z3 constant array.
4627 return is_app_of(a, Z3_OP_CONST_ARRAY)
4631 """Return `
True`
if `a`
is a Z3 constant array.
4640 return is_app_of(a, Z3_OP_CONST_ARRAY)
4644 """Return `
True`
if `a`
is a Z3 map array expression.
4656 return is_app_of(a, Z3_OP_ARRAY_MAP)
4660 """Return `
True`
if `a`
is a Z3 default array expression.
4665 return is_app_of(a, Z3_OP_ARRAY_DEFAULT)
4668 def get_map_func(a):
4669 """Return the function declaration associated with a Z3 map array expression.
4682 _z3_assert(is_map(a), "Z3 array map expression expected.")
4686 Z3_get_decl_ast_parameter(a.ctx_ref(), a.decl().ast, 0),
4692 def ArraySort(*sig):
4693 """Return the Z3 array sort with the given domain
and range sorts.
4706 sig = _get_args(sig)
4708 _z3_assert(len(sig) > 1, "At least two arguments expected")
4709 arity = len(sig) - 1
4714 _z3_assert(is_sort(s), "Z3 sort expected")
4715 _z3_assert(s.ctx == r.ctx, "Context mismatch")
4718 return ArraySortRef(Z3_mk_array_sort(ctx.ref(), d.ast, r.ast), ctx)
4719 dom = (Sort * arity)()
4720 for i in range(arity):
4722 return ArraySortRef(Z3_mk_array_sort_n(ctx.ref(), arity, dom, r.ast), ctx)
4725 def Array(name, *sorts):
4726 """Return an array constant named `name` with the given domain
and range sorts.
4734 s = ArraySort(sorts)
4736 return ArrayRef(Z3_mk_const(ctx.ref(), to_symbol(name, ctx), s.ast), ctx)
4739 def Update(a, *args):
4740 """Return a Z3 store array expression.
4743 >>> i, v =
Ints(
'i v')
4747 >>>
prove(s[i] == v)
4754 _z3_assert(is_array_sort(a), "First argument must be a Z3 array expression")
4755 args = _get_args(args)
4758 raise Z3Exception("array update requires index and value arguments")
4762 i = a.sort().domain().cast(i)
4763 v = a.sort().range().cast(v)
4764 return _to_expr_ref(Z3_mk_store(ctx.ref(), a.as_ast(), i.as_ast(), v.as_ast()), ctx)
4765 v = a.sort().range().cast(args[-1])
4766 idxs = [a.sort().domain_n(i).cast(args[i]) for i in range(len(args)-1)]
4767 _args, sz = _to_ast_array(idxs)
4768 return _to_expr_ref(Z3_mk_store_n(ctx.ref(), a.as_ast(), sz, _args, v.as_ast()), ctx)
4772 """ Return a default value
for array expression.
4778 _z3_assert(is_array_sort(a), "First argument must be a Z3 array expression")
4782 def Store(a, *args):
4783 """Return a Z3 store array expression.
4786 >>> i, v =
Ints(
'i v')
4787 >>> s =
Store(a, i, v)
4790 >>>
prove(s[i] == v)
4796 return Update(a, args)
4799 def Select(a, *args):
4800 """Return a Z3 select array expression.
4809 args = _get_args(args)
4811 _z3_assert(is_array_sort(a), "First argument must be a Z3 array expression")
4816 """Return a Z3 map array expression.
4821 >>> b =
Map(f, a1, a2)
4824 >>>
prove(b[0] == f(a1[0], a2[0]))
4827 args = _get_args(args)
4829 _z3_assert(len(args) > 0, "At least one Z3 array expression expected")
4830 _z3_assert(is_func_decl(f), "First argument must be a Z3 function declaration")
4831 _z3_assert(all([is_array(a) for a in args]), "Z3 array expected expected")
4832 _z3_assert(len(args) == f.arity(), "Number of arguments mismatch")
4833 _args, sz = _to_ast_array(args)
4835 return ArrayRef(Z3_mk_map(ctx.ref(), f.ast, sz, _args), ctx)
4839 """Return a Z3 constant array expression.
4853 _z3_assert(is_sort(dom), "Z3 sort expected")
4856 v = _py2expr(v, ctx)
4857 return ArrayRef(Z3_mk_const_array(ctx.ref(), dom.ast, v.as_ast()), ctx)
4861 """Return extensionality index
for one-dimensional arrays.
4868 _z3_assert(is_array_sort(a) and (is_array(b) or b.is_lambda()), "arguments must be arrays")
4869 return _to_expr_ref(Z3_mk_array_ext(ctx.ref(), a.as_ast(), b.as_ast()), ctx)
4872 def SetHasSize(a, k):
4874 k = _py2expr(k, ctx)
4875 return _to_expr_ref(Z3_mk_set_has_size(ctx.ref(), a.as_ast(), k.as_ast()), ctx)
4879 """Return `
True`
if `a`
is a Z3 array select application.
4888 return is_app_of(a, Z3_OP_SELECT)
4892 """Return `
True`
if `a`
is a Z3 array store application.
4900 return is_app_of(a, Z3_OP_STORE)
4902 #########################################
4906 #########################################
4910 """ Create a set sort over element sort s
"""
4911 return ArraySort(s, BoolSort())
4915 """Create the empty set
4920 return ArrayRef(Z3_mk_empty_set(ctx.ref(), s.ast), ctx)
4924 """Create the full set
4929 return ArrayRef(Z3_mk_full_set(ctx.ref(), s.ast), ctx)
4932 def SetUnion(*args):
4933 """ Take the union of sets
4939 args = _get_args(args)
4940 ctx = _ctx_from_ast_arg_list(args)
4941 _args, sz = _to_ast_array(args)
4942 return ArrayRef(Z3_mk_set_union(ctx.ref(), sz, _args), ctx)
4945 def SetIntersect(*args):
4946 """ Take the union of sets
4952 args = _get_args(args)
4953 ctx = _ctx_from_ast_arg_list(args)
4954 _args, sz = _to_ast_array(args)
4955 return ArrayRef(Z3_mk_set_intersect(ctx.ref(), sz, _args), ctx)
4959 """ Add element e to set s
4964 ctx = _ctx_from_ast_arg_list([s, e])
4965 e = _py2expr(e, ctx)
4966 return ArrayRef(Z3_mk_set_add(ctx.ref(), s.as_ast(), e.as_ast()), ctx)
4970 """ Remove element e to set s
4975 ctx = _ctx_from_ast_arg_list([s, e])
4976 e = _py2expr(e, ctx)
4977 return ArrayRef(Z3_mk_set_del(ctx.ref(), s.as_ast(), e.as_ast()), ctx)
4980 def SetComplement(s):
4981 """ The complement of set s
4987 return ArrayRef(Z3_mk_set_complement(ctx.ref(), s.as_ast()), ctx)
4990 def SetDifference(a, b):
4991 """ The set difference of a
and b
4997 ctx = _ctx_from_ast_arg_list([a, b])
4998 return ArrayRef(Z3_mk_set_difference(ctx.ref(), a.as_ast(), b.as_ast()), ctx)
5002 """ Check
if e
is a member of set s
5007 ctx = _ctx_from_ast_arg_list([s, e])
5008 e = _py2expr(e, ctx)
5009 return BoolRef(Z3_mk_set_member(ctx.ref(), e.as_ast(), s.as_ast()), ctx)
5013 """ Check
if a
is a subset of b
5019 ctx = _ctx_from_ast_arg_list([a, b])
5020 return BoolRef(Z3_mk_set_subset(ctx.ref(), a.as_ast(), b.as_ast()), ctx)
5023 #########################################
5027 #########################################
5029 def _valid_accessor(acc):
5030 """Return `
True`
if acc
is pair of the form (String, Datatype
or Sort).
"""
5031 if not isinstance(acc, tuple):
5035 return isinstance(acc[0], str) and (isinstance(acc[1], Datatype) or is_sort(acc[1]))
5039 """Helper
class for declaring Z3 datatypes.
5042 >>> List.declare(
'cons', (
'car',
IntSort()), (
'cdr', List))
5043 >>> List.declare(
'nil')
5044 >>> List = List.create()
5048 >>> List.cons(10, List.nil)
5050 >>> List.cons(10, List.nil).sort()
5052 >>> cons = List.cons
5056 >>> n = cons(1, cons(0, nil))
5058 cons(1, cons(0, nil))
5065 def __init__(self, name, ctx=None):
5066 self.ctx = _get_ctx(ctx)
5068 self.constructors = []
5070 def __deepcopy__(self, memo={}):
5071 r = Datatype(self.name, self.ctx)
5072 r.constructors = copy.deepcopy(self.constructors)
5075 def declare_core(self, name, rec_name, *args):
5077 _z3_assert(isinstance(name, str), "String expected")
5078 _z3_assert(isinstance(rec_name, str), "String expected")
5080 all([_valid_accessor(a) for a in args]),
5081 "Valid list of accessors expected. An accessor is a pair of the form (String, Datatype|Sort)",
5083 self.constructors.append((name, rec_name, args))
5085 def declare(self, name, *args):
5086 """Declare constructor named `name` with the given accessors `args`.
5087 Each accessor
is a pair `(name, sort)`, where `name`
is a string
and `sort` a Z3 sort
5088 or a reference to the datatypes being declared.
5090 In the following example `List.declare(
'cons', (
'car',
IntSort()), (
'cdr', List))`
5091 declares the constructor named `cons` that builds a new List using an integer
and a List.
5092 It also declares the accessors `car`
and `cdr`. The accessor `car` extracts the integer
5093 of a `cons` cell,
and `cdr` the list of a `cons` cell. After all constructors were declared,
5094 we use the method
create() to create the actual datatype
in Z3.
5097 >>> List.declare(
'cons', (
'car',
IntSort()), (
'cdr', List))
5098 >>> List.declare(
'nil')
5099 >>> List = List.create()
5102 _z3_assert(isinstance(name, str), "String expected")
5103 _z3_assert(name != "", "Constructor name cannot be empty")
5104 return self.declare_core(name, "is-" + name, *args)
5107 return "Datatype(%s, %s)" % (self.name, self.constructors)
5110 """Create a Z3 datatype based on the constructors declared using the method `
declare()`.
5112 The function `
CreateDatatypes()` must be used to define mutually recursive datatypes.
5115 >>> List.declare(
'cons', (
'car',
IntSort()), (
'cdr', List))
5116 >>> List.declare(
'nil')
5117 >>> List = List.create()
5120 >>> List.cons(10, List.nil)
5123 return CreateDatatypes([self])[0]
5126 class ScopedConstructor:
5127 """Auxiliary object used to create Z3 datatypes.
"""
5129 def __init__(self, c, ctx):
5134 if self.ctx.ref() is not None and Z3_del_constructor is not None:
5135 Z3_del_constructor(self.ctx.ref(), self.c)
5138 class ScopedConstructorList:
5139 """Auxiliary object used to create Z3 datatypes.
"""
5141 def __init__(self, c, ctx):
5146 if self.ctx.ref() is not None and Z3_del_constructor_list is not None:
5147 Z3_del_constructor_list(self.ctx.ref(), self.c)
5150 def CreateDatatypes(*ds):
5151 """Create mutually recursive Z3 datatypes using 1
or more Datatype helper objects.
5153 In the following example we define a Tree-List using two mutually recursive datatypes.
5155 >>> TreeList =
Datatype(
'TreeList')
5158 >>> Tree.declare(
'leaf', (
'val',
IntSort()))
5160 >>> Tree.declare(
'node', (
'children', TreeList))
5161 >>> TreeList.declare(
'nil')
5162 >>> TreeList.declare(
'cons', (
'car', Tree), (
'cdr', TreeList))
5164 >>> Tree.val(Tree.leaf(10))
5166 >>>
simplify(Tree.val(Tree.leaf(10)))
5168 >>> n1 = Tree.node(TreeList.cons(Tree.leaf(10), TreeList.cons(Tree.leaf(20), TreeList.nil)))
5170 node(cons(leaf(10), cons(leaf(20), nil)))
5171 >>> n2 = Tree.node(TreeList.cons(n1, TreeList.nil))
5174 >>>
simplify(TreeList.car(Tree.children(n2)) == n1)
5179 _z3_assert(len(ds) > 0, "At least one Datatype must be specified")
5180 _z3_assert(all([isinstance(d, Datatype) for d in ds]), "Arguments must be Datatypes")
5181 _z3_assert(all([d.ctx == ds[0].ctx for d in ds]), "Context mismatch")
5182 _z3_assert(all([d.constructors != [] for d in ds]), "Non-empty Datatypes expected")
5185 names = (Symbol * num)()
5186 out = (Sort * num)()
5187 clists = (ConstructorList * num)()
5189 for i in range(num):
5191 names[i] = to_symbol(d.name, ctx)
5192 num_cs = len(d.constructors)
5193 cs = (Constructor * num_cs)()
5194 for j in range(num_cs):
5195 c = d.constructors[j]
5196 cname = to_symbol(c[0], ctx)
5197 rname = to_symbol(c[1], ctx)
5200 fnames = (Symbol * num_fs)()
5201 sorts = (Sort * num_fs)()
5202 refs = (ctypes.c_uint * num_fs)()
5203 for k in range(num_fs):
5206 fnames[k] = to_symbol(fname, ctx)
5207 if isinstance(ftype, Datatype):
5210 ds.count(ftype) == 1,
5211 "One and only one occurrence of each datatype is expected",
5214 refs[k] = ds.index(ftype)
5217 _z3_assert(is_sort(ftype), "Z3 sort expected")
5218 sorts[k] = ftype.ast
5220 cs[j] = Z3_mk_constructor(ctx.ref(), cname, rname, num_fs, fnames, sorts, refs)
5221 to_delete.append(ScopedConstructor(cs[j], ctx))
5222 clists[i] = Z3_mk_constructor_list(ctx.ref(), num_cs, cs)
5223 to_delete.append(ScopedConstructorList(clists[i], ctx))
5224 Z3_mk_datatypes(ctx.ref(), num, names, out, clists)
5226 # Create a field for every constructor, recognizer and accessor
5227 for i in range(num):
5228 dref = DatatypeSortRef(out[i], ctx)
5229 num_cs = dref.num_constructors()
5230 for j in range(num_cs):
5231 cref = dref.constructor(j)
5232 cref_name = cref.name()
5233 cref_arity = cref.arity()
5234 if cref.arity() == 0:
5236 setattr(dref, cref_name, cref)
5237 rref = dref.recognizer(j)
5238 setattr(dref, "is_" + cref_name, rref)
5239 for k in range(cref_arity):
5240 aref = dref.accessor(j, k)
5241 setattr(dref, aref.name(), aref)
5243 return tuple(result)
5246 class DatatypeSortRef(SortRef):
5247 """Datatype sorts.
"""
5249 def num_constructors(self):
5250 """Return the number of constructors
in the given Z3 datatype.
5253 >>> List.declare(
'cons', (
'car',
IntSort()), (
'cdr', List))
5254 >>> List.declare(
'nil')
5255 >>> List = List.create()
5257 >>> List.num_constructors()
5260 return int(Z3_get_datatype_sort_num_constructors(self.ctx_ref(), self.ast))
5262 def constructor(self, idx):
5263 """Return a constructor of the datatype `self`.
5266 >>> List.declare(
'cons', (
'car',
IntSort()), (
'cdr', List))
5267 >>> List.declare(
'nil')
5268 >>> List = List.create()
5270 >>> List.num_constructors()
5272 >>> List.constructor(0)
5274 >>> List.constructor(1)
5278 _z3_assert(idx < self.num_constructors(), "Invalid constructor index")
5279 return FuncDeclRef(Z3_get_datatype_sort_constructor(self.ctx_ref(), self.ast, idx), self.ctx)
5281 def recognizer(self, idx):
5282 """In Z3, each constructor has an associated recognizer predicate.
5284 If the constructor
is named `name`, then the recognizer `is_name`.
5287 >>> List.declare(
'cons', (
'car',
IntSort()), (
'cdr', List))
5288 >>> List.declare(
'nil')
5289 >>> List = List.create()
5291 >>> List.num_constructors()
5293 >>> List.recognizer(0)
5295 >>> List.recognizer(1)
5297 >>>
simplify(List.is_nil(List.cons(10, List.nil)))
5299 >>>
simplify(List.is_cons(List.cons(10, List.nil)))
5301 >>> l =
Const(
'l', List)
5306 _z3_assert(idx < self.num_constructors(), "Invalid recognizer index")
5307 return FuncDeclRef(Z3_get_datatype_sort_recognizer(self.ctx_ref(), self.ast, idx), self.ctx)
5309 def accessor(self, i, j):
5310 """In Z3, each constructor has 0
or more accessor.
5311 The number of accessors
is equal to the arity of the constructor.
5314 >>> List.declare(
'cons', (
'car',
IntSort()), (
'cdr', List))
5315 >>> List.declare(
'nil')
5316 >>> List = List.create()
5317 >>> List.num_constructors()
5319 >>> List.constructor(0)
5321 >>> num_accs = List.constructor(0).arity()
5324 >>> List.accessor(0, 0)
5326 >>> List.accessor(0, 1)
5328 >>> List.constructor(1)
5330 >>> num_accs = List.constructor(1).arity()
5335 _z3_assert(i < self.num_constructors(), "Invalid constructor index")
5336 _z3_assert(j < self.constructor(i).arity(), "Invalid accessor index")
5338 Z3_get_datatype_sort_constructor_accessor(self.ctx_ref(), self.ast, i, j),
5343 class DatatypeRef(ExprRef):
5344 """Datatype expressions.
"""
5347 """Return the datatype sort of the datatype expression `self`.
"""
5348 return DatatypeSortRef(Z3_get_sort(self.ctx_ref(), self.as_ast()), self.ctx)
5350 def DatatypeSort(name, ctx = None):
5351 """Create a reference to a sort that was declared,
or will be declared,
as a recursive datatype
"""
5353 return DatatypeSortRef(Z3_mk_datatype_sort(ctx.ref(), to_symbol(name, ctx)), ctx)
5355 def TupleSort(name, sorts, ctx=None):
5356 """Create a named tuple sort base on a set of underlying sorts
5360 tuple = Datatype(name, ctx)
5361 projects = [("project%d" % i, sorts[i]) for i in range(len(sorts))]
5362 tuple.declare(name, *projects)
5363 tuple = tuple.create()
5364 return tuple, tuple.constructor(0), [tuple.accessor(0, i) for i in range(len(sorts))]
5367 def DisjointSum(name, sorts, ctx=None):
5368 """Create a named tagged union sort base on a set of underlying sorts
5372 sum = Datatype(name, ctx)
5373 for i in range(len(sorts)):
5374 sum.declare("inject%d" % i, ("project%d" % i, sorts[i]))
5376 return sum, [(sum.constructor(i), sum.accessor(i, 0)) for i in range(len(sorts))]
5379 def EnumSort(name, values, ctx=None):
5380 """Return a new enumeration sort named `name` containing the given values.
5382 The result
is a pair (sort, list of constants).
5384 >>> Color, (red, green, blue) =
EnumSort(
'Color', [
'red',
'green',
'blue'])
5387 _z3_assert(isinstance(name, str), "Name must be a string")
5388 _z3_assert(all([isinstance(v, str) for v in values]), "Eumeration sort values must be strings")
5389 _z3_assert(len(values) > 0, "At least one value expected")
5392 _val_names = (Symbol * num)()
5393 for i in range(num):
5394 _val_names[i] = to_symbol(values[i])
5395 _values = (FuncDecl * num)()
5396 _testers = (FuncDecl * num)()
5397 name = to_symbol(name)
5398 S = DatatypeSortRef(Z3_mk_enumeration_sort(ctx.ref(), name, num, _val_names, _values, _testers), ctx)
5400 for i in range(num):
5401 V.append(FuncDeclRef(_values[i], ctx))
5402 V = [a() for a in V]
5405 #########################################
5409 #########################################
5413 """Set of parameters used to configure Solvers, Tactics
and Simplifiers
in Z3.
5415 Consider using the function `args2params` to create instances of this object.
5418 def __init__(self, ctx=None, params=None):
5419 self.ctx = _get_ctx(ctx)
5421 self.params = Z3_mk_params(self.ctx.ref())
5423 self.params = params
5424 Z3_params_inc_ref(self.ctx.ref(), self.params)
5426 def __deepcopy__(self, memo={}):
5427 return ParamsRef(self.ctx, self.params)
5430 if self.ctx.ref() is not None and Z3_params_dec_ref is not None:
5431 Z3_params_dec_ref(self.ctx.ref(), self.params)
5433 def set(self, name, val):
5434 """Set parameter name with value val.
"""
5436 _z3_assert(isinstance(name, str), "parameter name must be a string")
5437 name_sym = to_symbol(name, self.ctx)
5438 if isinstance(val, bool):
5439 Z3_params_set_bool(self.ctx.ref(), self.params, name_sym, val)
5441 Z3_params_set_uint(self.ctx.ref(), self.params, name_sym, val)
5442 elif isinstance(val, float):
5443 Z3_params_set_double(self.ctx.ref(), self.params, name_sym, val)
5444 elif isinstance(val, str):
5445 Z3_params_set_symbol(self.ctx.ref(), self.params, name_sym, to_symbol(val, self.ctx))
5448 _z3_assert(False, "invalid parameter value")
5451 return Z3_params_to_string(self.ctx.ref(), self.params)
5453 def validate(self, ds):
5454 _z3_assert(isinstance(ds, ParamDescrsRef), "parameter description set expected")
5455 Z3_params_validate(self.ctx.ref(), self.params, ds.descr)
5458 def args2params(arguments, keywords, ctx=None):
5459 """Convert python arguments into a Z3_params object.
5460 A
':' is added to the keywords,
and '_' is replaced with
'-'
5462 >>>
args2params([
'model',
True,
'relevancy', 2], {
'elim_and' :
True})
5463 (params model true relevancy 2 elim_and true)
5466 _z3_assert(len(arguments) % 2 == 0, "Argument list must have an even number of elements.")
5481 class ParamDescrsRef:
5482 """Set of parameter descriptions
for Solvers, Tactics
and Simplifiers
in Z3.
5485 def __init__(self, descr, ctx=None):
5486 _z3_assert(isinstance(descr, ParamDescrs), "parameter description object expected")
5487 self.ctx = _get_ctx(ctx)
5489 Z3_param_descrs_inc_ref(self.ctx.ref(), self.descr)
5491 def __deepcopy__(self, memo={}):
5492 return ParamsDescrsRef(self.descr, self.ctx)
5495 if self.ctx.ref() is not None and Z3_param_descrs_dec_ref is not None:
5496 Z3_param_descrs_dec_ref(self.ctx.ref(), self.descr)
5499 """Return the size of
in the parameter description `self`.
5501 return int(Z3_param_descrs_size(self.ctx.ref(), self.descr))
5504 """Return the size of
in the parameter description `self`.
5508 def get_name(self, i):
5509 """Return the i-th parameter name
in the parameter description `self`.
5511 return _symbol2py(self.ctx, Z3_param_descrs_get_name(self.ctx.ref(), self.descr, i))
5513 def get_kind(self, n):
5514 """Return the kind of the parameter named `n`.
5516 return Z3_param_descrs_get_kind(self.ctx.ref(), self.descr, to_symbol(n, self.ctx))
5518 def get_documentation(self, n):
5519 """Return the documentation string of the parameter named `n`.
5521 return Z3_param_descrs_get_documentation(self.ctx.ref(), self.descr, to_symbol(n, self.ctx))
5523 def __getitem__(self, arg):
5525 return self.get_name(arg)
5527 return self.get_kind(arg)
5530 return Z3_param_descrs_to_string(self.ctx.ref(), self.descr)
5532 #########################################
5536 #########################################
5539 class Goal(Z3PPObject):
5540 """Goal
is a collection of constraints we want to find a solution
or show to be unsatisfiable (infeasible).
5542 Goals are processed using Tactics. A Tactic transforms a goal into a set of subgoals.
5543 A goal has a solution
if one of its subgoals has a solution.
5544 A goal
is unsatisfiable
if all subgoals are unsatisfiable.
5547 def __init__(self, models=True, unsat_cores=False, proofs=False, ctx=None, goal=None):
5549 _z3_assert(goal is None or ctx is not None,
5550 "If goal is different from None, then ctx must be also different from None")
5551 self.ctx = _get_ctx(ctx)
5553 if self.goal is None:
5554 self.goal = Z3_mk_goal(self.ctx.ref(), models, unsat_cores, proofs)
5555 Z3_goal_inc_ref(self.ctx.ref(), self.goal)
5558 if self.goal is not None and self.ctx.ref() is not None and Z3_goal_dec_ref is not None:
5559 Z3_goal_dec_ref(self.ctx.ref(), self.goal)
5562 """Return the depth of the goal `self`.
5563 The depth corresponds to the number of tactics applied to `self`.
5565 >>> x, y =
Ints(
'x y')
5567 >>> g.add(x == 0, y >= x + 1)
5570 >>> r =
Then(
'simplify',
'solve-eqs')(g)
5577 return int(Z3_goal_depth(self.ctx.ref(), self.goal))
5579 def inconsistent(self):
5580 """Return `
True`
if `self` contains the `
False` constraints.
5582 >>> x, y =
Ints(
'x y')
5584 >>> g.inconsistent()
5586 >>> g.add(x == 0, x == 1)
5589 >>> g.inconsistent()
5591 >>> g2 =
Tactic(
'propagate-values')(g)[0]
5592 >>> g2.inconsistent()
5595 return Z3_goal_inconsistent(self.ctx.ref(), self.goal)
5598 """Return the precision (under-approximation, over-approximation,
or precise) of the goal `self`.
5601 >>> g.prec() == Z3_GOAL_PRECISE
5603 >>> x, y =
Ints(
'x y')
5604 >>> g.add(x == y + 1)
5605 >>> g.prec() == Z3_GOAL_PRECISE
5607 >>> t =
With(
Tactic(
'add-bounds'), add_bound_lower=0, add_bound_upper=10)
5610 [x == y + 1, x <= 10, x >= 0, y <= 10, y >= 0]
5611 >>> g2.prec() == Z3_GOAL_PRECISE
5613 >>> g2.prec() == Z3_GOAL_UNDER
5616 return Z3_goal_precision(self.ctx.ref(), self.goal)
5618 def precision(self):
5619 """Alias
for `
prec()`.
5622 >>> g.precision() == Z3_GOAL_PRECISE
5628 """Return the number of constraints
in the goal `self`.
5633 >>> x, y =
Ints(
'x y')
5634 >>> g.add(x == 0, y > x)
5638 return int(Z3_goal_size(self.ctx.ref(), self.goal))
5641 """Return the number of constraints
in the goal `self`.
5646 >>> x, y =
Ints(
'x y')
5647 >>> g.add(x == 0, y > x)
5654 """Return a constraint
in the goal `self`.
5657 >>> x, y =
Ints(
'x y')
5658 >>> g.add(x == 0, y > x)
5664 return _to_expr_ref(Z3_goal_formula(self.ctx.ref(), self.goal, i), self.ctx)
5666 def __getitem__(self, arg):
5667 """Return a constraint
in the goal `self`.
5670 >>> x, y =
Ints(
'x y')
5671 >>> g.add(x == 0, y > x)
5677 if arg >= len(self):
5679 return self.get(arg)
5681 def assert_exprs(self, *args):
5682 """Assert constraints into the goal.
5686 >>> g.assert_exprs(x > 0, x < 2)
5690 args = _get_args(args)
5691 s = BoolSort(self.ctx)
5694 Z3_goal_assert(self.ctx.ref(), self.goal, arg.as_ast())
5696 def append(self, *args):
5701 >>> g.append(x > 0, x < 2)
5705 self.assert_exprs(*args)
5707 def insert(self, *args):
5712 >>> g.insert(x > 0, x < 2)
5716 self.assert_exprs(*args)
5718 def add(self, *args):
5723 >>> g.add(x > 0, x < 2)
5727 self.assert_exprs(*args)
5729 def convert_model(self, model):
5730 """Retrieve model
from a satisfiable goal
5731 >>> a, b =
Ints(
'a b')
5733 >>> g.add(
Or(a == 0, a == 1),
Or(b == 0, b == 1), a > b)
5737 [
Or(b == 0, b == 1),
Not(0 <= b)]
5739 [
Or(b == 0, b == 1),
Not(1 <= b)]
5755 _z3_assert(isinstance(model, ModelRef), "Z3 Model expected")
5756 return ModelRef(Z3_goal_convert_model(self.ctx.ref(), self.goal, model.model), self.ctx)
5759 return obj_to_string(self)
5762 """Return a textual representation of the s-expression representing the goal.
"""
5763 return Z3_goal_to_string(self.ctx.ref(), self.goal)
5765 def dimacs(self, include_names=True):
5766 """Return a textual representation of the goal
in DIMACS format.
"""
5767 return Z3_goal_to_dimacs_string(self.ctx.ref(), self.goal, include_names)
5769 def translate(self, target):
5770 """Copy goal `self` to context `target`.
5778 >>> g2 = g.translate(c2)
5789 _z3_assert(isinstance(target, Context), "target must be a context")
5790 return Goal(goal=Z3_goal_translate(self.ctx.ref(), self.goal, target.ref()), ctx=target)
5793 return self.translate(self.ctx)
5795 def __deepcopy__(self, memo={}):
5796 return self.translate(self.ctx)
5798 def simplify(self, *arguments, **keywords):
5799 """Return a new simplified goal.
5801 This method
is essentially invoking the simplify tactic.
5805 >>> g.add(x + 1 >= 2)
5808 >>> g2 = g.simplify()
5815 t = Tactic("simplify")
5816 return t.apply(self, *arguments, **keywords)[0]
5819 """Return goal `self`
as a single Z3 expression.
5834 return BoolVal(True, self.ctx)
5838 return And([self.get(i) for i in range(len(self))], self.ctx)
5840 #########################################
5844 #########################################
5847 class AstVector(Z3PPObject):
5848 """A collection (vector) of ASTs.
"""
5850 def __init__(self, v=None, ctx=None):
5853 self.ctx = _get_ctx(ctx)
5854 self.vector = Z3_mk_ast_vector(self.ctx.ref())
5857 assert ctx is not None
5859 Z3_ast_vector_inc_ref(self.ctx.ref(), self.vector)
5862 if self.vector is not None and self.ctx.ref() is not None and Z3_ast_vector_dec_ref is not None:
5863 Z3_ast_vector_dec_ref(self.ctx.ref(), self.vector)
5866 """Return the size of the vector `self`.
5871 >>> A.push(
Int(
'x'))
5872 >>> A.push(
Int(
'x'))
5876 return int(Z3_ast_vector_size(self.ctx.ref(), self.vector))
5878 def __getitem__(self, i):
5879 """Return the AST at position `i`.
5882 >>> A.push(
Int(
'x') + 1)
5883 >>> A.push(
Int(
'y'))
5890 if isinstance(i, int):
5894 if i >= self.__len__():
5896 return _to_ast_ref(Z3_ast_vector_get(self.ctx.ref(), self.vector, i), self.ctx)
5898 elif isinstance(i, slice):
5900 for ii in range(*i.indices(self.__len__())):
5901 result.append(_to_ast_ref(
5902 Z3_ast_vector_get(self.ctx.ref(), self.vector, ii),
5907 def __setitem__(self, i, v):
5908 """Update AST at position `i`.
5911 >>> A.push(
Int(
'x') + 1)
5912 >>> A.push(
Int(
'y'))
5919 if i >= self.__len__():
5921 Z3_ast_vector_set(self.ctx.ref(), self.vector, i, v.as_ast())
5924 """Add `v`
in the end of the vector.
5929 >>> A.push(
Int(
'x'))
5933 Z3_ast_vector_push(self.ctx.ref(), self.vector, v.as_ast())
5935 def resize(self, sz):
5936 """Resize the vector to `sz` elements.
5942 >>>
for i
in range(10): A[i] =
Int(
'x')
5946 Z3_ast_vector_resize(self.ctx.ref(), self.vector, sz)
5948 def __contains__(self, item):
5949 """Return `
True`
if the vector contains `item`.
5971 def translate(self, other_ctx):
5972 """Copy vector `self` to context `other_ctx`.
5978 >>> B = A.translate(c2)
5983 Z3_ast_vector_translate(self.ctx.ref(), self.vector, other_ctx.ref()),
5988 return self.translate(self.ctx)
5990 def __deepcopy__(self, memo={}):
5991 return self.translate(self.ctx)
5994 return obj_to_string(self)
5997 """Return a textual representation of the s-expression representing the vector.
"""
5998 return Z3_ast_vector_to_string(self.ctx.ref(), self.vector)
6000 #########################################
6004 #########################################
6008 """A mapping
from ASTs to ASTs.
"""
6010 def __init__(self, m=None, ctx=None):
6013 self.ctx = _get_ctx(ctx)
6014 self.map = Z3_mk_ast_map(self.ctx.ref())
6017 assert ctx is not None
6019 Z3_ast_map_inc_ref(self.ctx.ref(), self.map)
6021 def __deepcopy__(self, memo={}):
6022 return AstMap(self.map, self.ctx)
6025 if self.map is not None and self.ctx.ref() is not None and Z3_ast_map_dec_ref is not None:
6026 Z3_ast_map_dec_ref(self.ctx.ref(), self.map)
6029 """Return the size of the map.
6039 return int(Z3_ast_map_size(self.ctx.ref(), self.map))
6041 def __contains__(self, key):
6042 """Return `
True`
if the map contains key `key`.
6052 return Z3_ast_map_contains(self.ctx.ref(), self.map, key.as_ast())
6054 def __getitem__(self, key):
6055 """Retrieve the value associated with key `key`.
6063 return _to_ast_ref(Z3_ast_map_find(self.ctx.ref(), self.map, key.as_ast()), self.ctx)
6065 def __setitem__(self, k, v):
6066 """Add/Update key `k` with value `v`.
6079 Z3_ast_map_insert(self.ctx.ref(), self.map, k.as_ast(), v.as_ast())
6082 return Z3_ast_map_to_string(self.ctx.ref(), self.map)
6085 """Remove the entry associated with key `k`.
6096 Z3_ast_map_erase(self.ctx.ref(), self.map, k.as_ast())
6099 """Remove all entries
from the map.
6111 Z3_ast_map_reset(self.ctx.ref(), self.map)
6114 """Return an AstVector containing all keys
in the map.
6123 return AstVector(Z3_ast_map_keys(self.ctx.ref(), self.map), self.ctx)
6125 #########################################
6129 #########################################
6133 """Store the value of the interpretation of a function
in a particular point.
"""
6135 def __init__(self, entry, ctx):
6138 Z3_func_entry_inc_ref(self.ctx.ref(), self.entry)
6140 def __deepcopy__(self, memo={}):
6141 return FuncEntry(self.entry, self.ctx)
6144 if self.ctx.ref() is not None and Z3_func_entry_dec_ref is not None:
6145 Z3_func_entry_dec_ref(self.ctx.ref(), self.entry)
6148 """Return the number of arguments
in the given entry.
6152 >>> s.add(f(0, 1) == 10, f(1, 2) == 20, f(1, 0) == 10)
6157 >>> f_i.num_entries()
6159 >>> e = f_i.entry(0)
6163 return int(Z3_func_entry_get_num_args(self.ctx.ref(), self.entry))
6165 def arg_value(self, idx):
6166 """Return the value of argument `idx`.
6170 >>> s.add(f(0, 1) == 10, f(1, 2) == 20, f(1, 0) == 10)
6175 >>> f_i.num_entries()
6177 >>> e = f_i.entry(0)
6188 ...
except IndexError:
6189 ... print(
"index error")
6192 if idx >= self.num_args():
6194 return _to_expr_ref(Z3_func_entry_get_arg(self.ctx.ref(), self.entry, idx), self.ctx)
6197 """Return the value of the function at point `self`.
6201 >>> s.add(f(0, 1) == 10, f(1, 2) == 20, f(1, 0) == 10)
6206 >>> f_i.num_entries()
6208 >>> e = f_i.entry(0)
6216 return _to_expr_ref(Z3_func_entry_get_value(self.ctx.ref(), self.entry), self.ctx)
6219 """Return entry `self`
as a Python list.
6222 >>> s.add(f(0, 1) == 10, f(1, 2) == 20, f(1, 0) == 10)
6227 >>> f_i.num_entries()
6229 >>> e = f_i.entry(0)
6233 args = [self.arg_value(i) for i in range(self.num_args())]
6234 args.append(self.value())
6238 return repr(self.as_list())
6241 class FuncInterp(Z3PPObject):
6242 """Stores the interpretation of a function
in a Z3 model.
"""
6244 def __init__(self, f, ctx):
6247 if self.f is not None:
6248 Z3_func_interp_inc_ref(self.ctx.ref(), self.f)
6251 if self.f is not None and self.ctx.ref() is not None and Z3_func_interp_dec_ref is not None:
6252 Z3_func_interp_dec_ref(self.ctx.ref(), self.f)
6254 def else_value(self):
6256 Return the `
else` value
for a function interpretation.
6257 Return
None if Z3 did
not specify the `
else` value
for
6262 >>> s.add(
f(0) == 1,
f(1) == 1,
f(2) == 0)
6271 r = Z3_func_interp_get_else(self.ctx.ref(), self.f)
6273 return _to_expr_ref(r, self.ctx)
6277 def num_entries(self):
6278 """Return the number of entries/points
in the function interpretation `self`.
6282 >>> s.add(
f(0) == 1,
f(1) == 1,
f(2) == 0)
6291 return int(Z3_func_interp_get_num_entries(self.ctx.ref(), self.f))
6294 """Return the number of arguments
for each entry
in the function interpretation `self`.
6298 >>> s.add(
f(0) == 1,
f(1) == 1,
f(2) == 0)
6305 return int(Z3_func_interp_get_arity(self.ctx.ref(), self.f))
6307 def entry(self, idx):
6308 """Return an entry at position `idx < self.
num_entries()`
in the function interpretation `self`.
6312 >>> s.add(
f(0) == 1,
f(1) == 1,
f(2) == 0)
6323 if idx >= self.num_entries():
6325 return FuncEntry(Z3_func_interp_get_entry(self.ctx.ref(), self.f, idx), self.ctx)
6327 def translate(self, other_ctx):
6328 """Copy model
'self' to context
'other_ctx'.
6330 return ModelRef(Z3_model_translate(self.ctx.ref(), self.model, other_ctx.ref()), other_ctx)
6333 return self.translate(self.ctx)
6335 def __deepcopy__(self, memo={}):
6336 return self.translate(self.ctx)
6339 """Return the function interpretation
as a Python list.
6342 >>> s.add(
f(0) == 1,
f(1) == 1,
f(2) == 0)
6351 r = [self.entry(i).as_list() for i in range(self.num_entries())]
6352 r.append(self.else_value())
6356 return obj_to_string(self)
6359 class ModelRef(Z3PPObject):
6360 """Model/Solution of a satisfiability problem (aka system of constraints).
"""
6362 def __init__(self, m, ctx):
6363 assert ctx is not None
6366 Z3_model_inc_ref(self.ctx.ref(), self.model)
6369 if self.ctx.ref() is not None and Z3_model_dec_ref is not None:
6370 Z3_model_dec_ref(self.ctx.ref(), self.model)
6373 return obj_to_string(self)
6376 """Return a textual representation of the s-expression representing the model.
"""
6377 return Z3_model_to_string(self.ctx.ref(), self.model)
6379 def eval(self, t, model_completion=False):
6380 """Evaluate the expression `t`
in the model `self`.
6381 If `model_completion`
is enabled, then a default interpretation
is automatically added
6382 for symbols that do
not have an interpretation
in the model `self`.
6386 >>> s.add(x > 0, x < 2)
6399 >>> m.eval(y, model_completion=
True)
6406 if Z3_model_eval(self.ctx.ref(), self.model, t.as_ast(), model_completion, r):
6407 return _to_expr_ref(r[0], self.ctx)
6408 raise Z3Exception("failed to evaluate expression in the model")
6410 def evaluate(self, t, model_completion=False):
6411 """Alias
for `eval`.
6415 >>> s.add(x > 0, x < 2)
6419 >>> m.evaluate(x + 1)
6421 >>> m.evaluate(x == 1)
6424 >>> m.evaluate(y + x)
6428 >>> m.evaluate(y, model_completion=
True)
6431 >>> m.evaluate(y + x)
6434 return self.eval(t, model_completion)
6437 """Return the number of constant
and function declarations
in the model `self`.
6442 >>> s.add(x > 0, f(x) != x)
6449 num_consts = int(Z3_model_get_num_consts(self.ctx.ref(), self.model))
6450 num_funcs = int(Z3_model_get_num_funcs(self.ctx.ref(), self.model))
6451 return num_consts + num_funcs
6453 def get_interp(self, decl):
6454 """Return the interpretation
for a given declaration
or constant.
6459 >>> s.add(x > 0, x < 2, f(x) == 0)
6469 _z3_assert(isinstance(decl, FuncDeclRef) or is_const(decl), "Z3 declaration expected")
6473 if decl.arity() == 0:
6474 _r = Z3_model_get_const_interp(self.ctx.ref(), self.model, decl.ast)
6475 if _r.value is None:
6477 r = _to_expr_ref(_r, self.ctx)
6479 fi = self.get_interp(get_as_array_func(r))
6491 sz = fi.num_entries()
6495 e = Store(e, fe.arg_value(0), fe.value())
6501 return FuncInterp(Z3_model_get_func_interp(self.ctx.ref(), self.model, decl.ast), self.ctx)
6505 def num_sorts(self):
6506 """Return the number of uninterpreted sorts that contain an interpretation
in the model `self`.
6509 >>> a, b =
Consts(
'a b', A)
6518 return int(Z3_model_get_num_sorts(self.ctx.ref(), self.model))
6520 def get_sort(self, idx):
6521 """Return the uninterpreted sort at position `idx` < self.
num_sorts().
6525 >>> a1, a2 =
Consts(
'a1 a2', A)
6526 >>> b1, b2 =
Consts(
'b1 b2', B)
6528 >>> s.add(a1 != a2, b1 != b2)
6539 if idx >= self.num_sorts():
6541 return _to_sort_ref(Z3_model_get_sort(self.ctx.ref(), self.model, idx), self.ctx)
6544 """Return all uninterpreted sorts that have an interpretation
in the model `self`.
6548 >>> a1, a2 =
Consts(
'a1 a2', A)
6549 >>> b1, b2 =
Consts(
'b1 b2', B)
6551 >>> s.add(a1 != a2, b1 != b2)
6558 return [self.get_sort(i) for i in range(self.num_sorts())]
6560 def get_universe(self, s):
6561 """Return the interpretation
for the uninterpreted sort `s`
in the model `self`.
6564 >>> a, b =
Consts(
'a b', A)
6570 >>> m.get_universe(A)
6574 _z3_assert(isinstance(s, SortRef), "Z3 sort expected")
6576 return AstVector(Z3_model_get_sort_universe(self.ctx.ref(), self.model, s.ast), self.ctx)
6580 def __getitem__(self, idx):
6581 """If `idx`
is an integer, then the declaration at position `idx`
in the model `self`
is returned.
6582 If `idx`
is a declaration, then the actual interpretation
is returned.
6584 The elements can be retrieved using position
or the actual declaration.
6589 >>> s.add(x > 0, x < 2, f(x) == 0)
6603 >>>
for d
in m: print(
"%s -> %s" % (d, m[d]))
6608 if idx >= len(self):
6610 num_consts = Z3_model_get_num_consts(self.ctx.ref(), self.model)
6611 if (idx < num_consts):
6612 return FuncDeclRef(Z3_model_get_const_decl(self.ctx.ref(), self.model, idx), self.ctx)
6614 return FuncDeclRef(Z3_model_get_func_decl(self.ctx.ref(), self.model, idx - num_consts), self.ctx)
6615 if isinstance(idx, FuncDeclRef):
6616 return self.get_interp(idx)
6618 return self.get_interp(idx.decl())
6619 if isinstance(idx, SortRef):
6620 return self.get_universe(idx)
6622 _z3_assert(False, "Integer, Z3 declaration, or Z3 constant expected")
6626 """Return a list with all symbols that have an interpretation
in the model `self`.
6630 >>> s.add(x > 0, x < 2, f(x) == 0)
6638 for i in range(Z3_model_get_num_consts(self.ctx.ref(), self.model)):
6639 r.append(FuncDeclRef(Z3_model_get_const_decl(self.ctx.ref(), self.model, i), self.ctx))
6640 for i in range(Z3_model_get_num_funcs(self.ctx.ref(), self.model)):
6641 r.append(FuncDeclRef(Z3_model_get_func_decl(self.ctx.ref(), self.model, i), self.ctx))
6644 def update_value(self, x, value):
6645 """Update the interpretation of a constant
"""
6648 if is_func_decl(x) and x.arity() != 0 and isinstance(value, FuncInterp):
6650 fi2 = Z3_add_func_interp(x.ctx_ref(), self.model, x.ast, value.else_value().ast);
6651 fi2 = FuncInterp(fi2, x.ctx)
6652 for i in range(value.num_entries()):
6654 n = Z3_func_entry_get_num_args(x.ctx_ref(), e.entry)
6657 v.push(e.arg_value(j))
6658 val = Z3_func_entry_get_value(x.ctx_ref(), e.entry)
6659 Z3_func_interp_add_entry(x.ctx_ref(), fi2.f, v.vector, val)
6661 if not is_func_decl(x) or x.arity() != 0:
6662 raise Z3Exception("Expecting 0-ary function or constant expression")
6663 value = _py2expr(value)
6664 Z3_add_const_interp(x.ctx_ref(), self.model, x.ast, value.ast)
6666 def translate(self, target):
6667 """Translate `self` to the context `target`. That
is,
return a copy of `self`
in the context `target`.
6670 _z3_assert(isinstance(target, Context), "argument must be a Z3 context")
6671 model = Z3_model_translate(self.ctx.ref(), self.model, target.ref())
6672 return ModelRef(model, target)
6675 return self.translate(self.ctx)
6677 def __deepcopy__(self, memo={}):
6678 return self.translate(self.ctx)
6681 def Model(ctx=None):
6683 return ModelRef(Z3_mk_model(ctx.ref()), ctx)
6687 """Return true
if n
is a Z3 expression of the form (_
as-array f).
"""
6688 return isinstance(n, ExprRef) and Z3_is_as_array(n.ctx.ref(), n.as_ast())
6691 def get_as_array_func(n):
6692 """Return the function declaration f associated with a Z3 expression of the form (_
as-array f).
"""
6694 _z3_assert(is_as_array(n), "as-array Z3 expression expected.")
6695 return FuncDeclRef(Z3_get_as_array_func_decl(n.ctx.ref(), n.as_ast()), n.ctx)
6697 #########################################
6701 #########################################
6705 """Statistics
for `Solver.check()`.
"""
6707 def __init__(self, stats, ctx):
6710 Z3_stats_inc_ref(self.ctx.ref(), self.stats)
6712 def __deepcopy__(self, memo={}):
6713 return Statistics(self.stats, self.ctx)
6716 if self.ctx.ref() is not None and Z3_stats_dec_ref is not None:
6717 Z3_stats_dec_ref(self.ctx.ref(), self.stats)
6723 out.write(u('<table border="1" cellpadding="2" cellspacing="0">'))
6726 out.write(u('<tr style="background-color:#CFCFCF">'))
6729 out.write(u("<tr>"))
6731 out.write(u("<td>%s</td><td>%s</td></tr>" % (k, v)))
6732 out.write(u("</table>"))
6733 return out.getvalue()
6735 return Z3_stats_to_string(self.ctx.ref(), self.stats)
6738 """Return the number of statistical counters.
6741 >>> s =
Then(
'simplify',
'nlsat').solver()
6745 >>> st = s.statistics()
6749 return int(Z3_stats_size(self.ctx.ref(), self.stats))
6751 def __getitem__(self, idx):
6752 """Return the value of statistical counter at position `idx`. The result
is a pair (key, value).
6755 >>> s =
Then(
'simplify',
'nlsat').solver()
6759 >>> st = s.statistics()
6763 (
'nlsat propagations', 2)
6767 if idx >= len(self):
6769 if Z3_stats_is_uint(self.ctx.ref(), self.stats, idx):
6770 val = int(Z3_stats_get_uint_value(self.ctx.ref(), self.stats, idx))
6772 val = Z3_stats_get_double_value(self.ctx.ref(), self.stats, idx)
6773 return (Z3_stats_get_key(self.ctx.ref(), self.stats, idx), val)
6776 """Return the list of statistical counters.
6779 >>> s =
Then(
'simplify',
'nlsat').solver()
6783 >>> st = s.statistics()
6785 return [Z3_stats_get_key(self.ctx.ref(), self.stats, idx) for idx in range(len(self))]
6787 def get_key_value(self, key):
6788 """Return the value of a particular statistical counter.
6791 >>> s =
Then(
'simplify',
'nlsat').solver()
6795 >>> st = s.statistics()
6796 >>> st.get_key_value(
'nlsat propagations')
6799 for idx in range(len(self)):
6800 if key == Z3_stats_get_key(self.ctx.ref(), self.stats, idx):
6801 if Z3_stats_is_uint(self.ctx.ref(), self.stats, idx):
6802 return int(Z3_stats_get_uint_value(self.ctx.ref(), self.stats, idx))
6804 return Z3_stats_get_double_value(self.ctx.ref(), self.stats, idx)
6805 raise Z3Exception("unknown key")
6807 def __getattr__(self, name):
6808 """Access the value of statistical using attributes.
6810 Remark: to access a counter containing blank spaces (e.g.,
'nlsat propagations'),
6811 we should use
'_' (e.g.,
'nlsat_propagations').
6814 >>> s =
Then(
'simplify',
'nlsat').solver()
6818 >>> st = s.statistics()
6819 >>> st.nlsat_propagations
6824 key = name.replace("_", " ")
6826 return self.get_key_value(key)
6828 raise AttributeError
6830 #########################################
6834 #########################################
6837 class CheckSatResult:
6838 """Represents the result of a satisfiability check: sat, unsat, unknown.
6844 >>> isinstance(r, CheckSatResult)
6848 def __init__(self, r):
6851 def __deepcopy__(self, memo={}):
6852 return CheckSatResult(self.r)
6854 def __eq__(self, other):
6855 return isinstance(other, CheckSatResult) and self.r == other.r
6857 def __ne__(self, other):
6858 return not self.__eq__(other)
6862 if self.r == Z3_L_TRUE:
6864 elif self.r == Z3_L_FALSE:
6865 return "<b>unsat</b>"
6867 return "<b>unknown</b>"
6869 if self.r == Z3_L_TRUE:
6871 elif self.r == Z3_L_FALSE:
6876 def _repr_html_(self):
6877 in_html = in_html_mode()
6880 set_html_mode(in_html)
6884 sat = CheckSatResult(Z3_L_TRUE)
6885 unsat = CheckSatResult(Z3_L_FALSE)
6886 unknown = CheckSatResult(Z3_L_UNDEF)
6889 class Solver(Z3PPObject):
6891 Solver API provides methods
for implementing the main SMT 2.0 commands:
6892 push, pop, check, get-model, etc.
6895 def __init__(self, solver=None, ctx=None, logFile=None):
6896 assert solver is None or ctx is not None
6897 self.ctx = _get_ctx(ctx)
6898 self.backtrack_level = 4000000000
6901 self.solver = Z3_mk_solver(self.ctx.ref())
6903 self.solver = solver
6904 Z3_solver_inc_ref(self.ctx.ref(), self.solver)
6905 if logFile is not None:
6906 self.set("smtlib2_log", logFile)
6909 if self.solver is not None and self.ctx.ref() is not None and Z3_solver_dec_ref is not None:
6910 Z3_solver_dec_ref(self.ctx.ref(), self.solver)
6912 def set(self, *args, **keys):
6913 """Set a configuration option.
6914 The method `
help()`
return a string containing all available options.
6918 >>> s.set(mbqi=
True)
6919 >>> s.set(
'MBQI',
True)
6920 >>> s.set(
':mbqi',
True)
6922 p = args2params(args, keys, self.ctx)
6923 Z3_solver_set_params(self.ctx.ref(), self.solver, p.params)
6926 """Create a backtracking point.
6945 Z3_solver_push(self.ctx.ref(), self.solver)
6947 def pop(self, num=1):
6948 """Backtrack \\c num backtracking points.
6967 Z3_solver_pop(self.ctx.ref(), self.solver, num)
6969 def num_scopes(self):
6970 """Return the current number of backtracking points.
6985 return Z3_solver_get_num_scopes(self.ctx.ref(), self.solver)
6988 """Remove all asserted constraints
and backtracking points created using `
push()`.
6999 Z3_solver_reset(self.ctx.ref(), self.solver)
7001 def assert_exprs(self, *args):
7002 """Assert constraints into the solver.
7006 >>> s.assert_exprs(x > 0, x < 2)
7010 args = _get_args(args)
7011 s = BoolSort(self.ctx)
7013 if isinstance(arg, Goal) or isinstance(arg, AstVector):
7015 Z3_solver_assert(self.ctx.ref(), self.solver, f.as_ast())
7018 Z3_solver_assert(self.ctx.ref(), self.solver, arg.as_ast())
7020 def add(self, *args):
7021 """Assert constraints into the solver.
7025 >>> s.add(x > 0, x < 2)
7029 self.assert_exprs(*args)
7031 def __iadd__(self, fml):
7035 def append(self, *args):
7036 """Assert constraints into the solver.
7040 >>> s.append(x > 0, x < 2)
7044 self.assert_exprs(*args)
7046 def insert(self, *args):
7047 """Assert constraints into the solver.
7051 >>> s.insert(x > 0, x < 2)
7055 self.assert_exprs(*args)
7057 def assert_and_track(self, a, p):
7058 """Assert constraint `a`
and track it
in the unsat core using the Boolean constant `p`.
7060 If `p`
is a string, it will be automatically converted into a Boolean constant.
7065 >>> s.set(unsat_core=
True)
7066 >>> s.assert_and_track(x > 0,
'p1')
7067 >>> s.assert_and_track(x != 1,
'p2')
7068 >>> s.assert_and_track(x < 0, p3)
7069 >>> print(s.check())
7071 >>> c = s.unsat_core()
7081 if isinstance(p, str):
7082 p = Bool(p, self.ctx)
7083 _z3_assert(isinstance(a, BoolRef), "Boolean expression expected")
7084 _z3_assert(isinstance(p, BoolRef) and is_const(p), "Boolean expression expected")
7085 Z3_solver_assert_and_track(self.ctx.ref(), self.solver, a.as_ast(), p.as_ast())
7087 def check(self, *assumptions):
7088 """Check whether the assertions
in the given solver plus the optional assumptions are consistent
or not.
7094 >>> s.add(x > 0, x < 2)
7097 >>> s.model().eval(x)
7103 >>> s.add(2**x == 4)
7107 s = BoolSort(self.ctx)
7108 assumptions = _get_args(assumptions)
7109 num = len(assumptions)
7110 _assumptions = (Ast * num)()
7111 for i in range(num):
7112 _assumptions[i] = s.cast(assumptions[i]).as_ast()
7113 r = Z3_solver_check_assumptions(self.ctx.ref(), self.solver, num, _assumptions)
7114 return CheckSatResult(r)
7117 """Return a model
for the last `
check()`.
7119 This function raises an exception
if
7120 a model
is not available (e.g., last `
check()` returned unsat).
7124 >>> s.add(a + 2 == 0)
7131 return ModelRef(Z3_solver_get_model(self.ctx.ref(), self.solver), self.ctx)
7133 raise Z3Exception("model is not available")
7135 def import_model_converter(self, other):
7136 """Import model converter
from other into the current solver
"""
7137 Z3_solver_import_model_converter(self.ctx.ref(), other.solver, self.solver)
7139 def unsat_core(self):
7140 """Return a subset (
as an AST vector) of the assumptions provided to the last
check().
7142 These are the assumptions Z3 used
in the unsatisfiability proof.
7143 Assumptions are available
in Z3. They are used to extract unsatisfiable cores.
7144 They may be also used to
"retract" assumptions. Note that, assumptions are
not really
7145 "soft constraints", but they can be used to implement them.
7147 >>> p1, p2, p3 =
Bools(
'p1 p2 p3')
7148 >>> x, y =
Ints(
'x y')
7153 >>> s.add(
Implies(p3, y > -3))
7154 >>> s.check(p1, p2, p3)
7156 >>> core = s.unsat_core()
7169 return AstVector(Z3_solver_get_unsat_core(self.ctx.ref(), self.solver), self.ctx)
7171 def consequences(self, assumptions, variables):
7172 """Determine fixed values
for the variables based on the solver state
and assumptions.
7174 >>> a, b, c, d =
Bools(
'a b c d')
7176 >>> s.consequences([a],[b,c,d])
7178 >>> s.consequences([
Not(c),d],[a,b,c,d])
7181 if isinstance(assumptions, list):
7182 _asms = AstVector(None, self.ctx)
7183 for a in assumptions:
7186 if isinstance(variables, list):
7187 _vars = AstVector(None, self.ctx)
7191 _z3_assert(isinstance(assumptions, AstVector), "ast vector expected")
7192 _z3_assert(isinstance(variables, AstVector), "ast vector expected")
7193 consequences = AstVector(None, self.ctx)
7194 r = Z3_solver_get_consequences(self.ctx.ref(), self.solver, assumptions.vector,
7195 variables.vector, consequences.vector)
7196 sz = len(consequences)
7197 consequences = [consequences[i] for i in range(sz)]
7198 return CheckSatResult(r), consequences
7200 def from_file(self, filename):
7201 """Parse assertions
from a file
"""
7202 Z3_solver_from_file(self.ctx.ref(), self.solver, filename)
7204 def from_string(self, s):
7205 """Parse assertions
from a string
"""
7206 Z3_solver_from_string(self.ctx.ref(), self.solver, s)
7208 def cube(self, vars=None):
7210 The method takes an optional set of variables that restrict which
7211 variables may be used
as a starting point
for cubing.
7212 If vars
is not None, then the first case split
is based on a variable
in
7215 self.cube_vs = AstVector(None, self.ctx)
7216 if vars is not None:
7218 self.cube_vs.push(v)
7220 lvl = self.backtrack_level
7221 self.backtrack_level = 4000000000
7222 r = AstVector(Z3_solver_cube(self.ctx.ref(), self.solver, self.cube_vs.vector, lvl), self.ctx)
7223 if (len(r) == 1 and is_false(r[0])):
7229 def cube_vars(self):
7230 """Access the set of variables that were touched by the most recently generated cube.
7231 This set of variables can be used
as a starting point
for additional cubes.
7232 The idea
is that variables that appear
in clauses that are reduced by the most recent
7233 cube are likely more useful to cube on.
"""
7237 t = _py2expr(t, self.ctx)
7238 """Retrieve congruence closure root of the term t relative to the current search state
7239 The function primarily works
for SimpleSolver. Terms
and variables that are
7240 eliminated during pre-processing are
not visible to the congruence closure.
7242 return _to_expr_ref(Z3_solver_congruence_root(self.ctx.ref(), self.solver, t.ast), self.ctx)
7245 t = _py2expr(t, self.ctx)
7246 """Retrieve congruence closure sibling of the term t relative to the current search state
7247 The function primarily works
for SimpleSolver. Terms
and variables that are
7248 eliminated during pre-processing are
not visible to the congruence closure.
7250 return _to_expr_ref(Z3_solver_congruence_next(self.ctx.ref(), self.solver, t.ast), self.ctx)
7253 """Return a proof
for the last `
check()`. Proof construction must be enabled.
"""
7254 return _to_expr_ref(Z3_solver_get_proof(self.ctx.ref(), self.solver), self.ctx)
7256 def assertions(self):
7257 """Return an AST vector containing all added constraints.
7268 return AstVector(Z3_solver_get_assertions(self.ctx.ref(), self.solver), self.ctx)
7271 """Return an AST vector containing all currently inferred units.
7273 return AstVector(Z3_solver_get_units(self.ctx.ref(), self.solver), self.ctx)
7275 def non_units(self):
7276 """Return an AST vector containing all atomic formulas
in solver state that are
not units.
7278 return AstVector(Z3_solver_get_non_units(self.ctx.ref(), self.solver), self.ctx)
7280 def trail_levels(self):
7281 """Return trail
and decision levels of the solver state after a
check() call.
7283 trail = self.trail()
7284 levels = (ctypes.c_uint * len(trail))()
7285 Z3_solver_get_levels(self.ctx.ref(), self.solver, trail.vector, len(trail), levels)
7286 return trail, levels
7289 """Return trail of the solver state after a
check() call.
7291 return AstVector(Z3_solver_get_trail(self.ctx.ref(), self.solver), self.ctx)
7293 def statistics(self):
7294 """Return statistics
for the last `
check()`.
7301 >>> st = s.statistics()
7302 >>> st.get_key_value(
'final checks')
7309 return Statistics(Z3_solver_get_statistics(self.ctx.ref(), self.solver), self.ctx)
7311 def reason_unknown(self):
7312 """Return a string describing why the last `
check()` returned `unknown`.
7316 >>> s.add(2**x == 4)
7319 >>> s.reason_unknown()
7320 '(incomplete (theory arithmetic))'
7322 return Z3_solver_get_reason_unknown(self.ctx.ref(), self.solver)
7325 """Display a string describing all available options.
"""
7326 print(Z3_solver_get_help(self.ctx.ref(), self.solver))
7328 def param_descrs(self):
7329 """Return the parameter description set.
"""
7330 return ParamDescrsRef(Z3_solver_get_param_descrs(self.ctx.ref(), self.solver), self.ctx)
7333 """Return a formatted string with all added constraints.
"""
7334 return obj_to_string(self)
7336 def translate(self, target):
7337 """Translate `self` to the context `target`. That
is,
return a copy of `self`
in the context `target`.
7342 >>> s2 = s1.translate(c2)
7345 _z3_assert(isinstance(target, Context), "argument must be a Z3 context")
7346 solver = Z3_solver_translate(self.ctx.ref(), self.solver, target.ref())
7347 return Solver(solver, target)
7350 return self.translate(self.ctx)
7352 def __deepcopy__(self, memo={}):
7353 return self.translate(self.ctx)
7356 """Return a formatted string (
in Lisp-like format) with all added constraints.
7357 We say the string
is in s-expression format.
7365 return Z3_solver_to_string(self.ctx.ref(), self.solver)
7367 def dimacs(self, include_names=True):
7368 """Return a textual representation of the solver
in DIMACS format.
"""
7369 return Z3_solver_to_dimacs_string(self.ctx.ref(), self.solver, include_names)
7372 """return SMTLIB2 formatted benchmark
for solver
's assertions"""
7379 for i
in range(sz1):
7380 v[i] = es[i].as_ast()
7382 e = es[sz1].as_ast()
7386 self.ctx.ref(),
"benchmark generated from python API",
"",
"unknown",
"", sz1, v, e,
7391 """Create a solver customized for the given logic.
7393 The parameter `logic` is a string. It should be contains
7394 the name of a SMT-LIB logic.
7395 See http://www.smtlib.org/ for the name of all available logics.
7397 >>> s = SolverFor("QF_LIA")
7412 """Return a simple general purpose solver with limited amount of preprocessing.
7414 >>> s = SimpleSolver()
7431 """Fixedpoint API provides methods for solving with recursive predicates"""
7434 assert fixedpoint
is None or ctx
is not None
7437 if fixedpoint
is None:
7448 if self.
fixedpoint is not None and self.ctx.ref()
is not None and Z3_fixedpoint_dec_ref
is not None:
7452 """Set a configuration option. The method `help()` return a string containing all available options.
7458 """Display a string describing all available options."""
7462 """Return the parameter description set."""
7466 """Assert constraints as background axioms for the fixedpoint solver."""
7467 args = _get_args(args)
7470 if isinstance(arg, Goal)
or isinstance(arg, AstVector):
7480 """Assert constraints as background axioms for the fixedpoint solver. Alias for assert_expr."""
7488 """Assert constraints as background axioms for the fixedpoint solver. Alias for assert_expr."""
7492 """Assert constraints as background axioms for the fixedpoint solver. Alias for assert_expr."""
7496 """Assert rules defining recursive predicates to the fixedpoint solver.
7499 >>> s = Fixedpoint()
7500 >>> s.register_relation(a.decl())
7501 >>> s.register_relation(b.decl())
7514 body = _get_args(body)
7518 def rule(self, head, body=None, name=None):
7519 """Assert rules defining recursive predicates to the fixedpoint solver. Alias for add_rule."""
7523 """Assert facts defining recursive predicates to the fixedpoint solver. Alias for add_rule."""
7527 """Query the fixedpoint engine whether formula is derivable.
7528 You can also pass an tuple or list of recursive predicates.
7530 query = _get_args(query)
7532 if sz >= 1
and isinstance(query[0], FuncDeclRef):
7533 _decls = (FuncDecl * sz)()
7543 query =
And(query, self.
ctx)
7544 query = self.
abstract(query,
False)
7549 """Query the fixedpoint engine whether formula is derivable starting at the given query level.
7551 query = _get_args(query)
7553 if sz >= 1
and isinstance(query[0], FuncDecl):
7554 _z3_assert(
False,
"unsupported")
7560 query = self.
abstract(query,
False)
7561 r = Z3_fixedpoint_query_from_lvl(self.ctx.ref(), self.
fixedpoint, query.as_ast(), lvl)
7569 body = _get_args(body)
7574 """Retrieve answer from last query call."""
7576 return _to_expr_ref(r, self.
ctx)
7579 """Retrieve a ground cex from last query call."""
7580 r = Z3_fixedpoint_get_ground_sat_answer(self.ctx.ref(), self.
fixedpoint)
7581 return _to_expr_ref(r, self.
ctx)
7584 """retrieve rules along the counterexample trace"""
7588 """retrieve rule names along the counterexample trace"""
7591 names = _symbol2py(self.
ctx, Z3_fixedpoint_get_rule_names_along_trace(self.ctx.ref(), self.
fixedpoint))
7593 return names.split(
";")
7596 """Retrieve number of levels used for predicate in PDR engine"""
7600 """Retrieve properties known about predicate for the level'th unfolding.
7601 -1 is treated as the limit (infinity)
7604 return _to_expr_ref(r, self.
ctx)
7607 """Add property to predicate for the level'th unfolding.
7608 -1 is treated as infinity (infinity)
7613 """Register relation as recursive"""
7614 relations = _get_args(relations)
7619 """Control how relation is represented"""
7620 representations = _get_args(representations)
7621 representations = [
to_symbol(s)
for s
in representations]
7622 sz = len(representations)
7623 args = (Symbol * sz)()
7625 args[i] = representations[i]
7629 """Parse rules and queries from a string"""
7633 """Parse rules and queries from a file"""
7637 """retrieve rules that have been added to fixedpoint context"""
7641 """retrieve assertions that have been added to fixedpoint context"""
7645 """Return a formatted string with all added rules and constraints."""
7649 """Return a formatted string (in Lisp-like format) with all added constraints.
7650 We say the string is in s-expression format.
7655 """Return a formatted string (in Lisp-like format) with all added constraints.
7656 We say the string is in s-expression format.
7657 Include also queries.
7659 args, len = _to_ast_array(queries)
7663 """Return statistics for the last `query()`.
7668 """Return a string describing why the last `query()` returned `unknown`.
7673 """Add variable or several variables.
7674 The added variable or variables will be bound in the rules
7677 vars = _get_args(vars)
7697 """Finite domain sort."""
7700 """Return the size of the finite domain sort"""
7701 r = (ctypes.c_ulonglong * 1)()
7705 raise Z3Exception(
"Failed to retrieve finite domain sort size")
7709 """Create a named finite domain sort of a given size sz"""
7710 if not isinstance(name, Symbol):
7717 """Return True if `s` is a Z3 finite-domain sort.
7719 >>> is_finite_domain_sort(FiniteDomainSort('S', 100))
7721 >>> is_finite_domain_sort(IntSort())
7724 return isinstance(s, FiniteDomainSortRef)
7728 """Finite-domain expressions."""
7731 """Return the sort of the finite-domain expression `self`."""
7735 """Return a Z3 floating point expression as a Python string."""
7740 """Return `True` if `a` is a Z3 finite-domain expression.
7742 >>> s = FiniteDomainSort('S', 100)
7743 >>> b = Const('b', s)
7744 >>> is_finite_domain(b)
7746 >>> is_finite_domain(Int('x'))
7749 return isinstance(a, FiniteDomainRef)
7753 """Integer values."""
7756 """Return a Z3 finite-domain numeral as a Python long (bignum) numeral.
7758 >>> s = FiniteDomainSort('S', 100)
7759 >>> v = FiniteDomainVal(3, s)
7768 """Return a Z3 finite-domain numeral as a Python string.
7770 >>> s = FiniteDomainSort('S', 100)
7771 >>> v = FiniteDomainVal(42, s)
7779 """Return a Z3 finite-domain value. If `ctx=None`, then the global context is used.
7781 >>> s = FiniteDomainSort('S', 256)
7782 >>> FiniteDomainVal(255, s)
7784 >>> FiniteDomainVal('100', s)
7794 """Return `True` if `a` is a Z3 finite-domain value.
7796 >>> s = FiniteDomainSort('S', 100)
7797 >>> b = Const('b', s)
7798 >>> is_finite_domain_value(b)
7800 >>> b = FiniteDomainVal(10, s)
7803 >>> is_finite_domain_value(b)
7850 def _global_on_model(ctx):
7851 (fn, mdl) = _on_models[ctx]
7855 _on_model_eh = on_model_eh_type(_global_on_model)
7859 """Optimize API provides methods for solving using objective functions and weighted soft constraints"""
7871 if self.
optimize is not None and self.ctx.ref()
is not None and Z3_optimize_dec_ref
is not None:
7877 """Set a configuration option.
7878 The method `help()` return a string containing all available options.
7884 """Display a string describing all available options."""
7888 """Return the parameter description set."""
7892 """Assert constraints as background axioms for the optimize solver."""
7893 args = _get_args(args)
7896 if isinstance(arg, Goal)
or isinstance(arg, AstVector):
7904 """Assert constraints as background axioms for the optimize solver. Alias for assert_expr."""
7912 """Assert constraint `a` and track it in the unsat core using the Boolean constant `p`.
7914 If `p` is a string, it will be automatically converted into a Boolean constant.
7919 >>> s.assert_and_track(x > 0, 'p1')
7920 >>> s.assert_and_track(x != 1, 'p2')
7921 >>> s.assert_and_track(x < 0, p3)
7922 >>> print(s.check())
7924 >>> c = s.unsat_core()
7934 if isinstance(p, str):
7936 _z3_assert(isinstance(a, BoolRef),
"Boolean expression expected")
7937 _z3_assert(isinstance(p, BoolRef)
and is_const(p),
"Boolean expression expected")
7941 """Add soft constraint with optional weight and optional identifier.
7942 If no weight is supplied, then the penalty for violating the soft constraint
7944 Soft constraints are grouped by identifiers. Soft constraints that are
7945 added without identifiers are grouped by default.
7948 weight =
"%d" % weight
7949 elif isinstance(weight, float):
7950 weight =
"%f" % weight
7951 if not isinstance(weight, str):
7952 raise Z3Exception(
"weight should be a string or an integer")
7960 if sys.version_info.major >= 3
and isinstance(arg, Iterable):
7961 return [asoft(a)
for a
in arg]
7965 """Add objective function to maximize."""
7973 """Add objective function to minimize."""
7981 """create a backtracking point for added rules, facts and assertions"""
7985 """restore to previously created backtracking point"""
7989 """Check satisfiability while optimizing objective functions."""
7990 assumptions = _get_args(assumptions)
7991 num = len(assumptions)
7992 _assumptions = (Ast * num)()
7993 for i
in range(num):
7994 _assumptions[i] = assumptions[i].as_ast()
7998 """Return a string that describes why the last `check()` returned `unknown`."""
8002 """Return a model for the last check()."""
8006 raise Z3Exception(
"model is not available")
8012 if not isinstance(obj, OptimizeObjective):
8013 raise Z3Exception(
"Expecting objective handle returned by maximize/minimize")
8017 if not isinstance(obj, OptimizeObjective):
8018 raise Z3Exception(
"Expecting objective handle returned by maximize/minimize")
8022 if not isinstance(obj, OptimizeObjective):
8023 raise Z3Exception(
"Expecting objective handle returned by maximize/minimize")
8024 return obj.lower_values()
8027 if not isinstance(obj, OptimizeObjective):
8028 raise Z3Exception(
"Expecting objective handle returned by maximize/minimize")
8029 return obj.upper_values()
8032 """Parse assertions and objectives from a file"""
8036 """Parse assertions and objectives from a string"""
8040 """Return an AST vector containing all added constraints."""
8044 """returns set of objective functions"""
8048 """Return a formatted string with all added rules and constraints."""
8052 """Return a formatted string (in Lisp-like format) with all added constraints.
8053 We say the string is in s-expression format.
8058 """Return statistics for the last check`.
8063 """Register a callback that is invoked with every incremental improvement to
8064 objective values. The callback takes a model as argument.
8065 The life-time of the model is limited to the callback so the
8066 model has to be (deep) copied if it is to be used after the callback
8068 id = len(_on_models) + 41
8070 _on_models[id] = (on_model, mdl)
8073 self.ctx.ref(), self.
optimize, mdl.model, ctypes.c_void_p(id), _on_model_eh,
8083 """An ApplyResult object contains the subgoals produced by a tactic when applied to a goal.
8084 It also contains model and proof converters.
8096 if self.ctx.ref()
is not None and Z3_apply_result_dec_ref
is not None:
8100 """Return the number of subgoals in `self`.
8102 >>> a, b = Ints('a b')
8104 >>> g.add(Or(a == 0, a == 1), Or(b == 0, b == 1), a > b)
8105 >>> t = Tactic('split-clause')
8109 >>> t = Then(Tactic('split-clause'), Tactic('split-clause'))
8112 >>> t = Then(Tactic('split-clause'), Tactic('split-clause'), Tactic('propagate-values'))
8119 """Return one of the subgoals stored in ApplyResult object `self`.
8121 >>> a, b = Ints('a b')
8123 >>> g.add(Or(a == 0, a == 1), Or(b == 0, b == 1), a > b)
8124 >>> t = Tactic('split-clause')
8127 [a == 0, Or(b == 0, b == 1), a > b]
8129 [a == 1, Or(b == 0, b == 1), a > b]
8131 if idx >= len(self):
8136 return obj_to_string(self)
8139 """Return a textual representation of the s-expression representing the set of subgoals in `self`."""
8143 """Return a Z3 expression consisting of all subgoals.
8148 >>> g.add(Or(x == 2, x == 3))
8149 >>> r = Tactic('simplify')(g)
8151 [[Not(x <= 1), Or(x == 2, x == 3)]]
8153 And(Not(x <= 1), Or(x == 2, x == 3))
8154 >>> r = Tactic('split-clause')(g)
8156 [[x > 1, x == 2], [x > 1, x == 3]]
8158 Or(And(x > 1, x == 2), And(x > 1, x == 3))
8175 """Simplifiers act as pre-processing utilities for solvers.
8176 Build a custom simplifier and add it to a solver"""
8181 if isinstance(simplifier, SimplifierObj):
8183 elif isinstance(simplifier, list):
8184 simps = [
Simplifier(s, ctx)
for s
in simplifier]
8186 for i
in range(1, len(simps)):
8192 _z3_assert(isinstance(simplifier, str),
"simplifier name expected")
8196 raise Z3Exception(
"unknown simplifier '%s'" % simplifier)
8203 if self.
simplifier is not None and self.ctx.ref()
is not None and Z3_simplifier_dec_ref
is not None:
8207 """Return a simplifier that uses the given configuration options"""
8212 """Return a solver that applies the simplification pre-processing specified by the simplifier"""
8216 """Display a string containing a description of the available options for the `self` simplifier."""
8220 """Return the parameter description set."""
8232 """Tactics transform, solver and/or simplify sets of constraints (Goal).
8233 A Tactic can be converted into a Solver using the method solver().
8235 Several combinators are available for creating new tactics using the built-in ones:
8236 Then(), OrElse(), FailIf(), Repeat(), When(), Cond().
8242 if isinstance(tactic, TacticObj):
8246 _z3_assert(isinstance(tactic, str),
"tactic name expected")
8250 raise Z3Exception(
"unknown tactic '%s'" % tactic)
8257 if self.
tactic is not None and self.ctx.ref()
is not None and Z3_tactic_dec_ref
is not None:
8261 """Create a solver using the tactic `self`.
8263 The solver supports the methods `push()` and `pop()`, but it
8264 will always solve each `check()` from scratch.
8266 >>> t = Then('simplify', 'nlsat')
8269 >>> s.add(x**2 == 2, x > 0)
8277 def apply(self, goal, *arguments, **keywords):
8278 """Apply tactic `self` to the given goal or Z3 Boolean expression using the given options.
8280 >>> x, y = Ints('x y')
8281 >>> t = Tactic('solve-eqs')
8282 >>> t.apply(And(x == 0, y >= x + 1))
8286 _z3_assert(isinstance(goal, (Goal, BoolRef)),
"Z3 Goal or Boolean expressions expected")
8287 goal = _to_goal(goal)
8288 if len(arguments) > 0
or len(keywords) > 0:
8295 """Apply tactic `self` to the given goal or Z3 Boolean expression using the given options.
8297 >>> x, y = Ints('x y')
8298 >>> t = Tactic('solve-eqs')
8299 >>> t(And(x == 0, y >= x + 1))
8302 return self.
apply(goal, *arguments, **keywords)
8305 """Display a string containing a description of the available options for the `self` tactic."""
8309 """Return the parameter description set."""
8314 if isinstance(a, BoolRef):
8315 goal =
Goal(ctx=a.ctx)
8322 def _to_tactic(t, ctx=None):
8323 if isinstance(t, Tactic):
8329 def _and_then(t1, t2, ctx=None):
8330 t1 = _to_tactic(t1, ctx)
8331 t2 = _to_tactic(t2, ctx)
8333 _z3_assert(t1.ctx == t2.ctx,
"Context mismatch")
8337 def _or_else(t1, t2, ctx=None):
8338 t1 = _to_tactic(t1, ctx)
8339 t2 = _to_tactic(t2, ctx)
8341 _z3_assert(t1.ctx == t2.ctx,
"Context mismatch")
8346 """Return a tactic that applies the tactics in `*ts` in sequence.
8348 >>> x, y = Ints('x y')
8349 >>> t = AndThen(Tactic('simplify'), Tactic('solve-eqs'))
8350 >>> t(And(x == 0, y > x + 1))
8352 >>> t(And(x == 0, y > x + 1)).as_expr()
8356 _z3_assert(len(ts) >= 2,
"At least two arguments expected")
8357 ctx = ks.get(
"ctx",
None)
8360 for i
in range(num - 1):
8361 r = _and_then(r, ts[i + 1], ctx)
8366 """Return a tactic that applies the tactics in `*ts` in sequence. Shorthand for AndThen(*ts, **ks).
8368 >>> x, y = Ints('x y')
8369 >>> t = Then(Tactic('simplify'), Tactic('solve-eqs'))
8370 >>> t(And(x == 0, y > x + 1))
8372 >>> t(And(x == 0, y > x + 1)).as_expr()
8379 """Return a tactic that applies the tactics in `*ts` until one of them succeeds (it doesn't fail).
8382 >>> t = OrElse(Tactic('split-clause'), Tactic('skip'))
8383 >>> # Tactic split-clause fails if there is no clause in the given goal.
8386 >>> t(Or(x == 0, x == 1))
8387 [[x == 0], [x == 1]]
8390 _z3_assert(len(ts) >= 2,
"At least two arguments expected")
8391 ctx = ks.get(
"ctx",
None)
8394 for i
in range(num - 1):
8395 r = _or_else(r, ts[i + 1], ctx)
8400 """Return a tactic that applies the tactics in `*ts` in parallel until one of them succeeds (it doesn't fail).
8403 >>> t = ParOr(Tactic('simplify'), Tactic('fail'))
8408 _z3_assert(len(ts) >= 2,
"At least two arguments expected")
8409 ctx = _get_ctx(ks.get(
"ctx",
None))
8410 ts = [_to_tactic(t, ctx)
for t
in ts]
8412 _args = (TacticObj * sz)()
8414 _args[i] = ts[i].tactic
8419 """Return a tactic that applies t1 and then t2 to every subgoal produced by t1.
8420 The subgoals are processed in parallel.
8422 >>> x, y = Ints('x y')
8423 >>> t = ParThen(Tactic('split-clause'), Tactic('propagate-values'))
8424 >>> t(And(Or(x == 1, x == 2), y == x + 1))
8425 [[x == 1, y == 2], [x == 2, y == 3]]
8427 t1 = _to_tactic(t1, ctx)
8428 t2 = _to_tactic(t2, ctx)
8430 _z3_assert(t1.ctx == t2.ctx,
"Context mismatch")
8435 """Alias for ParThen(t1, t2, ctx)."""
8440 """Return a tactic that applies tactic `t` using the given configuration options.
8442 >>> x, y = Ints('x y')
8443 >>> t = With(Tactic('simplify'), som=True)
8444 >>> t((x + 1)*(y + 2) == 0)
8445 [[2*x + y + x*y == -2]]
8447 ctx = keys.pop(
"ctx",
None)
8448 t = _to_tactic(t, ctx)
8454 """Return a tactic that applies tactic `t` using the given configuration options.
8456 >>> x, y = Ints('x y')
8458 >>> p.set("som", True)
8459 >>> t = WithParams(Tactic('simplify'), p)
8460 >>> t((x + 1)*(y + 2) == 0)
8461 [[2*x + y + x*y == -2]]
8463 t = _to_tactic(t,
None)
8468 """Return a tactic that keeps applying `t` until the goal is not modified anymore
8469 or the maximum number of iterations `max` is reached.
8471 >>> x, y = Ints('x y')
8472 >>> c = And(Or(x == 0, x == 1), Or(y == 0, y == 1), x > y)
8473 >>> t = Repeat(OrElse(Tactic('split-clause'), Tactic('skip')))
8475 >>> for subgoal in r: print(subgoal)
8476 [x == 0, y == 0, x > y]
8477 [x == 0, y == 1, x > y]
8478 [x == 1, y == 0, x > y]
8479 [x == 1, y == 1, x > y]
8480 >>> t = Then(t, Tactic('propagate-values'))
8484 t = _to_tactic(t, ctx)
8489 """Return a tactic that applies `t` to a given goal for `ms` milliseconds.
8491 If `t` does not terminate in `ms` milliseconds, then it fails.
8493 t = _to_tactic(t, ctx)
8498 """Return a list of all available tactics in Z3.
8501 >>> l.count('simplify') == 1
8509 """Return a short description for the tactic named `name`.
8511 >>> d = tactic_description('simplify')
8518 """Display a (tabular) description of all available tactics in Z3."""
8521 print(
'<table border="1" cellpadding="2" cellspacing="0">')
8524 print(
'<tr style="background-color:#CFCFCF">')
8529 print(
"<td>%s</td><td>%s</td></tr>" % (t, insert_line_breaks(
tactic_description(t), 40)))
8537 """Probes are used to inspect a goal (aka problem) and collect information that may be used
8538 to decide which solver and/or preprocessing step will be used.
8544 if isinstance(probe, ProbeObj):
8546 elif isinstance(probe, float):
8548 elif _is_int(probe):
8550 elif isinstance(probe, bool):
8557 _z3_assert(isinstance(probe, str),
"probe name expected")
8561 raise Z3Exception(
"unknown probe '%s'" % probe)
8568 if self.
probe is not None and self.ctx.ref()
is not None and Z3_probe_dec_ref
is not None:
8572 """Return a probe that evaluates to "true" when the value returned by `self`
8573 is less than the value returned by `other`.
8575 >>> p = Probe('size') < 10
8586 """Return a probe that evaluates to "true" when the value returned by `self`
8587 is greater than the value returned by `other`.
8589 >>> p = Probe('size') > 10
8600 """Return a probe that evaluates to "true" when the value returned by `self`
8601 is less than or equal to the value returned by `other`.
8603 >>> p = Probe('size') <= 2
8614 """Return a probe that evaluates to "true" when the value returned by `self`
8615 is greater than or equal to the value returned by `other`.
8617 >>> p = Probe('size') >= 2
8628 """Return a probe that evaluates to "true" when the value returned by `self`
8629 is equal to the value returned by `other`.
8631 >>> p = Probe('size') == 2
8642 """Return a probe that evaluates to "true" when the value returned by `self`
8643 is not equal to the value returned by `other`.
8645 >>> p = Probe('size') != 2
8657 """Evaluate the probe `self` in the given goal.
8659 >>> p = Probe('size')
8669 >>> p = Probe('num-consts')
8672 >>> p = Probe('is-propositional')
8675 >>> p = Probe('is-qflia')
8680 _z3_assert(isinstance(goal, (Goal, BoolRef)),
"Z3 Goal or Boolean expression expected")
8681 goal = _to_goal(goal)
8686 """Return `True` if `p` is a Z3 probe.
8688 >>> is_probe(Int('x'))
8690 >>> is_probe(Probe('memory'))
8693 return isinstance(p, Probe)
8696 def _to_probe(p, ctx=None):
8700 return Probe(p, ctx)
8704 """Return a list of all available probes in Z3.
8707 >>> l.count('memory') == 1
8715 """Return a short description for the probe named `name`.
8717 >>> d = probe_description('memory')
8724 """Display a (tabular) description of all available probes in Z3."""
8727 print(
'<table border="1" cellpadding="2" cellspacing="0">')
8730 print(
'<tr style="background-color:#CFCFCF">')
8735 print(
"<td>%s</td><td>%s</td></tr>" % (p, insert_line_breaks(
probe_description(p), 40)))
8742 def _probe_nary(f, args, ctx):
8744 _z3_assert(len(args) > 0,
"At least one argument expected")
8746 r = _to_probe(args[0], ctx)
8747 for i
in range(num - 1):
8748 r =
Probe(f(ctx.ref(), r.probe, _to_probe(args[i + 1], ctx).probe), ctx)
8752 def _probe_and(args, ctx):
8753 return _probe_nary(Z3_probe_and, args, ctx)
8756 def _probe_or(args, ctx):
8757 return _probe_nary(Z3_probe_or, args, ctx)
8761 """Return a tactic that fails if the probe `p` evaluates to true.
8762 Otherwise, it returns the input goal unmodified.
8764 In the following example, the tactic applies 'simplify' if and only if there are
8765 more than 2 constraints in the goal.
8767 >>> t = OrElse(FailIf(Probe('size') > 2), Tactic('simplify'))
8768 >>> x, y = Ints('x y')
8774 >>> g.add(x == y + 1)
8776 [[Not(x <= 0), Not(y <= 0), x == 1 + y]]
8778 p = _to_probe(p, ctx)
8783 """Return a tactic that applies tactic `t` only if probe `p` evaluates to true.
8784 Otherwise, it returns the input goal unmodified.
8786 >>> t = When(Probe('size') > 2, Tactic('simplify'))
8787 >>> x, y = Ints('x y')
8793 >>> g.add(x == y + 1)
8795 [[Not(x <= 0), Not(y <= 0), x == 1 + y]]
8797 p = _to_probe(p, ctx)
8798 t = _to_tactic(t, ctx)
8803 """Return a tactic that applies tactic `t1` to a goal if probe `p` evaluates to true, and `t2` otherwise.
8805 >>> t = Cond(Probe('is-qfnra'), Tactic('qfnra'), Tactic('smt'))
8807 p = _to_probe(p, ctx)
8808 t1 = _to_tactic(t1, ctx)
8809 t2 = _to_tactic(t2, ctx)
8820 """Simplify the expression `a` using the given options.
8822 This function has many options. Use `help_simplify` to obtain the complete list.
8826 >>> simplify(x + 1 + y + x + 1)
8828 >>> simplify((x + 1)*(y + 1), som=True)
8830 >>> simplify(Distinct(x, y, 1), blast_distinct=True)
8831 And(Not(x == y), Not(x == 1), Not(y == 1))
8832 >>> simplify(And(x == 0, y == 1), elim_and=True)
8833 Not(Or(Not(x == 0), Not(y == 1)))
8836 _z3_assert(
is_expr(a),
"Z3 expression expected")
8837 if len(arguments) > 0
or len(keywords) > 0:
8839 return _to_expr_ref(
Z3_simplify_ex(a.ctx_ref(), a.as_ast(), p.params), a.ctx)
8841 return _to_expr_ref(
Z3_simplify(a.ctx_ref(), a.as_ast()), a.ctx)
8845 """Return a string describing all options available for Z3 `simplify` procedure."""
8850 """Return the set of parameter descriptions for Z3 `simplify` procedure."""
8855 """Apply substitution m on t, m is a list of pairs of the form (from, to).
8856 Every occurrence in t of from is replaced with to.
8860 >>> substitute(x + 1, (x, y + 1))
8862 >>> f = Function('f', IntSort(), IntSort())
8863 >>> substitute(f(x) + f(y), (f(x), IntVal(1)), (f(y), IntVal(1)))
8866 if isinstance(m, tuple):
8868 if isinstance(m1, list)
and all(isinstance(p, tuple)
for p
in m1):
8871 _z3_assert(
is_expr(t),
"Z3 expression expected")
8873 all([isinstance(p, tuple)
and is_expr(p[0])
and is_expr(p[1])
for p
in m]),
8874 "Z3 invalid substitution, expression pairs expected.")
8876 all([p[0].sort().
eq(p[1].sort())
for p
in m]),
8877 'Z3 invalid substitution, mismatching "from" and "to" sorts.')
8879 _from = (Ast * num)()
8881 for i
in range(num):
8882 _from[i] = m[i][0].as_ast()
8883 _to[i] = m[i][1].as_ast()
8884 return _to_expr_ref(
Z3_substitute(t.ctx.ref(), t.as_ast(), num, _from, _to), t.ctx)
8888 """Substitute the free variables in t with the expression in m.
8890 >>> v0 = Var(0, IntSort())
8891 >>> v1 = Var(1, IntSort())
8893 >>> f = Function('f', IntSort(), IntSort(), IntSort())
8894 >>> # replace v0 with x+1 and v1 with x
8895 >>> substitute_vars(f(v0, v1), x + 1, x)
8899 _z3_assert(
is_expr(t),
"Z3 expression expected")
8900 _z3_assert(all([
is_expr(n)
for n
in m]),
"Z3 invalid substitution, list of expressions expected.")
8903 for i
in range(num):
8904 _to[i] = m[i].as_ast()
8908 """Apply substitution m on t, m is a list of pairs of a function and expression (from, to)
8909 Every occurrence in to of the function from is replaced with the expression to.
8910 The expression to can have free variables, that refer to the arguments of from.
8913 if isinstance(m, tuple):
8915 if isinstance(m1, list)
and all(isinstance(p, tuple)
for p
in m1):
8918 _z3_assert(
is_expr(t),
"Z3 expression expected")
8919 _z3_assert(all([isinstance(p, tuple)
and is_func_decl(p[0])
and is_expr(p[1])
for p
in m]),
"Z3 invalid substitution, funcion pairs expected.")
8921 _from = (FuncDecl * num)()
8923 for i
in range(num):
8924 _from[i] = m[i][0].as_func_decl()
8925 _to[i] = m[i][1].as_ast()
8926 return _to_expr_ref(
Z3_substitute_funs(t.ctx.ref(), t.as_ast(), num, _from, _to), t.ctx)
8930 """Create the sum of the Z3 expressions.
8932 >>> a, b, c = Ints('a b c')
8937 >>> A = IntVector('a', 5)
8939 a__0 + a__1 + a__2 + a__3 + a__4
8941 args = _get_args(args)
8944 ctx = _ctx_from_ast_arg_list(args)
8946 return _reduce(
lambda a, b: a + b, args, 0)
8947 args = _coerce_expr_list(args, ctx)
8949 return _reduce(
lambda a, b: a + b, args, 0)
8951 _args, sz = _to_ast_array(args)
8956 """Create the product of the Z3 expressions.
8958 >>> a, b, c = Ints('a b c')
8959 >>> Product(a, b, c)
8961 >>> Product([a, b, c])
8963 >>> A = IntVector('a', 5)
8965 a__0*a__1*a__2*a__3*a__4
8967 args = _get_args(args)
8970 ctx = _ctx_from_ast_arg_list(args)
8972 return _reduce(
lambda a, b: a * b, args, 1)
8973 args = _coerce_expr_list(args, ctx)
8975 return _reduce(
lambda a, b: a * b, args, 1)
8977 _args, sz = _to_ast_array(args)
8981 """Create the absolute value of an arithmetic expression"""
8982 return If(arg > 0, arg, -arg)
8986 """Create an at-most Pseudo-Boolean k constraint.
8988 >>> a, b, c = Bools('a b c')
8989 >>> f = AtMost(a, b, c, 2)
8991 args = _get_args(args)
8993 _z3_assert(len(args) > 1,
"Non empty list of arguments expected")
8994 ctx = _ctx_from_ast_arg_list(args)
8996 _z3_assert(ctx
is not None,
"At least one of the arguments must be a Z3 expression")
8997 args1 = _coerce_expr_list(args[:-1], ctx)
8999 _args, sz = _to_ast_array(args1)
9004 """Create an at-most Pseudo-Boolean k constraint.
9006 >>> a, b, c = Bools('a b c')
9007 >>> f = AtLeast(a, b, c, 2)
9009 args = _get_args(args)
9011 _z3_assert(len(args) > 1,
"Non empty list of arguments expected")
9012 ctx = _ctx_from_ast_arg_list(args)
9014 _z3_assert(ctx
is not None,
"At least one of the arguments must be a Z3 expression")
9015 args1 = _coerce_expr_list(args[:-1], ctx)
9017 _args, sz = _to_ast_array(args1)
9021 def _reorder_pb_arg(arg):
9023 if not _is_int(b)
and _is_int(a):
9028 def _pb_args_coeffs(args, default_ctx=None):
9029 args = _get_args_ast_list(args)
9031 return _get_ctx(default_ctx), 0, (Ast * 0)(), (ctypes.c_int * 0)()
9032 args = [_reorder_pb_arg(arg)
for arg
in args]
9033 args, coeffs = zip(*args)
9035 _z3_assert(len(args) > 0,
"Non empty list of arguments expected")
9036 ctx = _ctx_from_ast_arg_list(args)
9038 _z3_assert(ctx
is not None,
"At least one of the arguments must be a Z3 expression")
9039 args = _coerce_expr_list(args, ctx)
9040 _args, sz = _to_ast_array(args)
9041 _coeffs = (ctypes.c_int * len(coeffs))()
9042 for i
in range(len(coeffs)):
9043 _z3_check_cint_overflow(coeffs[i],
"coefficient")
9044 _coeffs[i] = coeffs[i]
9045 return ctx, sz, _args, _coeffs, args
9049 """Create a Pseudo-Boolean inequality k constraint.
9051 >>> a, b, c = Bools('a b c')
9052 >>> f = PbLe(((a,1),(b,3),(c,2)), 3)
9054 _z3_check_cint_overflow(k,
"k")
9055 ctx, sz, _args, _coeffs, args = _pb_args_coeffs(args)
9060 """Create a Pseudo-Boolean inequality k constraint.
9062 >>> a, b, c = Bools('a b c')
9063 >>> f = PbGe(((a,1),(b,3),(c,2)), 3)
9065 _z3_check_cint_overflow(k,
"k")
9066 ctx, sz, _args, _coeffs, args = _pb_args_coeffs(args)
9071 """Create a Pseudo-Boolean equality k constraint.
9073 >>> a, b, c = Bools('a b c')
9074 >>> f = PbEq(((a,1),(b,3),(c,2)), 3)
9076 _z3_check_cint_overflow(k,
"k")
9077 ctx, sz, _args, _coeffs, args = _pb_args_coeffs(args)
9082 """Solve the constraints `*args`.
9084 This is a simple function for creating demonstrations. It creates a solver,
9085 configure it using the options in `keywords`, adds the constraints
9086 in `args`, and invokes check.
9089 >>> solve(a > 0, a < 2)
9092 show = keywords.pop(
"show",
False)
9100 print(
"no solution")
9102 print(
"failed to solve")
9112 """Solve the constraints `*args` using solver `s`.
9114 This is a simple function for creating demonstrations. It is similar to `solve`,
9115 but it uses the given solver `s`.
9116 It configures solver `s` using the options in `keywords`, adds the constraints
9117 in `args`, and invokes check.
9119 show = keywords.pop(
"show",
False)
9121 _z3_assert(isinstance(s, Solver),
"Solver object expected")
9129 print(
"no solution")
9131 print(
"failed to solve")
9142 def prove(claim, show=False, **keywords):
9143 """Try to prove the given claim.
9145 This is a simple function for creating demonstrations. It tries to prove
9146 `claim` by showing the negation is unsatisfiable.
9148 >>> p, q = Bools('p q')
9149 >>> prove(Not(And(p, q)) == Or(Not(p), Not(q)))
9153 _z3_assert(
is_bool(claim),
"Z3 Boolean expression expected")
9163 print(
"failed to prove")
9166 print(
"counterexample")
9170 def _solve_html(*args, **keywords):
9171 """Version of function `solve` that renders HTML output."""
9172 show = keywords.pop(
"show",
False)
9177 print(
"<b>Problem:</b>")
9181 print(
"<b>no solution</b>")
9183 print(
"<b>failed to solve</b>")
9190 print(
"<b>Solution:</b>")
9194 def _solve_using_html(s, *args, **keywords):
9195 """Version of function `solve_using` that renders HTML."""
9196 show = keywords.pop(
"show",
False)
9198 _z3_assert(isinstance(s, Solver),
"Solver object expected")
9202 print(
"<b>Problem:</b>")
9206 print(
"<b>no solution</b>")
9208 print(
"<b>failed to solve</b>")
9215 print(
"<b>Solution:</b>")
9219 def _prove_html(claim, show=False, **keywords):
9220 """Version of function `prove` that renders HTML."""
9222 _z3_assert(
is_bool(claim),
"Z3 Boolean expression expected")
9230 print(
"<b>proved</b>")
9232 print(
"<b>failed to prove</b>")
9235 print(
"<b>counterexample</b>")
9239 def _dict2sarray(sorts, ctx):
9241 _names = (Symbol * sz)()
9242 _sorts = (Sort * sz)()
9247 _z3_assert(isinstance(k, str),
"String expected")
9248 _z3_assert(
is_sort(v),
"Z3 sort expected")
9252 return sz, _names, _sorts
9255 def _dict2darray(decls, ctx):
9257 _names = (Symbol * sz)()
9258 _decls = (FuncDecl * sz)()
9263 _z3_assert(isinstance(k, str),
"String expected")
9267 _decls[i] = v.decl().ast
9271 return sz, _names, _decls
9280 if self.ctx.ref()
is not None and self.
pctx is not None and Z3_parser_context_dec_ref
is not None:
9294 """Parse a string in SMT 2.0 format using the given sorts and decls.
9296 The arguments sorts and decls are Python dictionaries used to initialize
9297 the symbol table used for the SMT 2.0 parser.
9299 >>> parse_smt2_string('(declare-const x Int) (assert (> x 0)) (assert (< x 10))')
9301 >>> x, y = Ints('x y')
9302 >>> f = Function('f', IntSort(), IntSort())
9303 >>> parse_smt2_string('(assert (> (+ foo (g bar)) 0))', decls={ 'foo' : x, 'bar' : y, 'g' : f})
9305 >>> parse_smt2_string('(declare-const a U) (assert (> a 0))', sorts={ 'U' : IntSort() })
9309 ssz, snames, ssorts = _dict2sarray(sorts, ctx)
9310 dsz, dnames, ddecls = _dict2darray(decls, ctx)
9311 return AstVector(Z3_parse_smtlib2_string(ctx.ref(), s, ssz, snames, ssorts, dsz, dnames, ddecls), ctx)
9314 def parse_smt2_file(f, sorts={}, decls={}, ctx=None):
9315 """Parse a file
in SMT 2.0 format using the given sorts
and decls.
9320 ssz, snames, ssorts = _dict2sarray(sorts, ctx)
9321 dsz, dnames, ddecls = _dict2darray(decls, ctx)
9322 return AstVector(Z3_parse_smtlib2_file(ctx.ref(), f, ssz, snames, ssorts, dsz, dnames, ddecls), ctx)
9325 #########################################
9327 # Floating-Point Arithmetic
9329 #########################################
9332 # Global default rounding mode
9333 _dflt_rounding_mode = Z3_OP_FPA_RM_NEAREST_TIES_TO_EVEN
9334 _dflt_fpsort_ebits = 11
9335 _dflt_fpsort_sbits = 53
9338 def get_default_rounding_mode(ctx=None):
9339 """Retrieves the
global default rounding mode.
"""
9340 global _dflt_rounding_mode
9341 if _dflt_rounding_mode == Z3_OP_FPA_RM_TOWARD_ZERO:
9343 elif _dflt_rounding_mode == Z3_OP_FPA_RM_TOWARD_NEGATIVE:
9345 elif _dflt_rounding_mode == Z3_OP_FPA_RM_TOWARD_POSITIVE:
9347 elif _dflt_rounding_mode == Z3_OP_FPA_RM_NEAREST_TIES_TO_EVEN:
9349 elif _dflt_rounding_mode == Z3_OP_FPA_RM_NEAREST_TIES_TO_AWAY:
9353 _ROUNDING_MODES = frozenset({
9354 Z3_OP_FPA_RM_TOWARD_ZERO,
9355 Z3_OP_FPA_RM_TOWARD_NEGATIVE,
9356 Z3_OP_FPA_RM_TOWARD_POSITIVE,
9357 Z3_OP_FPA_RM_NEAREST_TIES_TO_EVEN,
9358 Z3_OP_FPA_RM_NEAREST_TIES_TO_AWAY
9362 def set_default_rounding_mode(rm, ctx=None):
9363 global _dflt_rounding_mode
9364 if is_fprm_value(rm):
9365 _dflt_rounding_mode = rm.decl().kind()
9367 _z3_assert(_dflt_rounding_mode in _ROUNDING_MODES, "illegal rounding mode")
9368 _dflt_rounding_mode = rm
9371 def get_default_fp_sort(ctx=None):
9372 return FPSort(_dflt_fpsort_ebits, _dflt_fpsort_sbits, ctx)
9375 def set_default_fp_sort(ebits, sbits, ctx=None):
9376 global _dflt_fpsort_ebits
9377 global _dflt_fpsort_sbits
9378 _dflt_fpsort_ebits = ebits
9379 _dflt_fpsort_sbits = sbits
9382 def _dflt_rm(ctx=None):
9383 return get_default_rounding_mode(ctx)
9386 def _dflt_fps(ctx=None):
9387 return get_default_fp_sort(ctx)
9390 def _coerce_fp_expr_list(alist, ctx):
9391 first_fp_sort = None
9394 if first_fp_sort is None:
9395 first_fp_sort = a.sort()
9396 elif first_fp_sort == a.sort():
9397 pass # OK, same as before
9399 # we saw at least 2 different float sorts; something will
9400 # throw a sort mismatch later, for now assume None.
9401 first_fp_sort = None
9405 for i in range(len(alist)):
9407 is_repr = isinstance(a, str) and a.contains("2**(") and a.endswith(")")
9408 if is_repr or _is_int(a) or isinstance(a, (float, bool)):
9409 r.append(FPVal(a, None, first_fp_sort, ctx))
9412 return _coerce_expr_list(r, ctx)
9417 class FPSortRef(SortRef):
9418 """Floating-point sort.
"""
9421 """Retrieves the number of bits reserved
for the exponent
in the FloatingPoint sort `self`.
9426 return int(Z3_fpa_get_ebits(self.ctx_ref(), self.ast))
9429 """Retrieves the number of bits reserved
for the significand
in the FloatingPoint sort `self`.
9434 return int(Z3_fpa_get_sbits(self.ctx_ref(), self.ast))
9436 def cast(self, val):
9437 """Try to cast `val`
as a floating-point expression.
9441 >>> b.cast(1.0).
sexpr()
9442 '(fp #b0 #x7f #b00000000000000000000000)'
9446 _z3_assert(self.ctx == val.ctx, "Context mismatch")
9449 return FPVal(val, None, self, self.ctx)
9452 def Float16(ctx=None):
9453 """Floating-point 16-bit (half) sort.
"""
9455 return FPSortRef(Z3_mk_fpa_sort_16(ctx.ref()), ctx)
9458 def FloatHalf(ctx=None):
9459 """Floating-point 16-bit (half) sort.
"""
9461 return FPSortRef(Z3_mk_fpa_sort_half(ctx.ref()), ctx)
9464 def Float32(ctx=None):
9465 """Floating-point 32-bit (single) sort.
"""
9467 return FPSortRef(Z3_mk_fpa_sort_32(ctx.ref()), ctx)
9470 def FloatSingle(ctx=None):
9471 """Floating-point 32-bit (single) sort.
"""
9473 return FPSortRef(Z3_mk_fpa_sort_single(ctx.ref()), ctx)
9476 def Float64(ctx=None):
9477 """Floating-point 64-bit (double) sort.
"""
9479 return FPSortRef(Z3_mk_fpa_sort_64(ctx.ref()), ctx)
9482 def FloatDouble(ctx=None):
9483 """Floating-point 64-bit (double) sort.
"""
9485 return FPSortRef(Z3_mk_fpa_sort_double(ctx.ref()), ctx)
9488 def Float128(ctx=None):
9489 """Floating-point 128-bit (quadruple) sort.
"""
9491 return FPSortRef(Z3_mk_fpa_sort_128(ctx.ref()), ctx)
9494 def FloatQuadruple(ctx=None):
9495 """Floating-point 128-bit (quadruple) sort.
"""
9497 return FPSortRef(Z3_mk_fpa_sort_quadruple(ctx.ref()), ctx)
9500 class FPRMSortRef(SortRef):
9501 """"Floating-point rounding mode sort."""
9505 """Return True if `s` is a Z3 floating-point sort.
9512 return isinstance(s, FPSortRef)
9515 def is_fprm_sort(s):
9516 """Return
True if `s`
is a Z3 floating-point rounding mode sort.
9523 return isinstance(s, FPRMSortRef)
9528 class FPRef(ExprRef):
9529 """Floating-point expressions.
"""
9532 """Return the sort of the floating-point expression `self`.
9537 >>> x.sort() ==
FPSort(8, 24)
9540 return FPSortRef(Z3_get_sort(self.ctx_ref(), self.as_ast()), self.ctx)
9543 """Retrieves the number of bits reserved
for the exponent
in the FloatingPoint expression `self`.
9548 return self.sort().ebits()
9551 """Retrieves the number of bits reserved
for the exponent
in the FloatingPoint expression `self`.
9556 return self.sort().sbits()
9558 def as_string(self):
9559 """Return a Z3 floating point expression
as a Python string.
"""
9560 return Z3_ast_to_string(self.ctx_ref(), self.as_ast())
9562 def __le__(self, other):
9563 return fpLEQ(self, other, self.ctx)
9565 def __lt__(self, other):
9566 return fpLT(self, other, self.ctx)
9568 def __ge__(self, other):
9569 return fpGEQ(self, other, self.ctx)
9571 def __gt__(self, other):
9572 return fpGT(self, other, self.ctx)
9574 def __add__(self, other):
9575 """Create the Z3 expression `self + other`.
9584 [a, b] = _coerce_fp_expr_list([self, other], self.ctx)
9585 return fpAdd(_dflt_rm(), a, b, self.ctx)
9587 def __radd__(self, other):
9588 """Create the Z3 expression `other + self`.
9594 [a, b] = _coerce_fp_expr_list([other, self], self.ctx)
9595 return fpAdd(_dflt_rm(), a, b, self.ctx)
9597 def __sub__(self, other):
9598 """Create the Z3 expression `self - other`.
9607 [a, b] = _coerce_fp_expr_list([self, other], self.ctx)
9608 return fpSub(_dflt_rm(), a, b, self.ctx)
9610 def __rsub__(self, other):
9611 """Create the Z3 expression `other - self`.
9617 [a, b] = _coerce_fp_expr_list([other, self], self.ctx)
9618 return fpSub(_dflt_rm(), a, b, self.ctx)
9620 def __mul__(self, other):
9621 """Create the Z3 expression `self * other`.
9632 [a, b] = _coerce_fp_expr_list([self, other], self.ctx)
9633 return fpMul(_dflt_rm(), a, b, self.ctx)
9635 def __rmul__(self, other):
9636 """Create the Z3 expression `other * self`.
9645 [a, b] = _coerce_fp_expr_list([other, self], self.ctx)
9646 return fpMul(_dflt_rm(), a, b, self.ctx)
9649 """Create the Z3 expression `+self`.
"""
9653 """Create the Z3 expression `-self`.
9661 def __div__(self, other):
9662 """Create the Z3 expression `self / other`.
9673 [a, b] = _coerce_fp_expr_list([self, other], self.ctx)
9674 return fpDiv(_dflt_rm(), a, b, self.ctx)
9676 def __rdiv__(self, other):
9677 """Create the Z3 expression `other / self`.
9686 [a, b] = _coerce_fp_expr_list([other, self], self.ctx)
9687 return fpDiv(_dflt_rm(), a, b, self.ctx)
9689 def __truediv__(self, other):
9690 """Create the Z3 expression division `self / other`.
"""
9691 return self.__div__(other)
9693 def __rtruediv__(self, other):
9694 """Create the Z3 expression division `other / self`.
"""
9695 return self.__rdiv__(other)
9697 def __mod__(self, other):
9698 """Create the Z3 expression mod `self % other`.
"""
9699 return fpRem(self, other)
9701 def __rmod__(self, other):
9702 """Create the Z3 expression mod `other % self`.
"""
9703 return fpRem(other, self)
9706 class FPRMRef(ExprRef):
9707 """Floating-point rounding mode expressions
"""
9709 def as_string(self):
9710 """Return a Z3 floating point expression
as a Python string.
"""
9711 return Z3_ast_to_string(self.ctx_ref(), self.as_ast())
9714 def RoundNearestTiesToEven(ctx=None):
9716 return FPRMRef(Z3_mk_fpa_round_nearest_ties_to_even(ctx.ref()), ctx)
9721 return FPRMRef(Z3_mk_fpa_round_nearest_ties_to_even(ctx.ref()), ctx)
9724 def RoundNearestTiesToAway(ctx=None):
9726 return FPRMRef(Z3_mk_fpa_round_nearest_ties_to_away(ctx.ref()), ctx)
9731 return FPRMRef(Z3_mk_fpa_round_nearest_ties_to_away(ctx.ref()), ctx)
9734 def RoundTowardPositive(ctx=None):
9736 return FPRMRef(Z3_mk_fpa_round_toward_positive(ctx.ref()), ctx)
9741 return FPRMRef(Z3_mk_fpa_round_toward_positive(ctx.ref()), ctx)
9744 def RoundTowardNegative(ctx=None):
9746 return FPRMRef(Z3_mk_fpa_round_toward_negative(ctx.ref()), ctx)
9751 return FPRMRef(Z3_mk_fpa_round_toward_negative(ctx.ref()), ctx)
9754 def RoundTowardZero(ctx=None):
9756 return FPRMRef(Z3_mk_fpa_round_toward_zero(ctx.ref()), ctx)
9761 return FPRMRef(Z3_mk_fpa_round_toward_zero(ctx.ref()), ctx)
9765 """Return `
True`
if `a`
is a Z3 floating-point rounding mode expression.
9774 return isinstance(a, FPRMRef)
9777 def is_fprm_value(a):
9778 """Return `
True`
if `a`
is a Z3 floating-point rounding mode numeral value.
"""
9779 return is_fprm(a) and _is_numeral(a.ctx, a.ast)
9784 class FPNumRef(FPRef):
9785 """The sign of the numeral.
9796 num = (ctypes.c_int)()
9797 nsign = Z3_fpa_get_numeral_sign(self.ctx.ref(), self.as_ast(), byref(num))
9799 raise Z3Exception("error retrieving the sign of a numeral.")
9800 return num.value != 0
9802 """The sign of a floating-point numeral
as a bit-vector expression.
9804 Remark: NaN
's are invalid arguments.
9807 def sign_as_bv(self):
9808 return BitVecNumRef(Z3_fpa_get_numeral_sign_bv(self.ctx.ref(), self.as_ast()), self.ctx)
9810 """The significand of the numeral.
9817 def significand(self):
9818 return Z3_fpa_get_numeral_significand_string(self.ctx.ref(), self.as_ast())
9820 """The significand of the numeral
as a long.
9823 >>> x.significand_as_long()
9827 def significand_as_long(self):
9828 ptr = (ctypes.c_ulonglong * 1)()
9829 if not Z3_fpa_get_numeral_significand_uint64(self.ctx.ref(), self.as_ast(), ptr):
9830 raise Z3Exception("error retrieving the significand of a numeral.")
9833 """The significand of the numeral
as a bit-vector expression.
9835 Remark: NaN are invalid arguments.
9838 def significand_as_bv(self):
9839 return BitVecNumRef(Z3_fpa_get_numeral_significand_bv(self.ctx.ref(), self.as_ast()), self.ctx)
9841 """The exponent of the numeral.
9848 def exponent(self, biased=True):
9849 return Z3_fpa_get_numeral_exponent_string(self.ctx.ref(), self.as_ast(), biased)
9851 """The exponent of the numeral
as a long.
9854 >>> x.exponent_as_long()
9858 def exponent_as_long(self, biased=True):
9859 ptr = (ctypes.c_longlong * 1)()
9860 if not Z3_fpa_get_numeral_exponent_int64(self.ctx.ref(), self.as_ast(), ptr, biased):
9861 raise Z3Exception("error retrieving the exponent of a numeral.")
9864 """The exponent of the numeral
as a bit-vector expression.
9866 Remark: NaNs are invalid arguments.
9869 def exponent_as_bv(self, biased=True):
9870 return BitVecNumRef(Z3_fpa_get_numeral_exponent_bv(self.ctx.ref(), self.as_ast(), biased), self.ctx)
9872 """Indicates whether the numeral
is a NaN.
"""
9875 return Z3_fpa_is_numeral_nan(self.ctx.ref(), self.as_ast())
9877 """Indicates whether the numeral
is +oo
or -oo.
"""
9880 return Z3_fpa_is_numeral_inf(self.ctx.ref(), self.as_ast())
9882 """Indicates whether the numeral
is +zero
or -zero.
"""
9885 return Z3_fpa_is_numeral_zero(self.ctx.ref(), self.as_ast())
9887 """Indicates whether the numeral
is normal.
"""
9890 return Z3_fpa_is_numeral_normal(self.ctx.ref(), self.as_ast())
9892 """Indicates whether the numeral
is subnormal.
"""
9894 def isSubnormal(self):
9895 return Z3_fpa_is_numeral_subnormal(self.ctx.ref(), self.as_ast())
9897 """Indicates whether the numeral
is positive.
"""
9899 def isPositive(self):
9900 return Z3_fpa_is_numeral_positive(self.ctx.ref(), self.as_ast())
9902 """Indicates whether the numeral
is negative.
"""
9904 def isNegative(self):
9905 return Z3_fpa_is_numeral_negative(self.ctx.ref(), self.as_ast())
9908 The string representation of the numeral.
9915 def as_string(self):
9916 s = Z3_get_numeral_string(self.ctx.ref(), self.as_ast())
9917 return ("FPVal(%s, %s)" % (s, self.sort()))
9921 """Return `
True`
if `a`
is a Z3 floating-point expression.
9931 return isinstance(a, FPRef)
9935 """Return `
True`
if `a`
is a Z3 floating-point numeral value.
9946 return is_fp(a) and _is_numeral(a.ctx, a.ast)
9949 def FPSort(ebits, sbits, ctx=None):
9950 """Return a Z3 floating-point sort of the given sizes. If `ctx=
None`, then the
global context
is used.
9952 >>> Single =
FPSort(8, 24)
9953 >>> Double =
FPSort(11, 53)
9956 >>> x =
Const(
'x', Single)
9961 return FPSortRef(Z3_mk_fpa_sort(ctx.ref(), ebits, sbits), ctx)
9964 def _to_float_str(val, exp=0):
9965 if isinstance(val, float):
9969 sone = math.copysign(1.0, val)
9974 elif val == float("+inf"):
9976 elif val == float("-inf"):
9979 v = val.as_integer_ratio()
9982 rvs = str(num) + "/" + str(den)
9983 res = rvs + "p" + _to_int_str(exp)
9984 elif isinstance(val, bool):
9991 elif isinstance(val, str):
9992 inx = val.find("*(2**")
9995 elif val[-1] == ")":
9997 exp = str(int(val[inx + 5:-1]) + int(exp))
9999 _z3_assert(False, "String does not have floating-point numeral form.")
10001 _z3_assert(False, "Python value cannot be used to create floating-point numerals.")
10005 return res + "p" + exp
10009 """Create a Z3 floating-point NaN term.
10012 >>> set_fpa_pretty(
True)
10015 >>> pb = get_fpa_pretty()
10016 >>> set_fpa_pretty(
False)
10019 >>> set_fpa_pretty(pb)
10021 _z3_assert(isinstance(s, FPSortRef), "sort mismatch")
10022 return FPNumRef(Z3_mk_fpa_nan(s.ctx_ref(), s.ast), s.ctx)
10025 def fpPlusInfinity(s):
10026 """Create a Z3 floating-point +oo term.
10029 >>> pb = get_fpa_pretty()
10030 >>> set_fpa_pretty(
True)
10033 >>> set_fpa_pretty(
False)
10036 >>> set_fpa_pretty(pb)
10038 _z3_assert(isinstance(s, FPSortRef), "sort mismatch")
10039 return FPNumRef(Z3_mk_fpa_inf(s.ctx_ref(), s.ast, False), s.ctx)
10042 def fpMinusInfinity(s):
10043 """Create a Z3 floating-point -oo term.
"""
10044 _z3_assert(isinstance(s, FPSortRef), "sort mismatch")
10045 return FPNumRef(Z3_mk_fpa_inf(s.ctx_ref(), s.ast, True), s.ctx)
10048 def fpInfinity(s, negative):
10049 """Create a Z3 floating-point +oo
or -oo term.
"""
10050 _z3_assert(isinstance(s, FPSortRef), "sort mismatch")
10051 _z3_assert(isinstance(negative, bool), "expected Boolean flag")
10052 return FPNumRef(Z3_mk_fpa_inf(s.ctx_ref(), s.ast, negative), s.ctx)
10056 """Create a Z3 floating-point +0.0 term.
"""
10057 _z3_assert(isinstance(s, FPSortRef), "sort mismatch")
10058 return FPNumRef(Z3_mk_fpa_zero(s.ctx_ref(), s.ast, False), s.ctx)
10061 def fpMinusZero(s):
10062 """Create a Z3 floating-point -0.0 term.
"""
10063 _z3_assert(isinstance(s, FPSortRef), "sort mismatch")
10064 return FPNumRef(Z3_mk_fpa_zero(s.ctx_ref(), s.ast, True), s.ctx)
10067 def fpZero(s, negative):
10068 """Create a Z3 floating-point +0.0
or -0.0 term.
"""
10069 _z3_assert(isinstance(s, FPSortRef), "sort mismatch")
10070 _z3_assert(isinstance(negative, bool), "expected Boolean flag")
10071 return FPNumRef(Z3_mk_fpa_zero(s.ctx_ref(), s.ast, negative), s.ctx)
10074 def FPVal(sig, exp=None, fps=None, ctx=None):
10075 """Return a floating-point value of value `val`
and sort `fps`.
10076 If `ctx=
None`, then the
global context
is used.
10081 >>> print(
"0x%.8x" % v.exponent_as_long(
False))
10096 ctx = _get_ctx(ctx)
10097 if is_fp_sort(exp):
10101 fps = _dflt_fps(ctx)
10102 _z3_assert(is_fp_sort(fps), "sort mismatch")
10105 val = _to_float_str(sig)
10106 if val == "NaN" or val == "nan":
10108 elif val == "-0.0":
10109 return fpMinusZero(fps)
10110 elif val == "0.0" or val == "+0.0":
10111 return fpPlusZero(fps)
10112 elif val == "+oo" or val == "+inf" or val == "+Inf":
10113 return fpPlusInfinity(fps)
10114 elif val == "-oo" or val == "-inf" or val == "-Inf":
10115 return fpMinusInfinity(fps)
10117 return FPNumRef(Z3_mk_numeral(ctx.ref(), val, fps.ast), ctx)
10120 def FP(name, fpsort, ctx=None):
10121 """Return a floating-point constant named `name`.
10122 `fpsort`
is the floating-point sort.
10123 If `ctx=
None`, then the
global context
is used.
10132 >>> word =
FPSort(8, 24)
10133 >>> x2 =
FP(
'x', word)
10137 if isinstance(fpsort, FPSortRef) and ctx is None:
10140 ctx = _get_ctx(ctx)
10141 return FPRef(Z3_mk_const(ctx.ref(), to_symbol(name, ctx), fpsort.ast), ctx)
10144 def FPs(names, fpsort, ctx=None):
10145 """Return an array of floating-point constants.
10147 >>> x, y, z =
FPs(
'x y z',
FPSort(8, 24))
10157 ctx = _get_ctx(ctx)
10158 if isinstance(names, str):
10159 names = names.split(" ")
10160 return [FP(name, fpsort, ctx) for name in names]
10163 def fpAbs(a, ctx=None):
10164 """Create a Z3 floating-point absolute value expression.
10168 >>> x =
FPVal(1.0, s)
10171 >>> y =
FPVal(-20.0, s)
10175 fpAbs(-1.25*(2**4))
10176 >>>
fpAbs(-1.25*(2**4))
10177 fpAbs(-1.25*(2**4))
10178 >>>
fpAbs(x).sort()
10181 ctx = _get_ctx(ctx)
10182 [a] = _coerce_fp_expr_list([a], ctx)
10183 return FPRef(Z3_mk_fpa_abs(ctx.ref(), a.as_ast()), ctx)
10186 def fpNeg(a, ctx=None):
10187 """Create a Z3 floating-point addition expression.
10194 >>>
fpNeg(x).sort()
10197 ctx = _get_ctx(ctx)
10198 [a] = _coerce_fp_expr_list([a], ctx)
10199 return FPRef(Z3_mk_fpa_neg(ctx.ref(), a.as_ast()), ctx)
10202 def _mk_fp_unary(f, rm, a, ctx):
10203 ctx = _get_ctx(ctx)
10204 [a] = _coerce_fp_expr_list([a], ctx)
10206 _z3_assert(is_fprm(rm), "First argument must be a Z3 floating-point rounding mode expression")
10207 _z3_assert(is_fp(a), "Second argument must be a Z3 floating-point expression")
10208 return FPRef(f(ctx.ref(), rm.as_ast(), a.as_ast()), ctx)
10211 def _mk_fp_unary_pred(f, a, ctx):
10212 ctx = _get_ctx(ctx)
10213 [a] = _coerce_fp_expr_list([a], ctx)
10215 _z3_assert(is_fp(a), "First argument must be a Z3 floating-point expression")
10216 return BoolRef(f(ctx.ref(), a.as_ast()), ctx)
10219 def _mk_fp_bin(f, rm, a, b, ctx):
10220 ctx = _get_ctx(ctx)
10221 [a, b] = _coerce_fp_expr_list([a, b], ctx)
10223 _z3_assert(is_fprm(rm), "First argument must be a Z3 floating-point rounding mode expression")
10224 _z3_assert(is_fp(a) or is_fp(b), "Second or third argument must be a Z3 floating-point expression")
10225 return FPRef(f(ctx.ref(), rm.as_ast(), a.as_ast(), b.as_ast()), ctx)
10228 def _mk_fp_bin_norm(f, a, b, ctx):
10229 ctx = _get_ctx(ctx)
10230 [a, b] = _coerce_fp_expr_list([a, b], ctx)
10232 _z3_assert(is_fp(a) or is_fp(b), "First or second argument must be a Z3 floating-point expression")
10233 return FPRef(f(ctx.ref(), a.as_ast(), b.as_ast()), ctx)
10236 def _mk_fp_bin_pred(f, a, b, ctx):
10237 ctx = _get_ctx(ctx)
10238 [a, b] = _coerce_fp_expr_list([a, b], ctx)
10240 _z3_assert(is_fp(a) or is_fp(b), "First or second argument must be a Z3 floating-point expression")
10241 return BoolRef(f(ctx.ref(), a.as_ast(), b.as_ast()), ctx)
10244 def _mk_fp_tern(f, rm, a, b, c, ctx):
10245 ctx = _get_ctx(ctx)
10246 [a, b, c] = _coerce_fp_expr_list([a, b, c], ctx)
10248 _z3_assert(is_fprm(rm), "First argument must be a Z3 floating-point rounding mode expression")
10249 _z3_assert(is_fp(a) or is_fp(b) or is_fp(
10250 c), "Second, third or fourth argument must be a Z3 floating-point expression")
10251 return FPRef(f(ctx.ref(), rm.as_ast(), a.as_ast(), b.as_ast(), c.as_ast()), ctx)
10254 def fpAdd(rm, a, b, ctx=None):
10255 """Create a Z3 floating-point addition expression.
10261 >>>
fpAdd(rm, x, y)
10265 >>>
fpAdd(rm, x, y).sort()
10268 return _mk_fp_bin(Z3_mk_fpa_add, rm, a, b, ctx)
10271 def fpSub(rm, a, b, ctx=None):
10272 """Create a Z3 floating-point subtraction expression.
10278 >>>
fpSub(rm, x, y)
10280 >>>
fpSub(rm, x, y).sort()
10283 return _mk_fp_bin(Z3_mk_fpa_sub, rm, a, b, ctx)
10286 def fpMul(rm, a, b, ctx=None):
10287 """Create a Z3 floating-point multiplication expression.
10293 >>>
fpMul(rm, x, y)
10295 >>>
fpMul(rm, x, y).sort()
10298 return _mk_fp_bin(Z3_mk_fpa_mul, rm, a, b, ctx)
10301 def fpDiv(rm, a, b, ctx=None):
10302 """Create a Z3 floating-point division expression.
10308 >>>
fpDiv(rm, x, y)
10310 >>>
fpDiv(rm, x, y).sort()
10313 return _mk_fp_bin(Z3_mk_fpa_div, rm, a, b, ctx)
10316 def fpRem(a, b, ctx=None):
10317 """Create a Z3 floating-point remainder expression.
10324 >>>
fpRem(x, y).sort()
10327 return _mk_fp_bin_norm(Z3_mk_fpa_rem, a, b, ctx)
10330 def fpMin(a, b, ctx=None):
10331 """Create a Z3 floating-point minimum expression.
10339 >>>
fpMin(x, y).sort()
10342 return _mk_fp_bin_norm(Z3_mk_fpa_min, a, b, ctx)
10345 def fpMax(a, b, ctx=None):
10346 """Create a Z3 floating-point maximum expression.
10354 >>>
fpMax(x, y).sort()
10357 return _mk_fp_bin_norm(Z3_mk_fpa_max, a, b, ctx)
10360 def fpFMA(rm, a, b, c, ctx=None):
10361 """Create a Z3 floating-point fused multiply-add expression.
10363 return _mk_fp_tern(Z3_mk_fpa_fma, rm, a, b, c, ctx)
10366 def fpSqrt(rm, a, ctx=None):
10367 """Create a Z3 floating-point square root expression.
10369 return _mk_fp_unary(Z3_mk_fpa_sqrt, rm, a, ctx)
10372 def fpRoundToIntegral(rm, a, ctx=None):
10373 """Create a Z3 floating-point roundToIntegral expression.
10375 return _mk_fp_unary(Z3_mk_fpa_round_to_integral, rm, a, ctx)
10378 def fpIsNaN(a, ctx=None):
10379 """Create a Z3 floating-point isNaN expression.
10387 return _mk_fp_unary_pred(Z3_mk_fpa_is_nan, a, ctx)
10390 def fpIsInf(a, ctx=None):
10391 """Create a Z3 floating-point isInfinite expression.
10398 return _mk_fp_unary_pred(Z3_mk_fpa_is_infinite, a, ctx)
10401 def fpIsZero(a, ctx=None):
10402 """Create a Z3 floating-point isZero expression.
10404 return _mk_fp_unary_pred(Z3_mk_fpa_is_zero, a, ctx)
10407 def fpIsNormal(a, ctx=None):
10408 """Create a Z3 floating-point isNormal expression.
10410 return _mk_fp_unary_pred(Z3_mk_fpa_is_normal, a, ctx)
10413 def fpIsSubnormal(a, ctx=None):
10414 """Create a Z3 floating-point isSubnormal expression.
10416 return _mk_fp_unary_pred(Z3_mk_fpa_is_subnormal, a, ctx)
10419 def fpIsNegative(a, ctx=None):
10420 """Create a Z3 floating-point isNegative expression.
10422 return _mk_fp_unary_pred(Z3_mk_fpa_is_negative, a, ctx)
10425 def fpIsPositive(a, ctx=None):
10426 """Create a Z3 floating-point isPositive expression.
10428 return _mk_fp_unary_pred(Z3_mk_fpa_is_positive, a, ctx)
10431 def _check_fp_args(a, b):
10433 _z3_assert(is_fp(a) or is_fp(b), "First or second argument must be a Z3 floating-point expression")
10436 def fpLT(a, b, ctx=None):
10437 """Create the Z3 floating-point expression `other < self`.
10442 >>> (x < y).sexpr()
10445 return _mk_fp_bin_pred(Z3_mk_fpa_lt, a, b, ctx)
10448 def fpLEQ(a, b, ctx=None):
10449 """Create the Z3 floating-point expression `other <= self`.
10454 >>> (x <= y).sexpr()
10457 return _mk_fp_bin_pred(Z3_mk_fpa_leq, a, b, ctx)
10460 def fpGT(a, b, ctx=None):
10461 """Create the Z3 floating-point expression `other > self`.
10466 >>> (x > y).sexpr()
10469 return _mk_fp_bin_pred(Z3_mk_fpa_gt, a, b, ctx)
10472 def fpGEQ(a, b, ctx=None):
10473 """Create the Z3 floating-point expression `other >= self`.
10478 >>> (x >= y).sexpr()
10481 return _mk_fp_bin_pred(Z3_mk_fpa_geq, a, b, ctx)
10484 def fpEQ(a, b, ctx=None):
10485 """Create the Z3 floating-point expression `
fpEQ(other, self)`.
10490 >>>
fpEQ(x, y).sexpr()
10493 return _mk_fp_bin_pred(Z3_mk_fpa_eq, a, b, ctx)
10496 def fpNEQ(a, b, ctx=None):
10497 """Create the Z3 floating-point expression `
Not(
fpEQ(other, self))`.
10502 >>> (x != y).sexpr()
10505 return Not(fpEQ(a, b, ctx))
10508 def fpFP(sgn, exp, sig, ctx=None):
10509 """Create the Z3 floating-point value `
fpFP(sgn, sig, exp)`
from the three bit-vectors sgn, sig,
and exp.
10514 fpFP(1, 127, 4194304)
10515 >>> xv =
FPVal(-1.5, s)
10519 >>> slvr.add(
fpEQ(x, xv))
10522 >>> xv =
FPVal(+1.5, s)
10526 >>> slvr.add(
fpEQ(x, xv))
10530 _z3_assert(is_bv(sgn) and is_bv(exp) and is_bv(sig), "sort mismatch")
10531 _z3_assert(sgn.sort().size() == 1, "sort mismatch")
10532 ctx = _get_ctx(ctx)
10533 _z3_assert(ctx == sgn.ctx == exp.ctx == sig.ctx, "context mismatch")
10534 return FPRef(Z3_mk_fpa_fp(ctx.ref(), sgn.ast, exp.ast, sig.ast), ctx)
10537 def fpToFP(a1, a2=None, a3=None, ctx=None):
10538 """Create a Z3 floating-point conversion expression
from other term sorts
10541 From a bit-vector term
in IEEE 754-2008 format:
10547 From a floating-point term with different precision:
10558 From a signed bit-vector term:
10563 ctx = _get_ctx(ctx)
10564 if is_bv(a1) and is_fp_sort(a2):
10565 return FPRef(Z3_mk_fpa_to_fp_bv(ctx.ref(), a1.ast, a2.ast), ctx)
10566 elif is_fprm(a1) and is_fp(a2) and is_fp_sort(a3):
10567 return FPRef(Z3_mk_fpa_to_fp_float(ctx.ref(), a1.ast, a2.ast, a3.ast), ctx)
10568 elif is_fprm(a1) and is_real(a2) and is_fp_sort(a3):
10569 return FPRef(Z3_mk_fpa_to_fp_real(ctx.ref(), a1.ast, a2.ast, a3.ast), ctx)
10570 elif is_fprm(a1) and is_bv(a2) and is_fp_sort(a3):
10571 return FPRef(Z3_mk_fpa_to_fp_signed(ctx.ref(), a1.ast, a2.ast, a3.ast), ctx)
10573 raise Z3Exception("Unsupported combination of arguments for conversion to floating-point term.")
10576 def fpBVToFP(v, sort, ctx=None):
10577 """Create a Z3 floating-point conversion expression that represents the
10578 conversion
from a bit-vector term to a floating-point term.
10587 _z3_assert(is_bv(v), "First argument must be a Z3 bit-vector expression")
10588 _z3_assert(is_fp_sort(sort), "Second argument must be a Z3 floating-point sort.")
10589 ctx = _get_ctx(ctx)
10590 return FPRef(Z3_mk_fpa_to_fp_bv(ctx.ref(), v.ast, sort.ast), ctx)
10593 def fpFPToFP(rm, v, sort, ctx=None):
10594 """Create a Z3 floating-point conversion expression that represents the
10595 conversion
from a floating-point term to a floating-point term of different precision.
10606 _z3_assert(is_fprm(rm), "First argument must be a Z3 floating-point rounding mode expression.")
10607 _z3_assert(is_fp(v), "Second argument must be a Z3 floating-point expression.")
10608 _z3_assert(is_fp_sort(sort), "Third argument must be a Z3 floating-point sort.")
10609 ctx = _get_ctx(ctx)
10610 return FPRef(Z3_mk_fpa_to_fp_float(ctx.ref(), rm.ast, v.ast, sort.ast), ctx)
10613 def fpRealToFP(rm, v, sort, ctx=None):
10614 """Create a Z3 floating-point conversion expression that represents the
10615 conversion
from a real term to a floating-point term.
10624 _z3_assert(is_fprm(rm), "First argument must be a Z3 floating-point rounding mode expression.")
10625 _z3_assert(is_real(v), "Second argument must be a Z3 expression or real sort.")
10626 _z3_assert(is_fp_sort(sort), "Third argument must be a Z3 floating-point sort.")
10627 ctx = _get_ctx(ctx)
10628 return FPRef(Z3_mk_fpa_to_fp_real(ctx.ref(), rm.ast, v.ast, sort.ast), ctx)
10631 def fpSignedToFP(rm, v, sort, ctx=None):
10632 """Create a Z3 floating-point conversion expression that represents the
10633 conversion
from a signed bit-vector term (encoding an integer) to a floating-point term.
10642 _z3_assert(is_fprm(rm), "First argument must be a Z3 floating-point rounding mode expression.")
10643 _z3_assert(is_bv(v), "Second argument must be a Z3 bit-vector expression")
10644 _z3_assert(is_fp_sort(sort), "Third argument must be a Z3 floating-point sort.")
10645 ctx = _get_ctx(ctx)
10646 return FPRef(Z3_mk_fpa_to_fp_signed(ctx.ref(), rm.ast, v.ast, sort.ast), ctx)
10649 def fpUnsignedToFP(rm, v, sort, ctx=None):
10650 """Create a Z3 floating-point conversion expression that represents the
10651 conversion
from an unsigned bit-vector term (encoding an integer) to a floating-point term.
10660 _z3_assert(is_fprm(rm), "First argument must be a Z3 floating-point rounding mode expression.")
10661 _z3_assert(is_bv(v), "Second argument must be a Z3 bit-vector expression")
10662 _z3_assert(is_fp_sort(sort), "Third argument must be a Z3 floating-point sort.")
10663 ctx = _get_ctx(ctx)
10664 return FPRef(Z3_mk_fpa_to_fp_unsigned(ctx.ref(), rm.ast, v.ast, sort.ast), ctx)
10667 def fpToFPUnsigned(rm, x, s, ctx=None):
10668 """Create a Z3 floating-point conversion expression,
from unsigned bit-vector to floating-point expression.
"""
10670 _z3_assert(is_fprm(rm), "First argument must be a Z3 floating-point rounding mode expression")
10671 _z3_assert(is_bv(x), "Second argument must be a Z3 bit-vector expression")
10672 _z3_assert(is_fp_sort(s), "Third argument must be Z3 floating-point sort")
10673 ctx = _get_ctx(ctx)
10674 return FPRef(Z3_mk_fpa_to_fp_unsigned(ctx.ref(), rm.ast, x.ast, s.ast), ctx)
10677 def fpToSBV(rm, x, s, ctx=None):
10678 """Create a Z3 floating-point conversion expression,
from floating-point expression to signed bit-vector.
10682 >>> print(
is_fp(x))
10684 >>> print(
is_bv(y))
10686 >>> print(
is_fp(y))
10688 >>> print(
is_bv(x))
10692 _z3_assert(is_fprm(rm), "First argument must be a Z3 floating-point rounding mode expression")
10693 _z3_assert(is_fp(x), "Second argument must be a Z3 floating-point expression")
10694 _z3_assert(is_bv_sort(s), "Third argument must be Z3 bit-vector sort")
10695 ctx = _get_ctx(ctx)
10696 return BitVecRef(Z3_mk_fpa_to_sbv(ctx.ref(), rm.ast, x.ast, s.size()), ctx)
10699 def fpToUBV(rm, x, s, ctx=None):
10700 """Create a Z3 floating-point conversion expression,
from floating-point expression to unsigned bit-vector.
10704 >>> print(
is_fp(x))
10706 >>> print(
is_bv(y))
10708 >>> print(
is_fp(y))
10710 >>> print(
is_bv(x))
10714 _z3_assert(is_fprm(rm), "First argument must be a Z3 floating-point rounding mode expression")
10715 _z3_assert(is_fp(x), "Second argument must be a Z3 floating-point expression")
10716 _z3_assert(is_bv_sort(s), "Third argument must be Z3 bit-vector sort")
10717 ctx = _get_ctx(ctx)
10718 return BitVecRef(Z3_mk_fpa_to_ubv(ctx.ref(), rm.ast, x.ast, s.size()), ctx)
10721 def fpToReal(x, ctx=None):
10722 """Create a Z3 floating-point conversion expression,
from floating-point expression to real.
10726 >>> print(
is_fp(x))
10730 >>> print(
is_fp(y))
10736 _z3_assert(is_fp(x), "First argument must be a Z3 floating-point expression")
10737 ctx = _get_ctx(ctx)
10738 return ArithRef(Z3_mk_fpa_to_real(ctx.ref(), x.ast), ctx)
10741 def fpToIEEEBV(x, ctx=None):
10742 """\brief Conversion of a floating-point term into a bit-vector term
in IEEE 754-2008 format.
10744 The size of the resulting bit-vector
is automatically determined.
10746 Note that IEEE 754-2008 allows multiple different representations of NaN. This conversion
10747 knows only one NaN
and it will always produce the same bit-vector representation of
10752 >>> print(
is_fp(x))
10754 >>> print(
is_bv(y))
10756 >>> print(
is_fp(y))
10758 >>> print(
is_bv(x))
10762 _z3_assert(is_fp(x), "First argument must be a Z3 floating-point expression")
10763 ctx = _get_ctx(ctx)
10764 return BitVecRef(Z3_mk_fpa_to_ieee_bv(ctx.ref(), x.ast), ctx)
10767 #########################################
10769 # Strings, Sequences and Regular expressions
10771 #########################################
10773 class SeqSortRef(SortRef):
10774 """Sequence sort.
"""
10776 def is_string(self):
10777 """Determine
if sort
is a string
10785 return Z3_is_string_sort(self.ctx_ref(), self.ast)
10788 return _to_sort_ref(Z3_get_seq_sort_basis(self.ctx_ref(), self.ast), self.ctx)
10790 class CharSortRef(SortRef):
10791 """Character sort.
"""
10794 def StringSort(ctx=None):
10795 """Create a string sort
10800 ctx = _get_ctx(ctx)
10801 return SeqSortRef(Z3_mk_string_sort(ctx.ref()), ctx)
10803 def CharSort(ctx=None):
10804 """Create a character sort
10809 ctx = _get_ctx(ctx)
10810 return CharSortRef(Z3_mk_char_sort(ctx.ref()), ctx)
10814 """Create a sequence sort over elements provided
in the argument
10819 return SeqSortRef(Z3_mk_seq_sort(s.ctx_ref(), s.ast), s.ctx)
10822 class SeqRef(ExprRef):
10823 """Sequence expression.
"""
10826 return SeqSortRef(Z3_get_sort(self.ctx_ref(), self.as_ast()), self.ctx)
10828 def __add__(self, other):
10829 return Concat(self, other)
10831 def __radd__(self, other):
10832 return Concat(other, self)
10834 def __getitem__(self, i):
10836 i = IntVal(i, self.ctx)
10837 return _to_expr_ref(Z3_mk_seq_nth(self.ctx_ref(), self.as_ast(), i.as_ast()), self.ctx)
10841 i = IntVal(i, self.ctx)
10842 return SeqRef(Z3_mk_seq_at(self.ctx_ref(), self.as_ast(), i.as_ast()), self.ctx)
10844 def is_string(self):
10845 return Z3_is_string_sort(self.ctx_ref(), Z3_get_sort(self.ctx_ref(), self.as_ast()))
10847 def is_string_value(self):
10848 return Z3_is_string(self.ctx_ref(), self.as_ast())
10850 def as_string(self):
10851 """Return a string representation of sequence expression.
"""
10852 if self.is_string_value():
10853 string_length = ctypes.c_uint()
10854 chars = Z3_get_lstring(self.ctx_ref(), self.as_ast(), byref(string_length))
10855 return string_at(chars, size=string_length.value).decode("latin-1")
10856 return Z3_ast_to_string(self.ctx_ref(), self.as_ast())
10858 def __le__(self, other):
10859 return _to_expr_ref(Z3_mk_str_le(self.ctx_ref(), self.as_ast(), other.as_ast()), self.ctx)
10861 def __lt__(self, other):
10862 return _to_expr_ref(Z3_mk_str_lt(self.ctx_ref(), self.as_ast(), other.as_ast()), self.ctx)
10864 def __ge__(self, other):
10865 return _to_expr_ref(Z3_mk_str_le(self.ctx_ref(), other.as_ast(), self.as_ast()), self.ctx)
10867 def __gt__(self, other):
10868 return _to_expr_ref(Z3_mk_str_lt(self.ctx_ref(), other.as_ast(), self.as_ast()), self.ctx)
10871 def _coerce_char(ch, ctx=None):
10872 if isinstance(ch, str):
10873 ctx = _get_ctx(ctx)
10874 ch = CharVal(ch, ctx)
10875 if not is_expr(ch):
10876 raise Z3Exception("Character expression expected")
10879 class CharRef(ExprRef):
10880 """Character expression.
"""
10882 def __le__(self, other):
10883 other = _coerce_char(other, self.ctx)
10884 return _to_expr_ref(Z3_mk_char_le(self.ctx_ref(), self.as_ast(), other.as_ast()), self.ctx)
10887 return _to_expr_ref(Z3_mk_char_to_int(self.ctx_ref(), self.as_ast()), self.ctx)
10890 return _to_expr_ref(Z3_mk_char_to_bv(self.ctx_ref(), self.as_ast()), self.ctx)
10892 def is_digit(self):
10893 return _to_expr_ref(Z3_mk_char_is_digit(self.ctx_ref(), self.as_ast()), self.ctx)
10896 def CharVal(ch, ctx=None):
10897 ctx = _get_ctx(ctx)
10898 if isinstance(ch, str):
10900 if not isinstance(ch, int):
10901 raise Z3Exception("character value should be an ordinal")
10902 return _to_expr_ref(Z3_mk_char(ctx.ref(), ch), ctx)
10904 def CharFromBv(ch, ctx=None):
10905 if not is_expr(ch):
10906 raise Z3Expression("Bit-vector expression needed")
10907 return _to_expr_ref(Z3_mk_char_from_bv(ch.ctx_ref(), ch.as_ast()), ch.ctx)
10909 def CharToBv(ch, ctx=None):
10910 ch = _coerce_char(ch, ctx)
10913 def CharToInt(ch, ctx=None):
10914 ch = _coerce_char(ch, ctx)
10917 def CharIsDigit(ch, ctx=None):
10918 ch = _coerce_char(ch, ctx)
10919 return ch.is_digit()
10921 def _coerce_seq(s, ctx=None):
10922 if isinstance(s, str):
10923 ctx = _get_ctx(ctx)
10924 s = StringVal(s, ctx)
10926 raise Z3Exception("Non-expression passed as a sequence")
10928 raise Z3Exception("Non-sequence passed as a sequence")
10932 def _get_ctx2(a, b, ctx=None):
10943 """Return `
True`
if `a`
is a Z3 sequence expression.
10949 return isinstance(a, SeqRef)
10953 """Return `
True`
if `a`
is a Z3 string expression.
10957 return isinstance(a, SeqRef) and a.is_string()
10960 def is_string_value(a):
10961 """return 'True' if 'a' is a Z3 string constant expression.
10967 return isinstance(a, SeqRef) and a.is_string_value()
10969 def StringVal(s, ctx=None):
10970 """create a string expression
"""
10971 s = "".join(str(ch) if 32 <= ord(ch) and ord(ch) < 127 else "\\u{%x}" % (ord(ch)) for ch in s)
10972 ctx = _get_ctx(ctx)
10973 return SeqRef(Z3_mk_string(ctx.ref(), s), ctx)
10976 def String(name, ctx=None):
10977 """Return a string constant named `name`. If `ctx=
None`, then the
global context
is used.
10981 ctx = _get_ctx(ctx)
10982 return SeqRef(Z3_mk_const(ctx.ref(), to_symbol(name, ctx), StringSort(ctx).ast), ctx)
10985 def Strings(names, ctx=None):
10986 """Return a tuple of String constants.
"""
10987 ctx = _get_ctx(ctx)
10988 if isinstance(names, str):
10989 names = names.split(" ")
10990 return [String(name, ctx) for name in names]
10993 def SubString(s, offset, length):
10994 """Extract substring
or subsequence starting at offset
"""
10995 return Extract(s, offset, length)
10998 def SubSeq(s, offset, length):
10999 """Extract substring
or subsequence starting at offset
"""
11000 return Extract(s, offset, length)
11004 """Create the empty sequence of the given sort
11007 >>> print(e.eq(e2))
11016 if isinstance(s, SeqSortRef):
11017 return SeqRef(Z3_mk_seq_empty(s.ctx_ref(), s.ast), s.ctx)
11018 if isinstance(s, ReSortRef):
11019 return ReRef(Z3_mk_re_empty(s.ctx_ref(), s.ast), s.ctx)
11020 raise Z3Exception("Non-sequence, non-regular expression sort passed to Empty")
11024 """Create the regular expression that accepts the universal language
11032 if isinstance(s, ReSortRef):
11033 return ReRef(Z3_mk_re_full(s.ctx_ref(), s.ast), s.ctx)
11034 raise Z3Exception("Non-sequence, non-regular expression sort passed to Full")
11039 """Create a singleton sequence
"""
11040 return SeqRef(Z3_mk_seq_unit(a.ctx_ref(), a.as_ast()), a.ctx)
11043 def PrefixOf(a, b):
11044 """Check
if 'a' is a prefix of
'b'
11052 ctx = _get_ctx2(a, b)
11053 a = _coerce_seq(a, ctx)
11054 b = _coerce_seq(b, ctx)
11055 return BoolRef(Z3_mk_seq_prefix(a.ctx_ref(), a.as_ast(), b.as_ast()), a.ctx)
11058 def SuffixOf(a, b):
11059 """Check
if 'a' is a suffix of
'b'
11067 ctx = _get_ctx2(a, b)
11068 a = _coerce_seq(a, ctx)
11069 b = _coerce_seq(b, ctx)
11070 return BoolRef(Z3_mk_seq_suffix(a.ctx_ref(), a.as_ast(), b.as_ast()), a.ctx)
11073 def Contains(a, b):
11074 """Check
if 'a' contains
'b'
11081 >>> x, y, z =
Strings(
'x y z')
11086 ctx = _get_ctx2(a, b)
11087 a = _coerce_seq(a, ctx)
11088 b = _coerce_seq(b, ctx)
11089 return BoolRef(Z3_mk_seq_contains(a.ctx_ref(), a.as_ast(), b.as_ast()), a.ctx)
11092 def Replace(s, src, dst):
11093 """Replace the first occurrence of
'src' by
'dst' in 's'
11094 >>> r =
Replace(
"aaa",
"a",
"b")
11098 ctx = _get_ctx2(dst, s)
11099 if ctx is None and is_expr(src):
11101 src = _coerce_seq(src, ctx)
11102 dst = _coerce_seq(dst, ctx)
11103 s = _coerce_seq(s, ctx)
11104 return SeqRef(Z3_mk_seq_replace(src.ctx_ref(), s.as_ast(), src.as_ast(), dst.as_ast()), s.ctx)
11107 def IndexOf(s, substr, offset=None):
11108 """Retrieve the index of substring within a string starting at a specified offset.
11117 if is_expr(offset):
11119 ctx = _get_ctx2(s, substr, ctx)
11120 s = _coerce_seq(s, ctx)
11121 substr = _coerce_seq(substr, ctx)
11122 if _is_int(offset):
11123 offset = IntVal(offset, ctx)
11124 return ArithRef(Z3_mk_seq_index(s.ctx_ref(), s.as_ast(), substr.as_ast(), offset.as_ast()), s.ctx)
11127 def LastIndexOf(s, substr):
11128 """Retrieve the last index of substring within a string
"""
11130 ctx = _get_ctx2(s, substr, ctx)
11131 s = _coerce_seq(s, ctx)
11132 substr = _coerce_seq(substr, ctx)
11133 return ArithRef(Z3_mk_seq_last_index(s.ctx_ref(), s.as_ast(), substr.as_ast()), s.ctx)
11137 """Obtain the length of a sequence
's'
11143 return ArithRef(Z3_mk_seq_length(s.ctx_ref(), s.as_ast()), s.ctx)
11147 """Convert string expression to integer
11159 return ArithRef(Z3_mk_str_to_int(s.ctx_ref(), s.as_ast()), s.ctx)
11163 """Convert integer expression to string
"""
11166 return SeqRef(Z3_mk_int_to_str(s.ctx_ref(), s.as_ast()), s.ctx)
11170 """Convert a unit length string to integer code
"""
11173 return ArithRef(Z3_mk_string_to_code(s.ctx_ref(), s.as_ast()), s.ctx)
11175 def StrFromCode(c):
11176 """Convert code to a string
"""
11179 return SeqRef(Z3_mk_string_from_code(c.ctx_ref(), c.as_ast()), c.ctx)
11181 def Re(s, ctx=None):
11182 """The regular expression that accepts sequence
's'
11187 s = _coerce_seq(s, ctx)
11188 return ReRef(Z3_mk_seq_to_re(s.ctx_ref(), s.as_ast()), s.ctx)
11191 # Regular expressions
11193 class ReSortRef(SortRef):
11194 """Regular expression sort.
"""
11197 return _to_sort_ref(Z3_get_re_sort_basis(self.ctx_ref(), self.ast), self.ctx)
11202 return ReSortRef(Z3_mk_re_sort(s.ctx.ref(), s.ast), s.ctx)
11203 if s is None or isinstance(s, Context):
11205 return ReSortRef(Z3_mk_re_sort(ctx.ref(), Z3_mk_string_sort(ctx.ref())), s.ctx)
11206 raise Z3Exception("Regular expression sort constructor expects either a string or a context or no argument")
11209 class ReRef(ExprRef):
11210 """Regular expressions.
"""
11212 def __add__(self, other):
11213 return Union(self, other)
11217 return isinstance(s, ReRef)
11221 """Create regular expression membership test
11230 s = _coerce_seq(s, re.ctx)
11231 return BoolRef(Z3_mk_seq_in_re(s.ctx_ref(), s.as_ast(), re.as_ast()), s.ctx)
11235 """Create union of regular expressions.
11240 args = _get_args(args)
11243 _z3_assert(sz > 0, "At least one argument expected.")
11244 _z3_assert(all([is_re(a) for a in args]), "All arguments must be regular expressions.")
11249 for i in range(sz):
11250 v[i] = args[i].as_ast()
11251 return ReRef(Z3_mk_re_union(ctx.ref(), sz, v), ctx)
11254 def Intersect(*args):
11255 """Create intersection of regular expressions.
11258 args = _get_args(args)
11261 _z3_assert(sz > 0, "At least one argument expected.")
11262 _z3_assert(all([is_re(a) for a in args]), "All arguments must be regular expressions.")
11267 for i in range(sz):
11268 v[i] = args[i].as_ast()
11269 return ReRef(Z3_mk_re_intersect(ctx.ref(), sz, v), ctx)
11273 """Create the regular expression accepting one
or more repetitions of argument.
11282 return ReRef(Z3_mk_re_plus(re.ctx_ref(), re.as_ast()), re.ctx)
11286 """Create the regular expression that optionally accepts the argument.
11295 return ReRef(Z3_mk_re_option(re.ctx_ref(), re.as_ast()), re.ctx)
11298 def Complement(re):
11299 """Create the complement regular expression.
"""
11300 return ReRef(Z3_mk_re_complement(re.ctx_ref(), re.as_ast()), re.ctx)
11304 """Create the regular expression accepting zero
or more repetitions of argument.
11313 return ReRef(Z3_mk_re_star(re.ctx_ref(), re.as_ast()), re.ctx)
11316 def Loop(re, lo, hi=0):
11317 """Create the regular expression accepting between a lower
and upper bound repetitions
11318 >>> re =
Loop(
Re(
"a"), 1, 3)
11326 return ReRef(Z3_mk_re_loop(re.ctx_ref(), re.as_ast(), lo, hi), re.ctx)
11329 def Range(lo, hi, ctx=None):
11330 """Create the range regular expression over two sequences of length 1
11331 >>> range =
Range(
"a",
"z")
11337 lo = _coerce_seq(lo, ctx)
11338 hi = _coerce_seq(hi, ctx)
11339 return ReRef(Z3_mk_re_range(lo.ctx_ref(), lo.ast, hi.ast), lo.ctx)
11341 def Diff(a, b, ctx=None):
11342 """Create the difference regular expression
11344 return ReRef(Z3_mk_re_diff(a.ctx_ref(), a.ast, b.ast), a.ctx)
11346 def AllChar(regex_sort, ctx=None):
11347 """Create a regular expression that accepts all single character strings
11349 return ReRef(Z3_mk_re_allchar(regex_sort.ctx_ref(), regex_sort.ast), regex_sort.ctx)
11351 # Special Relations
11354 def PartialOrder(a, index):
11355 return FuncDeclRef(Z3_mk_partial_order(a.ctx_ref(), a.ast, index), a.ctx)
11358 def LinearOrder(a, index):
11359 return FuncDeclRef(Z3_mk_linear_order(a.ctx_ref(), a.ast, index), a.ctx)
11362 def TreeOrder(a, index):
11363 return FuncDeclRef(Z3_mk_tree_order(a.ctx_ref(), a.ast, index), a.ctx)
11366 def PiecewiseLinearOrder(a, index):
11367 return FuncDeclRef(Z3_mk_piecewise_linear_order(a.ctx_ref(), a.ast, index), a.ctx)
11370 def TransitiveClosure(f):
11371 """Given a binary relation R, such that the two arguments have the same sort
11372 create the transitive closure relation R+.
11373 The transitive closure R+
is a new relation.
11375 return FuncDeclRef(Z3_mk_transitive_closure(f.ctx_ref(), f.ast), f.ctx)
11379 super(ctypes.c_void_p, ast).__init__(ptr)
11382 def to_ContextObj(ptr,):
11383 ctx = ContextObj(ptr)
11384 super(ctypes.c_void_p, ctx).__init__(ptr)
11387 def to_AstVectorObj(ptr,):
11388 v = AstVectorObj(ptr)
11389 super(ctypes.c_void_p, v).__init__(ptr)
11392 # NB. my-hacky-class only works for a single instance of OnClause
11393 # it should be replaced with a proper correlation between OnClause
11394 # and object references that can be passed over the FFI.
11395 # for UserPropagator we use a global dictionary, which isn't great code.
11397 _my_hacky_class = None
11398 def on_clause_eh(ctx, p, clause):
11399 onc = _my_hacky_class
11400 p = _to_expr_ref(to_Ast(p), onc.ctx)
11401 clause = AstVector(to_AstVectorObj(clause), onc.ctx)
11402 onc.on_clause(p, clause)
11404 _on_clause_eh = Z3_on_clause_eh(on_clause_eh)
11407 def __init__(self, s, on_clause):
11410 self.on_clause = on_clause
11412 global _my_hacky_class
11413 _my_hacky_class = self
11414 Z3_solver_register_on_clause(self.ctx.ref(), self.s.solver, self.idx, _on_clause_eh)
11417 class PropClosures:
11418 def __init__(self):
11422 def set_threaded(self):
11423 if self.lock is None:
11425 self.lock = threading.Lock()
11427 def get(self, ctx):
11430 r = self.bases[ctx]
11432 r = self.bases[ctx]
11435 def set(self, ctx, r):
11438 self.bases[ctx] = r
11440 self.bases[ctx] = r
11442 def insert(self, r):
11445 id = len(self.bases) + 3
11448 id = len(self.bases) + 3
11453 _prop_closures = None
11456 def ensure_prop_closures():
11457 global _prop_closures
11458 if _prop_closures is None:
11459 _prop_closures = PropClosures()
11462 def user_prop_push(ctx, cb):
11463 prop = _prop_closures.get(ctx)
11468 def user_prop_pop(ctx, cb, num_scopes):
11469 prop = _prop_closures.get(ctx)
11471 prop.pop(num_scopes)
11474 def user_prop_fresh(ctx, _new_ctx):
11475 _prop_closures.set_threaded()
11476 prop = _prop_closures.get(ctx)
11478 Z3_del_context(nctx.ctx)
11479 new_ctx = to_ContextObj(_new_ctx)
11481 nctx.eh = Z3_set_error_handler(new_ctx, z3_error_handler)
11483 new_prop = prop.fresh(nctx)
11484 _prop_closures.set(new_prop.id, new_prop)
11488 def user_prop_fixed(ctx, cb, id, value):
11489 prop = _prop_closures.get(ctx)
11491 id = _to_expr_ref(to_Ast(id), prop.ctx())
11492 value = _to_expr_ref(to_Ast(value), prop.ctx())
11493 prop.fixed(id, value)
11496 def user_prop_created(ctx, cb, id):
11497 prop = _prop_closures.get(ctx)
11499 id = _to_expr_ref(to_Ast(id), prop.ctx())
11503 def user_prop_final(ctx, cb):
11504 prop = _prop_closures.get(ctx)
11509 def user_prop_eq(ctx, cb, x, y):
11510 prop = _prop_closures.get(ctx)
11512 x = _to_expr_ref(to_Ast(x), prop.ctx())
11513 y = _to_expr_ref(to_Ast(y), prop.ctx())
11517 def user_prop_diseq(ctx, cb, x, y):
11518 prop = _prop_closures.get(ctx)
11520 x = _to_expr_ref(to_Ast(x), prop.ctx())
11521 y = _to_expr_ref(to_Ast(y), prop.ctx())
11525 # TODO The decision callback is not fully implemented.
11526 # It needs to handle the ast*, unsigned* idx, and Z3_lbool*
11527 def user_prop_decide(ctx, cb, t_ref, idx_ref, phase_ref):
11528 prop = _prop_closures.get(ctx)
11530 t = _to_expr_ref(to_Ast(t_ref), prop.ctx())
11531 t, idx, phase = prop.decide(t, idx, phase)
11538 _user_prop_push = Z3_push_eh(user_prop_push)
11539 _user_prop_pop = Z3_pop_eh(user_prop_pop)
11540 _user_prop_fresh = Z3_fresh_eh(user_prop_fresh)
11541 _user_prop_fixed = Z3_fixed_eh(user_prop_fixed)
11542 _user_prop_created = Z3_created_eh(user_prop_created)
11543 _user_prop_final = Z3_final_eh(user_prop_final)
11544 _user_prop_eq = Z3_eq_eh(user_prop_eq)
11545 _user_prop_diseq = Z3_eq_eh(user_prop_diseq)
11546 _user_prop_decide = Z3_decide_eh(user_prop_decide)
11549 def PropagateFunction(name, *sig):
11550 """Create a function that gets tracked by user propagator.
11551 Every term headed by this function symbol
is tracked.
11552 If a term
is fixed
and the fixed callback
is registered a
11553 callback
is invoked that the term headed by this function
is fixed.
11555 sig = _get_args(sig)
11557 _z3_assert(len(sig) > 0, "At least two arguments expected")
11558 arity = len(sig) - 1
11561 _z3_assert(is_sort(rng), "Z3 sort expected")
11562 dom = (Sort * arity)()
11563 for i in range(arity):
11565 _z3_assert(is_sort(sig[i]), "Z3 sort expected")
11566 dom[i] = sig[i].ast
11568 return FuncDeclRef(Z3_solver_propagate_declare(ctx.ref(), to_symbol(name, ctx), arity, dom, rng.ast), ctx)
11572 class UserPropagateBase:
11575 # Either solver is set or ctx is set.
11576 # Propagators that are created throuh callbacks
11577 # to "fresh" inherit the context of that is supplied
11578 # as argument to the callback.
11579 # This context should not be deleted. It is owned by the solver.
11581 def __init__(self, s, ctx=None):
11582 assert s is None or ctx is None
11583 ensure_prop_closures()
11586 self.fresh_ctx = None
11588 self.id = _prop_closures.insert(self)
11593 self.created = None
11595 self.fresh_ctx = ctx
11597 Z3_solver_propagate_init(self.ctx_ref(),
11599 ctypes.c_void_p(self.id),
11606 self._ctx.ctx = None
11610 return self.fresh_ctx
11612 return self.solver.ctx
11615 return self.ctx().ref()
11617 def add_fixed(self, fixed):
11618 assert not self.fixed
11619 assert not self._ctx
11621 Z3_solver_propagate_fixed(self.ctx_ref(), self.solver.solver, _user_prop_fixed)
11624 def add_created(self, created):
11625 assert not self.created
11626 assert not self._ctx
11628 Z3_solver_propagate_created(self.ctx_ref(), self.solver.solver, _user_prop_created)
11629 self.created = created
11631 def add_final(self, final):
11632 assert not self.final
11633 assert not self._ctx
11635 Z3_solver_propagate_final(self.ctx_ref(), self.solver.solver, _user_prop_final)
11638 def add_eq(self, eq):
11640 assert not self._ctx
11642 Z3_solver_propagate_eq(self.ctx_ref(), self.solver.solver, _user_prop_eq)
11645 def add_diseq(self, diseq):
11646 assert not self.diseq
11647 assert not self._ctx
11649 Z3_solver_propagate_diseq(self.ctx_ref(), self.solver.solver, _user_prop_diseq)
11652 def add_decide(self, decide):
11653 assert not self.decide
11654 assert not self._ctx
11656 Z3_solver_propagate_decide(self.ctx_ref(), self.solver.solver, _user_prop_decide)
11657 self.decide = decide
11660 raise Z3Exception("push needs to be overwritten")
11662 def pop(self, num_scopes):
11663 raise Z3Exception("pop needs to be overwritten")
11665 def fresh(self, new_ctx):
11666 raise Z3Exception("fresh needs to be overwritten")
11669 assert not self._ctx
11671 Z3_solver_propagate_register(self.ctx_ref(), self.solver.solver, e.ast)
11673 Z3_solver_propagate_register_cb(self.ctx_ref(), ctypes.c_void_p(self.cb), e.ast)
11676 # Tell the solver to perform the next split on a given term
11677 # If the term is a bit-vector the index idx specifies the index of the Boolean variable being
11678 # split on. A phase of true = 1/false = -1/undef = 0 = let solver decide is the last argument.
11680 def next_split(self, t, idx, phase):
11681 Z3_solver_next_split(self.ctx_ref(), ctypes.c_void_p(self.cb), t.ast, idx, phase)
11684 # Propagation can only be invoked as during a fixed or final callback.
11686 def propagate(self, e, ids, eqs=[]):
11687 _ids, num_fixed = _to_ast_array(ids)
11689 _lhs, _num_lhs = _to_ast_array([x for x, y in eqs])
11690 _rhs, _num_rhs = _to_ast_array([y for x, y in eqs])
11691 Z3_solver_propagate_consequence(e.ctx.ref(), ctypes.c_void_p(
11692 self.cb), num_fixed, _ids, num_eqs, _lhs, _rhs, e.ast)
11694 def conflict(self, deps = [], eqs = []):
11695 self.propagate(BoolVal(False, self.ctx()), deps, eqs)
Z3_param_descrs Z3_API Z3_optimize_get_param_descrs(Z3_context c, Z3_optimize o)
Return the parameter description set for the given optimize object.
Z3_string Z3_API Z3_get_probe_name(Z3_context c, unsigned i)
Return the name of the i probe.
Z3_ast_vector Z3_API Z3_optimize_get_objectives(Z3_context c, Z3_optimize o)
Return objectives on the optimization context. If the objective function is a max-sat objective it is...
Z3_ast Z3_API Z3_mk_distinct(Z3_context c, unsigned num_args, Z3_ast const args[])
Create an AST node representing distinct(args[0], ..., args[num_args-1]).
Z3_fixedpoint Z3_API Z3_mk_fixedpoint(Z3_context c)
Create a new fixedpoint context.
Z3_probe Z3_API Z3_probe_le(Z3_context x, Z3_probe p1, Z3_probe p2)
Return a probe that evaluates to "true" when the value returned by p1 is less than or equal to the va...
def simplify(a, arguments, keywords)
Utils.
Z3_func_decl Z3_API Z3_mk_fresh_func_decl(Z3_context c, Z3_string prefix, unsigned domain_size, Z3_sort const domain[], Z3_sort range)
Declare a fresh constant or function.
void Z3_API Z3_global_param_set(Z3_string param_id, Z3_string param_value)
Set a global (or module) parameter. This setting is shared by all Z3 contexts.
Z3_string Z3_API Z3_apply_result_to_string(Z3_context c, Z3_apply_result r)
Convert the Z3_apply_result object returned by Z3_tactic_apply into a string.
Z3_string Z3_API Z3_get_decl_rational_parameter(Z3_context c, Z3_func_decl d, unsigned idx)
Return the rational value, as a string, associated with a rational parameter.
void Z3_API Z3_fixedpoint_add_rule(Z3_context c, Z3_fixedpoint d, Z3_ast rule, Z3_symbol name)
Add a universal Horn clause as a named rule. The horn_rule should be of the form: ...
def update_rule(self, head, body, name)
Z3_probe Z3_API Z3_probe_ge(Z3_context x, Z3_probe p1, Z3_probe p2)
Return a probe that evaluates to "true" when the value returned by p1 is greater than or equal to the...
Z3_param_descrs Z3_API Z3_tactic_get_param_descrs(Z3_context c, Z3_tactic t)
Return the parameter description set for the given tactic object.
def get_cover_delta(self, level, predicate)
Z3_tactic Z3_API Z3_tactic_when(Z3_context c, Z3_probe p, Z3_tactic t)
Return a tactic that applies t to a given goal is the probe p evaluates to true. If p evaluates to fa...
Z3_ast Z3_API Z3_mk_bound(Z3_context c, unsigned index, Z3_sort ty)
Create a variable.
def upper_values(self, obj)
Z3_ast Z3_API Z3_mk_mul(Z3_context c, unsigned num_args, Z3_ast const args[])
Create an AST node representing args[0] * ... * args[num_args-1].
def __getitem__(self, idx)
void Z3_API Z3_tactic_inc_ref(Z3_context c, Z3_tactic t)
Increment the reference counter of the given tactic.
Z3_symbol Z3_API Z3_get_decl_name(Z3_context c, Z3_func_decl d)
Return the constant declaration name as a symbol.
void Z3_API Z3_disable_trace(Z3_string tag)
Disable tracing messages tagged as tag when Z3 is compiled in debug mode. It is a NOOP otherwise...
void Z3_API Z3_simplifier_dec_ref(Z3_context c, Z3_simplifier g)
Decrement the reference counter of the given simplifier.
Z3_tactic Z3_API Z3_tactic_and_then(Z3_context c, Z3_tactic t1, Z3_tactic t2)
Return a tactic that applies t1 to a given goal and t2 to every subgoal produced by t1...
Z3_symbol_kind Z3_API Z3_get_symbol_kind(Z3_context c, Z3_symbol s)
Return Z3_INT_SYMBOL if the symbol was constructed using Z3_mk_int_symbol, and Z3_STRING_SYMBOL if th...
Z3_string Z3_API Z3_ast_to_string(Z3_context c, Z3_ast a)
Convert the given AST node into a string.
Z3_symbol Z3_API Z3_mk_string_symbol(Z3_context c, Z3_string s)
Create a Z3 symbol using a C string.
expr range(expr const &lo, expr const &hi)
Z3_ast_vector Z3_API Z3_fixedpoint_from_string(Z3_context c, Z3_fixedpoint f, Z3_string s)
Parse an SMT-LIB2 string with fixedpoint rules. Add the rules to the current fixedpoint context...
Z3_probe Z3_API Z3_probe_gt(Z3_context x, Z3_probe p1, Z3_probe p2)
Return a probe that evaluates to "true" when the value returned by p1 is greater than the value retur...
def substitute_vars(t, m)
Z3_ast Z3_API Z3_mk_const(Z3_context c, Z3_symbol s, Z3_sort ty)
Declare and create a constant.
Z3_simplifier Z3_API Z3_simplifier_and_then(Z3_context c, Z3_simplifier t1, Z3_simplifier t2)
Return a simplifier that applies t1 to a given goal and t2 to every subgoal produced by t1...
Z3_tactic Z3_API Z3_mk_tactic(Z3_context c, Z3_string name)
Return a tactic associated with the given name. The complete list of tactics may be obtained using th...
Z3_probe Z3_API Z3_probe_const(Z3_context x, double val)
Return a probe that always evaluates to val.
Z3_probe Z3_API Z3_probe_eq(Z3_context x, Z3_probe p1, Z3_probe p2)
Return a probe that evaluates to "true" when the value returned by p1 is equal to the value returned ...
def declare(self, name, args)
def assert_exprs(self, args)
def set_option(args, kws)
Z3_param_descrs Z3_API Z3_simplifier_get_param_descrs(Z3_context c, Z3_simplifier t)
Return the parameter description set for the given simplifier object.
Z3_ast Z3_API Z3_substitute(Z3_context c, Z3_ast a, unsigned num_exprs, Z3_ast const from[], Z3_ast const to[])
Substitute every occurrence of from[i] in a with to[i], for i smaller than num_exprs. The result is the new AST. The arrays from and to must have size num_exprs. For every i smaller than num_exprs, we must have that sort of from[i] must be equal to sort of to[i].
Z3_ast Z3_API Z3_mk_pbeq(Z3_context c, unsigned num_args, Z3_ast const args[], int const coeffs[], int k)
Pseudo-Boolean relations.
Z3_optimize Z3_API Z3_mk_optimize(Z3_context c)
Create a new optimize context.
void Z3_API Z3_optimize_assert(Z3_context c, Z3_optimize o, Z3_ast a)
Assert hard constraint to the optimization context.
void Z3_API Z3_del_context(Z3_context c)
Delete the given logical context.
Z3_ast Z3_API Z3_mk_app(Z3_context c, Z3_func_decl d, unsigned num_args, Z3_ast const args[])
Create a constant or function application.
bool Z3_API Z3_is_eq_sort(Z3_context c, Z3_sort s1, Z3_sort s2)
compare sorts.
bool Z3_API Z3_get_finite_domain_sort_size(Z3_context c, Z3_sort s, uint64_t *r)
Store the size of the sort in r. Return false if the call failed. That is, Z3_get_sort_kind(s) == Z3_...
unsigned Z3_API Z3_get_decl_num_parameters(Z3_context c, Z3_func_decl d)
Return the number of parameters associated with a declaration.
bool Z3_API Z3_is_eq_ast(Z3_context c, Z3_ast t1, Z3_ast t2)
Compare terms.
def assert_exprs(self, args)
Z3_probe Z3_API Z3_mk_probe(Z3_context c, Z3_string name)
Return a probe associated with the given name. The complete list of probes may be obtained using the ...
Z3_solver Z3_API Z3_mk_solver_for_logic(Z3_context c, Z3_symbol logic)
Create a new solver customized for the given logic. It behaves like Z3_mk_solver if the logic is unkn...
Z3_decl_kind Z3_API Z3_get_decl_kind(Z3_context c, Z3_func_decl d)
Return declaration kind corresponding to declaration.
Z3_string Z3_API Z3_get_tactic_name(Z3_context c, unsigned i)
Return the name of the idx tactic.
def lower_values(self, obj)
void Z3_API Z3_optimize_inc_ref(Z3_context c, Z3_optimize d)
Increment the reference counter of the given optimize context.
Z3_ast Z3_API Z3_func_decl_to_ast(Z3_context c, Z3_func_decl f)
Convert a Z3_func_decl into Z3_ast. This is just type casting.
Z3_ast Z3_API Z3_mk_add(Z3_context c, unsigned num_args, Z3_ast const args[])
Create an AST node representing args[0] + ... + args[num_args-1].
Z3_stats Z3_API Z3_fixedpoint_get_statistics(Z3_context c, Z3_fixedpoint d)
Retrieve statistics information from the last call to Z3_fixedpoint_query.
Z3_ast Z3_API Z3_simplify_ex(Z3_context c, Z3_ast a, Z3_params p)
Interface to simplifier.
Z3_context Z3_API Z3_mk_context_rc(Z3_config c)
Create a context using the given configuration. This function is similar to Z3_mk_context. However, in the context returned by this function, the user is responsible for managing Z3_ast reference counters. Managing reference counters is a burden and error-prone, but allows the user to use the memory more efficiently. The user must invoke Z3_inc_ref for any Z3_ast returned by Z3, and Z3_dec_ref whenever the Z3_ast is not needed anymore. This idiom is similar to the one used in BDD (binary decision diagrams) packages such as CUDD.
Z3_string Z3_API Z3_simplifier_get_help(Z3_context c, Z3_simplifier t)
Return a string containing a description of parameters accepted by the given simplifier.
Z3_apply_result Z3_API Z3_tactic_apply(Z3_context c, Z3_tactic t, Z3_goal g)
Apply tactic t to the goal g.
def register_relation(self, relations)
Z3_sort Z3_API Z3_mk_finite_domain_sort(Z3_context c, Z3_symbol name, uint64_t size)
Create a named finite domain sort.
Z3_parameter_kind Z3_API Z3_get_decl_parameter_kind(Z3_context c, Z3_func_decl d, unsigned idx)
Return the parameter type associated with a declaration.
Z3_ast Z3_API Z3_get_app_arg(Z3_context c, Z3_app a, unsigned i)
Return the i-th argument of the given application.
void Z3_API Z3_parser_context_dec_ref(Z3_context c, Z3_parser_context pc)
Decrement the reference counter of the given Z3_parser_context object.
bool Z3_API Z3_global_param_get(Z3_string param_id, Z3_string_ptr param_value)
Get a global (or module) parameter.
Z3_symbol Z3_API Z3_get_decl_symbol_parameter(Z3_context c, Z3_func_decl d, unsigned idx)
Return the double value associated with an double parameter.
Z3_func_decl Z3_API Z3_get_app_decl(Z3_context c, Z3_app a)
Return the declaration of a constant or function application.
void Z3_API Z3_fixedpoint_assert(Z3_context c, Z3_fixedpoint d, Z3_ast axiom)
Assert a constraint to the fixedpoint context.
void Z3_API Z3_parser_context_add_decl(Z3_context c, Z3_parser_context pc, Z3_func_decl f)
Add a function declaration.
Z3_apply_result Z3_API Z3_tactic_apply_ex(Z3_context c, Z3_tactic t, Z3_goal g, Z3_params p)
Apply tactic t to the goal g using the parameter set p.
void Z3_API Z3_append_log(Z3_string string)
Append user-defined string to interaction log.
unsigned Z3_API Z3_get_index_value(Z3_context c, Z3_ast a)
Return index of de-Bruijn bound variable.
def is_finite_domain_sort(s)
Z3_lbool Z3_API Z3_optimize_check(Z3_context c, Z3_optimize o, unsigned num_assumptions, Z3_ast const assumptions[])
Check consistency and produce optimal values.
def z3_error_handler(c, e)
void Z3_API Z3_optimize_set_params(Z3_context c, Z3_optimize o, Z3_params p)
Set parameters on optimization context.
Z3_tactic Z3_API Z3_tactic_or_else(Z3_context c, Z3_tactic t1, Z3_tactic t2)
Return a tactic that first applies t1 to a given goal, if it fails then returns the result of t2 appl...
Z3_ast Z3_API Z3_optimize_get_upper(Z3_context c, Z3_optimize o, unsigned idx)
Retrieve upper bound value or approximation for the i'th optimization objective.
Z3_ast_kind Z3_API Z3_get_ast_kind(Z3_context c, Z3_ast a)
Return the kind of the given AST.
bool Z3_API Z3_open_log(Z3_string filename)
Log interaction to a file.
void Z3_API Z3_set_ast_print_mode(Z3_context c, Z3_ast_print_mode mode)
Select mode for the format used for pretty-printing AST nodes.
void Z3_API Z3_optimize_assert_and_track(Z3_context c, Z3_optimize o, Z3_ast a, Z3_ast t)
Assert tracked hard constraint to the optimization context.
Z3_probe Z3_API Z3_probe_not(Z3_context x, Z3_probe p)
Return a probe that evaluates to "true" when p does not evaluate to true.
Z3_param_descrs Z3_API Z3_simplify_get_param_descrs(Z3_context c)
Return the parameter description set for the simplify procedure.
Z3_func_decl Z3_API Z3_mk_func_decl(Z3_context c, Z3_symbol s, unsigned domain_size, Z3_sort const domain[], Z3_sort range)
Declare a constant or function.
def get_rule_names_along_trace(self)
def simplify_param_descrs()
void Z3_API Z3_fixedpoint_inc_ref(Z3_context c, Z3_fixedpoint d)
Increment the reference counter of the given fixedpoint context.
void Z3_API Z3_probe_inc_ref(Z3_context c, Z3_probe p)
Increment the reference counter of the given probe.
Z3_func_decl Z3_API Z3_get_decl_func_decl_parameter(Z3_context c, Z3_func_decl d, unsigned idx)
Return the expression value associated with an expression parameter.
Z3_sort Z3_API Z3_mk_uninterpreted_sort(Z3_context c, Z3_symbol s)
Create a free (uninterpreted) type using the given name (symbol).
void Z3_API Z3_apply_result_inc_ref(Z3_context c, Z3_apply_result r)
Increment the reference counter of the given Z3_apply_result object.
void Z3_API Z3_dec_ref(Z3_context c, Z3_ast a)
Decrement the reference counter of the given AST. The context c should have been created using Z3_mk_...
void Z3_API Z3_del_config(Z3_config c)
Delete the given configuration object.
Z3_simplifier Z3_API Z3_simplifier_using_params(Z3_context c, Z3_simplifier t, Z3_params p)
Return a simplifier that applies t using the given set of parameters.
void Z3_API Z3_optimize_push(Z3_context c, Z3_optimize d)
Create a backtracking point.
def convert_model(self, model)
Z3_ast Z3_API Z3_substitute_vars(Z3_context c, Z3_ast a, unsigned num_exprs, Z3_ast const to[])
Substitute the variables in a with the expressions in to. For every i smaller than num_exprs...
def __init__(self, args, kws)
Z3_ast Z3_API Z3_optimize_get_lower(Z3_context c, Z3_optimize o, unsigned idx)
Retrieve lower bound value or approximation for the i'th optimization objective.
void Z3_API Z3_optimize_register_model_eh(Z3_context c, Z3_optimize o, Z3_model m, void *ctx, Z3_model_eh model_eh)
register a model event handler for new models.
void Z3_API Z3_parser_context_add_sort(Z3_context c, Z3_parser_context pc, Z3_sort s)
Add a sort declaration.
def using_params(self, args, keys)
double Z3_API Z3_get_decl_double_parameter(Z3_context c, Z3_func_decl d, unsigned idx)
Return the double value associated with an double parameter.
unsigned Z3_API Z3_get_ast_hash(Z3_context c, Z3_ast a)
Return a hash code for the given AST. The hash code is structural but two different AST objects can m...
def Extract(high, low, a)
Z3_string Z3_API Z3_optimize_to_string(Z3_context c, Z3_optimize o)
Print the current context as a string.
def solve_using(s, args, keywords)
Z3_string Z3_API Z3_get_full_version(void)
Return a string that fully describes the version of Z3 in use.
Z3_ast_vector Z3_API Z3_fixedpoint_from_file(Z3_context c, Z3_fixedpoint f, Z3_string s)
Parse an SMT-LIB2 file with fixedpoint rules. Add the rules to the current fixedpoint context...
def set_predicate_representation(self, f, representations)
Z3_ast_vector Z3_API Z3_parser_context_from_string(Z3_context c, Z3_parser_context pc, Z3_string s)
Parse a string of SMTLIB2 commands. Return assertions.
unsigned Z3_API Z3_get_app_num_args(Z3_context c, Z3_app a)
Return the number of argument of an application. If t is an constant, then the number of arguments is...
Z3_tactic Z3_API Z3_tactic_par_and_then(Z3_context c, Z3_tactic t1, Z3_tactic t2)
Return a tactic that applies t1 to a given goal and then t2 to every subgoal produced by t1...
Z3_string Z3_API Z3_fixedpoint_get_reason_unknown(Z3_context c, Z3_fixedpoint d)
Retrieve a string that describes the last status returned by Z3_fixedpoint_query. ...
def RecFunction(name, sig)
Z3_ast Z3_API Z3_sort_to_ast(Z3_context c, Z3_sort s)
Convert a Z3_sort into Z3_ast. This is just type casting.
void Z3_API Z3_set_error_handler(Z3_context c, Z3_error_handler h)
Register a Z3 error handler.
void Z3_API Z3_enable_trace(Z3_string tag)
Enable tracing messages tagged as tag when Z3 is compiled in debug mode. It is a NOOP otherwise...
Strings, Sequences and Regular expressions.
void Z3_API Z3_fixedpoint_dec_ref(Z3_context c, Z3_fixedpoint d)
Decrement the reference counter of the given fixedpoint context.
def apply(self, goal, arguments, keywords)
def solve(args, keywords)
def __init__(self, opt, value, is_max)
def check(self, assumptions)
Z3_ast_vector Z3_API Z3_fixedpoint_get_rules(Z3_context c, Z3_fixedpoint f)
Retrieve set of rules from fixedpoint context.
int Z3_API Z3_get_symbol_int(Z3_context c, Z3_symbol s)
Return the symbol int value.
def __call__(self, goal, arguments, keywords)
void Z3_API Z3_optimize_dec_ref(Z3_context c, Z3_optimize d)
Decrement the reference counter of the given optimize context.
double Z3_API Z3_probe_apply(Z3_context c, Z3_probe p, Z3_goal g)
Execute the probe over the goal. The probe always produce a double value. "Boolean" probes return 0...
unsigned Z3_API Z3_optimize_assert_soft(Z3_context c, Z3_optimize o, Z3_ast a, Z3_string weight, Z3_symbol id)
Assert soft constraint to the optimization context.
def prove(claim, show=False, keywords)
unsigned Z3_API Z3_get_num_tactics(Z3_context c)
Return the number of builtin tactics available in Z3.
def is_finite_domain_value(a)
Z3_string Z3_API Z3_get_numeral_string(Z3_context c, Z3_ast a)
Return numeral value, as a decimal string of a numeric constant term.
def get_rules_along_trace(self)
Z3_ast Z3_API Z3_simplify(Z3_context c, Z3_ast a)
Interface to simplifier.
Z3_model Z3_API Z3_optimize_get_model(Z3_context c, Z3_optimize o)
Retrieve the model for the last Z3_optimize_check.
void Z3_API Z3_interrupt(Z3_context c)
Interrupt the execution of a Z3 procedure. This procedure can be used to interrupt: solvers...
Z3_param_descrs Z3_API Z3_fixedpoint_get_param_descrs(Z3_context c, Z3_fixedpoint f)
Return the parameter description set for the given fixedpoint object.
def assert_and_track(self, a, p)
def translate(self, target)
def from_file(self, filename)
unsigned Z3_API Z3_fixedpoint_get_num_levels(Z3_context c, Z3_fixedpoint d, Z3_func_decl pred)
Query the PDR engine for the maximal levels properties are known about predicate. ...
Z3_ast Z3_API Z3_get_decl_ast_parameter(Z3_context c, Z3_func_decl d, unsigned idx)
Return the expression value associated with an expression parameter.
def query_from_lvl(self, lvl, query)
Z3_tactic Z3_API Z3_tactic_using_params(Z3_context c, Z3_tactic t, Z3_params p)
Return a tactic that applies t using the given set of parameters.
Z3_sort Z3_API Z3_get_domain(Z3_context c, Z3_func_decl d, unsigned i)
Return the sort of the i-th parameter of the given function declaration.
void Z3_API Z3_fixedpoint_add_cover(Z3_context c, Z3_fixedpoint d, int level, Z3_func_decl pred, Z3_ast property)
Add property about the predicate pred. Add a property of predicate pred at level. It gets pushed forw...
void Z3_API Z3_optimize_pop(Z3_context c, Z3_optimize d)
Backtrack one level.
unsigned Z3_API Z3_get_ast_id(Z3_context c, Z3_ast t)
Return a unique identifier for t. The identifier is unique up to structural equality. Thus, two ast nodes created by the same context and having the same children and same function symbols have the same identifiers. Ast nodes created in the same context, but having different children or different functions have different identifiers. Variables and quantifiers are also assigned different identifiers according to their structure.
Z3_config Z3_API Z3_mk_config(void)
Create a configuration object for the Z3 context object.
def to_string(self, queries)
Z3_sort Z3_API Z3_get_range(Z3_context c, Z3_func_decl d)
Return the range of the given declaration.
void Z3_API Z3_fixedpoint_update_rule(Z3_context c, Z3_fixedpoint d, Z3_ast a, Z3_symbol name)
Update a named rule. A rule with the same name must have been previously created. ...
Z3_tactic Z3_API Z3_tactic_repeat(Z3_context c, Z3_tactic t, unsigned max)
Return a tactic that keeps applying t until the goal is not modified anymore or the maximum number of...
Z3_stats Z3_API Z3_optimize_get_statistics(Z3_context c, Z3_optimize d)
Retrieve statistics information from the last call to Z3_optimize_check.
Z3_tactic Z3_API Z3_tactic_cond(Z3_context c, Z3_probe p, Z3_tactic t1, Z3_tactic t2)
Return a tactic that applies t1 to a given goal if the probe p evaluates to true, and t2 if p evaluat...
Z3_tactic Z3_API Z3_tactic_par_or(Z3_context c, unsigned num, Z3_tactic const ts[])
Return a tactic that applies the given tactics in parallel.
Z3_ast Z3_API Z3_mk_pble(Z3_context c, unsigned num_args, Z3_ast const args[], int const coeffs[], int k)
Pseudo-Boolean relations.
def set_on_model(self, on_model)
def parse_string(self, s)
Z3_solver Z3_API Z3_mk_simple_solver(Z3_context c)
Create a new incremental solver.
Z3_tactic Z3_API Z3_tactic_try_for(Z3_context c, Z3_tactic t, unsigned ms)
Return a tactic that applies t to a given goal for ms milliseconds. If t does not terminate in ms mil...
void Z3_API Z3_set_param_value(Z3_config c, Z3_string param_id, Z3_string param_value)
Set a configuration parameter.
def get_ground_sat_answer(self)
Z3_ast_vector Z3_API Z3_optimize_get_assertions(Z3_context c, Z3_optimize o)
Return the set of asserted formulas on the optimization context.
def declare_var(self, vars)
void Z3_API Z3_parser_context_inc_ref(Z3_context c, Z3_parser_context pc)
Increment the reference counter of the given Z3_parser_context object.
Z3_probe Z3_API Z3_probe_lt(Z3_context x, Z3_probe p1, Z3_probe p2)
Return a probe that evaluates to "true" when the value returned by p1 is less than the value returned...
Z3_string Z3_API Z3_fixedpoint_get_help(Z3_context c, Z3_fixedpoint f)
Return a string describing all fixedpoint available parameters.
void Z3_API Z3_simplifier_inc_ref(Z3_context c, Z3_simplifier t)
Increment the reference counter of the given simplifier.
Z3_tactic Z3_API Z3_tactic_fail_if(Z3_context c, Z3_probe p)
Return a tactic that fails if the probe p evaluates to false.
Z3_string Z3_API Z3_optimize_get_help(Z3_context c, Z3_optimize t)
Return a string containing a description of parameters accepted by optimize.
Z3_string Z3_API Z3_get_symbol_string(Z3_context c, Z3_symbol s)
Return the symbol name.
Z3_goal Z3_API Z3_apply_result_get_subgoal(Z3_context c, Z3_apply_result r, unsigned i)
Return one of the subgoals in the Z3_apply_result object returned by Z3_tactic_apply.
Z3_sort_kind Z3_API Z3_get_sort_kind(Z3_context c, Z3_sort t)
Return the sort kind (e.g., array, tuple, int, bool, etc).
def __rmul__(self, other)
Z3_param_descrs Z3_API Z3_get_global_param_descrs(Z3_context c)
Retrieve description of global parameters.
def RecAddDefinition(f, args, body)
Z3_ast Z3_API Z3_mk_pbge(Z3_context c, unsigned num_args, Z3_ast const args[], int const coeffs[], int k)
Pseudo-Boolean relations.
void Z3_API Z3_apply_result_dec_ref(Z3_context c, Z3_apply_result r)
Decrement the reference counter of the given Z3_apply_result object.
Z3_ast_vector Z3_API Z3_fixedpoint_get_assertions(Z3_context c, Z3_fixedpoint f)
Retrieve set of background assertions from fixedpoint context.
Z3_ast Z3_API Z3_mk_atleast(Z3_context c, unsigned num_args, Z3_ast const args[], unsigned k)
Pseudo-Boolean relations.
Z3_ast Z3_API Z3_fixedpoint_get_cover_delta(Z3_context c, Z3_fixedpoint d, int level, Z3_func_decl pred)
unsigned Z3_API Z3_get_num_probes(Z3_context c)
Return the number of builtin probes available in Z3.
Z3_ast Z3_API Z3_translate(Z3_context source, Z3_ast a, Z3_context target)
Translate/Copy the AST a from context source to context target. AST a must have been created using co...
void Z3_API Z3_get_version(unsigned *major, unsigned *minor, unsigned *build_number, unsigned *revision_number)
Return Z3 version number information.
Z3_lbool Z3_API Z3_fixedpoint_query(Z3_context c, Z3_fixedpoint d, Z3_ast query)
Pose a query against the asserted rules.
Z3_string Z3_API Z3_optimize_get_reason_unknown(Z3_context c, Z3_optimize d)
Retrieve a string that describes the last status returned by Z3_optimize_check.
Z3_solver Z3_API Z3_solver_add_simplifier(Z3_context c, Z3_solver solver, Z3_simplifier simplifier)
Attach simplifier to a solver. The solver will use the simplifier for incremental pre-processing...
Z3_string Z3_API Z3_tactic_get_help(Z3_context c, Z3_tactic t)
Return a string containing a description of parameters accepted by the given tactic.
void Z3_API Z3_global_param_reset_all(void)
Restore the value of all global (and module) parameters. This command will not affect already created...
unsigned Z3_API Z3_optimize_minimize(Z3_context c, Z3_optimize o, Z3_ast t)
Add a minimization constraint.
def get_num_levels(self, predicate)
Z3_string Z3_API Z3_simplify_get_help(Z3_context c)
Return a string describing all available parameters.
Z3_ast Z3_API Z3_mk_eq(Z3_context c, Z3_ast l, Z3_ast r)
Create an AST node representing l = r.
Z3_ast Z3_API Z3_mk_atmost(Z3_context c, unsigned num_args, Z3_ast const args[], unsigned k)
Pseudo-Boolean relations.
Z3_symbol Z3_API Z3_mk_int_symbol(Z3_context c, int i)
Create a Z3 symbol using an integer.
void Z3_API Z3_add_rec_def(Z3_context c, Z3_func_decl f, unsigned n, Z3_ast args[], Z3_ast body)
Define the body of a recursive function.
def __init__(self, result, ctx)
def set(self, args, keys)
Z3_ast Z3_API Z3_mk_ite(Z3_context c, Z3_ast t1, Z3_ast t2, Z3_ast t3)
Create an AST node representing an if-then-else: ite(t1, t2, t3).
Z3_solver Z3_API Z3_mk_solver_from_tactic(Z3_context c, Z3_tactic t)
Create a new solver that is implemented using the given tactic. The solver supports the commands Z3_s...
Z3_ast_vector Z3_API Z3_optimize_get_upper_as_vector(Z3_context c, Z3_optimize o, unsigned idx)
Retrieve upper bound value or approximation for the i'th optimization objective.
Z3_string Z3_API Z3_benchmark_to_smtlib_string(Z3_context c, Z3_string name, Z3_string logic, Z3_string status, Z3_string attributes, unsigned num_assumptions, Z3_ast const assumptions[], Z3_ast formula)
Convert the given benchmark into SMT-LIB formatted string.
def add_cover(self, level, predicate, property)
int Z3_API Z3_get_decl_int_parameter(Z3_context c, Z3_func_decl d, unsigned idx)
Return the integer value associated with an integer parameter.
unsigned Z3_API Z3_get_arity(Z3_context c, Z3_func_decl d)
Alias for Z3_get_domain_size.
Z3_sort Z3_API Z3_get_sort(Z3_context c, Z3_ast a)
Return the sort of an AST node.
Z3_parser_context Z3_API Z3_mk_parser_context(Z3_context c)
Create a parser context.
void Z3_API Z3_probe_dec_ref(Z3_context c, Z3_probe p)
Decrement the reference counter of the given probe.
void Z3_API Z3_optimize_from_file(Z3_context c, Z3_optimize o, Z3_string s)
Parse an SMT-LIB2 file with assertions, soft constraints and optimization objectives. Add the parsed constraints and objectives to the optimization context.
Z3_symbol Z3_API Z3_get_sort_name(Z3_context c, Z3_sort d)
Return the sort name as a symbol.
Z3_ast_vector Z3_API Z3_optimize_get_lower_as_vector(Z3_context c, Z3_optimize o, unsigned idx)
Retrieve lower bound value or approximation for the i'th optimization objective. The returned vector ...
void Z3_API Z3_fixedpoint_set_params(Z3_context c, Z3_fixedpoint f, Z3_params p)
Set parameters on fixedpoint context.
void Z3_API Z3_fixedpoint_set_predicate_representation(Z3_context c, Z3_fixedpoint d, Z3_func_decl f, unsigned num_relations, Z3_symbol const relation_kinds[])
Configure the predicate representation.
Z3_string Z3_API Z3_probe_get_descr(Z3_context c, Z3_string name)
Return a string containing a description of the probe with the given name.
def set(self, args, keys)
void Z3_API Z3_fixedpoint_register_relation(Z3_context c, Z3_fixedpoint d, Z3_func_decl f)
Register relation as Fixedpoint defined. Fixedpoint defined relations have least-fixedpoint semantics...
void Z3_API Z3_inc_ref(Z3_context c, Z3_ast a)
Increment the reference counter of the given AST. The context c should have been created using Z3_mk_...
Z3_ast Z3_API Z3_mk_numeral(Z3_context c, Z3_string numeral, Z3_sort ty)
Create a numeral of a given sort.
Z3_ast_vector Z3_API Z3_optimize_get_unsat_core(Z3_context c, Z3_optimize o)
Retrieve the unsat core for the last Z3_optimize_check The unsat core is a subset of the assumptions ...
def substitute_funs(t, m)
Z3_string Z3_API Z3_tactic_get_descr(Z3_context c, Z3_string name)
Return a string containing a description of the tactic with the given name.
unsigned Z3_API Z3_optimize_maximize(Z3_context c, Z3_optimize o, Z3_ast t)
Add a maximization constraint.
unsigned Z3_API Z3_apply_result_get_num_subgoals(Z3_context c, Z3_apply_result r)
Return the number of subgoals in the Z3_apply_result object returned by Z3_tactic_apply.
def check(self, assumptions)
Z3_ast Z3_API Z3_fixedpoint_get_answer(Z3_context c, Z3_fixedpoint d)
Retrieve a formula that encodes satisfying answers to the query.
Z3_string Z3_API Z3_fixedpoint_to_string(Z3_context c, Z3_fixedpoint f, unsigned num_queries, Z3_ast queries[])
Print the current rules and background axioms as a string.
Z3_lbool Z3_API Z3_fixedpoint_query_relations(Z3_context c, Z3_fixedpoint d, unsigned num_relations, Z3_func_decl const relations[])
Pose multiple queries against the asserted rules.
def is_algebraic_value(a)
void Z3_API Z3_tactic_dec_ref(Z3_context c, Z3_tactic g)
Decrement the reference counter of the given tactic.
Z3_func_decl Z3_API Z3_mk_rec_func_decl(Z3_context c, Z3_symbol s, unsigned domain_size, Z3_sort const domain[], Z3_sort range)
Declare a recursive function.
Z3_ast Z3_API Z3_substitute_funs(Z3_context c, Z3_ast a, unsigned num_funs, Z3_func_decl const from[], Z3_ast const to[])
Substitute funcions in from with new expressions in to.
Z3_simplifier Z3_API Z3_mk_simplifier(Z3_context c, Z3_string name)
Return a simplifier associated with the given name. The complete list of simplifiers may be obtained ...
Z3_sort Z3_API Z3_get_decl_sort_parameter(Z3_context c, Z3_func_decl d, unsigned idx)
Return the sort value associated with a sort parameter.
void Z3_API Z3_optimize_from_string(Z3_context c, Z3_optimize o, Z3_string s)
Parse an SMT-LIB2 string with assertions, soft constraints and optimization objectives. Add the parsed constraints and objectives to the optimization context.
Z3_ast Z3_API Z3_mk_fresh_const(Z3_context c, Z3_string prefix, Z3_sort ty)
Declare and create a fresh constant.