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75 lines
No EOL
1.8 KiB
C++
75 lines
No EOL
1.8 KiB
C++
/*++
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Copyright (c) 2025 Microsoft Corporation
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Module Name:
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finite_set_axioms.h
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Abstract:
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This module implements axiom schemas that are invoked by saturating constraints
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with respect to the semantics of set operations.
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--*/
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class finite_set_axioms {
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ast_manager& m;
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finite_set_util u;
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std::function<void(expr_ref_vector const &)> m_add_clause;
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public:
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finite_set_axioms(ast_manager &m) : m(m), u(m) {}
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void set_add_clause(std::function<void(expr_ref_vector const &)> &ac) {
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m_add_clause = ac;
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}
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// a ~ set.empty => not (x in a)
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void in_empty_axiom(expr *x);
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// a := set.union(b, c)
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// (x in a) <=> (x in b) or (x in c)
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void in_union_axiom(expr *x, expr *a);
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// a := set.intersect(b, c)
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// (x in a) <=> (x in b) and (x in c)
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void in_intersect_axiom(expr *x, expr *a);
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// a := set.difference(b, c)
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// (x in a) <=> (x in b) and not (x in c)
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void in_difference_axiom(expr *x, expr *a);
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// a := set.singleton(b)
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// (x in a) <=> (x == b)
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void in_singleton_axiom(expr *x, expr *a);
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// a := set.range(lo, hi)
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// (x in a) <=> (lo <= x <= hi)
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void in_range_axiom(expr *x, expr *a);
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// a := set.map(f, b)
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// (x in a) <=> set.map_inverse(f, x, b) in b
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void in_map_axiom(expr *x, expr *a);
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// a := set.map(f, b)
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// (x in b) => f(x) in a
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void in_map_image_axiom(expr *x, expr *a);
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// a := set.select(p, b)
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// (x in a) <=> (x in b) and p(x)
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void in_select_axiom(expr *x, expr *a);
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// a := set.subset(b, c)
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// (a) <=> (set.intersect(b, c) = b)
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void subset_axiom(expr *a);
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// a := set.singleton(b)
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// set.size(a) = 1
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void size_singleton_axiom(expr *a);
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// a != b => set.in (set.diff(a, b) a) != set.in (set.diff(a, b) b)
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void extensionality_axiom(expr *a, expr *b);
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}; |