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https://github.com/Z3Prover/z3
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enable conditional euf-completion with (optional) solver
This allows using z3 for limited E-saturation simplification.
The tactic rewrites all assertions using the E-graph induced by the equalities and instantiated equality axioms.
It does allow solving with conditionals, although this is a first inefficient cut.
The following is a sample use case that rewrites to false.
```
(declare-fun prime () Int)
(declare-fun add (Int Int) Int)
(declare-fun mul (Int Int) Int)
(declare-fun ^ (Int Int) Int)
(declare-fun sub (Int Int) Int)
(declare-fun i () Int)
(declare-fun j () Int)
(declare-fun base () Int)
(declare-fun S () (Seq Int))
(declare-fun hash ((Seq Int) Int Int Int Int) Int)
(assert (let ((a!1 (mul (seq.nth S i) (^ base (sub (sub j i) 1)))))
(let ((a!2 (mod (add (hash S base prime (add i 1) j) a!1) prime)))
(not (= (hash S base prime i j) a!2)))))
(assert (forall ((x Int))
(! (= (mod (mod x prime) prime) (mod x prime))
:pattern ((mod (mod x prime) prime)))))
(assert (forall ((x Int) (y Int))
(! (= (mod (mul x y) prime) (mod (mul (mod x prime) y) prime))
:pattern ((mod (mul x y) prime))
:pattern ((mod (mul (mod x prime) y) prime)))))
(assert (forall ((x Int) (y Int))
(! (= (mod (mul x y) prime) (mod (mul x (mod y prime)) prime))
:pattern ((mod (mul x y) prime))
:pattern ((mod (mul x (mod y prime)) prime)))))
(assert (forall ((x Int) (y Int))
(! (= (mod (add x y) prime) (mod (add x (mod y prime)) prime))
:pattern ((mod (add x y) prime))
:pattern ((mod (add x (mod y prime)) prime)))))
(assert (forall ((x Int) (y Int))
(! (= (mod (add x y) prime) (mod (add (mod x prime) y) prime))
:pattern ((mod (add x y) prime))
:pattern ((mod (add (mod x prime) y) prime)))))
(assert (forall ((x Int) (y Int))
(! (= (mul x (^ x y)) (^ x (add y 1))) :pattern ((mul x (^ x y))))))
(assert (forall ((x Int) (y Int)) (! (= (mul x y) (mul y x)) :pattern ((mul x y)))))
(assert (forall ((x Int) (y Int)) (! (= (add x y) (add y x)) :pattern ((add x y)))))
(assert (forall ((x Int) (y Int)) (! (= (mul x y) (mul y x)) :pattern ((mul x y)))))
(assert (forall ((x Int) (y Int) (z Int))
(! (= (add x (add y z)) (add (add x y) z))
:pattern ((add x (add y z)))
:pattern ((add (add x y) z)))))
(assert (forall ((x Int) (y Int) (z Int))
(! (= (mul x (mul y z)) (mul (mul x y) z))
:pattern ((mul x (mul y z)))
:pattern ((mul (mul x y) z)))))
(assert (forall ((x Int) (y Int) (z Int))
(! (= (sub (sub x y) z) (sub (sub x z) y)) :pattern ((sub (sub x y) z)))))
(assert (forall ((x Int) (y Int) (z Int))
(! (= (mul x (add y z)) (add (mul x y) (mul x z)))
:pattern ((mul x (add y z))))))
(assert (forall ((x Int)) (! (= (sub (add x 1) 1) x) :pattern ((add x 1)))))
(assert (forall ((x Int)) (! (= (add (sub x 1) 1) x) :pattern ((sub x 1)))))
(assert (let ((a!1 (^ base (sub (sub (sub j 1) i) 1))))
(let ((a!2 (mod (add (hash S base prime (add i 1) (sub j 1))
(mul (seq.nth S i) a!1))
prime)))
(= (hash S base prime i (sub j 1)) a!2))))
(assert (let ((a!1 (add (seq.nth S (- j 1)) (mul base (hash S base prime i (sub j 1))))))
(= (hash S base prime i j) (mod a!1 prime))))
(assert (let ((a!1 (add (seq.nth S (- j 1))
(mul base (hash S base prime (add i 1) (sub j 1))))))
(= (hash S base prime (add i 1) j) (mod a!1 prime))))
(apply euf-completion)
```
To use conditional rewriting you can
```
(assert (not (= 0 prime)))
```
and update axioms using modulus with prime to be of the form:
```
(=> (not (= 0 prime)) <original-body of quantifier>)
```
This commit is contained in:
parent
16452fec43
commit
564830ab31
6 changed files with 109 additions and 27 deletions
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@ -8,7 +8,6 @@ z3_add_component(core_tactics
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der_tactic.cpp
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elim_term_ite_tactic.cpp
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elim_uncnstr_tactic.cpp
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euf_completion_tactic.cpp
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injectivity_tactic.cpp
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nnf_tactic.cpp
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occf_tactic.cpp
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@ -38,7 +37,6 @@ z3_add_component(core_tactics
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elim_uncnstr_tactic.h
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elim_uncnstr2_tactic.h
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eliminate_predicates_tactic.h
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euf_completion_tactic.h
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injectivity_tactic.h
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nnf_tactic.h
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occf_tactic.h
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@ -1,24 +0,0 @@
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/*++
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Copyright (c) 2022 Microsoft Corporation
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Module Name:
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euf_completion_tactic.cpp
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Abstract:
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Tactic for simplifying with equations.
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Author:
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Nikolaj Bjorner (nbjorner) 2022-10-30
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--*/
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#include "tactic/tactic.h"
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#include "tactic/core/euf_completion_tactic.h"
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tactic * mk_euf_completion_tactic(ast_manager& m, params_ref const& p) {
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return alloc(dependent_expr_state_tactic, m, p,
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[](auto& m, auto& p, auto &s) -> dependent_expr_simplifier* { return alloc(euf::completion, m, s); });
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}
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@ -1,49 +0,0 @@
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/*++
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Copyright (c) 2022 Microsoft Corporation
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Module Name:
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euf_completion_tactic.h
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Abstract:
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Tactic for simplifying with equations.
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Author:
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Nikolaj Bjorner (nbjorner) 2022-10-30
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Tactic Documentation:
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## Tactic euf-completion
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### Short Description
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Uses the ground equalities as a rewrite system. The formulas are simplified
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using the rewrite system.
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### Long Description
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The tactic uses congruence closure to represent and orient the rewrite system. Equalities from the formula
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are inserted in the an E-graph (congruence closure structure) and then a representative that is most shallow
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is extracted.
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--*/
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#pragma once
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#include "util/params.h"
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#include "tactic/dependent_expr_state_tactic.h"
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#include "ast/simplifiers/euf_completion.h"
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class ast_manager;
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class tactic;
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tactic * mk_euf_completion_tactic(ast_manager & m, params_ref const & p = params_ref());
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/*
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ADD_TACTIC("euf-completion", "simplify using equalities.", "mk_euf_completion_tactic(m, p)")
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ADD_SIMPLIFIER("euf-completion", "simplify modulo congruence closure.", "alloc(euf::completion, m, s)")
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*/
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