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81 lines
2.3 KiB
C++
81 lines
2.3 KiB
C++
/*++
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Copyright (c) 2011 Microsoft Corporation
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Module Name:
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purify_arith_tactic.h
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Abstract:
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Tactic for eliminating arithmetic operators: DIV, IDIV, MOD,
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TO_INT, and optionally (OP_IRRATIONAL_ALGEBRAIC_NUM).
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This tactic uses the simplifier for also eliminating:
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OP_SUB, OP_UMINUS, OP_POWER (optionally), OP_REM, OP_IS_INT.
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Remarks:
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- The semantics of division by zero is not specified. Thus,
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uninterpreted functions are used. An ExRCF procedure may
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treat the uninterpreted function applications as fresh
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constants. Then, in any model produced by this procedure,
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the interpretation for division by zero must be checked.
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- POWER operator can only be handled if the second argument is a
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rational value. The tactic has an option for preserving POWER
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operator where the second argument is an integer.
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- The semantics of (^ t (/ 1 k)) is not specified when t < 0 and
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k is even. Similarly to the division by zero case,
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uninterpreted function symbols are created.
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- The semantics of (^ t 0) is not specified if t == 0. Thus,
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uninterpreted function symbols are created.
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- TO_REAL is not really outside of the RCF language
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since it is only used for "casting".
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- All quantifiers must occur with positive polarity.
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The tactic snf (with skolemization disabled) is applied
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to enforce that.
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Author:
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Leonardo de Moura (leonardo) 2011-12-30.
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Tactic Documentation:
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## Tactic purify-arith
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### Short Description
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Eliminate unnecessary operators: -, /, div, mod, rem, is-int, to-int, ^, root-objects.
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These operators can be replaced by introcing fresh variables and using multiplication and addition.
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### Example
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```z3
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(declare-const x Int)
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(declare-const y Int)
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(declare-const z Int)
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(declare-const u Int)
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(declare-const v Int)
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(declare-const w Int)
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(assert (= (div x 3) y))
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(assert (= (mod z 4) u))
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(assert (> (mod v w) u))
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(apply purify-arith)
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```
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--*/
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#pragma once
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#include "util/params.h"
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class ast_manager;
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class tactic;
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tactic * mk_purify_arith_tactic(ast_manager & m, params_ref const & p = params_ref());
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/*
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ADD_TACTIC("purify-arith", "eliminate unnecessary operators: -, /, div, mod, rem, is-int, to-int, ^, root-objects.", "mk_purify_arith_tactic(m, p)")
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*/
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