54 lines
2.4 KiB
Plaintext
54 lines
2.4 KiB
Plaintext
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//
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// Copyright (c) Microsoft Corporation. All rights reserved.
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//
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// Axioms about bit vectors, *not* enabling built-in Z3 support for bit vectors.
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// Note: the "/bv:z" option must still be used, because the type "bv32" appears
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// below. However, because the ":bvbuiltin" flag is omitted from the
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// declarations below, Z3 will treat "$add", "$sub" as uninterpreted functions
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// rather than bit vector operations. This is needed for efficiency.
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// Imports:
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// - Trusted.bpl
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axiom WORD_HI == 2147483647 + 2147483647 + 2;
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function $add(x:bv32, y:bv32) returns(bv32);
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function $sub(x:bv32, y:bv32) returns(bv32);
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function $mul(x:bv32, y:bv32) returns(bv32);
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function $and(x:bv32, y:bv32) returns(bv32);
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function $or(x:bv32, y:bv32) returns(bv32);
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function $shr(x:bv32, y:bv32) returns(bv32);
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function $shl(x:bv32, y:bv32) returns(bv32);
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function $not(x:bv32) returns(bv32);
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function $le(x:bv32, y:bv32) returns(bool);
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function{:expand false} TBV(b:bv32) returns(bool) { true }
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// meaning undefined if !word(i)
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function B(i:int) returns(bv32);
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function I(b:bv32) returns(int);
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axiom I(1bv32) == 1;
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axiom (forall i1:int, i2:int::{B(i1),B(i2)} word(i1) && word(i2) ==> (i1 == i2 <==> B(i1) == B(i2)));
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axiom (forall b1:bv32, b2:bv32::{I(b1),I(b2)} b1 == b2 <==> I(b1) == I(b2));
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axiom (forall b:bv32::{I(b)} word(I(b)));
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axiom (forall b:bv32::{B(I(b))} B(I(b)) == b);
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axiom (forall i:int::{I(B(i))} word(i) ==> I(B(i)) == i);
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axiom (forall b1:bv32, b2:bv32::{$add(b1, b2)}{TBV(b1),TBV(b2)} word(I(b1) + I(b2)) ==> I(b1) + I(b2) == I($add(b1, b2)));
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axiom (forall b1:bv32, b2:bv32::{$sub(b1, b2)}{TBV(b1),TBV(b2)} word(I(b1) - I(b2)) ==> I(b1) - I(b2) == I($sub(b1, b2)));
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axiom (forall b1:bv32, b2:bv32::{$mul(b1, b2)}{TBV(b1),TBV(b2)} word(I(b1) * I(b2)) ==> I(b1) * I(b2) == I($mul(b1, b2)));
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axiom (forall b1:bv32, b2:bv32::{$le(b1, b2)}{TBV(b1),TBV(b2)} I(b1) <= I(b2) <==> $le(b1, b2));
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axiom (forall i1:int, i2:int::{and(i1, i2)} and(i1, i2) == I($and(B(i1), B(i2))) );
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axiom (forall i1:int, i2:int::{or(i1, i2)} or(i1, i2) == I($or(B(i1), B(i2))) );
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axiom (forall i1:int, i2:int::{shl(i1, i2)} shl(i1, i2) == I($shl(B(i1), B(i2))) );
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axiom (forall i1:int, i2:int::{shr(i1, i2)} shr(i1, i2) == I($shr(B(i1), B(i2))) );
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axiom (forall i:int::{neg(i)} neg(i) == I($not(B(i))));
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axiom (forall b:bv32::{Aligned(I(b))} Aligned(I(b)) == ($and(b, 3bv32) == 0bv32));
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