feat: Add 'bv_div_unsafe' to support 'bv / bv' expressions. #3030
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This is useful when encoding LLVM IR semantics into FStar, where we are only concerned about partial correctness in the cases where the denominator is nonzero. Thus, we introduce a new 'bv_div_unsafe' operations, with both operands as bitvectors, along with a soundness axiom which asserts that 'bv_div_unsafe' behaves as 'bv_div' when the denominator is nonzero. We add a 'bv_div_unsafe' lowering in the smt2 encoding that mimics 'bv_div'.
bollu
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Hi @bollu, wondering if this really a useful model to represent UB. For instance, at the F* level, |
nikswamy
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Aug 24, 2023
ulib/FStar.BV.fsti
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| (** An unsafe version of 'bvdiv' that does not impose the precondition that the | ||
| denominator is nonzero. The behaviour of the solver when the denominator | ||
| is zero is implementation-defined. *) |
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I think it would be more accurate to say that bvdiv_unsafe is an uninterpreted function on bv_t n, modeling the corresponding operator from SMT-LIB. When its second argument is zero, the lemma below says that it is equivalent to bvdiv.
nikswamy
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Aug 24, 2023
nikswamy
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Aug 24, 2023
ulib/FStar.BV.fst
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| @@ -90,6 +90,11 @@ let bvdiv #n a b = | |||
| let int2bv_div #n #x #y #z pf = | |||
| inverse_vec_lemma #n (bvdiv #n (int2bv #n x) y) | |||
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| let bvdiv_unsafe #n a b = admit () | |||
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| let bvdiv_unsafe_sound #n #a #b b_nonzero_pf = admit () | |||
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Under that revised implementation above, this lemma should be provable
This convention is used by most proof assistants. https://xenaproject.wordpress.com/2020/07/05/division-by-zero-in-type-theory-a-faq/
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Thanks Sid! |
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This is useful when encoding LLVM IR semantics into FStar, where we are only concerned about partial correctness in the cases where the denominator is nonzero. Thus, we introduce a new 'bv_div_unsafe' operations, with both operands as bitvectors, along with a soundness axiom which asserts that 'bv_div_unsafe' behaves as 'bv_div' when the denominator is nonzero.
We add a 'bv_div_unsafe' lowering in the smt2 encoding that mimics 'bv_div'.