Fast LCF-Style Proof Reconstruction for Z3
نویسندگان
چکیده
The Satisfiability Modulo Theories (SMT) solver Z3 can generate proofs of unsatisfiability. We present independent reconstruction of these proofs in the theorem provers Isabelle/HOL and HOL4 with particular focus on efficiency. Our highly optimized implementations outperform previous LCF-style proof checkers for SMT, often by orders of magnitude. Detailed performance data shows that LCF-style proof reconstruction can be faster than proof search in Z3.
منابع مشابه
Reconstruction of Z3's Bit-Vector Proofs in HOL4 and Isabelle/HOL
The Satisfiability Modulo Theories (SMT) solver Z3 can generate proofs of unsatisfiability. We present independent reconstruction of unsatisfiability proofs for bit-vector theories in the theorem provers HOL4 and Isabelle/HOL. Our work shows that LCF-style proof reconstruction for the theory of fixed-size bit-vectors, although difficult because Z3’s proofs provide limited detail, is often possi...
متن کاملChallenges Implementing an LCF-Style Proof System with Haskell
The predominant, root design among current proof assistants, the LCF style, is traditionally realized through impure, functional languages. Thus, languages that eschew side-effects in the name of purity collectively represent a largely untapped platform for exploring alternate implementations of LCF-style provers. The work in this paper details the challenges we have encountered in the developm...
متن کاملUsing a SAT Solver as a Fast Decision Procedure for Propositional Logic in an LCF-style Theorem Prover
This paper describes the integration of a leading SAT solver with Isabelle/HOL, a popular interactive theorem prover. The SAT solver generates resolution-style proofs for (instances of) propositional tautologies. These proofs are verified by the theorem prover. The presented approach significantly improves Isabelle’s performance on propositional problems, and furthermore exhibits counterexample...
متن کاملPropositional Simplification With BDDs and SAT Solvers
We show how LCF-style interactive theorem provers might use BDD engines and SAT solvers to perform normalization, simplification of terms and theorems, and assist with interactive proof. The treatment builds on recent work integrating SAT solvers as non-trusted decision procedures for LCF-style theorem provers. We limit ourselves to propositional logic, but briefly note that the results may be ...
متن کاملLCF-Style Bit-Blasting in HOL4
This paper describes a new proof tool for deciding bit-vector problems in HOL4. The approach is based on “bit-blasting”, wherein word expressions are mapped into propositional formulas, which are then handed to a SAT solver. Significantly, the implementation uses the LCF approach, which means that the soundness of the tool is guaranteed by the soundness of HOL4’s logical kernel.
متن کامل