A Verified SAT Solver Framework with Learn, Forget, Restart, and Incrementality

Blanchette, Jasmin Christian; Fleury, Mathias; Weidenbach, Christoph

doi:10.24963/ijcai.2017/667

Cited by 3 publications

(1 citation statement)

References 7 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…There are many quite recent machine-checked formalizations of checkers or solvers, e.g. the works by [39,40], and many others-such as [41][42][43][44][45]-that also benefit from code generation tools and techniques to obtain executable code from formalization.…”

Section: Introductionmentioning

confidence: 99%

Verified Model Checking for Conjunctive Positive Logic

et al. 2021

View full text Add to dashboard Cite

We formalize, in the Dafny language and verifier, a proof system PS for deciding the model checking problem of the fragment of first-order logic, denoted FO(∀, ∃, ∧), known as conjunctive positive logic (CPL). We mechanize the proofs of soundness and completeness of PS ensuring its correctness. Our formalization is representative of how various popular verification systems can be used to verify the correctness of rule-based formal systems on the basis of the least fixpoint semantics. Further, exploiting Dafny's automatic code generation, from the completeness proof we achieve a mechanically verified prototype implementation of a proof search mechanism that is a model checker for CPL. The model checking problem of FO(∀, ∃, ∧) is equivalent to the quantified constraint satisfaction problem (QCSP), and it is PSPACE-complete. The formalized proof system decides the general QCSP and it can be applied to arbitrary formulae of CPL.

show abstract

Section: Introductionmentioning

confidence: 99%

Verified Model Checking for Conjunctive Positive Logic

et al. 2021

View full text Add to dashboard Cite

show abstract

Verified Verifying: SMT-LIB for Strings in Isabelle

Lotz

Kulczynski

Nowotka

et al. 2023

Lecture Notes in Computer Science

View full text Add to dashboard Cite

A formal foundation for symbolic evaluation with merging

Porncharoenwase

Nelson

Wang

et al. 2022

Proc. ACM Program. Lang.

View full text Add to dashboard Cite

Reusable symbolic evaluators are a key building block of solver-aided verification and synthesis tools. A reusable evaluator reduces the semantics of all paths in a program to logical constraints, and a client tool uses these constraints to formulate a satisfiability query that is discharged with SAT or SMT solvers. The correctness of the evaluator is critical to the soundness of the tool and the domain properties it aims to guarantee. Yet so far, the trust in these evaluators has been based on an ad-hoc foundation of testing and manual reasoning. This paper presents the first formal framework for reasoning about the behavior of reusable symbolic evaluators. We develop a new symbolic semantics for these evaluators that incorporates state merging. Symbolic evaluators use state merging to avoid path explosion and generate compact encodings. To accommodate a wide range of implementations, our semantics is parameterized by a symbolic factory, which abstracts away the details of merging and creation of symbolic values. The semantics targets a rich language that extends Core Scheme with assumptions and assertions, and thus supports branching, loops, and (first-class) procedures. The semantics is designed to support reusability, by guaranteeing two key properties: legality of the generated symbolic states, and the reducibility of symbolic evaluation to concrete evaluation. Legality makes it simpler for client tools to formulate queries, and reducibility enables testing of client tools on concrete inputs. We use the Lean theorem prover to mechanize our symbolic semantics, prove that it is sound and complete with respect to the concrete semantics, and prove that it guarantees legality and reducibility. To demonstrate the generality of our semantics, we develop Leanette, a reference evaluator written in Lean, and Rosette 4, an optimized evaluator written in Racket. We prove Leanette correct with respect to the semantics, and validate Rosette 4 against Leanette via solver-aided differential testing. To demonstrate the practicality of our approach, we port 16 published verification and synthesis tools from Rosette 3 to Rosette 4. Rosette 3 is an existing reusable evaluator that implements the classic merging semantics, adopted from bounded model checking. Rosette 4 replaces the semantic core of Rosette 3 but keeps its optimized symbolic factory. Our results show that Rosette 4 matches the performance of Rosette 3 across a wide range of benchmarks, while providing a cleaner interface that simplifies the implementation of client tools.

show abstract

A Verified SAT Solver Framework with Learn, Forget, Restart, and Incrementality

Cited by 3 publications

References 7 publications

Verified Model Checking for Conjunctive Positive Logic

Verified Model Checking for Conjunctive Positive Logic

Verified Verifying: SMT-LIB for Strings in Isabelle

A formal foundation for symbolic evaluation with merging

Contact Info

Product

Resources

About