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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.
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Symbolic types for lenient symbolic execution
We present lambda_sym, a typed λ-calculus forlenient symbolic execution, where some language constructs do not recognize symbolic values. Its type system, however, ensures safe behavior of all symbolic values in a program. Our calculus extends a base occurrence typing system with symbolic types and mutable state, making it a suitable model for both functional and imperative symbolically executed languages. Naively allowing mutation in this mixed setting introduces soundness issues, however, so we further addconcreteness polymorphism, which restores soundness without rejecting too many valid programs. To show that our calculus is a useful model for a real language, we implemented Typed Rosette, a typed extension of the solver-aided Rosette language. We evaluate Typed Rosette by porting a large code base, demonstrating that our type system accommodates a wide variety of symbolically executed programs.
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- Award ID(s):
- 1651225
- PAR ID:
- 10601698
- Publisher / Repository:
- Association for Computing Machinery (ACM)
- Date Published:
- Journal Name:
- Proceedings of the ACM on Programming Languages
- Volume:
- 2
- Issue:
- POPL
- ISSN:
- 2475-1421
- Format(s):
- Medium: X Size: p. 1-29
- Size(s):
- p. 1-29
- Sponsoring Org:
- National Science Foundation
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