Generic Automatic Proof Tools

2008 IEEE International High Level Design Validation and Test Workshop, 2008

Modern assertion languages, such as PSL and SVA, include many constructs that are best handled by rewriting to a small set of base cases. Since previous rewrite attempts have shown that the rules could be quite involved, sometimes counterintuitive, and that they can make a significant difference in the complexity of interpreting assertions, workable procedures for proving the correctness of these rules must be established. In this paper, we outline the methodology for computer-assisted proofs of a set of previously published rewrite rules for PSL properties. We show how to express PSL's syntax and semantics in the PVS theorem prover, and proceed to prove the correctness of a set of thirty rewrite rules. In doing so, we also demonstrate how to circumvent issues with PSL semantics regarding the never and eventually! operators.

Lecture Notes in Computer Science, 2010

Rewriting is a form of inference, and one that interacts in several ways with other forms of inference such as decision procedures and proof search. We discuss a range of issues at the intersection of rewriting and inference. How can other inference procedures be combined with rewriting? Can rewriting be used to describe inference procedures? What are some of the theoretical challenges and practical applications of combining rewriting and inference? How can rewriters, decision procedures, and their combination be certified? We discuss these problems in the context of our ongoing effort to use PVS as a metatheoretic framework to construct a proof kernel for justifying the claims of theorem provers, rewriters, model checkers, and satisfiability solvers.

International Joint Conference on Artificial Intelligence, 1985

A new approach for proving theorems in first-order predi cate calculus is developed based on term rewriting and polynomial simplification methods. A formula is translat ed into an equivalent set of formulae expressed in terms of 'true', 'false', 'exclusive-or', and 'and' by analyzing the semantics of its top-level operator. In this representation, formulae are polynomials over atomic formulae with 'and' as multiplication and 'exclusive-or' as addition, and they can be manipulated just like polynomials using familiar rules of multiplication and addition. Polynomials representing a formula are converted into rewrite rules which are used to simplify polynomials. New rules are generated by overlapping polynomials using a critical-pair completion procedure closely related to the Knuth-Bendix procedure. This process is repeated until a contradiction is reached or it is no longer possible to gen erate new rules. It is shown that resolution is subsumed by this method.

Computing Research Repository, 2006

Program analysis and verification require decision procedures to reason on theories of data structures. Many problems can be reduced to the satisfiability of sets of ground literals in theory T . If a sound and complete inference system for first-order logic is guaranteed to terminate on T -satisfiability problems, any theorem-proving strategy with that system and a fair search plan is a T -satisfiability procedure. We prove termination of a rewrite-based first-order engine on the theories of records, integer offsets, integer offsets modulo and lists. We give a modularity theorem stating sufficient conditions for termination on a combination of theories, given termination on each. The above theories, as well as others, satisfy these conditions. We introduce several sets of benchmarks on these theories and their combinations, including both parametric synthetic benchmarks to test scalability, and real-world problems to test performances on huge sets of literals. We compare the rewrite-based theorem prover E with the validity checkers CVC and CVC Lite. Contrary to the folklore that a general-purpose prover cannot compete with reasoners with built-in theories, the experiments are overall favorable to the theorem prover, showing that not only the rewriting approach is elegant and conceptually simple, but has important practical implications.

IEEE Transactions on Computer-Aided Design of Integrated Circuits and Systems, 2000

Modern assertion languages such as property specification language (PSL) and SystemVerilog assertions include many language constructs. By far, the most economical way to process the full languages in automated tools is to rewrite the majority of operators to a small set of base cases, which are then processed in an efficient way. Since recent rewrite attempts in the literature have shown that the rules could be quite involved, sometimes counterintuitive, and that they can make a significant difference in the complexity of interpreting assertions, ensuring that the rewrite rules are correct is a major contribution toward ensuring that the tools are correct, and even that the semantics of the assertion languages are well founded. This paper outlines the methodology for computer-assisted proofs of several publicly known rewrite rules for PSL properties. We first present the ways to express the PSL syntax and semantics in the prototype verification system (PVS) theorem prover, and then prove or disprove the correctness of over 50 rewrite rules published without proofs in various sources in the literature. In doing so, we also demonstrate how to circumvent known issues with PSL semantics regarding the never and eventually! operators, and offer our proposals on assertion language semantics.

Annual Review in Automatic Programming, 1973

J. A. Robinson's resolution principle has given rise to much research work and has contributed to the establishment of automatic theorem proving as a field of its own in artificial intelligence. The present paper is addressed to two kinds of readers: by its elementary introduction, it should enable a non-specialist in resolution theorem proving to grasp the essence of the method and read virtually any paper on the subject, whereas the researcher in artificial intelligence will find in specialized sections a collection of results on resolution-based procedures connected to the relevant papers in the literature.

Rewriting Logic and Its Applications, 2020

ρLog is a system for rule-based programming implemented in Mathematica, a state-of-the-art system for computer algebra. It is based on the usage of (1) conditional rewrite rules to express both computation and deduction, and of (2) patterns with sequence variables, context variables, ordinary variables, and function variables, which enable natural and concise specifications beyond the expressive power of first-order logic. Rules can be labeled with various kinds of strategies, which control their application. Our implementation is based on a rewriting-based calculus proposed by us, called ρLog too. We describe the capabilities of our system, the underlying ρLog calculus and its main properties, and indicate some applications.

Theoretical Computer Science, 1985

This paper describes a theorem proving procedure which combines the approach of Resolution with that of Rewriting. The basic-theoretical result is the completeness of a strong restriction of paramodulation for locking resolution procedures. Its oriented character suggests to consider the restricted paramodulation as a form of superposition (the Rewriting operation). This is achieved by means of a new formalism of clauses, named equational clauses, in which each literal is converted into an equation. Thereby, superposition on equational clauses is shown to embody not only paramodulation but also binary resolution; so clausal superposition will build up our major rule of inference. In addition, term simplification is incorporated in our procedure as well as subsumption. Experimental results and potential applications for our theorem prover are lastly reported.

Proc. XXXI Conferencia …, 2005

Abstract. Recent works point out the application of rewriting-logic environ-ments for the specification of hardware. When these specification are proved to be correct one can additionally apply them for the simulation, testing and even analysis of the conceived specified hardware. But ...

Data & Knowledge Engineering, 1994

There has been a considerable amount of research into the provision of explicit representation of control regimes for resolution-based theorem provers. However, most of the existing systems are either not adequate in that they do not allow the user to express any arbitrary control regime, or are too inefficient to be of practical use. In this paper a theorem prover, ACT-P, which is adequate but retains satisfactory efficiency is presented. It does so by providing a number of user-changeable heuristics which are called at specific points during the search for a proof. The set of user-changeable heuristics was determined on the basis of a classification of the heuristics used by existing resolution-based theorem provers.