Abstract

The first-order theory of rewriting is a decidable theory for linear variable-separated rewrite systems. The decision procedure is based on tree automata techniques and recently we completed a formalization in the Isabelle proof assistant. In this paper we present a certificate language that enables the output of software tools implementing the decision procedure to be formally verified. To show the feasibility of this approach, we present FORT-h, a reincarnation of the decision tool FORT with certifiable output, and the formally verified certifier FORTify.

Highlights

  • Many properties of rewrite systems can be expressed as logical formulas in the first-order theory of rewriting

  • FORT takes as input one or more rewrite systems R0, R1, . . . and a formula φ, and determines whether or not the rewrite systems satisfy the property expressed by φ, in which case it reports yes or no

  • 1. present a certificate language which is rich enough to express the various automata operations in decision procedures for the first-order theory of rewriting as well as numerous predicate symbols that may appear in formulas in this theory, 2. describe the tasks required to turn the formalization described in [14] into verified code to check certificates within reasonable time, 3. present a new reincarnation of FORT in Haskell, named FORT-h, which is capable of producing certificates

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Summary

Introduction

Many properties of rewrite systems can be expressed as logical formulas in the first-order theory of rewriting. The decision procedure is based on tree automata techniques and goes back to Dauchet and Tison [7] It is implemented in FORT [17, 18]. Certified categories were created in which tools must output a formal certificate This certificate is verified by CeTA [21], an automatically generated Haskell program using the code generation feature of Isabelle. The certifier CeTA supports a great many techniques for establishing concrete properties like termination and confluence, but the formalizations in the underlying Isabelle Formalization of Rewriting (IsaFoR) are orthogonal to the ones required for supporting the decision procedure underlying FORT. 1. present a certificate language which is rich enough to express the various automata operations in decision procedures for the first-order theory of rewriting as well as numerous predicate symbols that may appear in formulas in this theory, 2.

Preliminaries
Formulas
Certificates
FORTify
FORT-h
Experiments
Conclusion
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