Ground Confluence Prover based on Rewriting Induction
نویسندگان
چکیده
Ground confluence of term rewriting systems guarantees that all ground terms are confluent. Recently, interests in proving confluence of term rewriting systems automatically has grown, and confluence provers have been developed. But they mainly focus on confluence and not ground confluence. In fact, little interest has been paid to developing tools for proving ground confluence automatically. We report an implementation of a ground confluence prover based on rewriting induction, which is a method originally developed for proving inductive theorems. 1998 ACM Subject Classification F.4.2 Grammars and Other Rewriting Systems, I.2.3 Deduction and Theorem Proving
منابع مشابه
Proving Confluence of Term Rewriting Systems Automatically
We have developed an automated confluence prover for term rewriting systems (TRSs). This paper presents theoretical and technical ingredients that have been used in our prover. A distinctive feature of our prover is incorporation of several divide–and–conquer criteria such as those for commutative (Toyama, 1988), layer-preserving (Ohlebusch, 1994) and persistent (Aoto & Toyama, 1997) combinatio...
متن کاملRascal Tooling for Datatype Defining Rewrite Systems
It has been argued in [7] that using automated provers such as AProVE [4] and CSI [3] can benefit research projects on the topic of datatype defining rewrite systems (DDRSs), as the size of these DDRSs make manual completeness proofs long and error-prone. The authors of [7] note that no similar software exists for the ground-confluence property, and in [1] it is argued that such software should...
متن کاملConfluence of Orthogonal Nominal Rewriting Systems Revisited
Nominal rewriting systems (Fernández, Gabbay & Mackie, 2004; Fernández & Gabbay, 2007) have been introduced as a new framework of higher-order rewriting systems based on the nominal approach (Gabbay & Pitts, 2002; Pitts, 2003), which deals with variable binding via permutations and freshness conditions on atoms. Confluence of orthogonal nominal rewriting systems has been shown in (Fernández & G...
متن کاملA Prover for the μ CRL Toolset with Applications —
This document describes an automated theorem prover, based on an extension of binary decision diagrams. The prover transforms quantifier-free formulae into equivalent BDD-forms, w.r.t. to some algebraic data specification. The prover is used by four tools for the symbolic analysis of distributed systems specified in μCRL (i.e. process algebra plus algebraic data types). The main techniques are ...
متن کاملDeciding Confluence of Certain Term Rewriting Systems in Polynomial Time
We present a polynomial time algorithm for deciding confluence of ground term rewrite systems. We generalize the decision procedure to get a polynomial time algorithm, assuming that the maximum arity of a symbol in the signature is a constant, for deciding confluence of rewrite systems where each rule contains a shallow linear term on one side and a ground term on the other. The existence of a ...
متن کامل