Equational rules for rewriting logic

Reflection in membership equational logic, many-sorted equational logic, Horn logic with equality, and rewriting logic

We show that the generalized variant of formal systems where the underlying equational specifications are membership equational theories, and where the rules are conditional and can have equations, memberships and rewrites in the conditions is reflective. We also show that membership equational logic, many-sorted equational logic, and Horn logic with equality are likewise reflective. These resu...

Term-Rewriting Implementation of Equational Logic Programming

1987 ABSTRACT In 1975 I started a small project to explore the consequences of implementing equational programs with no semantic compromises. Latest results include a compiler that executes exactly the logical consequences of an equa-tional program, with run-time speed comparable to compiled Franz LISP. This paper describes the accomplishments of the project very brieey, concentrating on shortc...

Coinductive Foundations of Infinitary Rewriting and Infinitary Equational Logic

We present a coinductive framework for defining and reasoning about the infinitary analogues of equational logic and term rewriting in a uniform way. We define ∞ =, the infinitary extension of a given equational theory =R, and →∞, the standard notion of infinitary rewriting associated to a reduction relation →R, as follows: ∞ = := νR. (=R ∪ R) → := μR. νS. (→R ∪ R) ; S Here μ and ν are the leas...

A Rewriting Strategy to Generate Prime Implicates in Equational Logic

Generating the prime implicates of a formula consists in finding its most general consequences. This has many fields of application in automated reasoning, like planning and diagnosis, and although the subject has been extensively studied (and still is) in propositional logic, very few have approached the problem in more expressive logics because of its intrinsic complexity. This paper presents...

Dependency Pairs for Equational Rewriting