Equational specifications, complete term rewriting systems, and computable and semicomputable algebras

Equational Reasoning and Term Rewriting Systems

Equational Term Graph Rewriting

We present an equational framework for term graph rewriting with cycles. The usual notion of homomorphism is phrased in terms of the notion of bisimulation, which is well-known in process algebra and concurrency theory. Speciically, a homomorphism is a functional bisimulation. We prove that the bisimilarity class of a term graph, partially ordered by functional bisimulation, is a complete latti...

Nondeterministic Algebraic Specifications and Nonconfluent Term Rewriting

Algebraic specifications are generalized to the case of nondeterministic operations by admitting models with set-valued functions (multi-algebras). General (in particular, non-confluent) term rewriting systems are studied as a specification language for this semantic framework. A calculus for nondeterministic specifications is given which is similar to term rewriting but which employs an additi...

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...

Using Induction and Rewriting to Verify and Complete Parameterized Specifications

In software engineering there is a growing demand for formal methods for the specii-cation and validation of software systems. The formal development of a system might give rise to many proof obligations. We must prove the completeness of the speciication and the validity of some inductive properties. In this framework, many provers have been developed. However they require much user interactio...