Abs t rac t This paper is part of a long-term effort to increase expressiveness of algebraic specification languages while at the same time having a simple semantic basis on which efficient execution by rewriting and powerful theorem-proving tools can be based. In particular, our rewriting techniques provide semantic foundations for Maude's functional sublanguage, where they have been efficient...

Systems In this chapter we define the abstract versions of the systems that we are going to deal with for the rest of the thesis. They qualify as abstract because their semantics intend to give an abstract account of the concepts of dependence and independence, and do not refer to any particular version of these notions. The variants of dependence and independence that are conceivable are sever...

Equational logic serves as the underlying logic in many formal approaches to program specification. The algebraic data types specified in this formal way can be viewed as abstract machines on which the programs are to be run. This is one way of giving a precise algebraic semantics for programs, against which the correctness of a program can be tested. Object oriented (OO) programs, however, pre...

The recent development of abstract algebraic logic has led to a reconsideration of the universal algebraic theory of ordered algebras from a new perspective. The familiar equational logic of Birkhoff can be naturally viewed as one of the deductive systems that constitute the main object of study in abstract algebraic logic; technically it is a deductive system of dimension two. Large parts of u...

In Floyd-Hoare logic, programs are dynamic while assertions are static (hold at states). In action logic the two notions become one, with programs viewed as on-the-fly assertions whose truth is evaluated along intervals instead of at states. Action logic is an equational theory ACT conservatively extending the equational theory REG of regular expressions with operations preimplication a→b (had ...

Coalgebras When I started my PhD, the idea that the theory of coalgebras might serve as a general theory of systems had emerged. But there were only a few ad hoc descriptions of speci cation languages for coalgebras which were built, in analogy with logics for algebras, on equational logic and extensions. [2] was one of the rst papers to put forward the idea that modal logics should be used as ...

Nominal unification is a generalisation of first-order unification that takes α-equivalence into account. In this paper, we study nominal unification in the context of equational theories. We introduce nominal narrowing and design a general nominal E-unification procedure, which is sound and complete for a wide class of equational theories. We give examples of application. 1998 ACM Subject Clas...

We propose a general framework for first-order functional logic programming, supporting lazy functions, non-determinism and polymorphic datatypes whose data constructors obey a set C of equational axioms. On top of a given C, we specify a program as a set R of Cbased conditional rewriting rules for defined functions. We argue that equational logic does not supply the proper semantics for such p...

This document explains the design and use of the Church-Rosser checker tool CRC 3, which checks whether a (possibly conditional) equational specification satisfies the ChurchRosser property modulo any combination of associativity, and/or commutativity, and/or identity axioms (combinations of associativity without commutativity are handled only under certain conditions). This tool can be used to...

Narrowing was originally introduced to solve equational E-unification problems. It has also been recognized as a key mechanism to unify functional and logic programming. In both cases, narrowing supports equational reasoning and assumes confluent equations. The main goal of this work is to show that narrowing can be greatly generalized, so as to support a much wider range of applications, when ...