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 CAFE: An Industrial-Strength Algebraic Formal Method eBook

CAFE: An Industrial-Strength Algebraic Formal Method


Imprint: Elsevier Science

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This book contains selected papers on the language, applications, and environments of CafeOBJ, which is a state-of -the-art algebraic specification language. The authors are speakers at a workshop held in 1998 to commemorate a large industrial/academic project dedicated to CafeOBJ. The project involved more than 40 people from more than 10 organisations, of which 6 are industrial. The workshop attracted about 30 talks and more than 70 attendees.


The papers in the book however, are either heavily revised versions presented at the workshop, to reflect recent advancements or research; or completely new ones, written especially for this book. In this regard, the book is not a usual postpublication after a workshop. Also, although it is a compendium of papers that are related to CafeOBJ, the book is not a manual, reference, or tutorial of CafeOBJ. Probably the best description is that it is a collection of papers that investigate how to use, or to make it easy to use, CafeOBJ. Reflecting the diverse nature of the project and its participants (most of the authors are participants to the project), the papers, put together, offer a comprehensive picture from this methodological perspective.


Some papers deal with various advanced aspects of the language, such as rewriting logic and behavioural logic. For rewriting logic, a couple of significant applications were reported. In particular, UML, now considered de facto standard language for modelling systems, is the subject of one paper. For behavioural logic, new methodological guidelines are presented. Some papers shed new light on a more traditional paradigm in the language; order-sorted equational specifications. One paper, in particular, deal with a way to associate CafeOBJ with object-oriented programming. The other papers deal with environments for writing and vertifying specifications written in CafeOBJ. Underlying those papers are two major considerations: user interfaces for manipulating specifications, and systematic supports for proofs. All the environments explained in the papers assume and support distributed computing, and de facto standard network technologies, such as WWW and http, are incorporated.

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Title of Computers eBook: CAFE: An Industrial-Strength Algebraic Formal Method
Release Date: 10-06-2000
Publisher: Elsevier Science

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CAFE: An Industrial-Strength Algebraic Formal Method


Chapter One

Building Equational Proving Tools by Reflection in Rewriting Logic M. Clavel and F. Duran and S. Eker and J. Meseguer

This paper explains the design and use of two equational proving tools, namely an inductive theorem prover—to prove theorems about equational specifications with an initial algebra semantics—and a Church-Rosser checker—to check whether such specifications satisfy the Church-Rosser property. These tools can be used to prove properties of order-sorted equational specifications in CafeOBJ and of membership equational logic specifications in Maude. The tools have been written entirely in Maude and are in fact executable specifications in rewriting logic of the formal inference systems that they implement. The fact that rewriting logic is a reflective logic, and that Maude efficiently supports reflective rewriting logic computations is systematically exploited in the design of the tools.

1. Introduction

This paper explains the design and use of two proving tools, namely an inductive theorem prover—to prove theorems about equational specifications with an initial algebra semantics—and a Church-Rosser checker—to check whether such specifications satisfy the Church-Rosser property. These tools have been developed as part of the Cafe project [6, 20], and have been integrated, thanks to the efforts of our colleagues in Japan, within the overall Cafe environment. Through that integration, they can be used to prove formal properties of order-sorted equational specifications in CafeOBJ, They can also be used on their own to prove properties of equational specifications in Maude; t

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