Fundamentals of Algebraic Specification 1: Equations and Initial Semantics

Fundamentals of Algebraic Specification 1: Equations and Initial Semantics

by Hartmut Ehrig, Bernd Mahr

Paperback(Softcover reprint of the original 1st ed. 1985)

View All Available Formats & Editions
Choose Expedited Shipping at checkout for guaranteed delivery by Friday, August 23


The aim of this book is to present fundamentals of algebraic specifications with respect to the following three aspects:
fundamentals in the sense of a carefully motivated introduction to algebraic specifications, which is easy to understand for computer scientists and mathematicians;
fundamentals in the sense of mathematical theories which are the basis for precise definitions, constructions, results,
and correctness proofs; and fundamentals in the sense of concepts, which are introduced on a conceptual level and formalized in mathematical terms.
The book is equally suitableas a text book for graduate courses and as a reference for researchers and system developers.

Product Details

ISBN-13: 9783642699641
Publisher: Springer Berlin Heidelberg
Publication date: 11/23/2011
Series: Monographs in Theoretical Computer Science. An EATCS Series , #6
Edition description: Softcover reprint of the original 1st ed. 1985
Pages: 321
Product dimensions: 6.69(w) x 9.61(h) x 0.03(d)

Table of Contents

Historical Remarks.- The Chapters of this Volume.- Further Topics.- 1 Equational Specifications and Algebras.- Basic Examples.- Signatures, Terms, and Algebras.- Equational Specifications and Derivations.- Bibliographic Notes for Chapter 1.- 2 Specifications of Abstract Data Types.- Abstract Data Types.- Quotient Term Algebras.- Semantics and Correctness of Specifications.- Bibliographic Notes for Chapter 2.- 3 Initial Semantics of Specifications.- Facts about Homomorphisms.- Term Algebras, Initial and Free Algebras.- Congruences and Quotients.- Initial and Free SPEC-Algebras.- Bibliographic Notes for Chapter 3.- 4 Specifiability and Characterization of Equational Classes.- Equational Theory and Equational Classes.- Subalgebras.- Products.- Homomorphic Images.- Birkhoff-Characterizations of Equational Classes.- Bibliographic Notes for Chapter 4.- 5 Equational Calculus and Term Rewriting.- Formal Proofs by Equations.- Correctness and Completeness of the Equational Calculus.- Term Rewriting with Equations.- Equivalence of Proofs and Term Rewriting with Equations.- Bibliographic Notes for Chapter 5.- 6 Correctness and Extension of Specifications.- Initial Correctness of Specifications.- Correctness of Specifications with Hidden Functions.- Stepwise Specification by Extensions.- Correctness of Example Specifications.- Bibliographic Notes for Chapter 6.- 7 Parameterized Specifications and Functors.- Parameterized Specifications.- Categories and Functors.- Free Constructions and Free Functors.- Semantics and Correctness of Parameterized Specifications.- Bibliographic Notes for Chapter 7.- 8 Parameter Passing.- Specification Morphisms.- Standard Parameter Passing and Pushouts.- Amalgamation.- Persistency and Extension of Functors.- Correctness of Standard Parameter Passing.- Parameterized Parameter Passing.- Iterated Parameter Passing.- Bibliographic Notes for Chapter 8.- 9 Concepts of a Specification Language.- Basic Specifications.- Combination.- Renaming.- Actualization.- Modularization.- Syntax of the Specification Language ACT ONE.- 10 Semantics of the Specification Language ACT ONE.- First Level of Semantics.- Second Level of Semantics.- Semantical Properties and Context-Conditions.- Initial Algebra Semantics.- Bibliographic Notes for the Appendix.

Customer Reviews

Most Helpful Customer Reviews

See All Customer Reviews