Fundamentals of Algebraic Specification 1
Equations and Initial Semantics
Published on 23. November 2011
Book
Paperback/Softback
XI, 321 pages
978-3-642-69964-1 (ISBN)
Description
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.
More details
Series
Edition
Softcover reprint of the original 1st ed. 1985
Language
English
Place of publication
Berlin
Germany
Publishing group
Springer Berlin
Target group
Professional and scholarly
Research
Illustrations
XI, 321 p.
Dimensions
Height: 244 mm
Width: 170 mm
Thickness: 19 mm
Weight
588 gr
ISBN-13
978-3-642-69964-1 (9783642699641)
DOI
10.1007/978-3-642-69962-7
Schweitzer Classification
Other editions
Additional editions
Book
03/1985
Springer
€85.55
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Content
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.