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.
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ISBN-13
978-3-642-69962-7 (9783642699627)
DOI
10.1007/978-3-642-69962-7
Schweitzer Klassifikation
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.
