Fundamentals of Algebraic Specification 1: Equations and Initial Semantics [Paperback]

The aim of this book is to present fundamentals of algebraicspecifications with respect to the following three aspects:fundamentals in the sense of a carefully motivatedintroduction to algebraic specifications, which is easy tounderstand for computer scientists and mathematicians;fundamentals in the sense of mathematical theories which arethe basis for precise definitions, constructions, results,and correctness proofs; and fundamentals in the sense ofconcepts, which are introduced on a conceptual level andformalized in mathematical terms.The book is equally suitableas a text book for graduatecourses and as a reference for researchers and systemdevelopers.The aim of this book is to present fundamentals of algebraicspecifications with respect to the following three aspects:fundamentals in the sense of a carefully motivatedintroduction to algebraic specifications, which is easy tounderstand for computer scientists and mathematicians;fundamentals in the sense of mathematical theories which arethe basis for precise definitions, constructions, results,and correctness proofs; and fundamentals in the sense ofconcepts, which are introduced on a conceptual level andformalized in mathematical terms.The book is equally suitableas a text book for graduatecourses and as a reference for researchers and systemdevelopers.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 Specifiabilitl.