Universal Algebra for Computer Science by Eric G. Wagner

About this book :-
Universal Algebra for Computer Scientists by Wolfgang Wechler is a rigorous and well-structured textbook that introduces universal algebra through a model-theoretic lens, specifically tailored for computer science applications. The book offers a self-contained and clean exposition of core algebraic concepts, making it accessible to readers with a background in computer science rather than pure mathematics. It covers algebraic characterizations of classes of algebras—such as equational, implicational, and universal Horn classes—extending classical results like Birkhoff’s Variety Theorem. A significant portion is dedicated to term rewriting systems, including techniques like Knuth–Bendix completion and termination proofs, which are vital for program transformation and automated reasoning. The book also explores fix-point theory and complete ordered algebras, which are foundational for defining the semantics of recursive programs. Applications include formal specification of abstract data types and semantics of recursive schemes, bridging theoretical foundations with practical computing concerns. While not as widely known as some algebra texts, Wechler's work fills a unique niche by aligning universal algebra closely with the needs of theoretical computer science.

Book Detail :-
Title: Universal Algebra for Computer Science by Eric G. Wagner
Publisher: Wagner Mathematics
Year: 2006
Pages: 100
Type: PDF
Language: English
ISBN-10 #: N\A
ISBN-13 #: N\A
License: Linked Content Owned by Author
Amazon: Amazon

About Author :-
The author Eric G. Wagner is an American computer scientist who has made foundational contributions to the use of universal algebra in computer science, particularly in programming language semantics and data types. His work laid important groundwork for algebraic specifications, compiler verification, and the formal development of programming languages.

Book Contents :-
Part-I 1. Introduction to Part I 2. The UA-Calculators, Guide and Tutorial 3. Preliminaries 4. Algebras, Signatures and Homomorphisms 5. Initial Algebras 6. Trees over Signatures 7. Free Algebras, Derived Operations and Substitution 8. Context-free Grammars 9. A Grammar for a Structured Programming Language, LANG1 Part-II 10. The Limitations of LANG1 and of Context-free Grammars for programming languages 11. Parameterized Grammars

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