## Browse content

### Table of contents

#### Actions for selected chapters

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- Book chapterAbstract only
#### 1 - Bisimulation in Algebraic Specifications

EGIDIO ASTESIANO and MARTIN WIRSING

Pages 1-31 - Book chapterAbstract only
#### 2 - Characteristic Sets and Gröbner Bases in Geometry Theorem Proving

SHANG-CHING CHOU, WILLIAM F. SCHELTER and JIN-GEN YANG

Pages 33-92 - Book chapterAbstract only
#### 3 - On Recognizable Sets and Tree Automata

B. COURCELLE

Pages 93-126 - Book chapterAbstract only
#### 4 - The Idea of a Diagram

DESMOND FEARNLEY-SANDER

Pages 127-150 - Book chapterAbstract only
#### 5 - Rigid

*E*-Unification and, Its Applications to Equational MatingsJEAN GALLIER, WAYNE SNYDER and STAN RAATZ

Pages 151-216 - Book chapterAbstract only
#### 6 - What Is Unification?: A Categorical View of Substitution, Equation and Solution

JOSEPH A. GOGUEN

Pages 217-261 - Book chapterAbstract only
#### 7 - Some Fixpoint Techniques in Algebraic Structures and Applications to Computer Science

IRÈNE GUESSARIAN

Pages 263-292 - Book chapterAbstract only
#### 8 - Canonical Representatives for Observational Equivalence Classes

UGO MONTANARI and MARCELLO SGAMMA

Pages 293-319 - Book chapterAbstract only
#### 9 - Minimizing Expansions of Recursions

JEFFREY F. NAUGHTON and YEHOSHUA SAGIV

Pages 321-349 - Book chapterAbstract only
#### 10 - Tree Monoids and Recognizability of Sets of Finite Trees

MAURICE NIVAT and ANDREAS PODELSKI

Pages 351-367 - Book chapterAbstract only
#### 11 - Recursively Defined Types in Constructive Type Theory

PRAKASH PANANGADEN, PAUL MENDLER and MICHAEL I. SCHWARTZBACH

Pages 369-410 - Book chapterAbstract only
#### 12 - Rule Transformation Methods in the Implementation of Logic Based Languages

DOMENICO SACCA and CARLO ZANIOLO

Pages 411-444 - Book chapterNo access
#### Index

Pages 445-452

## About the book

### Description

Resolution of Equations in Algebraic Structures: Volume 1, Algebraic Techniques is a collection of papers from the "Colloquium on Resolution of Equations in Algebraic Structures" held in Texas in May 1987. The papers discuss equations and algebraic structures relevant to symbolic computation and to the foundation of programming. One paper discusses the complete lattice of simulation congruences associated with the ground atomic theory of hierarchical specification, retrieving as the lattice's maximum element Milner's strong bisimulation for CCS. Another paper explains algebraic recognizability of subsets of free T-algebras, or equational theories, and covers discrete structures like those of words, terms, finite trees, and finite graphs. One paper proposes a general theory of unification using a category theoretic framework for various substitution systems including classical unification, E-unification, and order-sorted unification. Another paper shows the universality of algebraic equations in computer science. Fixpoint theorems in ordered algebraic structures can be applied in computer science. These theorems, or their variations, include semantics and proof theory, logic programming, as well as efficient strategies for answering recursive queries in deductive data bases. The collection is suitable for programmers, mathematicians, students, and instructors involved in computer science and computer technology.

Resolution of Equations in Algebraic Structures: Volume 1, Algebraic Techniques is a collection of papers from the "Colloquium on Resolution of Equations in Algebraic Structures" held in Texas in May 1987. The papers discuss equations and algebraic structures relevant to symbolic computation and to the foundation of programming. One paper discusses the complete lattice of simulation congruences associated with the ground atomic theory of hierarchical specification, retrieving as the lattice's maximum element Milner's strong bisimulation for CCS. Another paper explains algebraic recognizability of subsets of free T-algebras, or equational theories, and covers discrete structures like those of words, terms, finite trees, and finite graphs. One paper proposes a general theory of unification using a category theoretic framework for various substitution systems including classical unification, E-unification, and order-sorted unification. Another paper shows the universality of algebraic equations in computer science. Fixpoint theorems in ordered algebraic structures can be applied in computer science. These theorems, or their variations, include semantics and proof theory, logic programming, as well as efficient strategies for answering recursive queries in deductive data bases. The collection is suitable for programmers, mathematicians, students, and instructors involved in computer science and computer technology.

## Details

### ISBN

978-0-12-046370-1

### Language

English

### Published

1989

### Copyright

Copyright © 1989 Elsevier Inc. All rights reserved.

### Imprint

Academic Press