The Clausal Theory of Types (Cambridge Tracts in Theoretical Computer Science, Series Number 21) - Softcover

Wolfram, D. A.

Softcover

ISBN 10: 0521117909 ISBN 13: 9780521117906

Publisher: Cambridge University Press, 2009

Synopsis

This book presents the theoretical foundation of a higher-order logic programming language with equality, based on the clausal theory of types. A long-sought goal of logic programming, the clausal theory of types is a logic programming language that allows functional computation as a primitive operation while having rigorous, sound, and complete declarative and operational semantics. The language is very powerful, supporting higher-order equational deduction and functional computation. Its higher order syntax makes it concise and expressive, abstract data types can be expressed in it, and searching for multiple solutions is a basic operation. The author proves a number of important and surprising results: a Skolem-Herbrand-Gödel theorem for higher-order logic; a Higher-Order Resolution Theorem, which includes as special cases some previously unproven conjectures about equational matching and higher-order matching.

About this title

Book Description:

Logic programming was based on first-order logic. Higher-order logics can also lead to theories of theorem-proving. This book introduces just such a theory, based on a lambda-calculus formulation of a clausal logic with equality, known as the Clausal Theory of Types, and derives a form of logic programming that incorporates functional programming. The book can be used for graduate courses in theorem-proving, but will be of interest to all working in declarative programming.

About this edition

• Publisher: Cambridge University Press
• Publication date: 2009
• ISBN 10: 0521117909
• ISBN 13: 9780521117906
• Binding: Paperback
• Edition number: 1
• Number of pages: 136