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  3. The Clausal Theory of Types
  • Cited by 44
Publisher:
Cambridge University Press
Online publication date:
January 2010
Print publication year:
1993
Online ISBN:
9780511569906
DOI:
https://doi.org/10.1017/CBO9780511569906
Subjects:
Algorithmics, Complexity, Computer Algebra, Computational Geometry, Computer Science, Programming Languages and Applied Logic
Series:
Cambridge Tracts in Theoretical Computer Science (21)
Information

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. By restricting this logic to Horn clauses, a concise form of logic programming that incorporates functional programming is achieved. The book begins by reviewing the fundamental Skolem-Herbrand-Gödel Theorem and resolution, which are then extrapolated to a higher-order setting; this requires introducing higher-order equational unification which builds in higher-order equational theories and uses higher-order rewriting. The logic programming language derived has the unique property of being sound and complete with respect to Henkin-Andrews general models, and consequently of treating equivalent terms as identical. First published in 1993, the book can be used for graduate courses in theorem-proving, but will be of interest to all working in declarative programming.

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