The Clausal Theory of Types (Cambridge Tracts in Theoretical Computer Science)

  • Publish Date: 1993-06-25
  • Binding: Hardcover
  • Author: D. A. Wolfram
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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-Gdel 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.