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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-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.
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.
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.
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.
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- Rewriting Techniques and Applications: 14th International Conference, RTA 2003, Valencia, Spain, June 9-11, 2003, Proceedings (Lecture Notes in Computer Science) by Robert Nieuwenhuis on page 122, and page 137
- Automated Deduction - CADE-16: 16th International Conference on Automated Deduction, Trento, Italy, July 7-10, 1999, Proceedings (Lecture Notes in Computer Science) by Harald Ganzinger on page 96, and page 413
- Rewriting Techniques and Applications: 6th International Conference, RTA-95, Kaiserslautern, Germany, April 5 - 7, 1995. Proceedings (Lecture Notes in Computer Science) by Jieh Hsiang on page 255, and page 323
- Higher-Order Algebra, Logic, and Term Rewriting: First International Workshop, HOA '93, Amsterdam, The Netherlands, September 23 - 24, 1993. Selected Papers (Lecture Notes in Computer Science) by Jan Heering on page 304, and page 325
- Basic Simple Type Theory (Cambridge Tracts in Theoretical Computer Science) by J. Roger Hindley in Front Matter
See all 37 books citing this book