Programming with Higher-Order Logic
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Formal systems that describe computations over syntactic structures occur frequently in computer science. Logic programming provides a natural framework for encoding and animating such systems. However, these systems often embody variable binding, a notion that must be treated carefully at a computational level. This book aims to show that a programming language based on a simply typed version of higher-order logic provides an elegant, declarative means for providing such a treatment. Three broad topics are covered in pursuit of this goal. First, a proof-theoretic framework that supports a general view of logic programming is identified. Second, an actual language called λProlog is developed by applying this view to higher-order logic. Finally, a methodology for programming with specifications is exposed by showing how several computations over formal objects such as logical formulas, functional programs, and λ-terms and π-calculus expressions can be encoded in λProlog.Read more
- All code fragments in the book are available via the author website associated with the book
- Shows that a programming language based on a simply typed version of higher-order logic provides an elegant, declarative means for providing such a treatment
Reviews & endorsements
"Overall, I am impressed with the depth of the discussion and the clearly well-produced book. The authors have argued successfully for the power and versatility of the fundamental ideas underlying λProlog."
Sara Kalvala, Computing Reviews
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- Date Published: June 2012
- format: Adobe eBook Reader
- isbn: 9781139512121
- contains: 81 b/w illus.
- availability: This ISBN is for an eBook version which is distributed on our behalf by a third party.
Table of Contents
1. First-order terms and representations of data
2. First-order horn clauses
3. First-order hereditary Harrop formulas
4. Typed lambda terms and formulas
5. Using quantification at higher-order types
6. Mechanisms for structuring large programs
7. Computations over λ-terms
8. Unification of λ-terms
9. Implementing proof systems
10. Computations over functional programs
11. Encoding a process calculus language
Appendix: the Teyjus system.
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