Programming with Higher-Order Logic

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 Ï -calculus expressions can be encoded in λ more

Product details

  • Electronic book text
  • Cambridge University Press (Virtual Publishing)
  • Cambridge, United Kingdom
  • English
  • 81 b/w illus.
  • 113902132X
  • 9781139021326

Review quote

'... 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 Reviewsshow more

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 more

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