Programming with Higher-Order Logic

Miller, Dale/ Nadathur, Gopalan

Cambridge University Press（2012/06発売）

• 製本 Hardcover:ハードカバー版／ページ数 320 p.／サイズ 81 b/w illus.
• 言語 ENG
• 商品コード 9780521879408
• DDC分類 005.101

Full Description

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.

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.