Programming with Higher-Order Logic

A programming language based on a higher-order logic provides a declarative approach to capturing computations involving types, proofs and other syntactic structures.

Dale Miller (Author), Gopalan Nadathur (Author)

9780521879408, Cambridge University Press

Hardback, published 11 June 2012

320 pages, 81 b/w illus.
23.5 x 15.8 x 1.9 cm, 0.55 kg

'… 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 ?Prolog.' Sara Kalvala, Computing Reviews

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 ?Prolog 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 ?-terms and ?-calculus expressions can be encoded in ?Prolog.

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 ?-terms
8. Unification of ?-terms
9. Implementing proof systems
10. Computations over functional programs
11. Encoding a process calculus language
Appendix: the Teyjus system.

Subject Areas: Computer science [UY], Programming & scripting languages: general [UMX]