Programming with Higher-Order Logic - Miller, Dale

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

Biographie:
Dale Miller is currently Director of Research at INRIA-Saclay where he is the Scientific Leader of the Parsifal team. He has been a professor at the University of Pennsylvania, Pennsylvania State University and the ?cole Polytechnique, France. Miller is the Editor-in-Chief of the ACM Transactions on Computational Logic and has editorial duties on several other journals. He was awarded an ERC Advanced Investigators Grant in 2011 and is the recipient of the 2011 Test-of-Time award of the IEEE Symposium on Logic in Computer Science. He works on many topics in the general area of computational logic, including automated reasoning, logic programming, proof theory, unification theory, operational semantics and, most recently, proof certificates.

Sommaire:
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....