Implementing type theory in higher order constraint logic programming

Implementing Type Theory in Higher Order Constraint Logic Programming

In this paper we are interested in high-level programming languages to implement the core components of an interactive theorem prover for a dependently typed language: the kernel — responsible for type-checking closed terms — and the elaborator — that manipulates terms with holes or, equivalently, partial proof terms. In the first part of the paper we confirm that λProlog, the language develope...

Higher-Order Logic Programming as Constraint Logic Programming

Higher-order logic programming (HOLP) languages are particularly useful for various kinds of metaprogramming and theorem proving tasks because of the logical support for variable binding via λabstraction. They have been used for a wide range of applications including theorem proving, programming language interpretation, type inference, compilation, and natural language parsing. Despite their ut...

A Logic Programming Approach to Implementing Higher-Order Term Rewriting

Term rewriting has proven to be an important technique in theorem proving. In this paper, we illustrate that rewrite systems and strategies for higher-order term rewriting, which includes the usual notion of rst-order rewriting, can be naturally speciied and implemented in a higher-order logic programming language. We adopt a notion of higher-order rewrite system which uses the simply typed-cal...

Higher-Order Logic Programming

Implementing Randomised Algorithms in Constraint Logic Programming

Synopsis Algorithms where the ow of information is determined by an element of random choice (a \coin ipping" device), aka randomised algorithms, have known in the last decade a tremendous growth of interest, especially in the eld of complexity theory. Up to now such algorithms have been implemented mostly by means of probabilistic programs written in imperative languages. These programs have b...