Definitions by rewriting in the Calculus of Constructions

Details Definitions by rewriting in the Calculus of Constructions Definitions by rewriting in the Calculus of Constructions

2006-10-12

arxiv.org/abs/cs/0610072v1

Mathematical Structures in Computer Science 15, 1 (2005) 37-92

Computer Science

Logic in Computer Science

Journal version of LICS'01

Scientific paper

10.1017/S0960129504004426

This paper presents general syntactic conditions ensuring the strong normalization and the logical consistency of the Calculus of Algebraic Constructions, an extension of the Calculus of Constructions with functions and predicates defined by higher-order rewrite rules. On the one hand, the Calculus of Constructions is a powerful type system in which one can formalize the propositions and natural deduction proofs of higher-order logic. On the other hand, rewriting is a simple and powerful computation paradigm. The combination of both allows, among other things, to develop formal proofs with a reduced size and more automation compared with more traditional proof assistants. The main novelty is to consider a general form of rewriting at the predicate-level which generalizes the strong elimination of the Calculus of Inductive Constructions.

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