The calculus of algebraic constructions

摘要

This paper is concerned with the foundations of the Calculus of Algebraic Constructions (CAC),an extension of the Calculus of Constructions by inductive data types.CAC generalizes inductive types equipped with higher-order primitive recursion,by providing definitions of functions by pattern-matching which capture recursor definitions for arbitrary non-dependent and non-polymorphic inductive types satisfying a strictly positivity condition.CAC dependent types and higher-order rewrite rules.Full proofs are available at http://www.lri.fr/-blanqui/publis/rta99full.ps.gz.