Article

# The Calculus of Algebraic Constructions

11/2006;
Source: arXiv

ABSTRACT 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 also generalizes the first-order framework of abstract data types by providing dependent types and higher-order rewrite rules.

0 0
·
0 Bookmarks
·
48 Views
• ##### Article: An Introduction to Generalized Type Systems
Journal of Functional Programming. 01/1991; 1(2):125-154.
• Source
##### Article: Theorem Proving Modulo
[hide abstract]
ABSTRACT: : iTheorem proving moduloj is a way to remove computational arguments from proofs by reasoning modulo a congruence on propositions. Such a technique, issued from automated theorem proving, is of wider interest because it aims at separating deductions and computations. The rst contribution of this paper is to provide a isequent calculus moduloj that gives a clear distinction between the decidable (computation) and the undecidable (deduction). The congruence on propositions is handled via rewrite rules and equational axioms. Usually rewriting applies only to terms. The second contribution of this paper is to allow rewriting atomic propositions into non atomic ones and to give a complete proof search method, called iExtended Narrowing and Resolutionj (ENAR), modulo such congruences. The completeness of this method is proved using the sequent calculus modulo. An important application is that this Extended Narrowing and Resolution method subsumes full higher-order resolution when applied ...
Journal of Automated Reasoning 05/1998; · 0.57 Impact Factor
• Source
##### Article: A short and flexible proof of Strong Normalization for the Calculus of Constructions
[hide abstract]
ABSTRACT: this paper can still go through (with slightly more technical effort) in case one can distinguish cases according to whether a specific subterm is a type or kind in a fixed context. The other property of type systems that is really actually required for the constructions in this paper to go through is a slight strengthening of the Stripping property (also called Generation). This property says, for example, that if Gamma ` v:T:M : U has a derivation D, then one can find a subderivation of D with conclusion Gamma
01/1997;