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Conference Papers Year : 2009

A New Elimination Rule for the Calculus of Inductive Constructions

Abstract

In Type Theory, definition by dependently-typed case analysis can be expressed by means of a set of equations — the semantic approach — or by an explicit pattern-matching construction — the syntactic approach. We aim at putting together the best of both approaches by extending the pattern-matching construction found in the Coq proof assistant in order to obtain the expressivity and flexibility of equation-based case analysis while remaining in a syntax-based setting, thus making dependently-typed programming more tractable in the Coq system. We provide a new rule that permits the omission of impossible cases, handles the propagation of inversion constraints, and allows to derive Streicher's K axiom. We show that subject reduction holds, and sketch a proof of relative consistency.
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Dates and versions

inria-00524938 , version 1 (29-10-2010)

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Bruno Barras, Pierre Corbineau, Benjamin Grégoire, Hugo Herbelin, Jorge Luis Sacchini. A New Elimination Rule for the Calculus of Inductive Constructions. Types for Proofs and Programs, Mar 2008, Torino, Italy. pp.32-48, ⟨10.1007/978-3-642-02444-3_3⟩. ⟨inria-00524938⟩
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