Inductive Definitions in the system Coq - Rules and Properties
TLCA '93 Proceedings of the International Conference on Typed Lambda Calculi and Applications
Journal of Functional Programming
Pattern matching coverage checking with dependent types using set approximations
PLPV '07 Proceedings of the 2007 workshop on Programming languages meets program verification
TYPES'06 Proceedings of the 2006 international conference on Types for proofs and programs
Epigram: practical programming with dependent types
AFP'04 Proceedings of the 5th international conference on Advanced Functional Programming
Equations: a dependent pattern-matching compiler
ITP'10 Proceedings of the First international conference on Interactive Theorem Proving
| Hi-index | 0.00 |
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.