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| HAL: inria-00583136, version 1 |
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| Twenty-Sixth Annual IEEE Symposium on "Logic in Computer Science" - LICS 2011, Toronto : Canada (2011) |
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| CoqMTU: a higher-order type theory with a predicative hierarchy of universes parametrized by a decidable first-order theory |
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| Bruno Barras 1, 2Jean-Pierre Jouannaud 3 |
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| (2011) |
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| We study a complex type theory, a Calculus of Inductive Constructions with a predicative hierarchy of universes and a first-order theory T built in its conversion relation. The theory T is specified abstractly, by a set of constructors, a set of defined symbols, axioms expressing that constructors are free and defined symbols completely defined, and a generic elimination principle relying on crucial properties of first-order structures satisfying the axioms. We first show that CoqMTU enjoys all basic meta-theoretical properties of such calculi, confluence, subject reduction and strong normalization when restricted to weak-elimination, implying the decidability of type-checking in this case as well as consistency. The case of strong elimination is left open. |
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| 1: | Laboratoire d'informatique de l'école polytechnique (LIX) |
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CNRS : UMR7161 – Polytechnique - X |
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| 2: | TYPICAL (INRIA Saclay - Ile de France) |
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INRIA – CNRS : UMR – Polytechnique - X |
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| 3: | FORMES (LIAMA) |
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INRIA – Tsinghua University / Beijing – LIAMA |
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| 4: | Microsoft Research - Inria Joint Centre (MSR - INRIA) |
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INRIA – Microsoft – Microsoft Research Laboratory Cambridge |
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| Domain | : | Computer Science/Logic in Computer Science |
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| Attached file list to this document: | |||||
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| inria-00583136, version 1 | |
| http://hal.inria.fr/inria-00583136 | |
| oai:hal.inria.fr:inria-00583136 | |
| From: Pierre-Yves Strub | |
| Submitted on: Monday, 4 April 2011 21:43:34 | |
| Updated on: Wednesday, 7 December 2011 09:57:20 | |
