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Untyping Typed Algebraic Structures and Colouring Proof Nets of Cyclic Linear Logic

Damien Pous 1
1 SARDES - System architecture for reflective distributed computing environments
Inria Grenoble - Rhône-Alpes, LIG - Laboratoire d'Informatique de Grenoble [2007-2015]
Abstract : We prove ''untyping'' theorems: in some typed theories (semirings, Kleene algebras, residuated lattices, involutive residuated lattices), typed equations can be derived from the underlying untyped equations. As a consequence, the corresponding untyped decision procedures can be extended for free to the typed settings. Some of these theorems are obtained via a detour through fragments of cyclic linear logic, and give rise to a substantial optimisation of standard proof search algorithms.
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Submitted on : Monday, June 14, 2010 - 10:24:12 AM
Last modification on : Wednesday, July 1, 2020 - 9:36:07 AM
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Damien Pous. Untyping Typed Algebraic Structures and Colouring Proof Nets of Cyclic Linear Logic. Computer Science Logic, Aug 2010, Brno, Czech Republic. pp.484-498, ⟨10.1007/978-3-642-15205-4_37⟩. ⟨hal-00421158v4⟩

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