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arXiv · 1205.3612

Untyping Typed Algebras and Colouring Cyclic Linear Logic

Damien Pous
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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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Damien Pous. 2012-05-16. Untyping Typed Algebras and Colouring Cyclic Linear Logic. https://doi.org/10.2168/lmcs-8(2:13)2012

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