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 Untyping Typed Algebras and Colouring Cyclic Linear Logic


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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.



Author: Damien Pous

Source: https://archive.org/







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