Untyping typed algebraic structures and colouring proof nets of cyclic linear logic

Authors:
Damien Pous
Affiliations:
CNRS, LIG, UMR
Venue:
CSL'10/EACSL'10 Proceedings of the 24th international conference/19th annual conference on Computer science logic
Year:
2010

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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.