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

  • Damien Pous
Part of the Lecture Notes in Computer Science book series (LNCS, volume 6247)


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.


Proof System Residuated Lattice Linear Logic Partial Algebra Equality Judgement 
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© Springer-Verlag Berlin Heidelberg 2010

Authors and Affiliations

  • Damien Pous
    • 1
  1. 1.CNRS (LIG, UMR 5217) 

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