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Untyping Typed Algebras and Colouring Cyclic Linear Logic

Damien Pous.

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&nbsp;[&hellip;]

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Deciding Kleene Algebras in Coq

Thomas Braibant ; Damien Pous.

We present a reflexive tactic for deciding the equational theory of Kleene algebras in the Coq proof assistant. This tactic relies on a careful implementation of efficient finite automata algorithms, so that it solves casual equations instantaneously and properly scales to larger expressions. The&nbsp;[&hellip;]

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Modular coinduction up-to for higher-order languages via first-order transition systems

Jean-Marie Madiot ; Damien Pous ; Davide Sangiorgi.

The bisimulation proof method can be enhanced by employing `bisimulations up-to' techniques. A comprehensive theory of such enhancements has been developed for first-order (i.e., CCS-like) labelled transition systems (LTSs) and bisimilarity, based on abstract fixed-point theory and compatible&nbsp;[&hellip;]

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