Thursday 15 February 2018, 13:30, LSV library: Intersection Types in Deduction Modulo Theory, Olivier Hermant (MINES Paris Tech).
In a 2012 paper, Richard Statman exhibited an inference system, based on second order monadic logic and non-terminating rewrite rules, that exactly types all strongly normalizable lambda-terms. We show that this system can be simplified to first-order minimal logic with rewrite rules, along the Deduction Modulo Theory lines.
We show that our rewrite system is terminating and that the conversion rule respects weak versions of invertibility of the arrow and of quantifiers. This requires additional care, in particular in the treatment of the latter. Then we study proof reduction, and show that every typable proof term is strongly normalizable and vice-versa.