General Recursion and Formal Topology.

Comment: In Proceedings PAR 2010, arXiv:1012.455

Construire les fonctions récursives totales en Coq

International audienceWe present a (relatively) short mechanized proof that Coq types any recursive function which is provably total in Coq. The well-founded (and terminating) induction scheme, which is the foundation of Coq recursion, is maximal. We implement an unbounded minimization scheme for decidable predicates. It can also be used to reify a whole category of undecidable predicates. This development is purely constructive and requires no axiom. Hence it can be integrated into any project that might assume additional axioms

General recursion and formal topology

It is well known that general recursion cannot be expressed within Martin-Löf’s type theory and various approaches have been proposed to overcome this problem still maintaining the termination of the computation of the typable terms. In this work we propose a new approach to this problem based on the use of inductively generated formal topologies.