We 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.
CITATION STYLE
Larchey-Wendling, D. (2017). Typing total recursive functions in Coq. In Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) (Vol. 10499 LNCS, pp. 371–388). Springer Verlag. https://doi.org/10.1007/978-3-319-66107-0_24
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