Totality for Mixed Inductive and Coinductive Types

Pierre Hyvernat (1)

1 LAMA - Laboratoire de Mathématiques

This paper introduces an ML / Haskell like programming language with nested inductive and coinductive algebraic datatypes called chariot. Functions are defined by arbitrary recursive definitions and can thus lead to non-termination and other “bad” behaviour. chariot comes with a totality checker that tags such bad definitions. Such a totality checker is mandatory in the context of proof assistants based on type theory like Agda. Proving correctness of this checker is far from trivial, and relies on (1) an interpretation of types as parity games due to L. Santocanale, (2) an interpretation of definitions as strategies for those games, (3) the Lee, Jones and Ben Amram’s size-change principle, used to check that those strategies are “total”. This paper develops the first two points, the last step being the subject of an upcoming paper. A prototype has been implemented and can be used to experiment with the resulting totality checker. It gives a practical argument in favor of this principle.

Mots clés: nested fixed points; coinductive types; size-change principle; functional programming; Circular proofs

Domaines: Logique en informatique [cs.LO]

Pierre Hyvernat. Totality for Mixed Inductive and Coinductive Types. 2023. ⟨hal-01989688v3⟩