Foundational extensible corecursion: a proof assistant perspective

Abstract

This paper presents a formalized framework for defining corecursive functions safely in a total setting, based on corecursion up-to and relational parametricity. The end product is a general corecursor that allows corecursive (and even recursive) calls under "friendly" operations, including constructors. Friendly corecursive functions can be registered as such, thereby increasing the corecursor's expressiveness. The metatheory is formalized in the Isabelle proof assistant and forms the core of a prototype tool. The corecursor is derived from first principles, without requiring new axioms or extensions of the logic.

A Formalized General Theory of Syntax with Bindings

“…Another exciting prospect is the integration of our framework with Isabelle's recent package for inductive and coinductive datatypes [11] based on bounded natural functors (BNFs), which follows a compositional design [58] and provides flexible ways to nest types [12] and mix recursion with corecursion [10,15], but does not yet cover terms with bindings. Achieving compositionality in the presence of bindings will require a substantial refinement of the notion of BNF (since terms with bindings form only partial functors w.r.t.…”