Foundational, compositional (co)datatypes for higher-order logic—Category theory applied to theorem proving
| Citations: | 2 - 2 self |
BibTeX
@MISC{Traytel_foundational,compositional,
author = {Dmitriy Traytel and Andrei Popescu and Jasmin Christian Blanchette and Technische Universität München},
title = {Foundational, compositional (co)datatypes for higher-order logic—Category theory applied to theorem proving},
year = {}
}
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Abstract
Abstract—Interactive theorem provers based on higher-order logic (HOL) traditionally follow the definitional approach, reducing high-level specifications to logical primitives. This also applies to the support for datatype definitions. However, the internal datatype construction used in HOL4, HOL Light, and Isabelle/HOL is fundamentally noncompositional, limiting its efficiency and flexibility, and it does not cater for codatatypes. We present a fully modular framework for constructing (co)datatypes in HOL, with support for mixed mutual and nested (co)recursion. Mixed (co)recursion enables type definitions involving both datatypes and codatatypes, such as the type of finitely branching trees of possibly infinite depth. Our framework draws heavily from category theory. The key notion is that of a bounded natural functor—an enriched type constructor satisfying specific properties preserved by interesting categorical operations. Our ideas are formalized in Isabelle and implemented as a new definitional package, addressing a frequent request from users. Keywords-•—Category theory, higher-order logic, interactive theorem proving, (co)datatypes, cardinals I.
