Foundational, compositional (co)datatypes for higher-order logic: category theory applied to theorem proving

Traytel, Dmitriy, Popescu, Andrei and Blanchette, Jasmin (2012) Foundational, compositional (co)datatypes for higher-order logic: category theory applied to theorem proving. In: 27th Annual IEEE Symposium on Logic in Computer Science (LICS), 25-28 June 2012, Dubrovnik, Croatia. (doi:10.1109/LICS.2012.75)

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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 implemented as a definitional package in Isabelle, addressing a frequent request from users.

Item Type: Conference or Workshop Item (Paper)
Research Areas: A. > School of Science and Technology > Computer Science > Foundations of Computing group
Item ID: 15168
Notes on copyright: © 2012 IEEE. Personal use of this material is permitted. Permission from IEEE must be obtained for all other uses, in any current or future media, including reprinting/republishing this material for advertising or promotional purposes, creating new collective works, for resale or redistribution to servers or lists, or reuse of any copyrighted component of this work in other works.
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Depositing User: Andrei Popescu
Date Deposited: 23 Apr 2015 09:24
Last Modified: 03 Jun 2019 09:38
ISBN: 9781467322638

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