Foundational, Compositional (Co)datatypes for Higher-Order Logic -- Category Theory Applied to Theorem Proving

Foundational, Compositional (Co)datatypes for Higher-Order Logic -- Category Theory Applied to Theorem Proving

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by Dmitriy Traytel , Andrei Popescu , Jasmin Christian Blanchette

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Datum	Value	Source
TITLE	Foundational, Compositional (Co)datatypes for Higher-Order Logic -- Category Theory Applied to Theorem Proving	user correction
AUTHOR NAME	Dmitriy Traytel	user correction
AUTHOR AFFIL	Technische Universität München	user correction
AUTHOR ADDR	Germany	user correction
AUTHOR NAME	Andrei Popescu	user correction
AUTHOR AFFIL	Technische Universität München	user correction
AUTHOR ADDR	Germany	user correction
AUTHOR NAME	Jasmin Christian Blanchette	user correction
AUTHOR AFFIL	Technische Universität München	user correction
AUTHOR ADDR	Germany	user correction
ABSTRACT	Higher-order logic (HOL) forms the basis of several popular interactive theorem provers. These 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 rich type constructor—a functor satisfying specific properties preserved by interesting categorical operations. Our ideas are formalized in Isabelle and implemented as a new definitional package, answering a long-standing user request.	user correction
CITATIONS	36 found	ParsCit 1.0