MoL-2023-03: Implementing a definitional (co)datatype package in Lean 4, based on quotients of polynomial functors

MoL-2023-03: Keizer, Alex C. (2023) Implementing a definitional (co)datatype package in Lean 4, based on quotients of polynomial functors. [Report]

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Abstract

Coinduction is the dual of induction. While inductive types are ubiquitous in functional programming languages, coinductive types, also known as codatatypes, are considerably less well-supported. Notably, Lean 4, the latest edition of an interactive theorem prover and dependently typed functional programming language developed at Microsoft Research, lacks support for coinduction.
I have implemented a (co)datatype package for Lean 4, which compiles high-level, definitional specifications for types, which may mix induction, coinduction and quotients, into a definition of that type in terms of quotients of polynomial functors. These QPFs were previously formalized in Lean 3, which I took as a starting point and ported to Lean 4. This thesis describes how the compilation procedure works, and dives into technical details of the Lean meta-programming system that influenced the implementation. The package adds data and codata commands for specifications of inductive, respectively coinductive, types. Additionally, a qpf command exposes a specific part of the procedure, called the composition pipeline, that is used to define new QPFs composed of other QPFs.

Item Type:	Report
Report Nr:	MoL-2023-03
Series Name:	Master of Logic Thesis (MoL) Series
Year:	2023
Subjects:	Computation Logic
Depositing User:	Dr Marco Vervoort
Date Deposited:	20 Mar 2023 12:25
Last Modified:	20 Mar 2023 12:25
URI:	https://eprints.illc.uva.nl/id/eprint/2239

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