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Scalar actions in Lean's mathlib

Accepted version
Peer-reviewed

Type

Article

Change log

Abstract

Scalar actions are ubiquitous in mathematics, and therefore it is valuable to be able to write them succinctly when formalizing. In this paper we explore how Lean 3's typeclasses are used by mathlib for scalar actions with examples, illustrate some of the problems which come up when using them such as compatibility of actions and non-definitionally-equal diamonds, and note how these problems can be solved. We outline where more work is needed in mathlib in this area.

Description

Keywords

68V20 (Primary), 68V35 (Secondary), cs.LO, cs.LO

Journal Title

CEUR Workshop Proceedings

Conference Name

FMM 2021 – Fifth Workshop on Formal Mathematics for Mathematicians

Journal ISSN

1613-0073

Volume Title

Publisher

CEUR Workshop Proceedings (CEUR-WS.org)

Publisher DOI