Scalar actions in Lean's mathlib

Workshop Papers of the 14th Conference on Intelligent Computer Mathematics (CICM 2021), Timisoara, Romania, July 26 - 31, 2021, https://ceur-ws.org/Vol-3377/fmm11.pdf 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.