In the typed functional programming communities, there is much talk about “reasoning with types”. But rarely is this elaborated into something concrete. Just how can we extract tangible information from types beyond playing mere type tetris? The secret sauce is called parametricity, first described by John C. Reynolds, and later applied to Haskell by Philip Wadler in his seminal paper “Theorems for free!”.
This talk expects basic understanding of type variables. Everything else – including the mathematics – will be introduced.