So this got me curious: which property of AlgDTs gave the name to “sum” and “product” type, and which properties were discovered later? As I continued to researched this the blog sort of blew up into an early history of algebraic data types.

In this talk, I will report on progress developing a fuzzy type theory, a project that started as part of the ACT 2022 Adjoint School. The motivation is to develop a logic which can model opinions, and we do this by generalizing Martin-Löf type theory. Martin-Löf type theory provides a system in which one can construct a proof (aka a term) of a proposition (aka a type), and we usually interpret such a term as saying that the proposition holds. Fuzzy type theory is a similar system in which one can provide or construct evidence (aka a fuzzy term) to support an opinion (aka a type), but the evidence (fuzzy term) comes with a parameter, for instance a real number between 0 and 1, which expresses to what extent the opinion holds.