Wadler

The guy used to read a lot of abstract algebra and symbolic logic, so he got the right intuitions and then formulated the right abstract concepts.

Monads allow composition of “lifted” (Kleisli arrows) “computations”, which implies “crossing off” an implicit abstraction barrier (at the type-level).

This abstraction barrier partitions the values of different kinds, while maintaining the crucial referential transparency property, upon which everything rests.

It is defined as a type-class, which means “all the types of this form”.

Type-classes define “shapes” of types, via required to implement sets of type-signatures. This is a systematization of Duck-Typing (walks like a duck, quacks like a duck).

For a person trained to think in terms of Sets, Logic and Relations (which is what all mathematics could be reduced to) coming up with a Set and a set of Operations (a product) – which is what a System in abstract algebra is – seems to be quite “natural” .

The main message is still to use mathematics as an illuminating candle in the darkness of ignorance.

Last but not least, he wrote the classic FP book with Richard Bird.