Lambda the Ultimate

Tropical Semirings, Jean-Éric Pin. Idempotency 1994.

It is a well-known fact that the boolean calculus is one of the mathematical foundations of electronic computers. This explains the important role of the boolean semiring in computer science. The aim of this paper is to present other semirings that occur in theoretical computer science. These semirings were baptized tropical semirings by Dominique Perrin in honour of the pioneering work of our brazilian colleague and friend Imre Simon, but are also commonly known as (min, +)-semirings.

In the previous post, Ohad Kammar asked for some more examples of why we should care about adjunctions, which reminded me of one of my favorite examples. You can understand solving many optimization problems as looking for a Galois connection between your problem and the tropical semiring. (Galois connections in general are one of the sources of the program derivation superpowers of the Squiggolists. So if you want to prove programs like Shin Cheng-Mu does, it's worth understanding!)