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Re:Abstract Algebra (2016) [pdf] by EdwardCoffin on Friday March 10, 2017 @06:17PM (#13842987)
Guy Steele [1] sometimes mentions it. He gave an interesting Google Tech Talk called Four Solutions to a Trivial Problem [2], and at 1:59 [3] he said:

Also, algebraic properties are important. I've got a background in applied algebra, and I think that has informed my programming. And I think that making programmers aware of algebraic properties of their code, and communicating some of those properties to the compiler, may be worthwhile.

The language Fortress [4], which he was one of the language designers of, allowed one to explicitly provide the compiler with such information - you could say that a certain operation was distributive or associative for instance, and the compiler could then do some refactorings and optimizations taking this knowledge into account.

[1] https://en.wikipedia.org/wiki/Guy_L._Steele_Jr.

[2] https://youtu.be/ftcIcn8AmSY

[3] https://youtu.be/ftcIcn8AmSY?t=1m59s

[4] https://en.wikipedia.org/wiki/Fortress_(programming_language...

Re:Abstract Algebra (2016) [pdf] by FullyFunctional on Saturday March 11, 2017 @03:18AM (#13844770)
GHC Haskell (not standard Haskell) supports this and it's heavily used. Look for "Rewrite rules".