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I have been thinking about this (computer algebra in a Haskell-ish language) on-and-off for quite a long time, and also spent time writing some small components (and even using them sometimes!) in Haskell (for example 1 2 3 4 5 )
I have been thinking about this (computer algebra in a Haskell-ish language) on-and-off for quite a long time, and also spent time writing some small components (and even using them sometimes!) in Haskell (for example 1 2 3 4 5 )
I used to use Maxima back in the day, which is embedded in Lisp. With a quick googling I found FriCAS https://github.com/fricas/fricas , which aims to be "world class" AND its libraries are built in a strongly-typed DSL called Spad.
This is normal math, however this is not CAS territory but formal proof territory. Things like the intermediate value theorem are already formalized in Mathlib in using Lean v3.