learn-you-a-haskell VS coq

you start that way, but don't do http://learnyouahaskell.com really?

Elm is a statically typed language inspired by Haskell. The natural step would be to use Elm on the frontend and Haskell on the backend. And that's what I tried to do. I read with some difficulty the Learn You a Haskell for Great Good! book (available for free here) and learned a lot of cool stuff. But creating a complete backend using Haskell proved to be more than I could chew. So I decided to look for alternatives...

Here y’go!

Definitely check out: http://learnyouahaskell.com

You see? It's not simple but you'll get there if you persist. Most Haskell and Purescript books cover it. Personally it clicked for me going through the "learn you a haskell" book. http://learnyouahaskell.com

You just wait until you start reading this http://learnyouahaskell.com/

This is my second time learning Haskell. I’ve learned it at the university in a course and through http://learnyouahaskell.com, but I’ve mostly forgotten everything but the basics.

Information about the Coq proof assistant: https://coq.inria.fr/ , https://en.wikipedia.org/wiki/Coq

This type of thing can help you formally verify code.

So, if your proof is correct, and your description of the (language/CPU) is correct, you can prove the code does what you think it does.

Formal proof systems are still growing up, though, and they are still pretty hard to use. See Coq for an introduction: https://coq.inria.fr/

Most of the proof assistants out there: Lean, Coq, Dafny, Isabelle, F*, Idris 2, and Agda. And the main concepts are dependent types, Homotopy Type Theory AKA HoTT, and Category Theory. Warning: HoTT and Category Theory are really dense, you're going to really need to research them.

If you're meaning "more similar to common mathematics" then look at Lean or Coq.

Coq, Agda, Lean, Isabelle, and probably some others which are not coming to my mind at the moment, but those would be considered the major ones.

Our approach to quantitative reasoning is not grounded in formal mathematics. Minerva parses questions and generates answers using a mix of natural language and LaTeX mathematical expressions, with no explicit underlying mathematical structure. This approach has an important limitation, in that the model’s answers cannot be automatically verified. Even when the final answer is known and can be verified, the model can arrive at a correct final answer using incorrect reasoning steps, which cannot be automatically detected. This limitation is not present in formal methods for theorem proving (e.g., see Coq, Isabelle, HOL, Lean, Metamath, and Mizar). On the other hand, an advantage of the informal approach is that it can be applied to a highly diverse set of problems which may not lend themselves to formalization.

The computer scientists who are figuring these things out are constructing the tools that software engineers need; just like the mathematicians who developed calculus and the physicists who extended Newtonian mechanics into something engineers can apply. Just as an engineer's tools and materials are calculus and physics (not hammers or concrete and steel), a software engineer's tools and materials are proof-assistants, category theory, linear polarized logic, and dependent type theory (not the Rust programming language or the UNIX platform).