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Haskell  Haskell  
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Agda
 Doom emacs and agdamode

Best Programming Language for Computational Proof
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.

Do you use Idris or Coq, and why?
Funny that you say this, because there are some obvious long standing open feature requests with looking up the type of the term under cursor — № 4295 and № 516. I am not blaming anyone in particular — this is the way it is. I wish I could find time to rewrite the proof search engine (how hard can it be), but I am already buried under a pile of other commitments and a good chunk of overwhelming sadness.

Haskell is the greatest programming language of all time ... the rational adult in a room full of children ... When I program in Haskell, I am in utopia. I am in a different world than 99.9% of what I see posted on Reddit.
"Haskal is a mess, that's why I use a language that's written with Haskal."

The comment with the most upvotes decides what language I write my finals in this year will be.
Do it in Agda.

Wren is a small, fast, classbased concurrent scripting language
Agda is fun[1]. And there's also Idris[2]  more programming language, less proof assistant.
[1] https://wiki.portal.chalmers.se/agda/pmwiki.php https://github.com/agda/agda

Do you feel static types have "won the war", so to speak?
At the most extreme level, you disappear into a meditative solitary retreat for a couple of years to seek enlightenment, and when you emerge you're no longer a programmer who writes programs, you're a theorist who proves theorems in Agda, and you have transcended above things that are tainted by the inherent evil of the material plane like "side effects" and "business needs" and "delivery timelines" and "could you stop doing that fancy math crap and just change the button's color like I asked for".

Can I write Agda using only ASCII characters?
(For example, the standard dependent pair definition Σ, which is defined in Agda's core, does not have any).

I solved collatz, but I have no idea how to write a paper.
Learn how to use a formal proof assistant. Coq and Agda are the most popular. Both allow you to write a proof as a program instead of as a paper, and provide various tools for formally checking your proof.

Today, Thanks to this sub Reddit. I discovered 3 awesome new languages....
If you're looking for stuff pushing the boundaries of PL research, Agda (especially Cubical Agda) might be cool to look at. It's got lots of cutting edge stuff in it, pushing the boundaries of what is currently possible with dependent type theory. It's not the only language out there with cubical features (see also: cooltt), but it's probably one of the more fleshedout implementations in terms of being practically useful. The 1Lab makes heavy use of it. There's also Introduction to Univalent Foundations of Mathematics with Agda that might be interesting to look at too!
What are some alternatives?
lean  Lean Theorem Prover
coq  Coq is a formal proof management system. It provides a formal language to write mathematical definitions, executable algorithms and theorems together with an environment for semiinteractive development of machinechecked proofs.
opentyperep  Open type representations and dynamic types
HoleyMonoid  Automatically exported from code.google.com/p/monoidcont
zig  Generalpurpose programming language and toolchain for maintaining robust, optimal, and reusable software.
distributive  Dual Traversable
fgl  A Functional Graph Library for Haskell
miso  :ramen: A tasty Haskell frontend framework
agda.nvim  NeoVim plugin for interacting with Agda written in Lua
eliminators  Dependently typed elimination functions using singletons
singletons  Fake dependent types in Haskell using singletons