On doing that in Idris (which is my dream language - the only reason I don't use it is its JS compiler is too slow), would it be possible to randomly generate elements of any data type, or would we have to write an `Arbitrary` instance for every type you want to test? I don't know/remember much about generics on Idris, would love to learn more.
(Seriously, though, why is the JS compiler still so slow? Again - I'm willing to put substantial money into funding a better one...)
Testing and proving aren't mutually exclusive; there's also a more fine-grained distinction, between proving things (say, with pen and paper, or an SMT solver, or whatever) and proving things using the type system of the language they're implemented in.
The nice thing about Idris is that it's specifically created with such "practical" issues in mind: it gives you powerful tools, but there's absolutely no obligation to use them. If you want to, you can avoid checking certain (or all) parts of a program. You need to define enough types to represent your computation/data, but not to prove its correctness; e.g. you can over-represent your domain using a bunch of sum types, stick infinite loops in the branches you know/think are unreachable, then turn off totality checking.
If we compare this to, say, Coq or Agda, not only must you prove everything-you-write-in-those-languages, you must also prove everything-you-write in those languages! (i.e. everything you write must be proved, and only proofs written in Coq/Agda will be accepted). You can assert axioms, but not their computational/runtime meaning, which is problematic when using them as a programming language.
Hmm, I imagine there's probably a generic way to do it; but I was imagining a straight port of the Haskell version. Note that it might be difficult to generate values of some heavily-constrained dependent type; you'd effectively be implementing a proof search!
On doing that in Idris (which is my dream language - the only reason I don't use it is its JS compiler is too slow), would it be possible to randomly generate elements of any data type, or would we have to write an `Arbitrary` instance for every type you want to test? I don't know/remember much about generics on Idris, would love to learn more.
(Seriously, though, why is the JS compiler still so slow? Again - I'm willing to put substantial money into funding a better one...)