About Haskell, I'm a noob too. I was hinting at the documentation eg. zipWith.

I don't even know where to put the initialization !

That's the neat part : nowhere. (Well kinda, but no spoil).

Finally about join : the order doesn't matter because it is not tested, but the tests still need to access some elements so they have to be at a reasonable position (something exponential would not be reasonable).

Ps : does your version of join really go through all elements ? If that's not the case then the tests may take elements forever.

• The order of the element doesn’t matter in join, you just need to have every element of the «  2D stream » in the output « 1D stream ». Trying to exhaust the first stream, then the second, etc … will not work because they are, well, infinite.

• Modifying signatures in general will most likely stop anything from even compiling. (but refactoring modules is possible, as written in the solution setup).

• tail and join, can (and should) be really lazy. After all it’s a ’a L.t (or a Stream of it), so no evaluation is needed right now.

• For fib_aux, let’s say it’s a bit like building a list recursively, but adding stuff to the tail side lazily in the future :

(* With list syntax : *)
(* Instead of *)
new_thing :: already_built
(* You do *)
currently_built :: will_do_in_the_future

• About tie specificaly, it’s hard to wrap your head around how it works - at least that’s my experience. So sorry I can’t help.

• This kata is quite under specified, yeah. In case you (or anyone) want to know what a function is supposed to do, it’s likely to be equivalent to the homonymous Haskell function.

I’ll try to answer some of your points without revealing too much of the solution. (Just in case I’ll split the answer so a spoiler flag will not hide everything).