http://stackoverflow.com/q/14713387/849891 SquareNumbersList

SquareNumbersList.hs

http://stackoverflow.com/q/14713387/849891

Write a recursive function squares that takes a list of integers, 
and returns a list of the squares of those integers in haskell [closed]

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For example, squares [1,2,10] should evaluate to [1,4,100], while squares [] 
should evaluate to []. Also try your function on an infinite list, for example 
squares [1..] or squares [1,3..].

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Here's what you could do: start typing what they say it must do:

    fun [1,2,10] = [1,4,100]  -- (1)

That's a perfectly valid Haskell code, a part of a Haskell function definition.

Why just a part? Because this function won't work with any other argument. But 
they say it must also work with empty lists - so write down that rule too, 
that the definition says our function must follow:

    fun [] = []           -- (2)

Now it says, our function must work also with an infinite list [1..]. 
Let's try to cook up something:

    fun [1..] = ... ?     -- (3)

Now we need to understand what is `[1..]`? It is a list. One thing we 
know for sure, its first element is `1`: `(1:xs) = [1..]`. What would 
be the first element of `xs`? `2`, right? So `[1..] == 1:[2..]` and we 
can also write, instead of `(3)`,

    fun (1:[2..]) = ys where  -- and then what?  -- (4)
      (y:t) = ys              -- what is the ys' frst element?
      y = square 1            -- right?

and what about `t`? It is

      t = fun [2..]           -- d'oh

So, must we now write out also the rule for `fun [2..]`?

    fun (2:[3..]) = ys where
      y:t = ys
      y = square 2
      t = fun [3..]

All perfectly valid Haskell, and following the specs fully so far. 
So, must we write out the infinite spec in full, by hand?
Or can we use *variables*? 

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end of part 1