[Haskell-beginners] Are these soloutions all valid and a good use of Haskell

Stefan Höck efasckenoth at gmail.com
Mon Nov 10 14:12:20 UTC 2014

Hi Roelof

It seems like you try to do too many things at once. Here's how you
could go about this step-by-step and let GHC help you implement your
functions along the way:

First, give the type signature of your function:

  last5 :: [a] -> Maybe a
  last5 = undefined

Now, load this into GHCi or compile with GHC. If it compiles, you're
on the right track. Now, you want to implement it using a fold
(try both, foldl and foldr):

  last5 :: [a] -> Maybe a
  last5 xs = foldr _ _ xs

The underscores are 'type holes'. This tells the compiler to give you
some information about what is supposed to be placed at the two
positions. For the moment, we are only interested in the types of the
things that go there. The compiler will tell you, that
the hole at the first position is of type

  a -> Maybe a -> Maybe a

and the hole at the second position is of type

  Maybe a

Now, instead of filling the holes in place, let's define two helper
functions together with their type signatures. You can later on inline
them in your definition of last5, but for the time being, let's get as
much help from the compiler as we can.

  last5 :: [a] -> Maybe a
  last5 xs = foldr acc initial xs

  acc :: a -> Maybe a -> Maybe a
  acc = undefined

  initial :: Maybe a
  initial = undefined

Again, compile or load into GHCi. If you did anything wrong, the 
compiler will tell you so. There is only one possible way to
implement function `initial` without cheating (= raising an error)

  initial :: Maybe a
  initial = Nothing

Function `acc` can be implemented in several ways. Only one of them
will lead to the desired behavior. Finding out the proper implementation
is the main point of this folding-exercise. Try also an implementation
using foldl. Does it behave as expected? What are the differences
compared to foldr?  When you feed your implementations a huge list -
say [1..20000000] - what happens?

Note that whenever you get an error message in a rather complex
function implementation, move local function definitions and lambdas
to the top level, give them a type signature and implement them
separately one at a time. Use type holes to let the compiler give
assistance with type signatures and possible implementations.
Once everything compiles and runs as expected, move the toplevel
definitions back to where you'd like them best.


PS: A more succint implementation of last5 would use currying:

    last5 = foldr acc initial

PPS: If you get a stack overflow with very large lists, try
     using foldl' from Data.List (or better, once you learned
     about the Foldable type class, from Data.Foldable).

On Mon, Nov 10, 2014 at 02:28:08PM +0100, Roelof Wobben wrote:
> I tried and so far I have this :
> last5 = foldl(\acc x -> if x=[] then x else acc xs) [] xs
> But now I get parse error on the -> part.
> Roelof
> Roelof Wobben schreef op 10-11-2014 13:47:
> >Thanks all,
> >
> >I will try to make a fold solution as soon as I see that functional
> >explained in the learnyouahaskell.
> >
> >Roelof
> >
> >
> >Frerich Raabe schreef op 10-11-2014 11:43:
> >>On 2014-11-10 11:16, Karl Voelker wrote:
> >>>On Mon, Nov 10, 2014, at 01:50 AM, Roelof Wobben wrote:
> >>>>What do you experts think of the different ways ?
> >>>
> >>>2 and 4 are quite similar, and both fine. 3 is not so good: guards
> >>>provide weaker guarantees than patterns, and head and tail are partial
> >>>functions.
> >>
> >>In addition to what Karl wrote, I'd like to suggest not using the
> >>semicolon all the time -- it's not needed and just adds noise.
> >>
> >>>All three implementations have in common that they do their own
> >>>recursion. It would be a good exercise to try implementing last as a
> >>>fold - in other words, letting the standard library do the recursion
> >>>for
> >>>you.
> >>
> >>Right - I suggest trying to express the problem with the most abstract
> >>function first, then consider using a fold, then use manual recursion.
> >>in
> >>your particular case you could exploit that for non-empty lists, getting
> >>the last element of a list is the same as getting the first element of
> >>a reversed list (and there are ready-made functions for reversing a list
> >>and getting the first element of a list).
> >>
> >
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