Mark partial functions as such

[Zemyla]

I feel like there's a difference between partial functions in the
sense of length and partial functions in the sense of head.

If you have a partiality monad like the free monad over Identity:

data Partial a = Done a | NotYet (Partial a)

instance Monad Partial where
  return = Done
  Done a >>= f = f a
  NotYet m >>= f = NotYet $ m >>= f

then length has a sensible and productive implementation in terms of it:

partialLength :: [a] -> Partial Int
partialLength = go 0 where
  go n ls = seq n $ case ls of
    [] -> Done n
    _:ls' -> NotYet $ go (n + 1) ls'

This is similar to the mechanism that Agda and Idris use to denote a
potentially non-terminating result; with it, these languages are
Turing complete.

head and tail aren't like that, and should be marked differently in
the documentation.

On Fri, Aug 31, 2018 at 7:28 AM, Andrew Martin
<andrew.thaddeus at gmail.com> wrote:
> I'm strongly +1 on this.
>
> On Thu, Aug 30, 2018 at 8:10 PM Richard Eisenberg <rae at cs.brynmawr.edu>
> wrote:
>>
>> Proposal: Mark partial functions in `base` as partial
>>
>> Motivation: I'm about to teach Haskell to a classful of beginners. In my
>> experience, they will soon reach for functions like `head` and `tail`,
>> because pattern-matching is foreign to them. I would love just to be able to
>> say "Don't use partial functions", but many students will not easily be able
>> to tell partial functions from total ones.
>>
>> I do expect this problem to work itself out rather quickly, and then
>> students will be able to identify partial functions, but loudly marking
>> partial functions as partial seems like a small service to everyone and a
>> bigger one to newbies. I don't see any downsides.
>>
>> Thoughts?
>>
>> Thanks,
>> Richard
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>
>
>
> --
> -Andrew Thaddeus Martin
>
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