map and fmap

[Jon Fairbairn]

On 2006-08-18 at 14:17+0200 John Hughes wrote:
> Jon Fairbairn wrote:
> 
> > ...
> >
> >The "beginners' prelude" would then consist of several
> >modules that provided classless versions of the
> >troublesome overloaded functions,
> >
> Hmmm.
> 
> I clearly don't teach the way you do.

Definitely! I clearly don't teach. (I'm unwell, condemmed
largely to snipe from the sidelines)

> "Folk who only get as far as doing arithmetic on Integers
> and Rationals with some simple stuff on Lists" doesn't
> include my students at the end of lecture 1! (That is, I
> start with different material).

That was really a guess about how your course must run,
based on your argument.

> I actually don't see much problem caused by the
> overloading of numbers, where teaching is concerned. Yes,
> it means that students see classes very early-- in error
> messages at least--but it's enough to tell them that Num a
> means a should be some kind of number (Integer or Double
> in my course). This is a small cost at the time I have to
> explain it. The good thing about doing so is that students
> start getting used to the idea of classes, and to
> distinguishing a class from a type, so that when I later
> introduce Eq and Ord constraints (which are very hard to
> get away from in reusable code), the concept of a class
> constraint is already familiar. Later on, when I show them
> wxHaskell, there are classes everywhere, but the basic
> idea is by then quite familiar.  So I'm dubious that your
> idea of a beginners' prelude would really work better,
> even for teaching beginners! Type classes are such an
> essential part of Haskell that even beginners need to
> learn about them... but constructor classes (Monad,
> Functor etc) are another kettle of fish altogether.

Well, for you the "beginners' prelude" would only affect
constructor classes, then.  Actually, having thought about
it further, I see a fundamental flaw in your argument. What
it amounts to is that you /do/ want a beginners' prelude,
but you want it to be the standard one.

This does have negative effects. Partly because it's deeply
ingrained, I find myself writing 'map' all over the place,
thus constraining functions that would work on any monad to
lists. I'm sure I'm not alone in this. I suspect that
another part of it is that 'fmap' is a "noisier" name. I
think Haskell should encourage people to think in terms of
code that is as reusable as possible, so the "ordinary" map
for Haskell should be the one for Functors.


So I think what we should do (in this specific case) is
essentially what Iavor suggested: provide a specialised
function for mapping on lists and rename fmap. Quite what
names we choose is another matter.

A reasonable choice (forestalling the objection that using
List.map, listMap or mapList would be too distracting for
students) would be
 
   lmap:: (t -> t') -> [t] -> [t']
   map:: Functor f => (t -> t') -> f t -> f t'

 Jón

-- 
Jón Fairbairn                              Jon.Fairbairn at cl.cam.ac.uk