[Haskell-beginners] No accumulation of partially applied functions allowed?

[Jay Sulzberger]

On Tue, 26 Jun 2012, Alec Story <avs38 at cornell.edu> wrote:

> Because of Haskell's type system, there are some expressions that you
> simply cannot compile.  Most of them you don't *want* to compile because
> they do bad things (like add two strings, for example).  Some things are
> legal in Lisp but don't typecheck in Haskell for exactly the reasons that
> Brent pointed out.  They might make sense in some contexts, but the
> compiler isn't able to reason about them.

Thanks, Alec.

What is a formalized version of

   It is not possible in Haskell to define `applyTo`.*
   * At least not without crazy type class hackery.

I think the difficulty must arise mainly from the *, meaning I
think, "any type" in the above `applyTo`.*.  Would it be
easy/convenient to define `applyTo`.(a, b, c) where a is a "type
variable"?  In general can we, for any finite number n, where n > 2,
easily/conveniently define `applyTo`.(a1, a2, ..., an) ?

Ah, I see that the problem is for lists of length 3, so for the
type, if it be such, that I might write as [a, a, a], ah, OK, I
will fire up GHCi and have a look.

oo--JS.


>
> On Tue, Jun 26, 2012 at 5:19 PM, Jay Sulzberger <jays at panix.com> wrote:
>
>>
>>
>> On Tue, 26 Jun 2012, Brent Yorgey <byorgey at seas.upenn.edu> wrote:
>>
>>  On Tue, Jun 26, 2012 at 10:08:49PM +0200, Obscaenvs wrote:
>>>
>>>> Sorry if this is a less than stellar question.
>>>>
>>>> The problem:
>>>> Given a function f :: a -> a -> a -> b, make it work on a list
>>>> instead: f `applyTo`[x,y,z] where [x,y,z] :: [a].
>>>> My stab at a general solution was
>>>> `
>>>> applyTo f [] = error "no arg"
>>>> applyTo f (x:xs) = go (f x) xs
>>>>    where
>>>>      go acc [] = acc
>>>>      go acc (y:[]) = acc y
>>>>      go acc (y:ys) = go (acc $ y) ys
>>>> `
>>>>
>>>> I thought this would work, functions being "first class citizens" but
>>>> ghci complains:
>>>>    "Occurs check: cannot construct the infinite type: t1 = t0 -> t1
>>>>    In the return type of a call of `acc'
>>>>    Probable cause: `acc' is applied to too many arguments
>>>>    In the expression: acc y
>>>>    In an equation for `go': go acc (y : []) = acc y"
>>>>
>>>> The 'probable cause' isn't the real cause here, but something to do
>>>> with the fact that it's impossible to accumulate functions in this
>>>> way...
>>>> Or am I just too tired too make it work? I can see that the type of
>>>> `go` could be a problem, but is it insurmountable?
>>>>
>>>
>>> The type of `go` is exactly the problem.  In particular, the type of
>>> acc's first parameter.  In the third clause of go's definition, we can
>>> see that `acc` and (acc $ y) are both used as the first argument to
>>> go, hence they must have the same type.  However, this is impossible
>>> -- if acc has type (t0 -> t1), then y must have type t0, and (acc $ y)
>>> has type t1, so it would have to be the case that t1 = t0 -> t1 --
>>> hence the error message.
>>>
>>> It is not possible in Haskell to define `applyTo`.* I know this
>>> function gets used a lot in lisp/scheme, but Haskell style is
>>> different.  If you explain the context in which you wanted this
>>> function, perhaps we can help you figure out a better way to structure
>>> things so it is not needed.
>>>
>>> -Brent
>>>
>>> * At least not without crazy type class hackery.
>>>
>>
>> What is the difficulty?
>>
>> Is the difficulty at the level of "syntax"?
>>
>> Or is it that the type "Haskell expression", perhaps "Haskell
>> form", to use an old and often confusing Lisp term, does not
>> exist in the Haskell System of Expression?  Here "exist" should be
>> read as "exist at the right level", right level for attaining
>> some objective.
>>
>> These alternatives, I think, need not be disjoint.
>>
>> I am ignorant of Haskell, but sometimes I write Perl in Lisp, and
>> the blurb for my last public rant mentioned a specific lambda
>> expression:
>>
>>  http://lists.gnu.org/archive/**html/gnu-misc-discuss/2012-03/**
>> msg00036.html<http://lists.gnu.org/archive/html/gnu-misc-discuss/2012-03/msg00036.html>
>>
>> oo--JS.
>>
>>
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>
>
>
> -- 
> Alec Story
> Cornell University
> Biological Sciences, Computer Science 2012
>