Well, I did say it could be a terminology issue. What are perhaps better
terms for;

-> = curried (only one argument) and used to represent arity-abstract
functions. This is clearly a curried function operator.

=> = may have more than one argument, and represents arity-concrete
functions (calls). This is clearly an uncurried function opertator.

Although one is curried, and one uncurried, I take your point that it may
not be the best terminology. The (un)curriedness is a property of each
arrow type....

Keean.

On 30 March 2015 at 14:23, Matt Oliveri <[email protected]> wrote:

> On Mon, Mar 30, 2015 at 7:17 AM, Keean Schupke <[email protected]> wrote:
> > Currying is the process of converting a multi-argument function into
> > functions that only accept one argument. Therefore a curried function has
> > only one argument.
> ...
> > Arity concrete functions can also return functions, I have not said they
> > cannot, however they can have more than one argument, so they are not
> all in
> > curried form.
>
> I see. Your use of "curried" is narrower than mine.
>
> > So re-recap my representations:
> >
> > - A curried arrow (can only accept one argument) is used to represent
> > arity-abstract functions. We can call this an abstract-curried arrow if
> you
> > like "->"
> >
> > - An uncurried arrow (can have more than one argument) is used to
> represent
> > concrete-arity functions. We can call this a concrete-arrow "=>"
>
> I really don't like the use of "curried" and "uncurried" to make this
> distinction, since the difference between arity-abstract and
> arity-concrete has nothing to do with whether you can have more than
> one argument.
>
> It's also misleading to use "curried" and "uncurried" here since it
> means something different for an arity-concrete function to be curried
> (called with one argument) than for an arity-abstract function to be
> curried (applied to one argument). Indeed, according to your terms, an
> arity-concrete function could be both curried and uncurried, in
> different senses.
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