Function Application is not Currying

[Xah Lee]

Function Application is not Currying

Xah Lee, 2009-01-28

In Jon Harrop's book Ocaml for Scientist at
http://www.ffconsultancy.com/products/ocaml_for_scientists/chapter1.html

It says:

    Currying

    A curried function is a function which returns a function as its
result.

LOL. That is incorrect.

Here are some examples of a function that returns a function as
result, but is not currying.

Mathematica example:

f[n_]:=Function[n^#];
f[7][2]
(* returns 49 *)

Emacs lisp example:

(defmacro f (n) (list 'lambda (list 'x) (list 'expt n 'x) ) )
(funcall (f 7) 2)

Perl example:

sub f {$n=$_[0]; sub { $n ** $_[0]} };
print &{ f(7) } (2);

Javascript example:

function f(n) {return function (x) {return Math.pow(x,n);}; }
alert (f(7) (2));

In the above, a function returns a function, and the result function
is applied to a value. They demonstrate 2 things:

    * The ability of the lang to have a function that returns a
function.
    * The ability to apply a value (of type function) to a value.

These, are 2 of the features that is part of often sloppily termed as
“function as first class citizens”.

However, the above are not languages that support currying, which is a
feature that Haskell & Ocaml has.

So what is Currying?

Wikipedia article Currying said it best:

    In computer science, currying, invented by Moses Schönfinkel and
Gottlob Frege, and independently by Haskell Curry,[1] is the technique
of transforming a function that takes multiple arguments (or more
accurately an n-tuple as argument) in such a way that it can be called
as a chain of functions each with a single argument.

Note how it says “is the technique of ...”.

To be more concrete, in the context of a given computer language, to
say that it support curring, is to mean that the compiler understand
the concept to certain degree. More to the point, the language is
inherently able to take a function of more than one arg and
deconstruct it to several functions of single arg.

To say that function returning function is Currying, is a confusion of
fundamental concepts.

Mathematically, currying is the concept of deconstructing a function
of multiple parameters to a composition of several functions all of
arity 1.

I like Jon, because i consider majority of his argument and
perspective are more correct or sensible in his trollish spats in
newsgroup fighting with tech geekers. But he is really a asshole, and
take every chance to peddle his book. Every mother fucking
opponitunity, he injects random opinion into discussions about how
static typing or greatness of Microsoft, which paves a way for him to
post a link to his book on Ocaml/F# or “study” or “speed comparison”
of his site. He does this repeatedly and intentionally, about every
week for the past 2 or so years, and write in a way to provoke irate
responses. In the past 2 or 3 years, i have for 2 or so times without
his or anyone's solicitation, publically supported him in ugly
newsgroup fights (such as some serious sounding post that accuse him
of spamming or or some real life threats about network abuse).
However, in the past year as i have had some debates on language
issues with jon, i find Jon to be a complete asshole as far as his
newsgroup demeanor goes.

PS see also: A Mathematica Optimization Problem ( story of a thread
where Jon started a fight with me )

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