[Python-Dev] Re: PEP 309 misuses the term "currying"

[Gareth McCaughan]

[Dave, this may be the second copy of this message you receive;
sorry about that.]

Dave Abrahams wrote:

> The operation performed by the operator described here is actually
> called "Partial Application". A good definition of currying can be
> found in http://tinyurl.com/3d6w6 and http://tinyurl.com/ly29.

I disagree. Currying is turning a function that takes its arguments
all at once as a tuple into a function that takes them one at a time
by partial application. So if f(1,2,3)=64 and F is the curried version
of f, then F(1)(2)(3)=64.

The idea of currying arose in a context where functions are
fundamentally single-argument; it's a way of converting between
two different ways of building multiple-argument functions
on top of a single-argument-only base. That's handy for
mathematicians and theoretical computer scientists, who
like to keep their underlying concepts as few and as simple
as possible. But in Python, and in many other programming
languages, functions with multiple arguments aren't built on
a single-argument substrate, so there are *three* options
for passing multiple arguments to a function.
  - Collect args into a tuple, pass that.
  - Just pass multiple arguments.
  - Pass arguments one at a time using partial application.
And the middle one, the one that isn't generally considered
by mathematicians doing lambda calculus, happens to be the
*usual* case. How you apply the notion of "currying" to Python,
then, depends on which pair of argument-passing conventions
you choose to assimilate; in other words, on which of the two
distinctions at work here you choose to emphasize. Currying
is ...

1. "Turning a function that takes a single tuple argument into
   one that takes multiple arguments."

2. "Turning a function that takes it arguments all at once into
   one that takes them one at a time."

According to #1, what PEP309 calls currying is no such thing.
According to #2, what PEP309 calls currying *is* currying.

It looks to me as if the second usage is the dominant one, in
which case I think PEP309 is fine.

-- 
g