operator on functions

[Ben Wolfson]

In article <9akpvh$74k$1 at news.mathworks.com>, "Joshua Marshall"
<jmarshal at mathworks.com> wrote:

> Szalay Zoltan <szz at philoslabs.com> wrote:
>> Hi everybody out there!
> 
>> It would be a nice feature of Python syntax providing an operator to
>> compose a function from another two:
>> h=f*g  . I mean (f*g)(x)=f(g(x).
> 
> Though maybe a little thought needs to go into multiple arguments (to
> f):
> 
>   (f*g)(x) => f(g(x))
> 
>   -vs-
> 
>   apply(f*g, x) => apply(f, apply(g, x))
> 
> or some hybrid.

This seems to work:

from __future__ import nested_scopes

class Function:
    def __init__(self, f):
        self.f=f
    def __call__(self, *a, **k):
        return self.f(*a, **k)
    def __mul__(self, o):
        return _compose(self, o)
    def __rmul__(self, o):
        return _compose(o, self)

def compose(f, g):
    def composed(*a, **k):
        result = g(*a, **k)
        if type(result) is not type(()):
            result = (result,)
        return f(*result)
    return composed

>>> import compose
>>> g = compose.Function(lambda a,b: (a+b, a*b, a-b)
>>> f = lambda a,b,c: ((a+b)*c, (a-b)/c)
>>> (f*g)(1,2)
(-5, -1)
>>> (g*f)(1,2,3)
(8, -9, 10)
>>> h = compose.Function(lambda a,b: a+b)
>>> i = lambda a: (-a, a+4)
>>> (h*i)(2)
4
>>> (i*h)(2,4)
(-6, 10)

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