Functional Python Programming

Chapter 14

Here's our first function that computes the product:

import operator

prod = myreduce(operator.mul)

This is based on our curried myreduce() function that was defined previously.
It uses the operator.mul() function to compute a "times-reduction" of an iterable:
we can call a product a times-reduce of a sequence.

Here's our second curried function that will produce a range of values:

@curry

def alt_range(n):

if n == 0: return range(1,2) # Only 1

if n % 2 == 0:

return range(2,n+1,2)

else:

return range(1,n+1,2)

The result of the alt_range() function will be even values or odd values. It will
have only values up to (and including) n, if n is odd. If n is even, it will have only
even values up to n. The sequences are important for implementing the semifactorial
or double factorial function, n!!.

Here's how we can combine the prod() and alt_range() functions into a new
curried function:

semi_fact= prod * alt_range

semi_fact(9)

945

The PyMonad * operator here combines two functions into a composite function,
named semi_fact. The alt_range() function is applied to the arguments. Then,
the prod() function is applied to the results of the alt_range function.

By doing this manually in Python, we're effectively creating a new lambda object:

semi_fact= lambda x: prod(alt_range(x))

The composition of curried functions involves somewhat less syntax than creating
a new lambda object.

Ideally, we would like to use functional composition and curried functions like this:

sumwhile= sum * takewhile(lambda x: x > 1E-7)