Functional Python Programming - Second Edition

Writing higher-order reductions

We'll look at an example of a higher-order reduction algorithm here. This will introduce a rather complex topic. The simplest kind of reduction develops a single value from a collection of values. Python has a number of built-in reductions, including any(), all(), max(), min(), sum(), and len().

As we noted in Chapter 4, Working with Collections, we can do a great deal of statistical calculation if we start with a few simple reductions such as the following:

def s0(data: Sequence) -> float:
    return sum(1 for x in data)  # or len(data)
def s1(data: Sequence) -> float:
    return sum(x for x in data)  # or sum(data)
def s2(data: Sequence) -> float:
    return sum(x*x for x in data)

This allows us to define mean, standard ...