
7.1.3 Functional Programming Tools
There are three builtin functions that are very useful when used with
lists: filter() , map() , and reduce() .
‘filter(function, sequence)’ returns a sequence (of
the same type, if possible) consisting of those items from the
sequence for which function(item) is true. For
example, to compute some primes:
>>> def f(x): return x % 2 != 0 and x % 3 != 0
...
>>> filter(f, range(2, 25))
[5, 7, 11, 13, 17, 19, 23]
‘map(function, sequence)’ calls
function(item) for each of the items in the sequence and
returns a list of the return values. For example, to compute some
cubes:
>>> def cube(x): return x*x*x
...
>>> map(cube, range(1, 11))
[1, 8, 27, 64, 125, 216, 343, 512, 729, 1000]
More than one sequence may be passed; the function must then have as
many arguments as there are sequences and is called with the
corresponding item from each sequence (or None if some sequence
is shorter than another). If None is passed for the function,
a function returning its argument(s) is substituted.
Combining these two special cases, we see that
‘map(None, list1, list2)’ is a convenient way of
turning a pair of lists into a list of pairs. For example:
>>> seq = range(8)
>>> def square(x): return x*x
...
>>> map(None, seq, map(square, seq))
[(0, 0), (1, 1), (2, 4), (3, 9), (4, 16), (5, 25),
(6, 36), (7, 49)]
‘reduce(func, sequence)’ returns a single value
constructed by calling the binary function func on the first two
items of the sequence, then on the result and the next item, and so
on. For example, to compute the sum of the numbers 1 through 10:
>>> def add(x,y): return x+y
...
>>> reduce(add, range(1, 11))
55
If there's only one item in the sequence, its value is returned; if
the sequence is empty, an exception is raised.
A third argument can be passed to indicate the starting value. In this
case the starting value is returned for an empty sequence, and the
function is first applied to the starting value and the first sequence
item, then to the result and the next item, and so on. For example,
>>> def sum(seq):
... def add(x,y): return x+y
... return reduce(add, seq, 0)
...
>>> sum(range(1, 11))
55
>>> sum([])
0

