Partial function application

Partial function application is the ability to take a function of many parameters and apply arguments to some of the parameters to create a new function that needs only the application of the remaining arguments to produce the equivalent of applying all arguments to the original function.

E.g:

Given values v1, v2

Given f(param1, param2)

Then partial(f, param1=v1) returns f'(param2)

And f(param1=v1, param2=v2) == f'(param2=v2) (for any value v2)

Task

Create a function fs( f, s ) that takes a function, f( n ), of one value and a sequence of values s.
Function fs should return an ordered sequence of the result of applying function f to every value of s in turn.

Create function f1 that takes a value and retuns it multiplied by 2.
Create function f2 that takes a value and returns it squared.

Partially apply f1 to fs to form function fsf1( s )
Partially apply f2 to fs to form function fsf2( s )

Test fsf1 and fsf2 by evaluating them with s being the sequence of integers from 0 to 3 inclusive and then the sequence of even integers from 2 to 8 inclusive.

Python

<lang python>from functools import partial

def fs(f, s): return [f(value) for value in s]

def f1(value): return value * 2

def f2(value): return value ** 2

fsf1 = partial(fs, f1) fsf2 = partial(fs, f2)

s = [0, 1, 2, 3] assert fs(f1, s) == fsf1(s) # == [0, 2, 4, 6] assert fs(f2, s) == fsf2(s) # == [0, 1, 4, 9]

s = [2, 4, 6, 8] assert fs(f1, s) == fsf1(s) # == [4, 8, 12, 16] assert fs(f2, s) == fsf2(s) # == [4, 16, 36, 64]</lang>

The program runs without triggering the assertions.