Function composition
You are encouraged to solve this task according to the task description, using any language you may know.
Create a function, compose, whose two arguments f and g, are both functions with one argument. The result of compose is to be a function of one argument, (lets call the argument x), which works like applying function f to the result of applying function g to x.
I.e:
compose(f, g)(x) == f( g(x) )
Reference: Function composition
ALGOL 68
Note: Returning PROC (REAL x)REAL: f1(f2(x))
from a function apparently
violates standard ALGOL 68's scoping rules. ALGOL 68G warns about this during
parsing, and then rejects during runtime.
<lang algol>MODE F = PROC(REAL)REAL; # ALGOL 68 is strong typed #
- As a procedure for real to real functions #
PROC compose = (F f, g)F: (REAL x)REAL: f(g(x));
OP (F,F)F O = compose; # or an OPerator that can be overloaded #
- Example use: #
F sin arc sin = compose(sin, arc sin); print((sin arc sin(0.5), (sin O arc sin)(0.5), new line))</lang> Output:
+.500000000000000e +0 +.500000000000000e +0
Python
<lang python>compose = lambda f, g: lambda x: f( g(x) )</lang> Example use: <lang python>>>> compose = lambda f, g: lambda x: f( g(x) ) >>> from math import sin, asin >>> sin_asin = compose(sin, asin) >>> sin_asin(0.5) 0.5 >>> </lang>
Scheme
<lang scheme>(define (compose f g) (lambda (x) (f (g x))))</lang> Example use: <lang scheme>> (define (compose f g) (lambda (x) (f (g x)))) > (define sin_asin (compose sin asin)) > (sin_asin 0.5) 0.5</lang>