Function composition: Difference between revisions
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Prelude> sin_asin 0.5 |
Prelude> sin_asin 0.5 |
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0.5</lang> |
0.5</lang> |
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=={{header|Java}}== |
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<lang java>public class Compose { |
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// Java doesn't have function type so we define an interface |
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// of function objects instead |
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public interface Fun<A,B> { |
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B call(A x); |
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} |
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public static <A,B,C> Fun<A,C> compose(final Fun<B,C> f, final Fun<A,B> g) { |
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return new Fun<A,C>() { |
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public C call(A x) { |
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return f.call(g.call(x)); |
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} |
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}; |
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} |
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public static void main(String[] args) { |
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Fun<Double,Double> sin = new Fun<Double,Double>() { |
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public Double call(Double x) { |
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return Math.sin(x); |
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} |
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}; |
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Fun<Double,Double> asin = new Fun<Double,Double>() { |
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public Double call(Double x) { |
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return Math.asin(x); |
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} |
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}; |
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Fun<Double,Double> sin_asin = compose(sin, asin); |
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System.out.println(sin_asin.call(0.5)); // prints "0.5" |
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} |
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}</lang> |
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=={{header|JavaScript}}== |
=={{header|JavaScript}}== |
Revision as of 20:54, 4 March 2009
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
Hint: Implementing compose correctly requires creating a closure. If your language does not support closures directly, you will need to implement it yourself.
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
C++
Note: this is already implemented as __gnu_cxx::compose1()
<lang cpp>#include <functional>
- include <cmath>
- include <iostream>
// functor class to be returned by compose function template <class Fun1, class Fun2> class compose_functor :
public std::unary_function<typename Fun2::argument_type, typename Fun1::result_type>
{ protected:
Fun1 f; Fun2 g;
public:
compose_functor(const Fun1& _f, const Fun2& _g) : f(_f), g(_g) { }
typename Fun1::result_type operator()(const typename Fun2::argument_type& x) const { return f(g(x)); }
};
// we wrap it in a function so the compiler infers the template arguments // whereas if we used the class directly we would have to specify them explicitly template <class Fun1, class Fun2> inline compose_functor<Fun1, Fun2> compose(const Fun1& f, const Fun2& g) { return compose_functor<Fun1,Fun2>(f, g); }
int main() {
std::cout << compose(std::ptr_fun(::sin), std::ptr_fun(::asin))(0.5) << std::endl;
return 0;
}</lang>
Common Lisp
<lang lisp>(defun compose (f g) (lambda (x) (funcall f (funcall g x))))</lang> Example use: <lang lisp>>(defun compose (f g) (lambda (x) (funcall f (funcall g x)))) COMPOSE >(let ((sin-asin (compose #'sin #'asin))))
(funcall sin-asin 0.5))
0.5</lang>
Haskell
This is already defined as the . (dot) operator in Haskell. <lang haskell>compose f g x = f (g x)</lang> Example use: <lang haskell>Prelude> let compose f g x = f (g x) Prelude> let sin_asin = compose sin asin Prelude> sin_asin 0.5 0.5</lang>
Java
<lang java>public class Compose {
// Java doesn't have function type so we define an interface // of function objects instead public interface Fun<A,B> { B call(A x); }
public static <A,B,C> Fun<A,C> compose(final Fun<B,C> f, final Fun<A,B> g) { return new Fun<A,C>() { public C call(A x) { return f.call(g.call(x)); } }; }
public static void main(String[] args) { Fun<Double,Double> sin = new Fun<Double,Double>() { public Double call(Double x) { return Math.sin(x); } }; Fun<Double,Double> asin = new Fun<Double,Double>() { public Double call(Double x) { return Math.asin(x); } };
Fun<Double,Double> sin_asin = compose(sin, asin);
System.out.println(sin_asin.call(0.5)); // prints "0.5" }
}</lang>
JavaScript
<lang javascript>
function compose(f, g) { return function(x) { return f(g(x)) } }
var id = compose(Math.sin, Math.asin) print id(0.5) // 0.5
</lang>
Joy
Composition is the default operation in Joy. The composition of two functions is the concatenation of those functions, in the order in which they are to be applied. <lang joy>
g f
</lang>
OCaml
<lang ocaml>let compose f g x = f (g x)</lang> Example use: <lang ocaml># let compose f g x = f (g x);; val compose : ('a -> 'b) -> ('c -> 'a) -> 'c -> 'b = <fun>
- let sin_asin = compose sin asin;;
val sin_asin : float -> float = <fun>
- sin_asin 0.5;;
- : float = 0.5</lang>
Perl
<lang perl>sub compose
{my ($f, $g) = @_; return sub {$f->($g->(@_))};}
use Math::Trig; print compose(sub {sin $_[0]}, \&asin)->(0.5), "\n";</lang>
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>