Function composition
From Rosetta Code
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: In some languages, implementing compose correctly requires creating a closure.
[edit] ActionScript
ActionScript supports closures, making function composition very straightforward.
function compose(f:Function, g:Function):Function {
return function(x:Object) {return f(g(x));};
}
function test() {
trace(compose(Math.atan, Math.tan)(0.5));
}
[edit] Ada
The interface of a generic functions package. The package can be instantiated with any type that has value semantics. Functions are composed using the operation '*'. The same operation applied to an argument evaluates it there: f * x. Functions can be composed with pointers to Ada functions. (In Ada functions are not first-class):
generic
type Argument is private;
package Functions is
type Primitive_Operation is not null
access function (Value : Argument) return Argument;
type Func (<>) is private;
function "*" (Left : Func; Right : Argument) return Argument;
function "*" (Left : Func; Right : Primitive_Operation) return Func;
function "*" (Left, Right : Primitive_Operation) return Func;
function "*" (Left, Right : Func) return Func;
private
type Func is array (Positive range <>) of Primitive_Operation;
end Functions;
Here is an implementation;
package body Functions is
function "*" (Left : Func; Right : Argument) return Argument is
Result : Argument := Right;
begin
for I in reverse Left'Range loop
Result := Left (I) (Result);
end loop;
return Result;
end "*";
function "*" (Left, Right : Func) return Func is
begin
return Left & Right;
end "*";
function "*" (Left : Func; Right : Primitive_Operation) return Func is
begin
return Left & (1 => Right);
end "*";
function "*" (Left, Right : Primitive_Operation) return Func is
begin
return (Left, Right);
end "*";
end Functions;
The following is an example of use:
with Ada.Numerics.Elementary_Functions; use Ada.Numerics.Elementary_Functions;
with Ada.Text_IO; use Ada.Text_IO;
with Functions;
procedure Test_Compose is
package Float_Functions is new Functions (Float);
use Float_Functions;
Sin_Arcsin : Func := Sin'Access * Arcsin'Access;
begin
Put_Line (Float'Image (Sin_Arcsin * 0.5));
end Test_Compose;
Sample output:
5.00000E-01
[edit] Aikido
import math
function compose (f, g) {
return function (x) { return f(g(x)) }
}
var func = compose(Math.sin, Math.asin)
println (func(0.5)) // 0.5
[edit] 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.
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))
Output:
+.500000000000000e +0 +.500000000000000e +0
ALGOL 68 is a stack based language, and the following apparently does not violate it's scoping rules.
MODE F = PROC(REAL)REAL; # ALGOL 68 is strong typed #
# As a procedure for real to real functions #
PROC compose = (F f, g)F: ((F f2, g2, REAL x)REAL: f2(g2(x)))(f, g, ); # Curry #
PRIO O = 7;
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))
[edit] Argile
Only works for functions taking real and returning real (double precision, 64 bits)
use std, math
let my_asin = new Function (.:<any,real x>:. -> real {asin x})
let my__sin = new Function (.:<any,real x>:. -> real { sin x})
let sinasin = my__sin o my_asin
print sin asin 0.5
print *my__sin 0.0
print *sinasin 0.5
~my_asin
~my__sin
~sinasin
=: <Function f> o <Function g> := -> Function {compose f g}
.:compose <Function f, Function g>:. -> Function
use array
let d = (new array of 2 Function)
(d[0]) = f ; (d[1]) = g
let c = new Function (.:<array of Function fg, real x>:. -> real {
*fg[0]( *fg[1](x) )
}) (d)
c.del = .:<any>:.{free any}
c
class Function
function(any)(real)->(real) func
any data
function(any) del
=: * <Function f> <real x> := -> real
Cgen "(*("(f.func)"))("(f.data)", "(x)")"
.: del Function <Function f> :.
unless f.del is nil
call f.del with f.data
free f
=: ~ <Function f> := {del Function f}
.: new Function <function(any)(real)-\>real func> (<any data>):. -> Function
let f = new Function
f.func = func
f.data = data
f
[edit] AutoHotkey
contributed by Laszlo on the ahk forum
MsgBox % compose("sin","cos",1.5)
compose(f,g,x) { ; function composition
Return %f%(%g%(x))
}
[edit] Bori
double sin (double v) { return Math.sin(v); }
double asin (double v) { return Math.asin(v); }
Var compose (Func f, Func g, double d) { return f(g(d)); }
void button1_onClick (Widget widget)
{
double d = compose(sin, asin, 0.5);
label1.setText(d.toString(9));
}
Output on Android phone:
0.500000000
[edit] Brat
compose = { f, g | { x | f g x } }
#Test
add1 = { x | x + 1 }
double = { x | x * 2 }
b = compose(->double ->add1)
p b 1 #should print 4
[edit] C
Only works for functions taking a double and returning a double:
#include <stdlib.h>
/* generic interface for functors from double to double */
typedef struct double_to_double {
double (*fn)(struct double_to_double *, double);
} double_to_double;
#define CALL(f, x) f->fn(f, x)
/* functor returned by compose */
typedef struct compose_functor {
double (*fn)(struct compose_functor *, double);
double_to_double *f;
double_to_double *g;
} compose_functor;
/* function to be used in "fn" in preceding functor */
double compose_call(compose_functor *this, double x) {
return CALL(this->f, CALL(this->g, x));
}
/* returns functor that is the composition of functors
f & g. caller is responsible for deallocating memory */
double_to_double *compose(double_to_double *f,
double_to_double *g) {
compose_functor *result = malloc(sizeof(compose_functor));
result->fn = &compose_call;
result->f = f;
result->g = g;
return (double_to_double *)result;
}
#include <math.h>
/* we can make functors for sin and asin by using
the following as "fn" in a functor */
double sin_call(double_to_double *this, double x) {
return sin(x);
}
double asin_call(double_to_double *this, double x) {
return asin(x);
}
#include <stdio.h>
int main() {
double_to_double *my_sin = malloc(sizeof(double_to_double));
my_sin->fn = &sin_call;
double_to_double *my_asin = malloc(sizeof(double_to_double));
my_asin->fn = &asin_call;
double_to_double *sin_asin = compose(my_sin, my_asin);
printf("%f\n", CALL(sin_asin, 0.5)); /* prints "0.500000" */
free(sin_asin);
free(my_sin);
free(my_asin);
return 0;
}
[edit] C++
#include <functional>composing
#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;
}
std::function
#include <iostream>GCC's C++ library has a built-in compose function
#include <functional>
#include <cmath>
template <typename A, typename B, typename C>
std::function<C(A)> compose(std::function<C(B)> f, std::function<B(A)> g) {
return [f,g](A x) { return f(g(x)); };
}
int main() {
std::function<double(double)> f = sin;
std::function<double(double)> g = asin;
std::cout << compose(f, g)(0.5) << std::endl;
return 0;
}
#include <iostream>
#include <cmath>
#include <ext/functional>
int main() {
std::cout << __gnu_cxx::compose1(std::ptr_fun(::sin), std::ptr_fun(::asin))(0.5) << std::endl;
return 0;
}
[edit] C#
using System;
class Program
{
static void Main(string[] args)
{
Func<int, int> outfunc = Composer<int, int, int>.Compose(functA, functB);
Console.WriteLine(outfunc(5)); //Prints 100
}
static int functA(int i) { return i * 10; }
static int functB(int i) { return i + 5; }
class Composer<A, B, C>
{
public static Func<C, A> Compose(Func<B, A> a, Func<C, B> b)
{
return delegate(C i) { return a(b(i)); };
}
}
}
[edit] Clojure
Function composition is built in to Clojure. Simply call the comp function.
A manual implementation could look like this:
(defn compose [f g]
(fn [x]
(f (g x))))
; Example
(def inc2 (compose inc inc))
(println (inc2 5)) ; prints 7
[edit] Common Lisp
compose returns a function that closes on the lexical variables f and g.
(defun compose (f g) (lambda (x) (funcall f (funcall g x))))
Example use:
>(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
This alternate solution, more ugly and more difficult, never closes on any lexical variables. Instead, it uses runtime evaluation to insert the values of f and g into new code. This is just a different way to create a closure.
(defun compose (f g)
(eval `(lambda (x) (funcall ',f (funcall ',g x))))
[edit] D
import std.stdio, std.math;
T delegate(S) compose(T, U, S)(T delegate(U) f, U delegate(S) g) {
return (S s) => f(g(s));
}
void main() {
//writeln(compose(x => x + 15, x => x ^^ 2)(10));
//writeln(compose(x => x ^^ 2, x => x + 15)(10));
int plus15(int x) { return x + 15; }
int sqr(int x) { return x * x; }
writeln(compose(&plus15, &sqr)(10));
writeln(compose(&sqr, &plus15)(10));
}
- Output:
115 625
[edit] Delphi
Anonymous methods were introduced in Delphi 2009, so next code works with Delphi 2009 and above:
program AnonCompose;
{$APPTYPE CONSOLE}
type
TFunc = reference to function(Value: Integer): Integer;
function Compose(F, G: TFunc): TFunc;
begin
Result:= function(Value: Integer): Integer
begin
Result:= F(G(Value));
end
end;
var
Func1, Func2, Func3: TFunc;
begin
Func1:=
function(Value: Integer): Integer
begin
Result:= Value * 2;
end;
Func2:=
function(Value: Integer): Integer
begin
Result:= Value * 3;
end;
Func3:= Compose(Func1, Func2);
Writeln(Func3(6)); // 36 = 6 * 3 * 2
Readln;
end.
[edit] Dylan
define method compose(f,g)
method(x) f(g(x)) end
end;
[edit] E
def compose(f, g) {
return fn x { return f(g(x)) }
}
[edit] Erlang
-module(fn).
-export([compose/1, multicompose/2]).
compose(F,G) -> fun(X) -> F(G(X)) end.
multicompose(Fs) ->
lists:foldl(fun compose/2, fun(X) -> X end, Fs).
Using them:
1> (fn:compose(fun math:sin/1, fun math:asin/1))(0.5).
0.5
2> Sin_asin_plus1 = fn:multicompose([fun math:sin/1, fun math:asin/1, fun(X) -> X + 1 end]).
#Fun<tests.0.59446746>
82> Sin_asin_plus1(0.5).
1.5
[edit] F#
The most-used composition operator in F# is >>. It implements forward composition, i.e. f >> g is a function which calls f first and then calls g on the result.
The reverse composition operator <<, on the other hand, exactly fulfills the requirements of the compose function described in this task.
We can implement composition manually like this (F# Interactive session):
> let compose f g x = f (g x);;
val compose : ('a -> 'b) -> ('c -> 'a) -> 'c -> 'b
Usage:
> let sin_asin = compose sin asin;;
val sin_asin : (float -> float)
> sin_asin 0.5;;
val it : float = 0.5
[edit] Factor
When passing functions around and creating anonymous functions, Factor uses so called quotations. There is already a word (compose) that provides composition of quotations.
( scratchpad ) [ 2 * ] [ 1 + ] compose .
[ 2 * 1 + ]
( scratchpad ) 4 [ 2 * ] [ 1 + ] compose call .
9
[edit] Fantom
class Compose
{
static |Obj -> Obj| compose (|Obj -> Obj| fn1, |Obj -> Obj| fn2)
{
return |Obj x -> Obj| { fn2 (fn1 (x)) }
}
public static Void main ()
{
double := |Int x -> Int| { 2 * x }
|Int -> Int| quad := compose(double, double)
echo ("Double 3 = ${double(3)}")
echo ("Quadruple 3 = ${quad (3)}")
}
}
[edit] Forth
: compose ( xt1 xt2 -- xt3 )
>r >r :noname
r> compile,
r> compile,
postpone ;
;
' 2* ' 1+ compose ( xt )
3 swap execute . \ 7
[edit] GAP
Composition := function(f, g)
return x -> f(g(x));
end;
h := Composition(x -> x+1, x -> x*x);
h(5);
# 26
[edit] Go
// Go doesn't have generics, but sometimes a type definition helps
// readability and maintainability. This example is written to
// the following function type, which uses float64.
type ffType func(float64) float64
// compose function requested by task
func compose(f, g ffType) ffType {
return func(x float64) float64 {
return f(g(x))
}
}
Example use:
package main
import "math"
import "fmt"
type ffType func(float64) float64
func compose(f, g ffType) ffType {
return func(x float64) float64 {
return f(g(x))
}
}
func main() {
sin_asin := compose(math.Sin, math.Asin)
fmt.Println(sin_asin(.5))
}
Output:
0.5
[edit] Groovy
Solution:
def compose = { f, g -> { x -> f(g(x)) } }
Test program:
def sq = { it * it }
def plus1 = { it + 1 }
def minus1 = { it - 1 }
def plus1sqd = compose(sq,plus1)
def sqminus1 = compose(minus1,sq)
def identity = compose(plus1,minus1)
def plus1sqdminus1 = compose(minus1,compose(sq,plus1))
def identity2 = compose(Math.&sin,Math.&asin)
println "(x+1)**2 = (0+1)**2 = " + plus1sqd(0)
println "x**2-1 = 20**2-1 = " + sqminus1(20)
println "(x+1)-1 = (12+1)-1 = " + identity(12)
println "(x+1)**2-1 = (3+1)**2-1 = " + plus1sqdminus1(3)
println "sin(asin(x)) = sin(asin(1)) = " + identity2(1)
Output:
(x+1)**2 = (0+1)**2 = 1 x**2-1 = 20**2-1 = 399 (x+1)-1 = (12+1)-1 = 12 (x+1)**2-1 = (3+1)**2-1 = 15 sin(asin(x)) = sin(asin(1)) = 1.0
[edit] Haskell
This is already defined as the . (dot) operator in Haskell.
compose f g x = f (g x)
Example use:
Prelude> let compose f g x = f (g x)
Prelude> let sin_asin = compose sin asin
Prelude> sin_asin 0.5
0.5
[edit] Icon and Unicon
Icon and Unicon don't have a lambda function or native closure; however, they do have co-expressions which are extremely versatile and can be used to achieve the same effect. The list of functions to compose can be a 'procedure', 'co-expression", or an invocable string (i.e. procedure name or unary operator). It will correctly handle compose(compose(...),..).
There are a few limitations to be aware of:
- type(compose(f,g)) returns a co-expression not a procedure
- this construction only handles functions of 1 argument (a closure construct is better for the general case)
The solution below can be adapted to work in Icon by reverting to the old syntax for invoking co-expressions.
x @ f # use this syntax in Icon instead of the Unicon f(x) to call co-expressions
every push(fL := [],!rfL) # use this instead of reverse(fL) as the Icon reverse applies only to strings
See Icon and Unicon Introduction:Minor Differences for more information
procedure main(arglist)
h := compose(sqrt,abs)
k := compose(integer,"sqrt",ord)
m := compose("-",k)
every write(i := -2 to 2, " h=(sqrt,abs)-> ", h(i))
every write(c := !"1@Q", " k=(integer,\"sqrt\",ord)-> ", k(c))
write(c := "1"," m=(\"-\",k) -> ",m(c))
end
invocable all # permit string invocations
procedure compose(fL[]) #: compose(f1,f2,...) returns the functional composition of f1,f2,... as a co-expression
local x,f,saveSource
every case type(x := !fL) of {
"procedure"|"co-expression": &null # procedures and co-expressions are fine
"string" : if not proc(x,1) then runnerr(123,fL) # as are invocable strings (unary operators, and procedures)
default: runerr(123,fL)
}
fL := reverse(fL) # reverse and isolate from mutable side-effects
cf := create { saveSource := &source # don't forget where we came from
repeat {
x := (x@saveSource)[1] # return result and resume here
saveSource := &source # ...
every f := !fL do x := f(x) # apply the list of 'functions'
}
}
return (@cf, cf) # 'prime' the co-expr before returning it
end
Sample Output:
-2 h=(sqrt,abs)-> 1.414213562373095
-1 h=(sqrt,abs)-> 1.0
0 h=(sqrt,abs)-> 0.0
1 h=(sqrt,abs)-> 1.0
2 h=(sqrt,abs)-> 1.414213562373095
1 k=(integer,"sqrt",ord)-> 7
@ k=(integer,"sqrt",ord)-> 8
Q k=(integer,"sqrt",ord)-> 9
1 m=("-",k) -> -7
[edit] J
Solution:
compose =: @
Example:
f compose g
Of course, given that @ is only one character long and is a built-in primitive, there is no need for the cover function compose. And @ is not the only composition primitive; composition is a very important concept in J. For more details, see the talk page.
[edit] 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"
}
}
[edit] 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
[edit] 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.
g f
[edit] K
Functions are automatically curried in K if called with missing arguments.
compose: {x@y@z}
Example:
sin_asin: compose[_sin;_asin]
sin_asin 0.5
0.5
[edit] Lua
function compose(f, g) return function(...) return f(g(...)) end end
[edit] Mathematica
Built-in function that takes any amount of function-arguments:
Composition[f, g][x]
Composition[f, g, h, i][x]
gives back:
f[g[x]]
f[g[h[i[x]]]]
Custom function:
compose[f_, g_][x_] := f[g[x]]
compose[Sin, Cos][r]
gives back:
Sin[Cos[r]]
Composition can be done in more than 1 way:
Composition[f,g,h][x]
f@g@h@x
x//h//g//f
all give back:
f[g[h[x]]]
The built-in function has a couple of automatic simplifications:
Composition[f, Identity, g]
Composition[f, InverseFunction[f], h][x]
becomes:
f[g[x]]
h[x]
[edit] Maxima
/* built-in */
load(to_poly_solver);
compose_functions([sin, cos]);
/* lambda([%g0],sin(cos(%g0)))*/
[edit] Nemerle
using System;
using System.Console;
using System.Math;
module Composition
{
Compose[T](f : T -> T, g : T -> T, x : T) : T
{
f(g(x))
}
Main() : void
{
def SinAsin = Compose(Sin, Asin, _);
WriteLine(SinAsin(0.5));
}
}
[edit] NewLISP
> (define (compose f g) (expand (lambda (x) (f (g x))) 'f 'g))
(lambda (f g) (expand (lambda (x) (f (g x))) 'f 'g))
> ((compose sin asin) 0.5)
0.5
[edit] Objective-C
The FunctionComposer is able to compose any object that conforms to the protocol FunctionCapsule (a selector/method accepting any object as argument and returning another object, i.e. computing a "function" of an object). A FunctionCaps class thought to encapsulate a function returning a double and with a double as argument is shown; anyway, as said, any object conforming to FunctionCapsule protocol can be composed with another object conforming to the same protocol. Argument passed and returned can be of any object type.
#include <Foundation/Foundation.h>
// the protocol of objects that can behave "like function"
@protocol FunctionCapsule <NSObject>
-(id)computeWith: (id)x;
@end
// a commodity for "encapsulating" double f(double)
typedef double (*func_t)(double);
@interface FunctionCaps : NSObject <FunctionCapsule>
{
func_t function;
}
+(id)capsuleFor: (func_t)f;
-(id)initWithFunc: (func_t)f;
@end
@implementation FunctionCaps
-(id)initWithFunc: (func_t)f
{
if ((self = [self init])) {
function = f;
}
return self;
}
+(id)capsuleFor: (func_t)f
{
return [[[self alloc] initWithFunc: f] autorelease];
}
-(id)computeWith: (id)x
{
return [NSNumber numberWithDouble: function([x doubleValue])];
}
@end
// the "functions" composer
@interface FunctionComposer : NSObject <FunctionCapsule>
{
id<FunctionCapsule> funcA;
id<FunctionCapsule> funcB;
}
+(id) createCompositeFunctionWith: (id<FunctionCapsule>)A and: (id<FunctionCapsule>)B;
-(id) initComposing: (id<FunctionCapsule>)A with: (id<FunctionCapsule>)B;
@end
@implementation FunctionComposer
+(id) createCompositeFunctionWith: (id<FunctionCapsule>)A and: (id<FunctionCapsule>)B
{
return [[[self alloc] initComposing: A with: B] autorelease];
}
-(id) init
{
[self release];
@throw [NSException exceptionWithName:NSInternalInconsistencyException
reason:@"FunctionComposer: init with initComposing!"
userInfo:nil];
return nil;
}
-(id) initComposing: (id<FunctionCapsule>)A with: (id<FunctionCapsule>)B
{
if ((self = [super init])) {
if ( [A respondsToSelector: @selector(computeWith:)] &&
[B respondsToSelector: @selector(computeWith:)] ) {
funcA = [A retain]; funcB = [B retain];
return self;
}
NSLog(@"FunctionComposer: cannot compose functions not responding to protocol FunctionCapsule!");
[self release];
}
return nil;
}
-(id)computeWith: (id)x
{
return [funcA computeWith: [funcB computeWith: x]];
}
-(void) dealloc
{
[funcA release];
[funcB release];
[super dealloc];
}
@end
// functions outside...
double my_f(double x)
{
return x+1.0;
}
double my_g(double x)
{
return x*x;
}
int main()
{
NSAutoreleasePool *pool = [[NSAutoreleasePool alloc] init];
id<FunctionCapsule> funcf = [FunctionCaps capsuleFor: my_f];
id<FunctionCapsule> funcg = [FunctionCaps capsuleFor: my_g];
id<FunctionCapsule> composed = [FunctionComposer
createCompositeFunctionWith: funcf and: funcg];
printf("g(2.0) = %lf\n", [[funcg computeWith: [NSNumber numberWithDouble: 2.0]] doubleValue]);
printf("f(2.0) = %lf\n", [[funcf computeWith: [NSNumber numberWithDouble: 2.0]] doubleValue]);
printf("f(g(2.0)) = %lf\n", [[composed computeWith: [NSNumber numberWithDouble: 2.0]] doubleValue]);
[pool release];
return 0;
}
[edit] Blocks
As above, we restrict ourselves to functions that take and return one object.
#include <Foundation/Foundation.h>
typedef id (^Function)(id);
// a commodity for "encapsulating" double f(double)
typedef double (*func_t)(double);
Function encapsulate(func_t f) {
return [[^(id x) { return [NSNumber numberWithDouble: f([x doubleValue])]; } copy] autorelease];
}
Function compose(Function a, Function b) {
return [[^(id x) { return a(b(x)); } copy] autorelease];
}
// functions outside...
double my_f(double x)
{
return x+1.0;
}
double my_g(double x)
{
return x*x;
}
int main()
{
NSAutoreleasePool *pool = [[NSAutoreleasePool alloc] init];
Function f = encapsulate(my_f);
Function g = encapsulate(my_g);
Function composed = compose(f, g);
printf("g(2.0) = %lf\n", [g([NSNumber numberWithDouble: 2.0]) doubleValue]);
printf("f(2.0) = %lf\n", [f([NSNumber numberWithDouble: 2.0]) doubleValue]);
printf("f(g(2.0)) = %lf\n", [composed([NSNumber numberWithDouble: 2.0]) doubleValue]);
[pool release];
return 0;
}
[edit] Objeck
bundle Default {
class Test {
@f : static : (Int) ~ Int;
@g : static : (Int) ~ Int;
function : Main(args : String[]) ~ Nil {
compose := Composer(F(Int) ~ Int, G(Int) ~ Int);
compose(13)->PrintLine();
}
function : F(a : Int) ~ Int {
return a + 14;
}
function : G(a : Int) ~ Int {
return a + 15;
}
function : Compose(x : Int) ~ Int {
return @f(@g(x));
}
function : Composer(f : (Int) ~ Int, g : (Int) ~ Int) ~ (Int) ~ Int {
@f := f;
@g := g;
return Compose(Int) ~ Int;
}
}
}
prints: 42
[edit] OCaml
let compose f g x = f (g x)
Example use:
# 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
[edit] Octave
function r = compose(f, g)
r = @(x) f(g(x));
endfunction
r = compose(@exp, @sin);
r(pi/3)
[edit] Oz
declare
fun {Compose F G}
fun {$ X}
{F {G X}}
end
end
SinAsin = {Compose Float.sin Float.asin}
in
{Show {SinAsin 0.5}}
[edit] PARI/GP
compose(f, g)={
x -> f(g(x))
};
compose(x->sin(x),x->cos(x)(1)
Usage note: In Pari/GP 2.4.3, this can be expressed more succinctly:
compose(sin,cos)(1)
[edit] Pascal
See Delphi
[edit] Perl
sub compose {
my ($f, $g) = @_;
sub {
$f -> ($g -> (@_))
};
}
use Math::Trig;
print compose(sub {sin $_[0]}, \&asin)->(0.5), "\n";
[edit] Perl 6
We'll define an infix compose operator from ∘, U+2218 RING OPERATOR.
sub infix:<∘> (&f, &g --> Block) {
-> \$args { f g |$args }
}
Example of composing a routine, an operator, and a lambda:
sub triple($n) { 3 * $n }
my $f = &triple ∘ &prefix:<-> ∘ { $^n + 2 };
say $f(5); # Prints "-21".
[edit] PHP
<?php
function compose($f, $g) {
return create_function('$x', "return $f($g(\$x));");
}
$trim_strlen = compose('strlen', 'trim');
echo $result = $trim_strlen(' Test '), "\n"; // prints 4
?>
<?php
function compose($f, $g) {
return function($x) use ($f, $g) { return $f($g($x)); };
}
$trim_strlen = compose('strlen', 'trim');
echo $result = $trim_strlen(' Test '), "\n"; // prints 4
?>
[edit] PicoLisp
(de compose (F G)
(curry (F G) (X)
(F (G X)) ) )
(def 'a (compose inc dec))
(def 'b (compose 'inc 'dec))
(def 'c (compose '((A) (inc A)) '((B) (dec B))))
: (a 7)
-> 7
: (b 7)
-> 7
: (c 7)
-> 7
[edit] PostScript
PostScript functions typically pops operand stack for argument, so calling two functions one after another naturally makes a compound function, and making a compound requires justdefing them:/square { dup mul } def
/plus1 { 1 add } def
/sqPlus1{ square plus1 } def
% if the task really demands we make a function called "compose", well
/compose { def } def % so now we can say:
/sqPlus1 { square plus1 } compose
[edit] Prolog
Works with SWI-Prolog and module lambda, written by Ulrich Neumerkel found there http://www.complang.tuwien.ac.at/ulrich/Prolog-inedit/lambda.pl
:- use_module(lambda).
compose(F,G, FG) :-
FG = \X^Z^(call(G,X,Y), call(F,Y,Z)).
Example of output :
?- compose(sin, asin, F), call(F, 0.5, Y). F = \_G4586^_G4589^ (call(asin,_G4586,_G4597),call(sin,_G4597,_G4589)), Y = 0.5.
[edit] PureBasic
;Declare how our function looks like
Prototype.i Func(Arg.i)
; Make a procedure that composes any functions of type "Func"
Procedure Compose(*a.Func,*b.Func, x)
ProcedureReturn *a(*b(x))
EndProcedure
; Just a procedure fitting "Func"
Procedure f(n)
ProcedureReturn 2*n
EndProcedure
; Yet another procedure fitting "Func"
Procedure g(n)
ProcedureReturn n+1
EndProcedure
;- Test it
X=Random(100)
Title$="With x="+Str(x)
Body$="Compose(f(),g(), x) ="+Str(Compose(@f(),@g(),X))
MessageRequester(Title$,Body$)
[edit] Purity
data compose = f => g => $f . $g
[edit] Python
compose = lambda f, g: lambda x: f( g(x) )
Example use:
>>> 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
>>>
[edit] Qi
Qi supports partial applications, but only when calling a function with one argument.
(define compose
F G -> (/. X
(F (G X))))
((compose (+ 1) (+ 2)) 3) \ (Outputs 6) \
Alternatively, it can be done like this:
(define compose F G X -> (F (G X)))
(((compose (+ 1)) (+ 2)) 3) \ (Outputs 6) \
[edit] R
compose <- function(f,g) function(x) { f(g(x)) }
r <- compose(sin, cos)
print(r(.5))
[edit] REBOL
rebol [
Title: "Functional Composition"
Author: oofoe
Date: 2009-12-06
URL: http://rosettacode.org/wiki/Functional_Composition
]
; "compose" means something else in REBOL, therefore I use a 'compose-functions name.
compose-functions: func [
{compose the given functions F and G}
f [any-function!]
g [any-function!]
] [
func [x] compose [(:f) (:g) x]
]
Functions "foo" and "bar" are used to prove that composition actually took place by attaching their signatures to the result.
foo: func [x] [reform ["foo:" x]]
bar: func [x] [reform ["bar:" x]]
foo-bar: compose-functions :foo :bar
print ["Composition of foo and bar:" mold foo-bar "test"]
sin-asin: compose-functions :sine :arcsine
print [crlf "Composition of sine and arcsine:" sin-asin 0.5]
Output:
Composition of foo and bar: "foo: bar: test" Composition of sine and arcsine: 0.5
[edit] REXX
compose: procedure; parse arg f,g,x; interpret 'return' f"("g'(' x "))"
exit /*control never gets here.*/
[edit] Ruby
This compose method gets passed two Method objects or Proc objects
def compose(f,g)
lambda {|x| f[g[x]]}
end
s = compose(Math.method(:sin), Math.method(:cos))
p s[0.5] # => 0.769196354841008
# verify
p Math.sin(Math.cos(0.5)) # => 0.769196354841008
[edit] Scala
def compose[A](f: A => A, g: A => A) = { x: A => f(g(x)) }
def add1(x: Int) = x+1
val add2 = compose(add1, add1)
We can achieve a more natural style by creating a container class for composable functions, which provides the compose method 'o':
class Composable[A](f: A => A) {
def o (g: A => A) = compose(f, g)
}
implicit def toComposable[A](f: A => A) = new Composable(f)
val add3 = (add1 _) o add2
> (add2 o add3)(37) res0: Int = 42
[edit] Scheme
(define (compose f g) (lambda (x) (f (g x))))
;; or:
(define ((compose f g) x) (f (g x)))
Example:
(display ((compose sin asin) 0.5))
(newline)
Output:
0.5
[edit] Slate
Function (method) composition is standard:
[| :x | x + 1] ** [| :x | x squared] applyTo: {3}
[edit] Smalltalk
| composer fg |
composer := [ :f :g | [ :x | f value: (g value: x) ] ].
fg := composer value: [ :x | x + 1 ]
value: [ :x | x * x ].
(fg value:3) displayNl.
[edit] Standard ML
This is already defined as the o operator in Standard ML.
fun compose (f, g) x = f (g x)
Example use:
- fun compose (f, g) x = f (g x);
val compose = fn : ('a -> 'b) * ('c -> 'a) -> 'c -> 'b
- val sin_asin = compose (Math.sin, Math.asin);
val sin_asin = fn : real -> real
- sin_asin 0.5;
val it = 0.5 : real
[edit] Tcl
This creates a compose procedure that returns an anonymous function term that should be expanded as part of application to its argument.
package require Tcl 8.5
namespace path {::tcl::mathfunc}
proc compose {f g} {
list apply [list {f g x} {{*}$f [{*}$g $x]}] $f $g]
}
set sin_asin [compose sin asin]
{*}$sin_asin 0.5 ;# ==> 0.5
{*}[compose abs int] -3.14 ;# ==> 3
[edit] UNIX Shell
Each function takes its argument from standard input, and puts its result to standard output. Then the composition of f and g is a shell pipeline, c() { g | f; }.
compose() {
eval "$1() { $3 | $2; }"
}
downvowel() { tr AEIOU aeiou; }
upcase() { tr a-z A-Z; }
compose c downvowel upcase
echo 'Cozy lummox gives smart squid who asks for job pen.' | c
# => CoZY LuMMoX GiVeS SMaRT SQuiD WHo aSKS FoR JoB PeN.
[edit] es
With shell pipelines:
fn compose f g {
result @ {$g | $f}
}
fn downvowel {tr AEIOU aeiou}
fn upcase {tr a-z A-Z}
fn-c = <={compose $fn-downvowel $fn-upcase}
echo 'Cozy lummox gives smart squid who asks for job pen.' | c
# => CoZY LuMMoX GiVeS SMaRT SQuiD WHo aSKS FoR JoB PeN.
With function arguments:
fn compose f g {
result @ x {result <={$f <={$g $x}}}
}
fn downvowel x {result `` '' {tr AEIOU aeiou <<< $x}}
fn upcase x {result `` '' {tr a-z A-Z <<< $x}}
fn-c = <={compose $fn-downvowel $fn-upcase}
echo <={c 'Cozy lummox gives smart squid who asks for job pen.'}
# => CoZY LuMMoX GiVeS SMaRT SQuiD WHo aSKS FoR JoB PeN.
[edit] Unlambda
``s`ksk
[edit] Ursala
Functional composition is a built in operation expressible as f+g for functions f and g, hence hardly worth defining. However, it could be defined without using the operator like this.
compose("f","g") "x" = "f" "g" "x"
test program:
#import nat
#cast %n
test = compose(successor,double) 3
output:
7
[edit] VBScript
I'm not convinced that this is really a 'closure'. It looks to me more like a cute trick with Eval().
Implementation
option explicit
class closure
private composition
sub compose( f1, f2 )
composition = f2 & "(" & f1 & "(p1))"
end sub
public default function apply( p1 )
apply = eval( composition )
end function
public property get formula
formula = composition
end property
end class
Invocation
dim c
set c = new closure
c.compose "ucase", "lcase"
wscript.echo c.formula
wscript.echo c("dog")
c.compose "log", "exp"
wscript.echo c.formula
wscript.echo c(12.3)
function inc( n )
inc = n + 1
end function
c.compose "inc", "inc"
wscript.echo c.formula
wscript.echo c(12.3)
function twice( n )
twice = n * 2
end function
c.compose "twice", "inc"
wscript.echo c.formula
wscript.echo c(12.3)
Output
lcase(ucase(p1)) dog exp(log(p1)) 12.3 inc(inc(p1)) 14.3 inc(twice(p1)) 25.6
Categories:
- Programming Tasks
- Higher-order functions
- ActionScript
- Ada
- Aikido
- ALGOL 68
- Argile
- AutoHotkey
- Bori
- Brat
- C
- C++
- C sharp
- Clojure
- Common Lisp
- D
- Delphi
- Dylan
- E
- Erlang
- Euphoria/Omit
- F Sharp
- Factor
- Fantom
- Forth
- GAP
- Go
- Groovy
- Haskell
- Icon
- Unicon
- J
- Java
- JavaScript
- Joy
- K
- Lua
- Mathematica
- Maxima
- Nemerle
- NewLISP
- Objective-C
- Objeck
- OCaml
- Octave
- Oz
- PARI/GP
- Pascal
- Perl
- Perl 6
- PHP
- PicoLisp
- PostScript
- Prolog
- PureBasic
- Purity
- Python
- Qi
- R
- REBOL
- REXX
- Ruby
- Scala
- Scheme
- Slate
- Smalltalk
- Standard ML
- Tcl
- UNIX Shell
- Es
- Unlambda
- Ursala
- TI-83 BASIC/Omit
- TI-89 BASIC/Omit
- Fortran/Omit
- VBScript
