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
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] BBC BASIC
REM Create some functions for testing:
DEF FNsqr(a) = SQR(a)
DEF FNabs(a) = ABS(a)
REM Create the function composition:
SqrAbs = FNcompose(FNsqr(), FNabs())
REM Test calling the composition:
x = -2 : PRINT ; x, FN(SqrAbs)(x)
END
DEF FNcompose(RETURN f%, RETURN g%)
LOCAL f$, p% : DIM p% 7 : p%!0 = f% : p%!4 = g%
f$ = "(x)=" + CHR$&A4 + "(&" + STR$~p% + ")(" + \
\ CHR$&A4 + "(&" + STR$~(p%+4) + ")(x))"
DIM p% LEN(f$) + 4 : $(p%+4) = f$ : !p% = p%+4
= p%
Output:
-2 1.41421356
[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))))
In this last example, a macro is used to compose any number of single parameter functions.
CL-USER> (defmacro compose (fn-name &rest args)
(labels ((rec1 (args)
(if (= (length args) 1)
`(funcall ,@args x)
`(funcall ,(first args) ,(rec1 (rest args))))))
`(defun ,fn-name (x) ,(rec1 args))))
Because this macro expands into a defun form, the function returned by compose is in the function namespace and the use of funcall is not necessary.
CL-USER> (compose f #'ceiling #'sin #'sqrt) F CL-USER> (compose g #'1+ #'abs #'cos) G CL-USER> (compose h #'f #'g) H CL-USER> (values (f pi) (g pi) (h pi)) 1 2.0L0 1 CL-USER>
[edit] D
import std.stdio;
T delegate(S) compose(T, U, S)(in T delegate(U) f,
in U delegate(S) g) {
return s => f(g(s));
}
void main() {
writeln(compose((int x) => x + 15, (int x) => x ^^ 2)(10));
writeln(compose((int x) => x ^^ 2, (int x) => x + 15)(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] Ela
It is already defined in standard prelude as (<<) operator.
let compose f g x = f (g x)
[edit] E
def compose(f, g) {
return fn x { return f(g(x)) }
}
[edit] Ela
It is already defined in standard prelude as (<<) operator.
compose f g x = 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.
Tentative new example:
f=: >.@(1&o.)@%:
g=: 1&+@|@(2&o.)
h=: f@g
Example use:
(f, g, h) 1p1
1 2 1
Note: 1&o. is sine (mnemonic: sine is an odd circular function), 2&o. is cosine (cosine is an even circular function), %: is square root, >. is ceiling, | is absolute value and 1&+ adds 1.
[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"
}
}
import java.util.function.Function;
public class Compose {
public static <A,B,C> Function<A,C> compose(Function<B,C> f, Function<A,B> g) {
return x -> f.apply(g.apply(x));
}
public static void main(String[] args) {
Function<Double,Double> sin_asin = compose(Math::sin, Math::asin);
System.out.println(sin_asin.apply(0.5)); // prints "0.5"
}
}
[edit] JavaScript
function compose(f, g) {
return function(x) {
return f(g(x));
};
}
Example:
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] LOLCODE
LOLCODE supports first-class functions only insofar as they may be stored in variables and returned from other functions. Alas, given the current lack of support for either lambdas or closures, function composition can only be reasonably simulated with the help of a few global variables.
HAI 1.3
I HAS A fx, I HAS A gx
HOW IZ I composin YR f AN YR g
fx R f, gx R g
HOW IZ I composed YR x
FOUND YR I IZ fx YR I IZ gx YR x MKAY MKAY
IF U SAY SO
FOUND YR composed
IF U SAY SO
HOW IZ I incin YR num
FOUND YR SUM OF num AN 1
IF U SAY SO
HOW IZ I sqrin YR num
FOUND YR PRODUKT OF num AN num
IF U SAY SO
I HAS A incsqrin ITZ I IZ composin YR incin AN YR sqrin MKAY
VISIBLE I IZ incsqrin YR 10 MKAY BTW, prints 101
I HAS A sqrincin ITZ I IZ composin YR sqrin AN YR incin MKAY
VISIBLE I IZ sqrincin YR 10 MKAY BTW, prints 121
KTHXBYE
[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)))*/
/* An implementation, to show a use of buildq */
compose(f, g) := buildq([f, g], lambda([x], f(g(x))));
[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] Order
Order supplies the built-in function 8compose for this purpose. However, a manual implementation might be:
#include <order/interpreter.h>
#define ORDER_PP_DEF_8comp ORDER_PP_FN( \
8fn(8F, 8G, 8fn(8X, 8ap(8F, 8ap(8G, 8X)))) )
Interpreter limitations mean that local variables containing functions must be called with the 8ap operator, but the functions themselves are still first-class values.
[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, $g) {
return function($x) use ($f, $g) { return $f($g($x)); };
}
$trim_strlen = compose('strlen', 'trim');
echo $result = $trim_strlen(' Test '), "\n"; // prints 4
?>
works with regular functions as well as functions created by create_function()
<?php
function compose($f, $g) {
return create_function('$x', 'return '.var_export($f,true).'('.var_export($g,true).'($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] Racket
(define (compose f g)
(lambda (x) (f (g x))))
Also available as a compose1 builtin, and a more general compose where one function can produce multiple arguments that are sent the the next function in the chain. (Note however that this is rarely desired.)
[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, but this was added just in case.*/
[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
- Programming Tasks
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