Function composition

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.

ActionScript

ActionScript supports closures, making function composition very straightforward. <lang ActionScript>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)); }</lang>

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): <lang ada>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;</lang> Here is an implementation; <lang ada>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;</lang> The following is an example of use: <lang ada>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;</lang>

Output:

 5.00000E-01

Aikido

<lang 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

</lang>

ALGOL 68

Translation of: Python

Works with: ELLA ALGOL 68 version Any (with appropriate job cards) - tested with release 1.8.8d.fc9.i386

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 algol68>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

ALGOL 68 is a stack based language, and the following apparently does not violate it's scoping rules.

Works with: ALGOL 68 version Standard - Jan 1975 Boston SC allowed Partial Parametrization.

Works with: ALGOL 68G version Any - tested with release mk15-0.8b.fc9.i386

<lang algol68>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))</lang>

AppleScript

<lang applescript>-- Compose two functions where each function is -- a script object with a call(x) handler. on compose(f, g) script on call(x) f's call(g's call(x)) end call end script end compose

script sqrt on call(x) x ^ 0.5 end call end script

script twice on call(x) 2 * x end call end script

compose(sqrt, twice)'s call(32) -- Result: 8.0</lang>

Applesoft BASIC

<lang ApplesoftBasic>10 F$ = "SIN" 20 DEF FN A(P) = ATN(P/SQR(-P*P+1)) 30 G$ = "FN A" 40 GOSUB 100"COMPOSE 50 SA$ = E$

60 X = .5 : E$ = SA$ 70 GOSUB 200"EXEC 80 PRINT R 90 END

100 E$ = F$ + "(" + G$ + "(X))" : RETURN : REMCOMPOSE F$ G$

200 D$ = CHR$(4) : FI$ = "TEMPORARY.EX" : M$ = CHR$(13) 210 PRINT D$"OPEN"FI$M$D$"CLOSE"FI$M$D$"DELETE"FI$ 220 PRINT D$"OPEN"FI$M$D$"WRITE"FI$ 230 PRINT "CALL-998:CALL-958:R="E$":CONT" 240 PRINT D$"CLOSE"FI$M$D$"EXEC"FI$:CALL-998:END:RETURN</lang>

Argile

Only works for functions taking real and returning real (double precision, 64 bits)

Works with: Argile version 1.0.0

<lang Argile>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</lang>

AutoHotkey

contributed by Laszlo on the ahk forum <lang AutoHotkey>MsgBox % compose("sin","cos",1.5)

compose(f,g,x) { ; function composition

  Return %f%(%g%(x))

}</lang>

BBC BASIC

Works with: BBC BASIC for Windows

<lang bbcbasic> 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%</lang>

Output:

-2        1.41421356

Bori

<lang 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)); }</lang>

Output:

on Android phone

Brat

<lang 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</lang>

C

Only works for functions taking a double and returning a double: <lang c>#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;

}</lang>

C++

<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>

Works with: C++11

composing std::function

<lang cpp>#include <iostream>

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;

}</lang>

Works with: GCC

GCC's C++ library has a built-in compose function

<lang cpp>#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;

}</lang>

C#

<lang csharp>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)); };
       }
   }

}</lang>

Clojure

Function composition is built in to Clojure. Simply call the comp function.

A manual implementation could look like this: <lang clojure>(defn compose [f g]

 (fn [x]
   (f (g x))))

Example

(def inc2 (compose inc inc)) (println (inc2 5)) ; prints 7</lang>

CoffeeScript

<lang coffeescript> compose = ( f, g ) -> ( x ) -> f g x

Example

add2 = ( x ) -> x + 2 mul2 = ( x ) -> x * 2

mulFirst = compose add2, mul2 addFirst = compose mul2, add2 multiple = compose mul2, compose add2, mul2

console.log "add2 2 #=> #{ add2 2 }" console.log "mul2 2 #=> #{ mul2 2 }" console.log "mulFirst 2 #=> #{ mulFirst 2 }" console.log "addFirst 2 #=> #{ addFirst 2 }" console.log "multiple 2 #=> #{ multiple 2 }" </lang>

Output:

add2 2 #=> 4
mul2 2 #=> 4
mulFirst 2 #=> 6
addFirst 2 #=> 8
multiple 2 #=> 12

Or, extending the Function prototype.

<lang coffeescript> Function::of = (f) -> (args...) => @ f args...

Example

add2 = (x) -> x + 2 mul2 = (x) -> x * 2

mulFirst = add2.of mul2 addFirst = mul2.of add2 multiple = mul2.of add2.of mul2

console.log "add2 2 #=> #{ add2 2 }" console.log "mul2 2 #=> #{ mul2 2 }" console.log "mulFirst 2 #=> #{ mulFirst 2 }" console.log "addFirst 2 #=> #{ addFirst 2 }" console.log "multiple 2 #=> #{ multiple 2 }" </lang>

Output is identical.

Common Lisp

compose returns a function that closes on the lexical variables f and g. <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>

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.

<lang lisp>(defun compose (f g)

 (eval `(lambda (x) (funcall ',f (funcall ',g x))))</lang>

In this last example, a macro is used to compose any number of single parameter functions. <lang lisp>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))))</lang> 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>

D

<lang 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));

}</lang>

Output:

115
625

Delphi

Anonymous methods were introduced in Delphi 2009, so next code works with Delphi 2009 and above:

<lang Delphi>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.</lang>

Déjà Vu

It is already defined in the standard library as $.

<lang dejavu>compose f g: labda: f g</lang>

Dylan

<lang dylan>define method compose(f,g)

  method(x) f(g(x)) end

end;</lang>

Ela

It is already defined in standard prelude as (<<) operator.

<lang ela>let compose f g x = f (g x)</lang>

E

<lang e>def compose(f, g) {

 return fn x { return f(g(x)) }

}</lang>

Ela

It is already defined in standard prelude as (<<) operator.

<lang ela>compose f g x = f (g x)</lang>

Emacs Lisp

A lambda form can be constructed with the desired f and g inserted. The result is simply a list. A list starting with lambda is a function.

<lang Lisp>(defun compose (f g)

 `(lambda (x) (,f (,g x))))

(let ((func (compose '1+ '1+)))

 (funcall func 5))

=> 7</lang>

A similar thing can be done with a macro like the following. It differs in that the arguments should be unquoted symbols, and if they're expressions then they're evaluated on every call to the resulting lambda.

<lang Lisp>(defmacro compose (f g)

 `(lambda (x) (,f (,g x))))

(let ((func (compose 1+ 1+)))

 (funcall func 5))

=> 7</lang>

Another possibility is the cl.el lexical-let to hold f and g for use in a new lambda.

<lang Lisp>(eval-when-compile (require 'cl)) ;; for `lexical-let' macro (defun compose (f g)

 (lexical-let ((f f)
               (g g))
   (lambda (x)
     (funcall f (funcall g x)))))

(let ((func (compose '1+ '1+)))

 (funcall func 5))

=> 7</lang>

Erlang

<lang 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).</lang>

Using them: <lang erlang>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</lang>

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): <lang fsharp>> let compose f g x = f (g x);;

val compose : ('a -> 'b) -> ('c -> 'a) -> 'c -> 'b</lang> Usage: <lang fsharp>> let sin_asin = compose sin asin;;

val sin_asin : (float -> float)

> sin_asin 0.5;; val it : float = 0.5</lang>

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. <lang factor>( scratchpad ) [ 2 * ] [ 1 + ] compose . [ 2 * 1 + ] ( scratchpad ) 4 [ 2 * ] [ 1 + ] compose call . 9</lang>

Fantom

<lang 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)}")
 }

} </lang>

Forth

<lang forth>: compose ( xt1 xt2 -- xt3 )

 >r >r :noname
    r> compile,
    r> compile,
    postpone ;

' 2* ' 1+ compose ( xt ) 3 swap execute . \ 7</lang>

FunL

<lang funl>import math.{sin, asin}

def compose( f, g ) = x -> f( g(x) )

sin_asin = compose( sin, asin )

println( sin_asin(0.5) )</lang>

Output:

0.5

GAP

<lang gap>Composition := function(f, g)

   return x -> f(g(x));

end;

h := Composition(x -> x+1, x -> x*x); h(5);

26</lang>

Go

<lang 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))
   }

}</lang> Example use: <lang go>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))

}</lang>

Output:

0.5

Groovy

Solution: <lang groovy>def compose = { f, g -> { x -> f(g(x)) } }</lang>

Test program: <lang groovy>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)</lang>

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

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>

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. <lang Icon> 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</lang>

See Icon and Unicon Introduction:Minor Differences for more information

<lang Unicon>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</lang>

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

J

Solution: <lang j>compose =: @</lang>

Example: <lang j>f compose g</lang>

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:

Example use: <lang j> (f, g, h) 1p1 1 2 1</lang>

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.

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>

Works with: Java version 8+

<lang java>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"
   }

}</lang>

JavaScript

<lang javascript>function compose(f, g) {

 return function(x) {
   return f(g(x));
 };

}</lang> Example: <lang javascript>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>

jq

The equivalent in jq of a function with one argument is a 0-arity filter. For example, in jq, exp is the exponential function and can be evaluated like so: 0.5 | exp.

We therefore illustrate here how a function that composes two 0-arity filters can be written: <lang jq>

apply g first and then f

def compose(f; g): g | f; </lang> Example: 0.5 | compose(asin, sin)

In practice, "compose" is rarely used since, given two 0-arity filters, f and g, the expression "g|f" is a first-class citizen. For example, it can be passed as an argument to other functions.

Julia

<lang julia>compose(f::Function, g::Function) = x->f(g(x))</lang>

Output:

julia> compose(asin,sin)(0.5)
0.5

K

Functions are automatically curried in K if called with missing arguments. <lang k>compose: {x@y@z}</lang> Example: <lang k> sin_asin: compose[_sin;_asin]

 sin_asin 0.5

0.5</lang>

LFE

<lang lisp> (defun compose (f g)

 (lambda (x)
   (funcall f
     (funcall g x))))

(defun compose (funcs)

 (lists:foldl #'compose/2
              (lambda (x) x)
              funcs))

(defun check ()

 (let* ((sin-asin (compose #'math:sin/1 #'math:asin/1))
        (expected (math:sin (math:asin 0.5)))
        (compose-result (funcall sin-asin 0.5)))
   (io:format '"Expected answer: ~p~n" (list expected))
   (io:format '"Answer with compose: ~p~n" (list compose-result))))

</lang>

If you pasted those into the LFE REPL, you can do the following: <lang lisp> > (funcall (compose #'math:sin/1 #'math:asin/1)

          0.5)

0.49999999999999994 > (funcall (compose `(,#'math:sin/1

                     ,#'math:asin/1
                     ,(lambda (x) (+ x 1))))
          0.5)

1.5 > (check) Expected answer: 0.49999999999999994 Answer with compose: 0.49999999999999994 ok > </lang>

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. <lang LOLCODE>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</lang>

Lua

<lang lua>function compose(f, g) return function(...) return f(g(...)) end end</lang>

Mathematica

Built-in function that takes any amount of function-arguments: <lang Mathematica>Composition[f, g][x] Composition[f, g, h, i][x]</lang> gives back: <lang Mathematica>f[g[x]] f[g[h[i[x]]]]</lang> Custom function: <lang Mathematica>compose[f_, g_][x_] := f[g[x]] compose[Sin, Cos][r]</lang> gives back: <lang Mathematica>Sin[Cos[r]]</lang> Composition can be done in more than 1 way: <lang Mathematica>Composition[f,g,h][x] f@g@h@x x//h//g//f</lang> all give back: <lang Mathematica>f[g[h[x]]]</lang> The built-in function has a couple of automatic simplifications: <lang Mathematica>Composition[f, Identity, g] Composition[f, InverseFunction[f], h][x]</lang> becomes: <lang Mathematica>f[g[x]] h[x]</lang>

Maxima

<lang 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))));</lang>

Nemerle

<lang 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));
   }

}</lang>

NewLISP

<lang 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 </lang>

Nim

<lang nim>import future

proc compose[A,B,C](f: A -> B, g: B -> C): A -> C = (x: A) => f(g(x))

proc plustwo(x: int): int = x + 2 proc minustwo(x: int): int = x - 2

var plusminustwo = compose(plustwo, minustwo) echo plusminustwo(10)</lang>

Objective-C

Works with: Mac OS X version 10.6+

We restrict ourselves to functions that take and return one object.

<lang objc>#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 @(f([x doubleValue])); };

}

Function compose(Function a, Function b) {

 return ^(id x) { return a(b(x)); };

}

// functions outside... double my_f(double x) {

 return x+1.0;

}

double my_g(double x) {

 return x*x;

}

int main() {

 @autoreleasepool {

   Function f = encapsulate(my_f);
   Function g = encapsulate(my_g);
 
   Function composed = compose(f, g);
 
   printf("g(2.0) = %lf\n", [g(@2.0) doubleValue]);
   printf("f(2.0) = %lf\n", [f(@2.0) doubleValue]);
   printf("f(g(2.0)) = %lf\n", [composed(@2.0) doubleValue]);

 }
 return 0;

}</lang>

Objeck

<lang 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;
   }
 }

} </lang> prints: 42

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>

Octave

<lang octave>function r = compose(f, g)

 r = @(x) f(g(x));

endfunction

r = compose(@exp, @sin); r(pi/3)</lang>

Oforth

Oforth uses RPN notation. Function composition of f and g is just calling : <lang Oforth>g f</lang> If a block is needed, a compose function can be implemented : <lang Oforth>func: compose(f, g) { #[ g perform f perform ] }</lang> Usage : <lang Oforth>1.2 compose(#asin, #sin) perform</lang>

Order

Order supplies the built-in function 8compose for this purpose. However, a manual implementation might be: <lang c>#include <order/interpreter.h>

define ORDER_PP_DEF_8comp ORDER_PP_FN( \

8fn(8F, 8G, 8fn(8X, 8ap(8F, 8ap(8G, 8X)))) )</lang> Interpreter limitations mean that local variables containing functions must be called with the 8ap operator, but the functions themselves are still first-class values.

Oz

<lang oz>declare

 fun {Compose F G}
    fun {$ X}
       {F {G X}}
    end
 end

 SinAsin = {Compose Float.sin Float.asin}

in

 {Show {SinAsin 0.5}}</lang>

PARI/GP

Works with: PARI/GP version 2.4.2 and above

<lang parigp>compose(f, g)={

 x -> f(g(x))

};

compose(x->sin(x),x->cos(x)(1)</lang>

Usage note: In Pari/GP 2.4.3, this can be expressed more succinctly: <lang parigp>compose(sin,cos)(1)</lang>

Pascal

See Delphi

Perl

<lang perl>sub compose {

   my ($f, $g) = @_;

   sub {
       $f -> ($g -> (@_))
   };

}

use Math::Trig; print compose(sub {sin $_[0]}, \&asin)->(0.5), "\n";</lang>

Perl 6

Works with: rakudo

We'll define an infix compose operator from ∘, U+2218 RING OPERATOR. <lang perl6>sub infix:<∘> (&f, &g --> Block) {

   -> |args { f g |args }

}</lang>

Example of composing a routine, an operator, and a lambda:

<lang perl6>sub triple($n) { 3 * $n } my &f = &triple ∘ &prefix:<-> ∘ { $^n + 2 }; say &f(5); # Prints "-21".</lang>

PHP

Works with: PHP version 5.3+

<lang 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 ?></lang>

Works with: PHP version pre-5.3 and 5.3+

works with regular functions as well as functions created by create_function() <lang php><?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 ?></lang>

PicoLisp

<lang PicoLisp>(de compose (F G)

  (curry (F G) (X)
     (F (G X)) ) )</lang>

<lang PicoLisp>(def 'a (compose inc dec)) (def 'b (compose 'inc 'dec)) (def 'c (compose '((A) (inc A)) '((B) (dec B))))</lang> <lang PicoLisp>: (a 7) -> 7

(b 7)

-> 7

(c 7)

-> 7</lang>

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 just defing them:<lang PostScript>/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</lang>

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 <lang Prolog>:- use_module(lambda).

compose(F,G, FG) :- FG = \X^Z^(call(G,X,Y), call(F,Y,Z)). </lang>

Output:

 ?- compose(sin, asin, F), call(F, 0.5, Y).
F = \_G4586^_G4589^ (call(asin,_G4586,_G4597),call(sin,_G4597,_G4589)),
Y = 0.5.

PureBasic

<lang 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$,Body$)</lang>

Purity

<lang Purity> data compose = f => g => $f . $g </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>

Qi

Qi supports partial applications, but only when calling a function with one argument. <lang qi> (define compose

 F G -> (/. X
            (F (G X))))

((compose (+ 1) (+ 2)) 3) \ (Outputs 6) \ </lang>

Alternatively, it can be done like this:

<lang qi> (define compose F G X -> (F (G X)))

(((compose (+ 1)) (+ 2)) 3) \ (Outputs 6) \ </lang>

R

<lang R>compose <- function(f,g) function(x) { f(g(x)) } r <- compose(sin, cos) print(r(.5))</lang>

Racket

<lang racket> (define (compose f g)

 (lambda (x) (f (g x))))

</lang>

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.)

REBOL

<lang 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]

]</lang>

Functions "foo" and "bar" are used to prove that composition actually took place by attaching their signatures to the result.

<lang REBOL>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]</lang>

Output:

Composition of foo and bar: "foo: bar: test"

Composition of sine and arcsine: 0.5

REXX

<lang 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.*/</lang>

Ruby

This compose method gets passed two Method objects or Proc objects <lang ruby>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</lang>

Scala

<lang 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)</lang>

We can achieve a more natural style by creating a container class for composable functions, which provides the compose method 'o':

<lang scala>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</lang>

> (add2 o add3)(37)
res0: Int = 42

Scheme

<lang scheme>(define (compose f g) (lambda (x) (f (g x))))

or

(define ((compose f g) x) (f (g x))) </lang> Example: <lang scheme> (display ((compose sin asin) 0.5)) (newline)</lang>

Output:

Sidef

<lang ruby>func compose(f, g) {

   func(x) { f(g(x)) }.copy;

}; var fg = compose(func(x){Math.sin(x)}, func(x){Math.cos(x)}); say fg(0.5); # => 0.7691963548410084218525147580510688880995</lang>

Slate

Function (method) composition is standard: <lang slate>[| :x | x + 1] ** [| :x | x squared] applyTo: {3}</lang>

Smalltalk

              value: [ :x | x * x ].

(fg value:3) displayNl.</lang>

Standard ML

This is already defined as the o operator in Standard ML. <lang sml>fun compose (f, g) x = f (g x)</lang> Example use: <lang sml>- 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</lang>

Swift

<lang swift>func compose<A,B,C>(f: (B) -> C, g: (A) -> B) -> (A) -> C {

 return { f(g($0)) }

}

let sin_asin = compose(sin, asin) println(sin_asin(0.5))</lang>

Output:

0.5

Tcl

Works with: Tcl version 8.5

This creates a compose procedure that returns an anonymous function term that should be expanded as part of application to its argument. <lang tcl>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</lang>

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; }.

Works with: Bourne Shell

<lang bash>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.</lang>

Works with: Bourne Again SHell

This solution uses no external tools, just Bash itself.

compose a new function consisting of the application of 2 unary functions

            compose () { f="$1"; g="$2"; x="$3"; "$f" "$("$g" "$x")";}

chartolowervowel()

Usage: chartolowervowel "A" --> "a"

Based on a to_upper script in Chris F. A. Johnson's book Pro Bash Programming Ch7. String Manipulation
(with minor tweaks to use local variables and return the value of the converted character
http://cfajohnson.com/books/cfajohnson/pbp/
highly recommended I have a copy and have bought another for a friend

{

  local LWR="";

case $1 in

                         A*) _LWR=a ;;

B*) _LWR=b ;;
C*) _LWR=c ;;
D*) _LWR=d ;;

E*) _LWR=e ;;

F*) _LWR=f ;;
G*) _LWR=g ;;
H*) _LWR=h ;;

I*) _LWR=i ;;

J*) _LWR=j ;;
K*) _LWR=k ;;
L*) _LWR=L ;;
M*) _LWR=m ;;
N*) _LWR=n ;;

O*) _LWR=o ;;

P*) _LWR=p ;;
Q*) _LWR=q ;;
R*) _LWR=r ;;
S*) _LWR=s ;;
T*) _LWR=t ;;

U*) _LWR=u ;;

V*) _LWR=v ;;
W*) _LWR=w ;;
X*) _LWR=x ;;
Y*) _LWR=y ;;
Z*) _LWR=z ;;

*) _LWR=${1%${1#?}} ;; esac; echo "$_LWR";

strdownvowel()

Usage: strdownvowel "STRING" --> "STRiNG"

Based on an upword script in Chris F. A. Johnson's book Pro Bash Programming Ch7. String Manipulation
(with minor tweaks to use local variables and return the value of the converted string
http://cfajohnson.com/books/cfajohnson/pbp/
highly recommended I have a copy and have bought another for a friend

{

 local _DWNWORD=""
 local word="$1"
 while [ -n "$word" ] ## loop until nothing is left in $word
 do
    chartolowervowel "$word" >> /dev/null
    _DWNWORD=$_DWNWORD$_LWR
    word=${word#?}  ## remove the first character from $word

 done
 Echo "$_DWNWORD"

}

chartoupper()

Usage: chartoupper "s" --> "S"

From Chris F. A. Johnson's book Pro Bash Programming Ch7. String Manipulation
(with minor tweaks to use local variables and return the value of the converted character
http://cfajohnson.com/books/cfajohnson/pbp/
highly recommended I have a copy and have bought another for a friend

{ 
    local UPR="";

      case $1  in
                         a*) _UPR=A ;;
                         b*) _UPR=B ;;

c*) _UPR=C ;; d*) _UPR=D ;; e*) _UPR=E ;; f*) _UPR=F ;; g*) _UPR=G ;; h*) _UPR=H ;; i*) _UPR=I ;; j*) _UPR=J ;; k*) _UPR=K ;; l*) _UPR=L ;; m*) _UPR=M ;; n*) _UPR=N ;; o*) _UPR=O ;; p*) _UPR=P ;; q*) _UPR=Q ;; r*) _UPR=R ;; s*) _UPR=S ;; t*) _UPR=T ;; u*) _UPR=U ;; v*) _UPR=V ;; w*) _UPR=W ;; x*) _UPR=X ;; y*) _UPR=Y ;; z*) _UPR=Z ;; *) _UPR=${1%${1#?}} ;; esac; echo "$_UPR"; }

strupcase()

Usage: strupcase "string" --> "STRING"

Based on an upword script in Chris F. A. Johnson's book Pro Bash Programming Ch7. String Manipulation
(with minor tweaks to use local variables and return the value of the converted string
http://cfajohnson.com/books/cfajohnson/pbp/
highly recommended I have a copy and have bought another for a friend

{

 local _UPWORD=""
 local word="$1"
 while [ -n "$word" ] ## loop until nothing is left in $word
 do
    chartoupper "$word" >> /dev/null
    _UPWORD=$_UPWORD$_UPR
    word=${word#?}  ## remove the first character from $word

 done
 Echo "$_UPWORD"

}

compose strdownvowel strupcase "Cozy lummox gives smart squid who asks for job pen."

--> CoZY LuMMoX GiVeS SMaRT SQuiD WHo aSKS FoR JoB PeN.</lang>

es

With shell pipelines:

<lang es>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.</lang>

With function arguments:

<lang es>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.</lang>

Unlambda

``s`ksk

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. <lang Ursala>compose("f","g") "x" = "f" "g" "x"</lang> test program: <lang Ursala>#import nat

cast %n

test = compose(successor,double) 3</lang>

Output:

VBScript

I'm not convinced that this is really a 'closure'. It looks to me more like a cute trick with Eval().

Implementation <lang vb> 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 </lang>

Invocation <lang vb> 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) </lang>

Output:

lcase(ucase(p1))
dog
exp(log(p1))
12.3
inc(inc(p1))
14.3
inc(twice(p1))
25.6

Wortel

The @ operator applied to a array literal will compose the functions in the array and ^ with a group literal will do the same, but also quotes operators. <lang wortel>! @[f g] x ; f(g(x))</lang> <lang wortel>! ^(f g) x ; f(g(x))</lang> Defining the compose function <lang wortel>@var compose &[f g] &x !f!g x</lang>

zkl

<lang zkl>Utils.Helpers.fcomp('+(1),'*(2))(5) //-->11</lang> Which is implemented with a closure (.fp), T is a read only list and L(x).apply(L(g,f)) --> L(g(f(x)):<lang zkl>fcn fcomp(f,g,h,etc){

  fcn(x,hgf){ T(x).apply(hgf)[0] }.fp1(vm.arglist.reverse()); }</lang>