Function composition

Task

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.

Example

 compose(f, g) (x) = f(g(x))

Reference: Function composition

Hint: In some languages, implementing compose correctly requires creating a closure.

11l

Translation of: Python

V compose = (f, g) -> (x -> @f(@g(x)))
V sin_asin = compose(x -> sin(x), x -> asin(x))
print(sin_asin(0.5))

Output:

0.5

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));
}

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;

Output:

 5.00000E-01

Agda

compose : ∀ {a b c} {A : Set a} {B : Set b} {C : Set c}
        → (B → C)
        → (A → B)
        → A → C
compose f g x = f (g x)

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

Aime

compose_i(,,)
{
    ($0)(($1)($2));
}

compose(,)
{
    compose_i.apply($0, $1);
}

double(real a)
{
    2 * a;
}

square(real a)
{
    a * a;
}

main(void)
{
    o_(compose(square, double)(40), "\n");

    0;
}

Output:

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.

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.

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

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))

Amazing Hopper

VERSION 1:

#defn   Compose(_FX_,_FY_)  _FX_,_FY_

main:
  0.5,Compose(sin,arcsin)
  "\n", print
{0}return

Output:

$ hopper3 basica/compose1.hop
0.500000

VERSION 2:

#define-a   «(_X_)   _X_ )
#define     Compose(_FX_,_FY_)  _FC_(_FX_,_FY_,
#define     _FC_(_X_,_Y_,*)  *,_X_,_Y_  

main:
  Compose(sin,arcsin)«( 0.5)
  "\n", print
{0}return

Output:

$ hopper3 basica/compose2.hop
0.500000

VERSION 3:

#define     «(_X_)   _X_ )
#define     Compose(_FX_,_FY_)  _FC_(_FX_,_FY_,
#define     _FC_(_X_,_Y_,*)  *,_X_,_Y_  

main:
  Compose(sin,arcsin)«( 0.5, mul by '2' )
  "\n", print
{0}return

Output:

$ hopper3 basica/compose2.hop
1.000000

The power of macro-substitution, by Hopper!

AntLang

/Apply g to exactly one argument
compose1: {f: x; g: y; {f[g[x]]}}
/Extra: apply to multiple arguments
compose: {f: x; g: y; {f[g apply args]}}

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

A limitation of AppleScript's handlers (functions), which can be seen in the example above, is that they are not in themselves composable first class objects, and have to be lifted into script objects before they can be composed or passed as arguments.

We can generalise this lifting with an mReturn or mInject function, which injects a handler into a script for us. This allows use to write higher-order composition and pipelining functions which take a pair (or sequence of) ordinary handlers as arguments, and return a first class script object. (We can also use mReturn to equip AppleScript with map and fold functions which take a list and an ordinary handler as arguments).

------------ COMPOSITION OF A LIST OF FUNCTIONS ----------

-- compose :: [(a -> a)] -> (a -> a)
on compose(fs)
    script
        on |λ|(x)
            script go
                on |λ|(a, f)
                    mReturn(f)'s |λ|(a)
                end |λ|
            end script
            
            foldr(go, x, fs)
        end |λ|
    end script
end compose


--------------------------- TEST -------------------------
on root(x)
    x ^ 0.5
end root

on succ(x)
    x + 1
end succ

on half(x)
    x / 2
end half

on run
    tell compose({half, succ, root})
        
        |λ|(5)
        
    end tell
    --> 1.61803398875
end run


-------------------- GENERIC FUNCTIONS -------------------

-- foldr :: (a -> b -> a) -> a -> [b] -> a
on foldr(f, startValue, xs)
    tell mReturn(f)
        set v to startValue
        set lng to length of xs
        repeat with i from lng to 1 by -1
            set v to |λ|(v, item i of xs, i, xs)
        end repeat
        return v
    end tell
end foldr

-- Lift 2nd class handler function into 1st class script wrapper 
-- mReturn :: Handler -> Script
on mReturn(f)
    if class of f is script then
        f
    else
        script
            property |λ| : f
        end script
    end if
end mReturn

Output:

1.61803398875

Applesoft BASIC

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

Argile

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

Works with: Argile version 1.0.0

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

Arturo

compose: function [f,g] ->
    return function [x].import:[f,g][
        call f @[call g @[x]]
    ]

splitupper: compose 'split 'upper

print call 'splitupper ["done"]

Output:

D O N E

ATS

If I may state in greater detail what the task requires, it is this:

That compose should return a new function, which will exist independently of compose once created. A person should never have to call compose merely to get the result of the composed computation.

Thus it is probably impossible, for instance, to really satisfy the requirement in standard C, if the result of composition is to be called like an ordinary function. However, the C solution shows it is possible, if the notion of a function is expanded to include structures requiring more than just a plain C function call. Also, there is at least one platform-dependent library for creating a "true" closure in C.

In ATS we have closures, but of more than one kind.

(*
   The task:

      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,
      (let's call the argument x), which works like applying function
      f to the result of applying function g to x.

   In ATS, we have to choose whether to use non-linear closures
   (cloref) or linear closures (cloptr). In the latter case, we also
   have to choose between closures allocated with malloc (or similar)
   and closures allocated on the stack.

   For simplicity, we will use non-linear closures and assume there is
   a garbage collector, or that the memory allocated for the closures
   can be allowed to leak. (This is often the case in a program that
   does not run continuously.)
*)

#include "share/atspre_staload.hats"

(* The following is actually a *template function*, rather than a
   function proper. It is expanded during template processing. *)

fn {t1, t2, t3 : t@ype}
compose (f : t2 -<cloref1> t3,
         g : t1 -<cloref1> t2) : t1 -<cloref1> t3 =
  lam x => f (g (x))


implement
main0 () =
  let
    val one_hundred = 100.0
    val char_zero = '0'
    val f = (lam y =<cloref1> add_double_int (one_hundred, y))
    val g = (lam x =<cloref1> char2i x - char2i char_zero)
    val z = compose (f, g) ('5')
    val fg = compose (f, g)
    val w = fg ('7')
  in
    println! (z : double);
    println! (w : double)
  end

Output:

$ patscc -O2 -DATS_MEMALLOC_GCBDW function_composition.dats -lgc && ./a.out
105.000000
107.000000

Incidentally, it is possible to instantiate the template function and obtain a true function that does the composition. What the template does for us is give us compile-time type polymorphism. In the following, the template is instantiated as a true function for specific types:

#include "share/atspre_staload.hats"

fn {t1, t2, t3 : t@ype}
compose (f : t2 -<cloref1> t3,
         g : t1 -<cloref1> t2) : t1 -<cloref1> t3 =
  lam x => f (g (x))

fn
compose_char2int2double
          (f : int -<cloref1> double,
           g : char -<cloref1> int) :
    char -<cloref1> double =
  compose<char, int, double> (f, g)

implement
main0 () =
  let
    val one_hundred = 100.0
    val char_zero = '0'
    val f = (lam y =<cloref1> add_double_int (one_hundred, y))
    val g = (lam x =<cloref1> char2i x - char2i char_zero)
    val z = compose_char2int2double (f, g) ('5')
    val fg = compose_char2int2double (f, g)
    val w = fg ('7')
  in
    println! (z : double);
    println! (w : double)
  end

Output:

$ patscc -O2 -DATS_MEMALLOC_GCBDW function_composition_2.dats -lgc && ./a.out
105.000000
107.000000

One could even make the composition procedures themselves be closures:

#include "share/atspre_staload.hats"

fn {t1, t2, t3 : t@ype}
compose (f : t2 -<cloref1> t3,
         g : t1 -<cloref1> t2) :<cloref1>
    t1 -<cloref1> t3 =
  lam x => f (g (x))

fn
compose_char2int2double
          (f : int -<cloref1> double,
           g : char -<cloref1> int) :<cloref1>
    char -<cloref1> double =
  compose<char, int, double> (f, g)

implement
main0 () =
  let
    val one_hundred = 100.0
    val char_zero = '0'
    val f = (lam y =<cloref1> add_double_int (one_hundred, y))
    val g = (lam x =<cloref1> char2i x - char2i char_zero)
    val z = compose_char2int2double (f, g) ('5')
    val fg = compose_char2int2double (f, g)
    val w = fg ('7')
  in
    println! (z : double);
    println! (w : double)
  end

Output:

$ patscc -O2 -DATS_MEMALLOC_GCBDW function_composition_3.dats -lgc && ./a.out
105.000000
107.000000

AutoHotkey

contributed by Laszlo on the ahk forum

MsgBox % compose("sin","cos",1.5)

compose(f,g,x) { ; function composition
   Return %f%(%g%(x))
}

BBC BASIC

Works with: BBC BASIC for Windows

      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

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

Binary Lambda Calculus

In lambda calculus, the compose functions happens to coincide with multiplication on Church numerals, namely compose = \f \g \x. f (g x) which in BLC is

00 00 00 01 1110 01 110 10

BQN

As a 2-modifier:

_compose_ ← ∘

Or:

_compose_ ← {𝔽𝔾𝕩}

As a dyadic function:

Compose ← {𝕏∘𝕎}

This is how you can use it:

   (Compose´ ⟨-,÷⟩) {𝕎𝕩} 2
¯0.5

Bracmat

This solution uses a macro in the body of the compose function.

Function composition is illustrated with a conversion from Fahrenheit to Celsius in two steps, followed by a conversion of the resulting rational number to a floating point expression. This shows that the returned value from the compose function indeed is a function and can be used as an argument to another call to compose.

( ( compose
  =   f g
    . !arg:(?f.?g)&'(.($f)$(($g)$!arg))
  )
&     compose
    $ ( (=.flt$(!arg,2))
      . compose$((=.!arg*5/9).(=.!arg+-32))
      )
  : (=?FahrenheitToCelsius)
& ( FahrenheitToCelsiusExample
  =   deg
    .   chu$(x2d$b0):?deg
      &   out
        $ ( str
          $ (!arg " " !deg "F in " !deg "C = " FahrenheitToCelsius$!arg)
          )
  )
& FahrenheitToCelsiusExample$0
& FahrenheitToCelsiusExample$100
)

0 °F in °C = -1,78*10E1
100 °F in °C = 3,78*10E1

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

Bruijn

Composition operators as defined in std/Combinator:

:import std/Number .

# 1x composition, bluebird combinator
…∘… [[[2 (1 0)]]]

:test (((inc ∘ (mul (+2))) (+3)) =? (+7)) ([[1]])

# 2x composition, blackbird combinator
…∘∘… [[[[3 (2 1 0)]]]]

:test (((inc ∘∘ mul) (+2) (+3)) =? (+7)) ([[1]])

# 3x composition, bunting combinator
…∘∘∘… [[[[[4 (3 2 1 0)]]]]]

:test (((inc ∘∘∘ (add ∘∘ mul)) (+1) (+2) (+4)) =? (+7)) ([[1]])

# reverse composition, queer bird combinator
…→… [[[1 (2 0)]]]

:test ((((mul (+2)) → inc) (+3)) =? (+7)) ([[1]])

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;
}

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)); };
        }
    }
}

C++

#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;
}

Works with: C++11

composing std::function

#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;
}

Works with: C++14

This much simpler version uses decltype(auto).

#include <iostream>
#include <cmath>
 
template <class F, class G>
decltype(auto) compose(F&& f, G&& g) {
    return [=](auto x) { return f(g(x)); };
}
 
int main() {
  std::cout << compose(sin, asin)(0.5) << "\n";
}

Works with: GCC

Not standard C++, but GCC has a built-in compose function

#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;
}

Works with: C++20

#include <iostream>
#include <cmath>
 
auto compose(auto f, auto g) {
     return [=](auto x) { return f(g(x)); };
}

int main() {
  std::cout << compose(sin, asin)(0.5) << "\n";
}

Output:

0.5

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

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 }"

Output:

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

Or, extending the Function prototype.

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 }"

Output is identical.

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>

Crystal

Crystal requires using closures for function composition. Since the only type the compiler can't infer for compose is the type of x, the type of the first argument to f has to be specified as the generic type T.

require "math"

def compose(f : Proc(T, _), g : Proc(_, _)) forall T
  return ->(x : T) { f.call(g.call(x)) }
end

compose(->Math.sin(Float64), ->Math.asin(Float64)).call(0.5)  #=> 0.5

The types for f's output, g's input and output, and the result of compose can all be inferred, but could be specified verbosely with def compose(f : Proc(T, U), g : Proc(U, V)) : Proc(T, V) forall T, U, V

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

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;
  // Alternative: TFunc = TFunc<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.

Diego

Function composition of two simple functions:

set_namespace(rosettacode);

begin_funct(compose)_arg(f, g);
    []_ret(x)_calc([f]([g]([x])));
end_funct[];

me_msg()_funct(compose)_arg(f)_sin()_arg(g)_asin()_var(x)_value(0.5);    // result: 0.5

reset_namespace[];

Function composition of two calculated functions:

set_namespace(rosettacode);

with_funct(f)_arg({int}, x)_ret()_calc([x] * [x]);
with_funct(g)_arg({int}, x)_ret()_calc([x] + 2);

begin_funct(compose)_arg(f, g);
    []_ret(x)_calc([f]([g]([x])));
end_funct[];

me_msg()_funct(compose)_arg(f)_funct(f)_arg(g)_funct(g)_var(x)_v(10);      // result: 144
// or me_msg()_funct(compose)_arg({f}, f)_arg({g}, g)_var(x)_v(10);

reset_ns[];

Dylan

compose[1] is already part of the language standard, with a more complete definition than this.

define method compose(f,g)
   method(x) f(g(x)) end
end;

Déjà Vu

It is already defined in the standard library as $.

compose f g:
	labda:
		f g

E

def compose(f, g) {
  return fn x { return f(g(x)) }
}

EchoLisp

;; By decreasing order of performance
;; 1) user definition : lambda and closure

(define (ucompose f g ) (lambda (x) ( f ( g x))))
(ucompose sin cos)
   → (🔒 λ (_x) (f (g _x)))

;; 2) built-in compose : lambda

(compose sin cos)
   → (λ (_#:g1002) (#apply-compose (#list #cos #sin) _#:g1002))

;; 3) compiled composition

(define (sincos x) (sin (cos x)))
sincos → (λ (_x) (⭕️ #sin (#cos _x)))

Output:

((ucompose sin cos) 3) → -0.8360218615377305
((compose sin cos) 3) → -0.8360218615377305
(sincos 3) → -0.8360218615377305

Ela

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

let compose f g x = f (g x)

==Ela ==

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

compose f g x = f (g x)

Elena

ELENA 6.x :

import extensions;
 
extension op : Func1
{
    compose(Func1 f)
        = (x => self(f(x)));
}
 
public program()
{
    var fg := (x => x + 1).compose::(x => x * x);
 
    console.printLine(fg(3))
}

Output:

Elixir

Translation of: Erlang

defmodule RC do
  def compose(f, g), do: fn(x) -> f.(g.(x)) end
  
  def multicompose(fs), do: List.foldl(fs, fn(x) -> x end, &compose/2)
end

sin_asin = RC.compose(&:math.sin/1, &:math.asin/1)
IO.puts sin_asin.(0.5)

IO.puts RC.multicompose([&:math.sin/1, &:math.asin/1, fn x->1/x end]).(0.5)
IO.puts RC.multicompose([&(&1*&1), &(1/&1), &(&1*&1)]).(0.5)

Output:

0.5
2.0
16.0

Emacs Lisp

Lexical binding is supported as of Emacs 24.1, allowing the use of a closure for function composition.

;; lexical-binding: t
(defun compose (f g)
  (lambda (x)
    (funcall f (funcall g x))))

(let ((func (compose '1+ '1+)))
  (funcall func 5)) ;=> 7

Alternatively, 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.

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

(let ((func (compose '1+ '1+)))
  (funcall func 5)) ;=> 7

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.

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

(let ((func (compose 1+ 1+)))
  (funcall func 5)) ;=> 7

Erlang

-module(fn).
-export([compose/2, multicompose/1]).

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

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

Factor

Factor is a concatenative language, so function composition is inherent. If the functions f and g are named, their composition is f g. Thanks to stack polymorphism, this holds true even if g consumes more values than f leaves behind. You always get every sort of composition for free. But watch out for stack underflows!

To compose quotations (anonymous functions), compose may be used:

( scratchpad ) [ 2 * ] [ 1 + ] compose .
[ 2 * 1 + ]
( scratchpad ) 4 [ 2 * ] [ 1 + ] compose call .
9

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)}")
  }
}

Forth

: compose ( xt1 xt2 -- xt3 )
  >r >r :noname
     r> compile,
     r> compile,
     postpone ;
;

' 2* ' 1+ compose  ( xt )
3 swap execute .   \ 7

Fortran

Modern Fortran standard has (limited) kind of higher-order functions (as result, argument, and with one level of nested functions) and optional arguments, and this enables to compose the following function (it is impure because Fortran has no closures). For simple cases function calls may be just nested to achieve the effect of function composition, because in fortran nested calls f(g(d(x))) generate a hierarchic set of function calls and the result of each function is transmitted to its calling function in a standard way for all functions.

module functions_module
   implicit none
   private ! all by default
   public :: f,g

contains

   pure function  f(x)
      implicit none
      real, intent(in) :: x
      real :: f
      f = sin(x)
   end function f

   pure function  g(x)
      implicit none
      real, intent(in) :: x
      real :: g
      g = cos(x)
   end function g

end module functions_module

module compose_module
   implicit none
   private ! all by default
   public :: compose

   interface
      pure function  f(x)
         implicit none
         real, intent(in) :: x
         real :: f
      end function f

      pure function  g(x)
         implicit none
         real, intent(in) :: x
         real :: g
      end function g
   end interface

contains

   impure function  compose(x, fi, gi)
      implicit none
      real, intent(in) :: x
      procedure(f), optional :: fi
      procedure(g), optional :: gi
      real :: compose

      procedure (f), pointer, save :: fpi => null()
      procedure (g), pointer, save :: gpi => null()

      if(present(fi) .and. present(gi))then
         fpi => fi
         gpi => gi
         compose = 0
         return
      endif

      if(.not. associated(fpi)) error stop "fpi"
      if(.not. associated(gpi)) error stop "gpi"

      compose = fpi(gpi(x))

   contains

   end function compose

end module compose_module

program test_compose
   use functions_module
   use compose_module
   implicit none
   write(*,*) "prepare compose:", compose(0.0, f,g)
   write(*,*) "run compose:", compose(0.5)
end program test_compose

Fortress

In Fortress, there are two ways that you can compose functions.

1. You can compose functions manually by writing your own composition function.

In this version, we allow any type of function to be used by defining our own types in the function definition and using those types to define how the composed function should behave. This version operates very similarly to the way that the COMPOSE operator, explained below, operates.

  compose[\A, B, C\](f:A->B, g:B->C, i:Any): A->C = do
    f(g(i))
  end

  composed(i:RR64): RR64 = compose(sin, cos, i)

Alternatively, you could explicitly define each type for improved type safety.

Due to the fact that alt_compose() is built around the idea that it is being used to compose two trigonometric functions, these will return identical functions. However, if you were to pass alt_composed() any other type of function, the interpreter would throw an error.

  alt_compose(f:Number->RR64, g:Number->RR64, i:RR64): ()->RR64 = do
    f(g(i))
  end

  alt_composed(i:RR64): RR64 = compose(sin, cos, i)

2. You can use the COMPOSE operator (or CIRC or RING). Because COMPOSE returns an anonymous function, it is necessary to wrap it in parentheses if you want to be able to use it in this manner.

  opr_composed(i:Number): Number->RR64 = (sin COMPOSE cos)(i)

Should you need to, you could also mix both methods by overloading the COMPOSE operator.

FreeBASIC

Illustrating with functions that take and return integers.

function compose( f as function(as integer) as integer,_
                  g as function(as integer) as integer,_
                  n as integer ) as integer
    return f(g(n))
end function

If you have functions named, say, foo and bar you would call compose with

compose( @foo, @bar, n )

for some integer n.

FunL

import math.{sin, asin}

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

sin_asin = compose( sin, asin )

println( sin_asin(0.5) )

Output:

0.5

Fōrmulæ

Fōrmulæ programs are not textual, visualization/edition of programs is done showing/manipulating structures but not text. Moreover, there can be multiple visual representations of the same program. Even though it is possible to have textual representation —i.e. XML, JSON— they are intended for storage and transfer purposes more than visualization and edition.

Programs in Fōrmulæ are created/edited online in its website.

In this page you can see and run the program(s) related to this task and their results. You can also change either the programs or the parameters they are called with, for experimentation, but remember that these programs were created with the main purpose of showing a clear solution of the task, and they generally lack any kind of validation.

Solution

The compose function returns a lambda expression, containing the actual composition of its arguments, and hence it can be called applied with its argument(s):

Test cases

Arguments of the functions to compose can be the same symbol, they are not "scrambled":

Because a function in Fōrmulæ is just a lambda expression, a lambda expression can be directly provided.

Since the composition function returns a lambda expression, it is not required to be applied:

GAP

Composition := function(f, g)
    return x -> f(g(x));
end;

h := Composition(x -> x+1, x -> x*x);
h(5);
# 26

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

Groovy

Test program:

final times2 = { it * 2 }
final plus1 = { it + 1 }

final plus1_then_times2 = times2 << plus1
final times2_then_plus1 = times2 >> plus1

assert plus1_then_times2(3) == 8
assert times2_then_plus1(3) == 7

Haskell

This is already defined as the . (dot) operator in Haskell:

Prelude> let sin_asin = sin . asin
Prelude> sin_asin 0.5
0.49999999999999994

Ways to use directly:

(sin . asin) 0.5

sin . asin $ 0.5

Implementing compose function from scratch:

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

Right to left composition of a list of functions could be defined as flip (foldr id):

composeList :: [a -> a] -> a -> a
composeList = flip (foldr id)

main :: IO ()
main = print $ composeList [(/ 2), succ, sqrt] 5

Output:

1.618033988749895

Hy

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

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

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:

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.

Janet

Janet supports function composition with the comp function.

(defn fahrenheit->celsius [deg-f]
  (/ (* (- deg-f 32) 5) 9))

(defn celsius->kelvin [deg-c]
  (+ deg-c 273.15))

(def fahrenheit->kelvin (comp celsius->kelvin fahrenheit->celsius))

(fahrenheit->kelvin 72) // 295.372

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"
    }
}

Java 8

Java 8's Function interface already has a .compose() default method:

Works with: Java version 8+

import java.util.function.Function;

public class Compose {
    public static void main(String[] args) {
        Function<Double,Double> sin_asin = ((Function<Double,Double>)Math::sin).compose(Math::asin);

        System.out.println(sin_asin.apply(0.5)); // prints "0.5"
    }
}

Implementing it yourself as a static method:

Works with: Java version 8+

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"
    }
}

JavaScript

ES5

Simple composition of two functions

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

Example:

var id = compose(Math.sin, Math.asin);
console.log(id(0.5)); // 0.5

Multiple composition

Recursion apart, multiple composition can be written in at least two general ways in JS:

Iteratively (faster to run, perhaps more fiddly to write)
With a fold / reduction (see http://rosettacode.org/wiki/Catamorphism). The fold is arguably simpler to write and reason about, though not quite as fast to execute.

(function () {
    'use strict';


    // iterativeComposed :: [f] -> f
    function iterativeComposed(fs) {

        return function (x) {
            var i = fs.length,
                e = x;

            while (i--) e = fs[i](e);
            return e;
        }
    }

    // foldComposed :: [f] -> f
    function foldComposed(fs) {

        return function (x) {
            return fs
                .reduceRight(function (a, f) {
                    return f(a);
                }, x);
        };
    }


    var sqrt = Math.sqrt,

        succ = function (x) {
            return x + 1;
        },

        half = function (x) {
            return x / 2;
        };


    // Testing two different multiple composition ([f] -> f) functions

    return [iterativeComposed, foldComposed]
        .map(function (compose) {

            // both functions compose from right to left
            return compose([half, succ, sqrt])(5);

        });
})();

Output:

[1.618033988749895, 1.618033988749895]

ES6

Simple composition of two functions

function compose(f, g) {
  return x => f(g(x));
}

or

var compose = (f, g) => x => f(g(x));

Example:

var id = compose(Math.sin, Math.asin);
console.log(id(0.5)); // 0.5

Multiple composition

(() => {
    "use strict";

    // -------------- MULTIPLE COMPOSITION ---------------

    // compose (<<<) :: (b -> c) -> (a -> b) -> a -> c
    const compose = (...fs) =>
        // A function defined by the right-to-left
        // composition of all the functions in fs.
        fs.reduce(
            (f, g) => x => f(g(x)),
            x => x
        );

    // ---------------------- TEST -----------------------
    const
        sqrt = Math.sqrt,
        succ = x => x + 1,
        half = x => x / 2;

    return compose(half, succ, sqrt)(5);

    // --> 1.618033988749895
})();

Output:

1.618033988749895

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

And yes, there should be a space between the two names.

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:

# apply g first and then f
def compose(f; g): g | f;

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" can be passed as an argument to other functions.

Julia

Works with: Julia version 0.6

Built-in:

@show (asin ∘ sin)(0.5)

Alternative:

compose(f::Function, g::Function) = (x) -> g(f(x))
@show compose(sin, asin)(0.5)

K

The K syntax for APL tacit (point free) function composition is the dyadic form of apostrophe ('), here is a cover function

compose:{'[x;y]}

An equivalent explicit definition would be

compose:{x[y[z]]}

Example:

  sin_asin:compose[sin;asin] // or compose . (sin;asin)
  sin_asin 0.5
0.5

Klingphix

include ..\Utilitys.tlhy

:*2 2 * ;
:++ 1 + ;
:composite swap exec swap exec ;
 
@++ @*2 3 composite ? { result: 7 }

"End " input

Kotlin

fun f(x: Int): Int = x * x

fun g(x: Int): Int = x + 2

fun <T, V, R> compose(f: (V) -> R,  g: (T) -> V): (T) -> R  = { f(g(it) }

fun main() {
   val x = 10
   println(compose(::f, ::g)(x))
}

Output:

Lambdatalk

{def compose
 {lambda {:f :g :x}
  {:f {:g :x}}}}
-> compose

{def funcA {lambda {:x} {* :x 10}}}
-> funcA

{def funcB {lambda {:x} {+ :x 5}}}
-> funcB

{def f {compose funcA funcB}}
-> f

{{f} 3}
-> 80

Lang

fp.f = ($x) -> return parser.op($x * 3)
fp.g = ($x) -> return parser.op($x + 2)

$x = 5

# In Lang this task can be achieved with the concat operator
fn.println(parser.op((fp.g ||| fp.f)($x))) # Prints 21 [Internal execution: fp.f(fp.g($x))]

# Creating a user-defined function doing the same thing is a bit more difficult
fp.compose = (fp.f, fp.g) -> {
	fp.innerFunc = (fp.f, fp.g, $x) -> return fp.f(fp.g($x))
		return fn.argCnt1(fn.combA3(fp.innerFunc, fp.f, fp.g)) # fn.combA3 must be used, because Lang does not support closures
}

fn.println(fp.compose(fp.f, fp.g)($x)) # Prints also 21

LFE

(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))))

If you pasted those into the LFE REPL, you can do the following:

> (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
>

Lingo

Lingo does not support functions as first-class objects. However, there is a way to achieve something similar:

In Lingo global functions (i.e. either built-in functions or custom functions defined in movie scripts) are methods of the _movie object. There are 2 ways to call such functions:

a) foo (1,2,3)
b) call (#foo, _movie, 1, 2, 3)

If we ignore the standard way a) and only concentrate on b), we can define a "call-function" (arbitrary word coining) as:

"Anything that supports the syntax 'call(<func>, _movie [, comma-separated arg list])' and might return a value."

As described above, this "call-function" definition includes all built-in and global user-defined functions.

For such "call-functions", function composition can be implemented using the following global (i.e. movie script) function compose() and the following parent script "Composer":

-- in some movie script
----------------------------------------
-- Composes 2 call-functions, returns a new call-function
-- @param {symbol|instance} f
-- @param {symbol|instance} g
-- @return {instance}
----------------------------------------
on compose (f, g)
  return script("Composer").new(f, g)
end

-- parent script "Composer"

property _f
property _g

----------------------------------------
-- @constructor
-- @param {symbol|instance} f
-- @param {symbol|instance} g
----------------------------------------
on new (me, f, g)
  me._f = f
  me._g = g
  return me
end

on call (me)
  if ilk(me._g)=#instance then
    cmd = "_movie.call(#call,me._g,VOID"
  else
    cmd = "_movie.call(me._g,_movie"
  end if
  a = [] -- local args list
  repeat with i = 1 to the paramCount-2
    a[i] = param(i+2)
    put ",a["&i&"]" after cmd
  end repeat
  put ")" after cmd
  if ilk(me._f)=#instance then
    return _movie.call(#call, me._f, VOID, value(cmd))
  else
    return _movie.call(me._f, _movie, value(cmd))
  end if
end

Usage:

-- compose new function based on built-in function 'sin' and user-defined function 'asin'
f1 = compose(#asin, #sin)
put call(f1, _movie, 0.5)
-- 0.5000

-- compose new function based on previously composed function 'f1' and user-defined function 'double'
f2 = compose(#double, f1)
put call(f2, _movie, 0.5)
-- 1.0000

-- compose new function based on 2 composed functions
f1 = compose(#asin, #sin)
f2 = compose(#double, #triple)
f3 = compose(f2, f1)
put call(f3, _movie, 0.5)
-- 3.0000

User-defined custom functions used in demo code above:

-- in some movie script
on asin (x)
  res = atan(sqrt(x*x/(1-x*x)))
  if x<0 then res = -res
  return res
end

on double (x)
  return x*2
end

on triple (x)
  return x*3
end

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

Lua

function compose(f, g) return function(...) return f(g(...)) end end

M2000 Interpreter

Using Lambda functions

Module CheckIt {
      Compose = lambda (f, g)->{
            =lambda f, g (x)->f(g(x))
      }
      Add5=lambda (x)->x+5
      Division2=lambda (x)->x/2
      Add5Div2=compose(Division2, Add5)
      Print Add5Div2(15)=10  ' True
}
CheckIt

Using EVAL and EVAL$

class Compose {
private:
	composition$
public:
	function formula$ {
		=.composition$
	}
	value (x){
		=Eval(.composition$)
	}
Class:
	module compose(a$, b$) {
		.composition$<=a$+"("+b$+"(x))"
	}
}
function Global Exp(x) {
	=round(2.7182818284590452**x)
}
class ComposeStr$ {
private:
	composition$
public:
	function formula$ {
		=.composition$
	}
	value (x$){
		=Eval$(.composition$.)  // NEED A DOT AFTER STRING VARIABLE
	}
Class:
	module composeStr(a$, b$) {
		.composition$<=a$+"("+b$+"(x$))"
	}
}
ExpLog=Compose("Exp", "Ln")
Print ExpLog(3)
UcaseLcase$=ComposeStr$("Ucase$", "Lcase$")
Print UcaseLcase$("GOOD")

Mathcad

Mathcad is a non-text-based programming environment. The expressions below are an approximations of the way that they are entered (and) displayed on a Mathcad worksheet. The worksheet is available at xxx_tbd_xxx

This particular version of Function Composition was created in Mathcad Prime Express 7.0, a free version of Mathcad Prime 7.0 with restrictions (such as no programming or symbolics). All Prime Express numbers are complex. There is a recursion depth limit of about 4,500.

compose(f,g,x):=f(g(x))

cube(x):=x³ cuberoot(x):=x^1/3

funlist:=[sin cos cube]^T invlist:=[asin acos cuberoot]^T

invfunlist(x):= {vectorize}compose(invlist,funlist,x){/vectorize}

x:= 0.5

invfunlist(x)= {results of evaluation appears here) invfunlist([x √2 3]^T)= {results)

apply(f,x):=f(x) apply(f,x):={vectorize}apply(f,x){/vectorize}

apply(funlist,x)= {results} + ... several more examples

Mathematica / Wolfram Language

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]

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))));

min

Works with: min version 0.19.3

Since min is both concatenative and homoiconic, function composition is equivalent to list concatenation. Example:

(1 +) (2 *) concat print

Output:

(1 + 2 *)

MiniScript

funcA = function(x)
    return x * 10
end function

funcB = function(x)
    return x + 5
end function

compose = function(f, g)
    return function(x)
        return f(g(x))
    end function
end function

f = compose(@funcA, @funcB)
print f(3)  // should be equal to (3+5)*10

Output:

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));
    }
}

Never

func compose(f(i : int) -> int, g(i : int) -> int) -> (int) -> int
{
    let func (i : int) -> int { f(g(i)) }
}

func dec(i : int) -> int { 10 * i }

func succ(i : int) -> int { i + 1 }

func main() -> int
{
    let h = compose(dec, succ);

    print(h(1));

    0
}

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

Nim

import sugar

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

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

ObjectIcon

Translation of: Icon and Unicon

# -*- ObjectIcon -*-
#
# The Rosetta Code function composition task, in Object Icon.
# Composition will result in a co-expression.
#
# Object Icon co-expressions are closures: they share the local
# variables of the context in which they are created. In Arizona Icon,
# co-expressions obtain only the *values* of those variables. However,
# this difference, despite its significance, is not really important
# to the notion of composition.
#
# This example is adapted from the Unicon implementation of the
# task. To simplify the example, I have removed support for string
# invocations.
#

import io

procedure main (arglist)
  local f, g

  # f gets a co-expression that is a composition of three procedures.
  f := compose(append_exclamation, string_repeat, double_it)
  write(123@f)

  # g gets a co-expression that is a composition of a procedure and f.
  g := compose(string_repeat, f)
  write(123@g)
end

procedure double_it (n)
  return n + n
end

procedure string_repeat (x)
  return string(x) || string(x)
end

procedure append_exclamation (s)
  return s || "!"
end

procedure compose (rfL[])
    local x, f, saveSource, fL, cf
 
    every push(fL := [], !rfL)
    cf := create {
      saveSource := &source
      repeat {
        x := x@saveSource
        saveSource := &source
        every f := !fL do {
          case type(f) of {
            "co-expression": x := x@f
            default: x := f(x)
          }
        }
      }
    }

    # Co-expressions often need to be "primed" before they can be
    # used.
    @cf

    return cf
end

Output:

$ oit -s function_composition-OI.icn && ./function_composition-OI
246246!
246246!246246!

Objective-C

Works with: Mac OS X version 10.6+

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 @(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;
}

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

Octave

function r = compose(f, g)
  r = @(x) f(g(x));
endfunction

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

Oforth

Oforth uses RPN notation. Function composition of f and g is just calling :

g f

If a block is needed, a compose function can be implemented :

: compose(f, g)  #[ g perform f perform ] ;

Usage :

1.2 compose(#asin, #sin) perform
[ 1, 2, 3, 4, 5 ] compose(#[ map(#sqrt) ], #[ filter(#isEven) ]) perform

The last line returns : [1.4142135623731, 2]

Ol

(define (compose f g)
   (lambda (x) (f (g x))))

;; or:

(define ((compose f g) x) (f (g x)))

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.

Oz

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

  SinAsin = {Compose Float.sin Float.asin}
in
  {Show {SinAsin 0.5}}

PARI/GP

Works with: PARI/GP version 2.4.2 and above

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)

PascalABC.NET

function Compose<T,T1,T2>(f: T1 -> T2; g: T -> T1): T -> T2 := x -> f(g(x));

begin
  Compose(Sin,ArcSin)(1.0).Print
end.

Output:

Pascal

See Delphi

Perl

sub compose {
    my ($f, $g) = @_;

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

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

Phix

There is not really any direct support for this sort of thing in Phix, but it is all pretty trivial to manage explicitly.
In the following, as it stands, you cannot use constant m in the same way as a routine_id, or pass a standard routine_id to call_composite(), but tagging the ctable entries so that you know precisely what to do with each entry does not sound the least bit difficult to me.

sequence ctable = {}
 
function compose(integer f, integer g)
    ctable = append(ctable,{f,g})
    return length(ctable)   
end function
 
function call_composite(integer f, atom x)
integer g
    {f,g} = ctable[f]
    return call_func(f,{call_func(g,{x})})
end function
 
function plus1(atom x)
    return x+1
end function
 
function halve(atom x)
    return x/2
end function
 
constant m = compose(routine_id("halve"),routine_id("plus1"))
 
?call_composite(m,1)    -- displays 1
?call_composite(m,4)    -- displays 2.5

Phixmonti

def *2 2 * enddef
def ++ 1 + enddef
def composite swap exec swap exec enddef

getid ++ getid *2 3 composite print /# result: 7 #/

PHP

Works with: PHP version 5.3+

<?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: PHP version pre-5.3 and 5.3+

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
?>

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

PostScript

/compose { % f g -> { g f }
  [ 3 1 roll exch
  % procedures are not executed when encountered directly
  % insert an 'exec' after procedures, but not after operators
  1 index type /operatortype ne { /exec cvx exch } if
  dup type /operatortype ne { /exec cvx } if
  ] cvx
} def

/square { dup mul } def
/plus1  { 1 add } def
/sqPlus1 /square load /plus1 load compose def

PowerShell

You can simply call g inside f like this:

function g ($x) {
    $x + $x
}
function f ($x) {
    $x*$x*$x
}  
f (g 1)

Or g and f can become paramaters of a new function fg

function fg (${function:f}, ${function:g}, $x) {
    f (g $x)
}
fg f g 1

In both cases the answer is:

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)).

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

;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$,Body$)

Purity

data compose = f => g => $f . $g

Python

Simple composition of two functions

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
>>>

Or, expanding slightly:

Works with: Python version 3

from math import (acos, cos, asin, sin)


# compose (<<<) :: (b -> c) -> (a -> b) -> a -> c
def compose(g, f):
    '''Right to left function composition.'''
    return lambda x: g(f(x))


# main :: IO ()
def main():
    '''Test'''

    print(list(map(
        lambda f: f(0.5),
        zipWith(compose)(
            [sin, cos, lambda x: x ** 3.0]
        )([asin, acos, lambda x: x ** (1 / 3.0)])
    )))


# GENERIC FUNCTIONS ---------------------------------------


# zipWith :: (a -> b -> c) -> [a] -> [b] -> [c]
def zipWith(f):
    '''A list constructed by zipping with a
       custom function, rather than with the
       default tuple constructor.'''
    return lambda xs: lambda ys: (
        map(f, xs, ys)
    )


if __name__ == '__main__':
    main()

Output:

[0.49999999999999994, 0.5000000000000001, 0.5000000000000001]

Multiple composition

Nested composition of several functions can be streamlined by using functools.reduce.

Works with: Python version 3

from functools import reduce
from math import sqrt


def compose(*fs):
    '''Composition, from right to left,
       of an arbitrary number of functions.
    '''
    def go(f, g):
        return lambda x: f(g(x))

    return reduce(go, fs, lambda x: x)


# ------------------------- TEST -------------------------
def main():
    '''Composition of three functions.'''

    f = compose(
        half,
        succ,
        sqrt
    )

    print(
        f(5)
    )


# ----------------------- GENERAL ------------------------
def half(n):
    return n / 2


def succ(n):
    return 1 + n


if __name__ == '__main__':
    main()

Output:

1.618033988749895

composition via operator overloading

Here need composition of several functions is reduced with classes.

Works with: Python version 3

# Contents of `pip install compositions'

class Compose(object):
    def __init__(self, func):
        self.func = func

    def __call__(self, x):
        return self.func(x)

    def __mul__(self, neighbour):
        return Compose(lambda x: self.func(neighbour.func(x)))

# from composition.composition import Compose
if __name__ == "__main__":
    # Syntax 1
    @Compose
    def f(x):
        return x

    # Syntax 2
    g = Compose(lambda x: x)

    print((f * g)(2))

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) \

Quackery

  [ nested swap 
    nested swap join ]  is compose ( g f --> [ )

  ( ----- demonstration ----- )

 ( create a named nest -- equivalent to a function )

  [ 2 * ]               is double  (   n --> n )

  ( "[ 4 + ]" is an unnamed nest 
               -- equivalent to a lambda function. ) 

  ( "quoting" a nest with ' puts it on the stack 
    rather than it being evaluated. "do" evaluates 
    the top of stack.                              )

  19   ' double   ' [ 4 + ]   compose do echo

Output:

R

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

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.)

Raku

(formerly Perl 6)

Works with: rakudo version 2018.03

The function composition operator is ∘, U+2218 RING OPERATOR (with a "Texas" version o for the Unicode challenged). Here we compose a routine, an operator, and a lambda:

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

REBOL

REBOL [
	Title: "Functional Composition"
	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

REXX

compose: procedure;  parse arg f,g,x;    interpret  'return'  f"("  g'('  x  "))"

exit        /*control should never gets here,  but this was added just in case.*/

Ring

# Project : Function composition

sumprod = func1(:func2,2,3)
see sumprod + nl

func func1(func2,x,y)
        temp = call func2(x,y)
        res = temp + x + y
        return res

func func2(x,y)
        res = x * y
        return res

Output:

RPL

Works with: HP version 48G

« →STR SWAP →STR + 
  DUP "»«" POS "  " REPL STR→
» 'FCOMP' STO     @   ( « f » « g » → « f o g » )

≪ ALOG ≫ ≪ COS ≫ FCOMP 
≪ ALOG ≫ ≪ COS ≫ FCOMP 0 EVAL
≪ ALOG ≫ ≪ COS ≫ FCOMP 'x' EVAL

Output:

3: ≪ COS ALOG ≫
2: 10
1: 'ALOG(COS(x))'

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

Rust

In order to return a closure (anonymous function) in Stable Rust, it must be wrapped in a layer of indirection via a heap allocation. However, there is a feature coming down the pipeline (currently available in Nightly) which makes this possible. Both of the versions below are in the most general form i.e. their arguments may be functions or closures with the only restriction being that the output of g is the same type as the input of f.

Stable

Function is allocated on the heap and is called via dynamic dispatch

fn compose<'a,F,G,T,U,V>(f: F, g: G) -> Box<Fn(T) -> V + 'a>
    where F: Fn(U) -> V + 'a,
          G: Fn(T) -> U + 'a,
{
   Box::new(move |x| f(g(x)))
}

Nightly

Function is returned on the stack and is called via static dispatch (monomorphized)

#![feature(conservative_impl_trait)]
fn compose<'a,F,G,T,U,V>(f: F, g: G) -> impl Fn(T) -> V + 'a
    where F: Fn(U) -> V + 'a,
          G: Fn(T) -> U + 'a,
{
   move |x| f(g(x))
}

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

Scheme

(define (compose f g) (lambda (x) (f (g x))))

;; or:

(define ((compose f g) x) (f (g x)))

;; or to compose an arbitrary list of 1 argument functions:

(define-syntax compose
  (lambda (x)
    (syntax-case x ()
      ((_) #'(lambda (y) y))
      ((_ f) #'f)
      ((_ f g h ...)  #'(lambda (y) (f ((compose g h ...) y)))))))

Example:

(display ((compose sin asin) 0.5))
(newline)

Output:

0.5

Sidef

func compose(f, g) {
    func(x) { f(g(x)) }
}

var fg = compose(func(x){ sin(x) }, func(x){ cos(x) })
say fg(0.5)      # => 0.76919635484100842185251475805107

Slate

Function (method) composition is standard:

[| :x | x + 1] ** [| :x | x squared] applyTo: {3}

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.

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

SuperCollider

has a function composition operator (the message `<>`):

f = { |x| x + 1 };
g = { |x| x * 2 };
h = g <> f;
h.(8); // returns 18

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))

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.

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

Transd

#lang transd

MainModule: {
    // Make a short alias for a function type that takes a string and
    // returns a string. Call it 'Shader'.

    Shader: typealias(Lambda<String String>),

    // 'composer' function takes two Shaders, combines them into
    // a single Shader, which is a capturing closure, аnd returns 
    // this closure to the caller.
    // [[f1,f2]] is a list of captured variables

	composer: (λ f1 Shader() f2 Shader()
        (ret Shader(λ[[f1,f2]] s String() (exec f1 (exec f2 s))))),

	_start: (λ 
        // create a combined shader as a local variable 'render'

        locals: render (composer 
            Shader(λ s String() (ret (toupper s)))
            Shader(λ s String() (ret (+ s "!"))))
        
        // call this combined shader as a usual shader with passing
        // a string to it, аnd receiving from it the combined result of 
        // its two captured shaders

        (textout (exec render "hello")))
}

Output:

HELLO!

TypeScript

function compose<T, U, V> (fn1: (input: T) => U, fn2: (input: U) => V){
    return function(value: T) {
        return fn2(fn1(value))
    } 
}

function size (s: string): number { return s.length; }

function isEven(x: number): boolean { return x % 2 === 0; }

const evenSize = compose(size, isEven);

console.log(evenSize("ABCD")) // true
console.log(evenSize("ABC")) // false

uBasic/4tH

Print FUNC(_Compose (_f, _g, 3))
End

_Compose Param (3) : Return (FUNC(a@(FUNC(b@(c@)))))
_f Param (1) : Return (a@ + 1)
_g Param (1) : Return (a@ * 2)

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

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.

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.

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.

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.

compose("f","g") "x" = "f" "g" "x"

test program:

#import nat
#cast %n

test =  compose(successor,double) 3

Output:

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

WDTE

The simplest way is with a lambda:

let compose f g => (@ c x => g x -> f);

Alternatively, you can take advantage of partial function calls:

let compose f g x => g x -> f;

Both can be used as follows:

(compose (io.writeln io.stdout) !) true;

Output:

false

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.

! @[f g] x ; f(g(x))

! ^(f g) x ; f(g(x))

Defining the compose function

@var compose &[f g] &x !f!g x

Wren

var compose = Fn.new { |f, g| Fn.new { |x| f.call(g.call(x)) } }

var double = Fn.new { |x| 2 * x }

var addOne = Fn.new { |x| x + 1 }

System.print(compose.call(double, addOne).call(3))

Output:

zkl

Utils.Helpers.fcomp('+(1),'*(2))(5) //-->11

Which is implemented with a closure (.fp1), which fixes the second paramter

fcn fcomp(f,g,h,etc){
   { fcn(x,hgf){ T(x).pump(Void,hgf.xplode()) }.fp1(vm.arglist.reverse()); }

ZX Spectrum Basic

DEF FN commands can be nested, making this appear trivial:

10 DEF FN f(x)=SQR x
20 DEF FN g(x)=ABS x
30 DEF FN c(x)=FN f(FN g(x))
40 PRINT FN c(-4)

Which gets you f(g(x)), for sure. But if you want g(f(x)) you need to DEF a whole new FN. Instead we can pass the function names as strings to a new function and numerically evaluate the string:

10 DEF FN f(x)=SQR x
20 DEF FN g(x)=ABS x
30 DEF FN c(a$,b$,x)=VAL ("FN "+a$+"(FN "+b$+"(x))")
40 PRINT FN c("f","g",-4)
50 PRINT FN c("g","f",-4)

Output:

2

A Invalid argument, 50:1