⚠️ Warning: This is a draft ⚠️

This means it might contain formatting issues, incorrect code, conceptual problems, or other severe issues.

If you want to help to improve and eventually enable this page, please fork RosettaGit's repository and open a merge request on GitHub.

A language has [[wp:First-class function|first-class functions]] if it can do each of the following without recursively invoking a compiler or interpreter or otherwise [[metaprogramming]]:

• Create new functions from preexisting functions at run-time
• Store functions in collections
• Use functions as arguments to other functions
• Use functions as return values of other functions

;Task: Write a program to create an ordered collection ''A'' of functions of a real number. At least one function should be built-in and at least one should be user-defined; try using the sine, cosine, and cubing functions. Fill another collection ''B'' with the inverse of each function in ''A''. Implement function composition as in [[Functional Composition]]. Finally, demonstrate that the result of applying the composition of each function in ''A'' and its inverse in ''B'' to a value, is the original value. (Within the limits of computational accuracy).

(A solution need not actually call the collections "A" and "B". These names are only used in the preceding paragraph for clarity.)

## ActionScript

{{trans|JavaScript}}


var cube:Function = function(x) {
return Math.pow(x, 3);
};
var cuberoot:Function = function(x) {
return Math.pow(x, 1/3);
};

function compose(f:Function, g:Function):Function {
return function(x:Number) {return f(g(x));};
}
var functions:Array = [Math.cos, Math.tan, cube];
var inverse:Array = [Math.acos, Math.atan, cuberoot];

function test() {
for (var i:uint = 0; i < functions.length; i++) {
// Applying the composition to 0.5
trace(compose(functions[i], inverse[i])(0.5));
}
}

test();


Output:


0.5000000000000001
0.5000000000000001
0.5000000000000001



Even if the example below solves the task, there are some limitations to how dynamically you can create, store and use functions in Ada, so it is debatable if Ada really has first class functions.

with Ada.Float_Text_IO,

procedure First_Class_Functions is

function Sqr (X : Float) return Float is
begin
return X ** 2;
end Sqr;

type A_Function is access function (X : Float) return Float;

generic
F, G : A_Function;
function Compose (X : Float) return Float;

function Compose (X : Float) return Float is
begin
return F (G (X));
end Compose;

Functions : array (Positive range <>) of A_Function := (Sin'Access,
Cos'Access,
Sqr'Access);
Inverses  : array (Positive range <>) of A_Function := (Arcsin'Access,
Arccos'Access,
Sqrt'Access);
begin
for I in Functions'Range loop
declare
function Identity is new Compose (Functions (I), Inverses (I));
Test_Value : Float := 0.5;
Result     : Float;
begin
Result := Identity (Test_Value);

if Result = Test_Value then
Put      ("Example ");
Put      (I, Width => 0);
Put_Line (" is perfect for the given test value.");
else
Put      ("Example ");
Put      (I, Width => 0);
Put      (" is off by");
Put      (abs (Result - Test_Value));
Put_Line (" for the given test value.");
end if;
end;
end loop;
end First_Class_Functions;


It is bad style (but an explicit requirement in the task description) to put the functions and their inverses in separate arrays rather than keeping each pair in a record and then having an array of that record type.

## Aikido

{{incomplete|Aikido|Fails to demonstrate that the result of applying the composition of each function in A and its inverse in B to a value, is the original value}} {{trans|Javascript}}


import math

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

var fn  = [Math.sin, Math.cos, function(x) { return x*x*x }]
var inv = [Math.asin, Math.acos, function(x) { return Math.pow(x, 1.0/3) }]

for (var i=0; i<3; i++) {
var f = compose(inv[i], fn[i])
println(f(0.5))    // 0.5
}



## ALGOL 68

{{trans|Python}}

{{works with|ALGOL 68|Standard - no extensions to language used}}

{{works with|ALGOL 68G|Any - tested with release mk15-0.8b.fc9.i386}}

{{works with|ELLA ALGOL 68|Any (with appropriate job cards) - tested with release 1.8.8d.fc9.i386 using non-standard compose}}

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 - if run out of scope - rejects during runtime.

MODE F = PROC (REAL)REAL;
OP ** = (REAL x, power)REAL: exp(ln(x)*power);

# Add a user defined function and its inverse #
PROC cube = (REAL x)REAL: x * x * x;
PROC cube root = (REAL x)REAL: x ** (1/3);

# First class functions allow run-time creation of functions from functions #
# return function compose(f,g)(x) == f(g(x)) #
PROC non standard compose = (F f1, f2)F: (REAL x)REAL: f1(f2(x)); # eg ELLA ALGOL 68RS #
PROC compose = (F f, g)F: ((F f2, g2, REAL x)REAL: f2(g2(x)))(f, g, );

# Or the classic "o" functional operator #
PRIO O = 5;
OP (F,F)F O = compose;

# first class functions should be able to be members of collection types #
[]F func list = (sin, cos, cube);
[]F arc func list = (arc sin, arc cos, cube root);

# Apply functions from lists as easily as integers #
FOR index TO UPB func list DO
STRUCT(F f, inverse f) this := (func list[index], arc func list[index]);
print(((inverse f OF this O f OF this)(.5), new line))
OD


Output:

+.500000000000000e +0
+.500000000000000e +0
+.500000000000000e +0


## AppleScript

AppleScript does not have built-in functions like sine or cosine.

-- 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 increment
on call(n)
n + 1
end call
end script

script decrement
on call(n)
n - 1
end call
end script

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

script half
on call(x)
x / 2
end call
end script

script cube
on call(x)
x ^ 3
end call
end script

script cuberoot
on call(x)
x ^ (1 / 3)
end call
end script

set functions to {increment, twice, cube}
set inverses to {decrement, half, cuberoot}
repeat with i from 1 to 3
set end of answers to ¬
compose(item i of inverses, ¬
item i of functions)'s ¬
call(0.5)
end repeat
answers -- Result: {0.5, 0.5, 0.5}


Putting math libraries aside for the moment (we can always shell out to bash functions like '''bc'''), a deeper issue is that the architectural position of functions in the AppleScript type system is simply a little too incoherent and second class to facilitate really frictionless work with first-class functions. (This is clearly not what AppleScript was originally designed for).

Incoherent, in the sense that built-in functions and operators do not have the same place in the type system as user functions. The former are described as 'commands' in parser errors, and have to be wrapped in user handlers if they are to be used interchangeably with other functions.

Second class, in the sense that user functions (or 'handlers' in the terminology of Apple's documentation), are properties of scripts. The scripts are autonomous first class objects, but the handlers are not. Functions which accept other functions as arguments will internally need to use an '''mReturn''' or '''mInject''' function which 'lifts' handlers into script object types. Functions which return functions will similarly have to return them embedded in such script objects.

Once we have a function like mReturn, however, we can readily write higher order functions like '''map''', '''zipWith''' and '''mCompose''' below.

on run

set fs to {sin_, cos_, cube_}
set afs to {asin_, acos_, croot_}

-- Form a list of three composed function objects,
-- and map testWithHalf() across the list to produce the results of
-- application of each composed function (base function composed with inverse) to 0.5

script testWithHalf
on |λ|(f)
mReturn(f)'s |λ|(0.5)
end |λ|
end script

map(testWithHalf, zipWith(mCompose, fs, afs))

--> {0.5, 0.5, 0.5}
end run

-- Simple composition of two unadorned handlers into
-- a method of a script object
on mCompose(f, g)
script
on |λ|(x)
mReturn(f)'s |λ|(mReturn(g)'s |λ|(x))
end |λ|
end script
end mCompose

-- map :: (a -> b) -> [a] -> [b]
on map(f, xs)
tell mReturn(f)
set lng to length of xs
set lst to {}
repeat with i from 1 to lng
set end of lst to |λ|(item i of xs, i, xs)
end repeat
return lst
end tell
end map

-- 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

-- zipWith :: (a -> b -> c) -> [a] -> [b] -> [c]
on zipWith(f, xs, ys)
set lng to min(length of xs, length of ys)
set lst to {}
tell mReturn(f)
repeat with i from 1 to lng
set end of lst to |λ|(item i of xs, item i of ys)
end repeat
return lst
end tell
end zipWith

-- min :: Ord a => a -> a -> a
on min(x, y)
if y < x then
y
else
x
end if
end min

on sin:r
(do shell script "echo 's(" & r & ")' | bc -l") as real
end sin:

on cos:r
(do shell script "echo 'c(" & r & ")' | bc -l") as real
end cos:

on cube:x
x ^ 3
end cube:

on croot:x
x ^ (1 / 3)
end croot:

on asin:r
(do shell script "echo 'a(" & r & "/sqrt(1-" & r & "^2))' | bc -l") as real
end asin:

on acos:r
(do shell script "echo 'a(sqrt(1-" & r & "^2)/" & r & ")' | bc -l") as real
end acos:


{{Out}}

{0.5, 0.5, 0.5}


## AutoHotkey

By '''just me'''. [http://ahkscript.org/boards/viewtopic.php?f=17&t=1363&p=16454#p16454 Forum Post]

#NoEnv
; Set the floating-point precision
SetFormat, Float, 0.15
; Super-global variables for function objects
Global F, G
; User-defined functions
Cube(X) {
Return X ** 3
}
CubeRoot(X) {
Return X ** (1/3)
}
; Function arrays, Sin/ASin and Cos/ACos are built-in
FuncArray1 := [Func("Sin"),  Func("Cos"),  Func("Cube")]
FuncArray2 := [Func("ASin"), Func("ACos"), Func("CubeRoot")]
; Compose
Compose(FN1, FN2) {
Static FG := Func("ComposedFunction")
F := FN1, G:= FN2
Return FG
}
ComposedFunction(X) {
Return F.(G.(X))
}
; Run
X := 0.5 + 0
Result := "Input:n" . X . "nnOutput:"
For Index In FuncArray1
Result .= "n" . Compose(FuncArray1[Index], FuncArray2[Index]).(X)
MsgBox, 0, First-Class Functions, % Result
ExitApp


{{Output}}

Input:
0.500000000000000

Output:
0.500000000000000
0.500000000000000
0.500000000000001


## Axiom

Using the interpreter:

fns := [sin$Float, cos$Float, (x:Float):Float +-> x^3]
inv := [asin$Float, acos$Float, (x:Float):Float +-> x^(1/3)]
[(f*g) 0.5 for f in fns for g in inv]


)abbrev package TESTP TestPackage
TestPackage(T:SetCategory) : with
_*: (List((T->T)),List((T->T))) -> (T -> List T)
import MappingPackage3(T,T,T)
fs * gs ==
((x:T):(List T) +-> [(f*g) x for f in fs for g in gs])


This would be called using:

(fns * inv) 0.5


Output:

[0.5,0.5,0.5]


## BBC BASIC

{{works with|BBC BASIC for Windows}} Strictly speaking you cannot return a ''function'', but you can return a ''function pointer'' which allows the task to be implemented.

      REM Create some functions and their inverses:
DEF FNsin(a) = SIN(a)
DEF FNasn(a) = ASN(a)
DEF FNcos(a) = COS(a)
DEF FNacs(a) = ACS(a)
DEF FNcube(a) = a^3
DEF FNroot(a) = a^(1/3)

dummy = FNsin(1)

REM Create the collections (here structures are used):
DIM cA{Sin%, Cos%, Cube%}
DIM cB{Asn%, Acs%, Root%}
cA.Sin% = ^FNsin() : cA.Cos% = ^FNcos() : cA.Cube% = ^FNcube()
cB.Asn% = ^FNasn() : cB.Acs% = ^FNacs() : cB.Root% = ^FNroot()

REM Create some function compositions:
AsnSin% = FNcompose(cB.Asn%, cA.Sin%)
AcsCos% = FNcompose(cB.Acs%, cA.Cos%)
RootCube% = FNcompose(cB.Root%, cA.Cube%)

REM Test applying the compositions:
x = 1.234567 : PRINT x, FN(AsnSin%)(x)
x = 2.345678 : PRINT x, FN(AcsCos%)(x)
x = 3.456789 : PRINT x, FN(RootCube%)(x)
END

DEF FNcompose(f%,g%)
LOCAL f$, p% f$ = "(x)=" + CHR$&A4 + "(&" + STR$~f% + ")(" + \
\             CHR$&A4 + "(&" + STR$~g% + ")(x))"
DIM p% LEN(f$) + 4$(p%+4) = f$: !p% = p%+4 = p%  '''Output:'''  1.234567 1.234567 2.345678 2.345678 3.456789 3.456789  ## Bori double acos (double d) { return Math.acos(d); } double asin (double d) { return Math.asin(d); } double cos (double d) { return Math.cos(d); } double sin (double d) { return Math.sin(d); } double croot (double d) { return Math.pow(d, 1/3); } double cube (double x) { return x * x * x; } Var compose (Var f, Var g, double x) { Func ff = f; Func fg = g; return ff(fg(x)); } void button1_onClick (Widget widget) { Array arr1 = [ sin, cos, cube ]; Array arr2 = [ asin, acos, croot ]; str s; for (int i = 1; i <= 3; i++) { s << compose(arr1.get(i), arr2.get(i), 0.5) << str.newline; } label1.setText(s); }  Output on Android phone: 0.5 0.4999999999999999 0.5000000000000001  ## Bracmat Bracmat has no built-in functions of real values. To say the truth, Bracmat has no real values. The only pair of currently defined built-in functions for which inverse functions exist are d2x and x2d for decimal to hexadecimal conversion and vice versa. These functions also happen to be each other's inverse. Because these two functions only take non-negative integer arguments, the example uses the argument 3210 for each pair of functions. The lists A and B contain a mix of function names and function definitions, which illustrates that they always can take each other's role, except when a function definition is assigned to a function name, as for example in the first and second lines. The compose function uses macro substitution. ( (sqrt=.!arg^1/2) & (log=.e\L!arg) & (A=x2d (=.!arg^2) log (=.!arg*pi)) & ( B = d2x sqrt (=.e^!arg) (=.!arg*pi^-1) ) & ( compose = f g . !arg:(?f.?g) & '(.($f)$(($g)$!arg)) ) & whl ' ( !A:%?F ?A & !B:%?G ?B & out$((compose$(!F.!G))$3210)
)
)


Output:

3210
3210
3210
3210


## C

Since one can't create new functions dynamically within a C program, C doesn't have first class functions. But you can pass references to functions as parameters and return values and you can have a list of function references, so I guess you can say C has second class functions.

Here goes.

#include <iostream>
#include <stdio.h>
#include <math.h>

/* declare a typedef for a function pointer */
typedef double (*Class2Func)(double);

/*A couple of functions with the above prototype */
double functionA( double v)
{
return v*v*v;
}
double functionB(double v)
{
return exp(log(v)/3);
}

/* A function taking a function as an argument */
double Function1( Class2Func f2, double val )
{
return f2(val);
}

/*A function returning a function */
Class2Func WhichFunc( int idx)
{
return (idx < 4) ? &functionA : &functionB;
}

/* A list of functions */
Class2Func funcListA[] = {&functionA, &sin, &cos, &tan };
Class2Func funcListB[] = {&functionB, &asin, &acos, &atan };

/* Composing Functions */
double InvokeComposed( Class2Func f1, Class2Func f2, double val )
{
return f1(f2(val));
}

typedef struct sComposition {
Class2Func f1;
Class2Func f2;
} *Composition;

Composition Compose( Class2Func f1, Class2Func f2)
{
Composition comp = malloc(sizeof(struct sComposition));
comp->f1 = f1;
comp->f2 = f2;
return comp;
}

double CallComposed( Composition comp, double val )
{
return comp->f1( comp->f2(val) );
}
/** * * * * * * * * * * * * * * * * * * * * * * * * * * */

int main(int argc, char *argv[])
{
int ix;
Composition c;

printf("Function1(functionA, 3.0) = %f\n", Function1(WhichFunc(0), 3.0));

for (ix=0; ix<4; ix++) {
c = Compose(funcListA[ix], funcListB[ix]);
printf("Compostion %d(0.9) = %f\n", ix, CallComposed(c, 0.9));
}

return 0;
}


===Non-portable function body duplication=== Following code generates true functions at run time. Extremely unportable, and [http://en.wikipedia.org/wiki/Considered_harmful should be considered harmful] in general, but it's one (again, harmful) way for the truly desperate (or perhaps for people supporting only one platform -- and note that some other languages only work on one platform).

#include <stdio.h>
#include <stdlib.h>
#include <string.h>
#include <math.h>

typedef double (*f_dbl)(double);

double dummy(double x)
{
f_dbl f = TAGF;
f_dbl g = TAGG;
return f(g(x));
}

f_dbl composite(f_dbl f, f_dbl g)
{
size_t len = (void*)composite - (void*)dummy;
f_dbl ret = malloc(len);
char *ptr;
memcpy(ret, dummy, len);
for (ptr = (char*)ret; ptr < (char*)ret + len - sizeof(f_dbl); ptr++) {
if (*(f_dbl*)ptr == TAGF)      *(f_dbl*)ptr = f;
else if (*(f_dbl*)ptr == TAGG) *(f_dbl*)ptr = g;
}
return ret;
}

double cube(double x)
{
return x * x * x;
}

/* uncomment next line if your math.h doesn't have cbrt() */
/* double cbrt(double x) { return pow(x, 1/3.); } */

int main()
{
int i;
double x;

f_dbl A[3] = { cube, exp, sin };
f_dbl B[3] = { cbrt, log, asin}; /* not sure about availablity of cbrt() */
f_dbl C[3];

for (i = 0; i < 3; i++)
C[i] = composite(A[i], B[i]);

for (i = 0; i < 3; i++) {
for (x = .2; x <= 1; x += .2)
printf("C%d(%g) = %g\n", i, x, C[i](x));
printf("\n");
}
return 0;
}


(Boring) outputC0(0.2) = 0.2 C0(0.4) = 0.4 C0(0.6) = 0.6 C0(0.8) = 0.8 C0(1) = 1

C1(0.2) = 0.2 C1(0.4) = 0.4 C1(0.6) = 0.6 C1(0.8) = 0.8 C1(1) = 1

C2(0.2) = 0.2 C2(0.4) = 0.4 C2(0.6) = 0.6 C2(0.8) = 0.8 C2(1) = 1



## C#

c#
using System;

class Program
{
static void Main(string[] args)
{
var cube = new Func<double, double>(x => Math.Pow(x, 3.0));
var croot = new Func<double, double>(x => Math.Pow(x, 1 / 3.0));

var functionTuples = new[]
{
(forward: Math.Sin, backward: Math.Asin),
(forward: Math.Cos, backward: Math.Acos),
(forward: cube,     backward: croot)
};

foreach (var ft in functionTuples)
{
Console.WriteLine(ft.backward(ft.forward(0.5)));
}
}
}



Output:

0.5
0.5
0.5


## C++

{{works with|C++11}}


#include <functional>
#include <algorithm>
#include <iostream>
#include <vector>
#include <cmath>

using std::cout;
using std::endl;
using std::vector;
using std::function;
using std::transform;
using std::back_inserter;

typedef function<double(double)> FunType;

vector<FunType> A = {sin, cos, tan, [](double x) { return x*x*x; } };
vector<FunType> B = {asin, acos, atan, [](double x) { return exp(log(x)/3); } };

template <typename A, typename B, typename C>
function<C(A)> compose(function<C(B)> f, function<B(A)> g) {
return [f,g](A x) { return f(g(x)); };
}

int main() {
vector<FunType> composedFuns;
auto exNums = {0.0, 0.2, 0.4, 0.6, 0.8, 1.0};

transform(B.begin(), B.end(),
A.begin(),
back_inserter(composedFuns),
compose<double, double, double>);

for (auto num: exNums)
for (auto fun: composedFuns)
cout << u8"f\u207B\u00B9.f(" << num << ") = " << fun(num) << endl;

return 0;
}



## Ceylon

{{works with|Ceylon 1.2.1}} First, you need to import the numeric module in you module.ceylon file

module rosetta "1.0.0" {
import ceylon.numeric "1.2.1";
}


And then you can use the math functions in your run.ceylon file

import ceylon.numeric.float {

sin, exp, asin, log
}

shared void run() {

function cube(Float x) => x ^ 3;
function cubeRoot(Float x) => x ^ (1.0 / 3.0);

value functions = {sin, exp, cube};
value inverses = {asin, log, cubeRoot};

for([func, inv] in zipPairs(functions, inverses)) {
print(compose(func, inv)(0.5));
}
}


## Clojure


(use 'clojure.contrib.math)
(let [fns [#(Math/sin %) #(Math/cos %) (fn [x] (* x x x))]
inv [#(Math/asin %) #(Math/acos %) #(expt % 1/3)]]
(map #(% 0.5) (map #(comp %1 %2) fns inv)))



Output:

(0.5 0.4999999999999999 0.5000000000000001)


## CoffeeScript

{{trans|JavaScript}}

# Functions as values of a variable
cube = (x) -> Math.pow x, 3
cuberoot = (x) -> Math.pow x, 1 / 3

# Higher order function
compose = (f, g) -> (x) -> f g(x)

# Storing functions in a array
fun = [Math.sin, Math.cos, cube]
inv = [Math.asin, Math.acos, cuberoot]

# Applying the composition to 0.5
console.log compose(inv[i], fun[i])(0.5) for i in [0..2]​​​​​​​


Output:

0.5
0.4999999999999999
0.5


## Common Lisp

(defun compose (f g) (lambda (x) (funcall f (funcall g x))))
(defun cube (x) (expt x 3))
(defun cube-root (x) (expt x (/ 3)))

(loop with value = 0.5
for func in (list #'sin  #'cos  #'cube     )
for inverse  in (list #'asin #'acos #'cube-root)
for composed = (compose inverse func)
do (format t "~&(~A ∘ ~A)(~A) = ~A~%"
inverse
func
value
(funcall composed value)))


Output:

(#<FUNCTION ASIN> ∘ #<FUNCTION SIN>)(0.5) = 0.5
(#<FUNCTION ACOS> ∘ #<FUNCTION COS>)(0.5) = 0.5
(#<FUNCTION CUBE-ROOT> ∘ #<FUNCTION CUBE>)(0.5) = 0.5


## D

### Using Standard Compose

void main() {
import std.stdio, std.math, std.typetuple, std.functional;

alias dir = TypeTuple!(sin,  cos,  x => x ^^ 3);
alias inv = TypeTuple!(asin, acos, cbrt);
// foreach (f, g; staticZip!(dir, inv))
foreach (immutable i, f; dir)
writefln("%6.3f", compose!(f, inv[i])(0.5));
}


{{out}}

 0.500
0.500
0.500


### Defining Compose

Here we need wrappers because the standard functions have different signatures (eg pure/nothrow). Same output.

void main() {
import std.stdio, std.math, std.range;

static T delegate(S) compose(T, U, S)(in T function(in U) f,
in U function(in S) g) {
return s => f(g(s));
}

immutable sin  = (in real x) pure nothrow => x.sin,
asin = (in real x) pure nothrow => x.asin,
cos  = (in real x) pure nothrow => x.cos,
acos = (in real x) pure nothrow => x.acos,
cube = (in real x) pure nothrow => x ^^ 3,
cbrt = (in real x) /*pure*/ nothrow => x.cbrt;

foreach (f, g; [sin, cos, cube].zip([asin, acos, cbrt]))
writefln("%6.3f", compose(f, g)(0.5));
}


## Dart

import 'dart:math' as Math;
cube(x) => x*x*x;
cuberoot(x)  => Math.pow(x, 1/3);
compose(f,g) => ((x)=>f(g(x)));
main(){
var functions = [Math.sin, Math.exp, cube];
var inverses = [Math.asin, Math.log, cuberoot];
for (int i = 0; i < 3; i++){
print(compose(functions[i], inverses[i])(0.5));
}
}


{{out}}


0.49999999999999994
0.5
0.5000000000000001



negate:
- 0

set :A [ @++ $@negate @-- ] set :B [ @--$ @++ @negate ]

test n:
for i range 0 -- len A:
if /= n call compose @B! i @A! i n:
return false
true

test to-num !prompt "Enter a number: "
if:
!print "f^-1(f(x)) = x"
else:
!print "Something went wrong."



{{out}}

Enter a number: 23
f^-1(f(x)) = x


## Dyalect

===Create new functions from preexisting functions at run-time===

Using partial application:

func apply(fun, x) { y => fun(x, y) }

func sum(x, y) { x + y }

func sum2 = apply(sum, 2)


### Store functions in collections

func sum(x, y) { x + y }
func doubleMe(x) { x + x }

var arr = []


### Use functions as arguments to other functions

func Iterator.filter(pred) {
for x in this when pred(x) {
yield x
}
}

[1,2,3,4,5].iter().filter(x => x % 2 == 0)


### Use functions as return values of other functions

func flip(fun, x, y) {
(y, x) => fun(x, y)
}


## E

First, a brief summary of the relevant semantics: In E, every value, including built-in and user-defined functions, "is an object" — it has methods which respond to messages. Methods are distinguished by the given name (''verb'') and the number of parameters (''arity''). By convention and syntactic sugar, a ''function'' is an object which has a method whose verb is "run".

The relevant mathematical operations are provided as methods on floats, so the first thing we must do is define them as functions.

def sin(x)  { return x.sin() }
def cos(x)  { return x.cos() }
def asin(x) { return x.asin() }
def acos(x) { return x.acos() }
def cube(x) { return x ** 3     }
def curt(x) { return x ** (1/3) }

def forward := [sin,  cos,  cube]
def reverse := [asin, acos, curt]


There are no built-in functions in this list, since the original author couldn't easily think of any which had one parameter and were inverses of each other, but composition would work just the same with them.

Defining composition. fn ''params'' { ''expr'' } is shorthand for an anonymous function returning a value.

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

? def x := 0.5  \
> for i => f in forward {
>     def g := reverse[i]
>     println(x = $x, f =$f, g = $g, compose($f, $g)($x) = ${compose(f, g)(x)}) > } x = 0.5, f = <sin>, g = <asin>, compose(<sin>, <asin>)(0.5) = 0.5 x = 0.5, f = <cos>, g = <acos>, compose(<cos>, <acos>)(0.5) = 0.4999999999999999 x = 0.5, f = <cube>, g = <curt>, compose(<cube>, <curt>)(0.5) = 0.5000000000000001  Note: def g := reverse[i] is needed here because E as yet has no defined protocol for iterating over collections in parallel. [http://wiki.erights.org/wiki/Parallel_iteration Page for this issue.] ## EchoLisp  ;; adapted from Racket ;; (compose f g h ... ) is a built-in defined as : ;; (define (compose f g) (λ (x) (f (g x)))) (define (cube x) (expt x 3)) (define (cube-root x) (expt x (// 1 3))) (define funlist (list sin cos cube)) (define ifunlist (list asin acos cube-root)) (for ([f funlist] [i ifunlist]) (writeln ((compose i f) 0.5))) → 0.5 0.4999999999999999 0.5  ## Ela Translation of Haskell: open number //sin,cos,asin,acos open list //zipWith cube x = x ** 3 croot x = x ** (1/3) funclist = [sin, cos, cube] funclisti = [asin, acos, croot] zipWith (\f inversef -> (inversef << f) 0.5) funclist funclisti  Function (<<) is defined in standard prelude as: (<<) f g x = f (g x)  Output (calculations are performed on 32-bit floats): [0.5,0.5,0.499999989671302]  ## Elena ELENA 4.1 : import system'routines; import system'math; import extensions'routines; import extensions'math; extension op { compose(f,g) = f(g(self)); } public program() { var fs := new::( mssgconst sin<mathOp>[0], mssgconst cos<mathOp>[0], (x => power(x, 3.0r)) ); var gs := new::( mssgconst arcsin<mathOp>[0], mssgconst arccos<mathOp>[0], (x => power(x, 1.0r / 3)) ); fs.zipBy(gs, (f,g => 0.5r.compose(f,g))) .forEach:printingLn }  {{out}}  0.5 0.5 0.5  ## Elixir defmodule First_class_functions do def task(val) do as = [&:math.sin/1, &:math.cos/1, fn x -> x * x * x end] bs = [&:math.asin/1, &:math.acos/1, fn x -> :math.pow(x, 1/3) end] Enum.zip(as, bs) |> Enum.each(fn {a,b} -> IO.puts compose([a,b], val) end) end defp compose(funs, x) do Enum.reduce(funs, x, fn f,acc -> f.(acc) end) end end First_class_functions.task(0.5)  {{out}}  0.5 0.4999999999999999 0.5  ## Erlang  -module( first_class_functions ). -export( [task/0] ). task() -> As = [fun math:sin/1, fun math:cos/1, fun cube/1], Bs = [fun math:asin/1, fun math:acos/1, fun square_inverse/1], [io:fwrite( "Value: 1.5 Result: ~p~n", [functional_composition([A, B], 1.5)]) || {A, B} <- lists:zip(As, Bs)]. functional_composition( Funs, X ) -> lists:foldl( fun(F, Acc) -> F(Acc) end, X, Funs ). square( X ) -> math:pow( X, 2 ). square_inverse( X ) -> math:sqrt( X ).  {{out}}  93> first_class_functions:task(). Value: 1.5 Result: 1.5000000000000002 Value: 1.5 Result: 1.5 Value: 1.5 Result: 1.5  =={{header|F_Sharp|F#}}== open System let cube x = x ** 3.0 let croot x = x ** (1.0/3.0) let funclist = [Math.Sin; Math.Cos; cube] let funclisti = [Math.Asin; Math.Acos; croot] let composed = List.map2 (<<) funclist funclisti let main() = for f in composed do printfn "%f" (f 0.5) main()  Output: 0.500000 0.500000 0.500000  ## Factor The constants A and B consist of arrays containing quotations (aka anonymous functions). USING: assocs combinators kernel math.functions prettyprint sequences ; IN: rosettacode.first-class-functions CONSTANT: A { [ sin ] [ cos ] [ 3 ^ ] } CONSTANT: B { [ asin ] [ acos ] [ 1/3 ^ ] } : compose-all ( seq1 seq2 -- seq ) [ compose ] 2map ; : test-fcf ( -- ) 0.5 A B compose-all [ call( x -- y ) ] with map . ;  {{out}} { 0.5 0.4999999999999999 0.5 }  ## Fantom Methods defined for classes can be pulled out into functions, e.g. "Float#sin.func" pulls the sine method for floats out into a function accepting a single argument. This function is then a first-class value.  class FirstClassFns { static |Obj -> Obj| compose (|Obj -> Obj| fn1, |Obj -> Obj| fn2) { return |Obj x -> Obj| { fn2 (fn1 (x)) } } public static Void main () { cube := |Float a -> Float| { a * a * a } cbrt := |Float a -> Float| { a.pow(1/3f) } |Float->Float|[] fns := [Float#sin.func, Float#cos.func, cube] |Float->Float|[] inv := [Float#asin.func, Float#acos.func, cbrt] |Float->Float|[] composed := fns.map |fn, i| { compose(fn, inv[i]) } composed.each |fn| { echo (fn(0.5f)) } } }  Output:  0.5 0.4999999999999999 0.5  ## Forth : compose ( xt1 xt2 -- xt3 ) >r >r :noname r> compile, r> compile, postpone ; ; : cube fdup fdup f* f* ; : cuberoot 1e 3e f/ f** ; : table create does> swap cells + @ ; table fn ' fsin , ' fcos , ' cube , table inverse ' fasin , ' facos , ' cuberoot , : main 3 0 do i fn i inverse compose ( xt ) 0.5e execute f. loop ; main \ 0.5 0.5 0.5  ## FreeBASIC Like C, FreeBASIC doesn't have first class functions so I've contented myself by translating their code: {{trans|C}} ' FB 1.05.0 Win64 #Include "crt/math.bi" '' include math functions in C runtime library ' Declare function pointer type ' This implicitly assumes default StdCall calling convention on Windows Type Class2Func As Function(As Double) As Double ' A couple of functions with the above prototype Function functionA(v As Double) As Double Return v*v*v '' cube of v End Function Function functionB(v As Double) As Double Return Exp(Log(v)/3) '' same as cube root of v which would normally be v ^ (1.0/3.0) in FB End Function ' A function taking a function as an argument Function function1(f2 As Class2Func, val_ As Double) As Double Return f2(val_) End Function ' A function returning a function Function whichFunc(idx As Long) As Class2Func Return IIf(idx < 4, @functionA, @functionB) End Function ' Additional function needed to treat CDecl function pointer as StdCall ' Get compiler warning otherwise Function cl2(f As Function CDecl(As Double) As Double) As Class2Func Return CPtr(Class2Func, f) End Function ' A list of functions ' Using C Runtime library versions of trig functions as it doesn't appear ' to be possible to apply address operator (@) to FB's built-in versions Dim funcListA(0 To 3) As Class2Func = {@functionA, cl2(@sin_), cl2(@cos_), cl2(@tan_)} Dim funcListB(0 To 3) As Class2Func = {@functionB, cl2(@asin_), cl2(@acos_), cl2(@atan_)} ' Composing Functions Function invokeComposed(f1 As Class2Func, f2 As Class2Func, val_ As double) As Double Return f1(f2(val_)) End Function Type Composition As Class2Func f1, f2 End Type Function compose(f1 As Class2Func, f2 As Class2Func) As Composition Ptr Dim comp As Composition Ptr = Allocate(SizeOf(Composition)) comp->f1 = f1 comp->f2 = f2 Return comp End Function Function callComposed(comp As Composition Ptr, val_ As Double ) As Double Return comp->f1(comp->f2(val_)) End Function Dim ix As Integer Dim c As Composition Ptr Print "function1(functionA, 3.0) = "; CSng(function1(whichFunc(0), 3.0)) Print For ix = 0 To 3 c = compose(funcListA(ix), funcListB(ix)) Print "Composition"; ix; "(0.9) = "; CSng(callComposed(c, 0.9)) Next Deallocate(c) Print Print "Press any key to quit" Sleep  {{out}}  function1(functionA, 3.0) = 27 Composition 0(0.9) = 0.9 Composition 1(0.9) = 0.9 Composition 2(0.9) = 0.9 Composition 3(0.9) = 0.9  ## GAP # Function composition Composition := function(f, g) local h; h := function(x) return f(g(x)); end; return h; end; # Apply each function in list u, to argument x ApplyList := function(u, x) local i, n, v; n := Size(u); v := [ ]; for i in [1 .. n] do v[i] := u[i](x); od; return v; end; # Inverse and Sqrt are in the built-in library. Note that Sqrt yields values in cyclotomic fields. # For example, # gap> Sqrt(7); # E(28)^3-E(28)^11-E(28)^15+E(28)^19-E(28)^23+E(28)^27 # where E(n) is a primitive n-th root of unity a := [ i -> i + 1, Inverse, Sqrt ]; # [ function( i ) ... end, <Operation "InverseImmutable">, <Operation "Sqrt"> ] b := [ i -> i - 1, Inverse, x -> x*x ]; # [ function( i ) ... end, <Operation "InverseImmutable">, function( x ) ... end ] # Compose each couple z := ListN(a, b, Composition); # Now a test ApplyList(z, 3); [ 3, 3, 3 ]  ## Go package main import "math" import "fmt" // user-defined function, per task. Other math functions used are built-in. func cube(x float64) float64 { return math.Pow(x, 3) } // ffType and compose function taken from Function composition task type ffType func(float64) float64 func compose(f, g ffType) ffType { return func(x float64) float64 { return f(g(x)) } } func main() { // collection A funclist := []ffType{math.Sin, math.Cos, cube} // collection B funclisti := []ffType{math.Asin, math.Acos, math.Cbrt} for i := 0; i < 3; i++ { // apply composition and show result fmt.Println(compose(funclisti[i], funclist[i])(.5)) } }  Output:  0.49999999999999994 0.5 0.5  ## Groovy Solution: def compose = { f, g -> { x -> f(g(x)) } }  Test program: def cube = { it * it * it } def cubeRoot = { it ** (1/3) } funcList = [ Math.&sin, Math.&cos, cube ] inverseList = [ Math.&asin, Math.&acos, cubeRoot ] println ([funcList, inverseList].transpose().collect { f, finv -> compose(f, finv) }.collect{ it(0.5) }) println ([inverseList, funcList].transpose().collect { finv, f -> compose(finv, f) }.collect{ it(0.5) })  Output: [0.5, 0.4999999999999999, 0.5000000000346574] [0.5, 0.4999999999999999, 0.5000000000346574]  ## Haskell  a -> a cube x = x ** 3.0 croot :: Floating a => a -> a croot x = x ** (1/3) -- compose already exists in Haskell as the . operator -- compose :: (a -> b) -> (b -> c) -> a -> c -- compose f g = \x -> g (f x) funclist :: Floating a => [a -> a] funclist = [sin, cos, cube ] invlist :: Floating a => [a -> a] invlist = [asin, acos, croot] main :: IO () main = print$ zipWith (\f i -> f . i $0.5) funclist invlist  {{output}} [0.5,0.4999999999999999,0.5000000000000001]  =={{header|Icon}} and {{header|Unicon}}== The Unicon solution can be modified to work in Icon. See [[Function_composition#Icon_and_Unicon]]. link compose procedure main(arglist) fun := [sin,cos,cube] inv := [asin,acos,cuberoot] x := 0.5 every i := 1 to *inv do write("f(",x,") := ", compose(inv[i],fun[i])(x)) end procedure cube(x) return x*x*x end procedure cuberoot(x) return x ^ (1./3) end  Please refer to See [[Function_composition#Icon_and_Unicon]] for 'compose'. Sample Output: f(0.5) := 0.5 f(0.5) := 0.4999999999999999 f(0.5) := 0.5  ## J ### Explicit version J has some subtleties which are not addressed in this specification (J functions have grammatical character and their [[wp:Gerund|gerundial form]] may be placed in data structures where the spec sort of implies that there be no such distinction - for those uncomfortable with this terminology it is best to think of these as type distinctions - the type which appears in data structures and the type which may be applied are distinct though each may be directly derived from the other). However, here are the basics which were requested:  sin=: 1&o. cos=: 2&o. cube=: ^&3 square=: *: unqo=: :6 unqcol=: :0 quot=: 1 :'{.u''''' A=: sincoscubesquare B=: monad def'y unqo inv quot'"0 A BA=. A dyad def'x unqo@(y unqo) quot'"0 B  A unqcol 0.5 0.479426 0.877583 0.125 0.25 BA unqcol 0.5 0.5 0.5 0.5 0.5  ===Tacit (unorthodox) version=== In J only adverbs and conjunctions (functionals) can produce verbs (functions)... Unless they are forced to cloak as verbs (functions). (Note that this takes advantage of a bug/feature of the interpreter ; see [http://rosettacode.org/wiki/Closures/Value_capture#Tacit_.28unorthodox.29_version unorthodox tacit] .) The resulting functions (which correspond to functionals) can take and produce functions: j train =. (<':')(0:)(,^:)&6 NB. Producing the function train corresponding to the functional :6 inverse=. (<'^:')(0:)(,^:)&_1 NB. Producing the function inverse corresponding to the functional ^:_1 compose=. (<'@:')(0:)(,^:) NB. Producing the function compose corresponding to the functional @: an =. <@:((,'0') ; ]) NB. Producing the atomic representation of a noun of =. train@:([ ; an) NB. Evaluating a function for an argument box =. < @: train"0 NB. Producing a boxed list of the trains of the components ]A =. box (1&o.)(2&o.)(^&3) NB. Producing a boxed list containing the Sin, Cos and Cubic functions ┌────┬────┬───┐ │1&o.│2&o.│^&3│ └────┴────┴───┘ ]B =. inverse &.> A NB. Producing their inverses ┌────────┬────────┬───────┐ │1&o.^:_1│2&o.^:_1│^&3^:_1│ └────────┴────────┴───────┘ ]BA=. B compose &.> A NB. Producing the compositions of the functions and their inverses ┌────────────────┬────────────────┬──────────────┐ │1&o.^:_1@:(1&o.)│2&o.^:_1@:(2&o.)│^&3^:_1@:(^&3)│ └────────────────┴────────────────┴──────────────┘ BA of &> 0.5 NB. Evaluating the compositions at 0.5 0.5 0.5 0.5  ## Java Java doesn't technically have first-class functions. Java can simulate first-class functions to a certain extent, with anonymous classes and generic function interface. {{works with|Java|1.5+}} import java.util.ArrayList; public class FirstClass{ public interface Function<A,B>{ B apply(A x); } public static <A,B,C> Function<A, C> compose( final Function<B, C> f, final Function<A, B> g) { return new Function<A, C>() { @Override public C apply(A x) { return f.apply(g.apply(x)); } }; } public static void main(String[] args){ ArrayList<Function<Double, Double>> functions = new ArrayList<Function<Double,Double>>(); functions.add( new Function<Double, Double>(){ @Override public Double apply(Double x){ return Math.cos(x); } }); functions.add( new Function<Double, Double>(){ @Override public Double apply(Double x){ return Math.tan(x); } }); functions.add( new Function<Double, Double>(){ @Override public Double apply(Double x){ return x * x; } }); ArrayList<Function<Double, Double>> inverse = new ArrayList<Function<Double,Double>>(); inverse.add( new Function<Double, Double>(){ @Override public Double apply(Double x){ return Math.acos(x); } }); inverse.add( new Function<Double, Double>(){ @Override public Double apply(Double x){ return Math.atan(x); } }); inverse.add( new Function<Double, Double>(){ @Override public Double apply(Double x){ return Math.sqrt(x); } }); System.out.println("Compositions:"); for(int i = 0; i < functions.size(); i++){ System.out.println(compose(functions.get(i), inverse.get(i)).apply(0.5)); } System.out.println("Hard-coded compositions:"); System.out.println(Math.cos(Math.acos(0.5))); System.out.println(Math.tan(Math.atan(0.5))); System.out.println(Math.pow(Math.sqrt(0.5), 2)); } }  Output: Compositions: 0.4999999999999999 0.49999999999999994 0.5000000000000001 Hard-coded compositions: 0.4999999999999999 0.49999999999999994 0.5000000000000001  {{works with|Java|8+}} import java.util.ArrayList; import java.util.function.Function; public class FirstClass{ public static void main(String... arguments){ ArrayList<Function<Double, Double>> functions = new ArrayList<>(); functions.add(Math::cos); functions.add(Math::tan); functions.add(x -> x * x); ArrayList<Function<Double, Double>> inverse = new ArrayList<>(); inverse.add(Math::acos); inverse.add(Math::atan); inverse.add(Math::sqrt); System.out.println("Compositions:"); for (int i = 0; i < functions.size(); i++){ System.out.println(functions.get(i).compose(inverse.get(i)).apply(0.5)); } System.out.println("Hard-coded compositions:"); System.out.println(Math.cos(Math.acos(0.5))); System.out.println(Math.tan(Math.atan(0.5))); System.out.println(Math.pow(Math.sqrt(0.5), 2)); } }  ## JavaScript ### ES5 // Functions as values of a variable var cube = function (x) { return Math.pow(x, 3); }; var cuberoot = function (x) { return Math.pow(x, 1 / 3); }; // Higher order function var compose = function (f, g) { return function (x) { return f(g(x)); }; }; // Storing functions in a array var fun = [Math.sin, Math.cos, cube]; var inv = [Math.asin, Math.acos, cuberoot]; for (var i = 0; i < 3; i++) { // Applying the composition to 0.5 console.log(compose(inv[i], fun[i])(0.5)); }  ### ES6 // Functions as values of a variable var cube = x => Math.pow(x, 3); var cuberoot = x => Math.pow(x, 1 / 3); // Higher order function var compose = (f, g) => (x => f(g(x))); // Storing functions in a array var fun = [ Math.sin, Math.cos, cube ]; var inv = [ Math.asin, Math.acos, cuberoot ]; for (var i = 0; i < 3; i++) { // Applying the composition to 0.5 console.log(compose(inv[i], fun[i])(0.5)); }  Result is always: 0.5 0.4999999999999999 0.5  ## Julia #!/usr/bin/julia function compose(f::Function, g::Function) return x -> f(g(x)) end value = 0.5 for pair in [(sin, asin), (cos, acos), (x -> x^3, x -> x^(1/3))] func, inverse = pair println(compose(func, inverse)(value)) end  Output: 0.5 0.4999999999999999 0.5000000000000001  ## Kotlin // version 1.0.6 fun compose(f: (Double) -> Double, g: (Double) -> Double ): (Double) -> Double = { f(g(it)) } fun cube(d: Double) = d * d * d fun main(args: Array<String>) { val listA = listOf(Math::sin, Math::cos, ::cube) val listB = listOf(Math::asin, Math::acos, Math::cbrt) val x = 0.5 for (i in 0..2) println(compose(listA[i], listB[i])(x)) }  {{out}}  0.5 0.4999999999999999 0.5000000000000001  ## Lambdatalk Tested in [http://epsilonwiki.free.fr/ELS_YAW/?view=p227]  {def cube {lambda {:x} {pow :x 3}}} {def cuberoot {lambda {:x} {pow :x {/ 1 3}}}} {def compose {lambda {:f :g :x} {:f {:g :x}}}} {def fun sin cos cube} {def inv asin acos cuberoot} {def display {lambda {:i} {br}{compose {nth :i {fun}} {nth :i {inv}} 0.5}}} {map display {serie 0 2}} Output: 0.5 0.49999999999999994 0.5000000000000001  ## Lasso #!/usr/bin/lasso9 define cube(x::decimal) => { return #x -> pow(3.0) } define cuberoot(x::decimal) => { return #x -> pow(1.0/3.0) } define compose(f, g, v) => { return { return #f -> detach -> invoke(#g -> detach -> invoke(#1)) } -> detach -> invoke(#v) } local(functions = array({return #1 -> sin}, {return #1 -> cos}, {return cube(#1)})) local(inverse = array({return #1 -> asin}, {return #1 -> acos}, {return cuberoot(#1)})) loop(3) stdoutnl( compose( #functions -> get(loop_count), #inverse -> get(loop_count), 0.5 ) ) /loop  Output: 0.500000 0.500000 0.500000  ## Lingo Lingo does not support functions as first-class objects. But with the limitations described under [https://www.rosettacode.org/wiki/Function_composition#Lingo Function composition] the task can be solved: -- sin, cos and sqrt are built-in, square, asin and acos are user-defined A = [#sin, #cos, #square] B = [#asin, #acos, #sqrt] testValue = 0.5 repeat with i = 1 to 3 -- for implementation details of compose() see https://www.rosettacode.org/wiki/Function_composition#Lingo f = compose(A[i], B[i]) res = call(f, _movie, testValue) put res = testValue end repeat  {{out}}  -- 1 -- 1 -- 1  User-defined arithmetic functions used in code above: on square (x) return x*x end on asin (x) res = atan(sqrt(x*x/(1-x*x))) if x<0 then res = -res return res end on acos (x) return PI/2 - asin(x) end  ## Lua function compose(f,g) return function(...) return f(g(...)) end end fn = {math.sin, math.cos, function(x) return x^3 end} inv = {math.asin, math.acos, function(x) return x^(1/3) end} for i, v in ipairs(fn) do local f = compose(v, inv[i]) print(f(0.5)) end  Output: 0.5 0.5 0.5  ## M2000 Interpreter Cos, Sin works with degrees, Number pop number from stack of values, so we didn't use a variable like this POW3INV =Lambda (x)->x**(1/3) M2000 Interpreter Module CheckFirst { RAD = lambda -> number/180*pi ASIN = lambda RAD -> { Read x : x=Round(x,10) If x>=0 and X<1 Then { =RAD(abs(2*Round(ATN(x/(1+SQRT(1-x**2)))))) } Else.if x==1 Then { =RAD(90) } Else error "asin exit limit" } ACOS=lambda ASIN (x) -> PI/2 - ASIN(x) POW3 = Lambda ->number**3 POW3INV =Lambda ->number**(1/3) COSRAD =lambda ->Cos(number*180/pi) SINRAD=lambda ->Sin(number*180/pi) Composed=lambda (f1, f2) -> { =lambda f1, f2 (x)->{ =f1(f2(x)) } } Dim Base 0, A(3), B(3), C(3) A(0)=ACOS, ASIN, POW3INV B(0)=COSRAD, SINRAD, POW3 C(0)=Composed(ACOS, COSRAD), Composed(ASIN, SINRAD), Composed(POW3INV, POW3) Print$("0.00")
For i=0 To 2 {
Print A(i)(B(i)(.5)), C(i)(.5)
}
}
CheckFirst



## Maple

The composition operator in Maple is denoted by "@". We use "zip" to produce the list of compositions. The cubing procedure and its inverse are each computed.


> A := [ sin, cos, x -> x^3 ]:
> B := [ arcsin, arccos, rcurry( surd, 3 ) ]:
> zip( @, A, B )( 2/3 );
[2/3, 2/3, 2/3]

> zip( @, B, A )( 2/3 );
[2/3, 2/3, 2/3]



=={{header|Mathematica}} / {{header|Wolfram Language}}== The built-in function Composition can do composition, a custom function that does the same would be compose[f_,g_]:=f[g[#]]&. However the latter only works with 2 arguments, Composition works with any number of arguments.

funcs = {Sin, Cos, #^3 &};
funcsi = {ArcSin, ArcCos, #^(1/3) &};
compositefuncs = Composition @@@ Transpose[{funcs, funcsi}];
Table[i[0.666], {i, compositefuncs}]


gives back:

{0.666, 0.666, 0.666}


Note that I implemented cube and cube-root as pure functions. This shows that Mathematica is fully able to handle functions as variables, functions can return functions, and functions can be given as an argument. 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]]]


## Maxima

a: [sin, cos, lambda([x], x^3)]$b: [asin, acos, lambda([x], x^(1/3))]$
compose(f, g) := buildq([f, g], lambda([x], f(g(x))))$map(lambda([fun], fun(x)), map(compose, a, b)); [x, x, x]  ## Mercury This solution uses the compose/3 function defined in std_util (part of the Mercury standard library) to demonstrate the use of first-class functions. The following process is followed: # A list of "forward" functions is provided (sin, cosine and a lambda that calls ln). # A list of "reverse" functions is provided (asin, acosine and a lambda that calls exp). # The lists are mapped in corresponding members through an anonymous function that composes the resulting pairs of functions and applies them to the value 0.5. # The results are returned and printed when all function pairs have been processed. ### firstclass.m  :- module firstclass. :- interface. :- import_module io. :- pred main(io::di, io::uo) is det. :- implementation. :- import_module exception, list, math, std_util. main(!IO) :- Forward = [sin, cos, (func(X) = ln(X))], Reverse = [asin, acos, (func(X) = exp(X))], Results = map_corresponding( (func(F, R) = compose(R, F, 0.5)), Forward, Reverse), write_list(Results, ", ", write_float, !IO), write_string("\n", !IO).  ### Use and output <nowiki>$ mmc -E firstclass.m && ./firstclass
0.5, 0.4999999999999999, 0.5</nowiki>


(Limitations of the IEEE floating point representation make the cos/acos pairing lose a little bit of accuracy.)

## min

{{works with|min|0.19.3}} Note concat is what performs the function composition, as functions are lists in min.

('sin 'cos (3 pow)) =A
('asin 'acos (1 3 / pow)) =B

(A bool) (
0.5 A first B first concat -> puts!
A rest #A
B rest #B
) while


{{out}}


0.5
0.4999999999999999
0.5



## Nemerle

{{trans|Python}}

using System;
using System.Console;
using System.Math;
using Nemerle.Collections.NCollectionsExtensions;

module FirstClassFunc
{
Main() : void
{
def cube = fun (x) {x * x * x};
def croot = fun (x) {Pow(x, 1.0/3.0)};
def compose = fun(f, g) {fun (x) {f(g(x))}};
def funcs = [Sin, Cos, cube];
def ifuncs = [Asin, Acos, croot];
WriteLine($[compose(f, g)(0.5) | (f, g) in ZipLazy(funcs, ifuncs)]); } }  ### Use and Output C:\Rosetta>ncc -o:FirstClassFunc FirstClassFunc.n C:Rosetta>FirstClassFunc [0.5, 0.5, 0.5] ## newLISP  (define (compose f g) (expand (lambda (x) (f (g x))) 'f 'g)) (lambda (f g) (expand (lambda (x) (f (g x))) 'f 'g)) > (define (cube x) (pow x 3)) (lambda (x) (pow x 3)) > (define (cube-root x) (pow x (div 1 3))) (lambda (x) (pow x (div 1 3))) > (define functions '(sin cos cube)) (sin cos cube) > (define inverses '(asin acos cube-root)) (asin acos cube-root) > (map (fn (f g) ((compose f g) 0.5)) functions inverses) (0.5 0.5 0.5)  ## Nim {{trans|ES6}} from math import nil proc cube(x: float64) : float64 {.procvar.} = math.pow(x, 3) proc cuberoot(x: float64) : float64 {.procvar.} = math.pow(x, 1/3) proc compose[A](f: proc(x: A): A, g: proc(x: A): A) : (proc(x: A): A) = proc c(x: A): A {.closure.} = f(g(x)) return c proc sin(x: float64) : float64 {.procvar.} = math.sin(x) proc asin(x: float64) : float64 {.procvar.}= math.arcsin(x) proc cos(x: float64) : float64 {.procvar.} = math.cos(x) proc acos(x: float64) : float64 {.procvar.} = math.arccos(x) var fun = @[sin, cos, cube] var inv = @[asin, acos, cuberoot] for i in 0..2: echo$compose(inv[i], fun[i])(0.5)


Output:

0.5
0.4999999999999999
0.5


## Objeck

use Collection.Generic;

lambdas Func {
Double : (FloatHolder) ~ FloatHolder
}

class FirstClass {
function : Main(args : String[]) ~ Nil {
vector := Vector->New()<Func2Holder <FloatHolder, FloatHolder> >;
# store functions in collections
=>  v * v)<FloatHolder, FloatHolder>);
# new function from preexisting function at run-time
=> Float->SquareRoot(v->Get()))<FloatHolder, FloatHolder>);
# process collection
each(i : vector) {
# return value of other functions and pass argument to other function
Show(vector->Get(i)<Func2Holder>->Get()<FloatHolder, FloatHolder>);
};
}

function : Show(func : (FloatHolder) ~ FloatHolder) ~ Nil {
func(13.5)->Get()->PrintLine();
}
}


## OCaml

# let cube x = x ** 3. ;;
val cube : float -> float = <fun>

# let croot x = x ** (1. /. 3.) ;;
val croot : float -> float = <fun>

# let compose f g = fun x -> f (g x) ;;  (* we could have written "let compose f g x = f (g x)" but we show this for clarity *)
val compose : ('a -> 'b) -> ('c -> 'a) -> 'c -> 'b = <fun>

# let funclist = [sin; cos; cube] ;;
val funclist : (float -> float) list = [<fun>; <fun>; <fun>]

# let funclisti = [asin; acos; croot] ;;
val funclisti : (float -> float) list = [<fun>; <fun>; <fun>]

# List.map2 (fun f inversef -> (compose inversef f) 0.5) funclist funclisti ;;
- : float list = [0.5; 0.499999999999999889; 0.5]


## Octave

function r = cube(x)
r = x.^3;
endfunction

function r = croot(x)
r = x.^(1/3);
endfunction

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

f1 = {@sin, @cos, @cube};
f2 = {@asin, @acos, @croot};

for i = 1:3
disp(compose(f1{i}, f2{i})(.5))
endfor


{{Out}}

 0.50000
0.50000
0.50000


## Oforth

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

[ #cos, #sin, #[ 3 pow ] ] [ #acos, #asin, #[ 3 inv powf ] ] zipWith(#compose)
map(#[ 0.5 swap perform ]) conform(#[ 0.5 == ]) println



{{Out}}


1



## Ol


; creation of new function from preexisting functions at run-time
(define (compose f g) (lambda (x) (f (g x))))

; storing functions in collection
(define (quad x) (* x x x x))
(define (quad-root x) (sqrt (sqrt x)))

; use functions as arguments to other functions
; and use functions as return values of other functions
(define identity (compose (ref collection 2) (ref collection 1)))
(print (identity 11211776))



## Oz

This is now also compatible with Oz v 2.0 (To be executed in the Oz OPI, by typing ctl+. ctl+b)

declare

fun {Compose F G}
my @flist2 = ( \&asin,               \&acos,               $croot ); print join "\n", map { compose($flist1[$_],$flist2[$_]) -> (0.5) } 0..2;  Output: 0.5 0.5 0.5  ## Perl 6 Here we use the Z ("zipwith") metaoperator to zip the 𝐴 and 𝐵 lists with a user-defined compose function, expressed as an infix operator, . The .() construct invokes the function contained in the$_ (current topic) variable.

sub infix:<∘> (&𝑔, &𝑓) { -> \x { 𝑔 𝑓 x } }

my \𝐴 = &sin,  &cos,  { $_ ** <3/1> } my \𝐵 = &asin, &acos, {$_ ** <1/3> }

say .(.5) for 𝐴 Z∘ 𝐵


Output:

0.5
0.5
0.5


Operators, both buildin and user-defined, are first class too.

my @a = 1,2,3;
my @op = &infix:<+>, &infix:<->, &infix:<*>;
for flat @a Z @op -> $v, &op { say 42.&op($v) }


{{output}}

43
40
126


## 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, constant m cannot be used the same way as a routine_id, and a standard routine_id cannot be passed to call_composite, but tagging ctable entries so that you know exactly what to do with them does not sound 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


## PHP

{{trans|JavaScript}} {{works with|PHP|5.3+}}

Non-anonymous functions can only be passed around by name, but the syntax for calling them is identical in both cases. Object or class methods require a different syntax involving array pseudo-types and call_user_func. So PHP could be said to have ''some'' first class functionality.

$compose = function ($f, $g) { return function ($x) use ($f,$g) {
return $f($g($x)); }; };$fn  = array('sin', 'cos', function ($x) { return pow($x, 3); });
$inv = array('asin', 'acos', function ($x) { return pow($x, 1/3); }); for ($i = 0; $i < 3;$i++) {
$f =$compose($inv[$i], $fn[$i]);
echo $f(0.5), PHP_EOL; }  Output: 0.5 0.5 0.5  ## PicoLisp (load "@lib/math.l") (de compose (F G) (curry (F G) (X) (F (G X)) ) ) (de cube (X) (pow X 3.0) ) (de cubeRoot (X) (pow X 0.3333333) ) (mapc '((Fun Inv) (prinl (format ((compose Inv Fun) 0.5) *Scl)) ) '(sin cos cube) '(asin acos cubeRoot) )  Output: 0.500001 0.499999 0.500000  ## PostScript  % PostScript has 'sin' and 'cos', but not these /asin { dup dup 1. add exch 1. exch sub mul sqrt atan } def /acos { dup dup 1. add exch 1. exch sub mul sqrt exch atan } def /cube { 3 exp } def /cuberoot { 1. 3. div exp } def /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 /funcs [ /sin load /cos load /cube load ] def /ifuncs [ /asin load /acos load /cuberoot load ] def 0 1 funcs length 1 sub { /i exch def ifuncs i get funcs i get compose .5 exch exec == } for  ## Prolog Works with SWI-Prolog and module lambda, written by Ulrich Neumerkel found here: http://www.complang.tuwien.ac.at/ulrich/Prolog-inedit/lambda.pl :- use_module(library(lambda)). compose(F,G, FG) :- FG = \X^Z^(call(G,X,Y), call(F,Y,Z)). cube(X, Y) :- Y is X ** 3. cube_root(X, Y) :- Y is X ** (1/3). first_class :- L = [sin, cos, cube], IL = [asin, acos, cube_root], % we create the composed functions maplist(compose, L, IL, Lst), % we call the functions maplist(call, Lst, [0.5,0.5,0.5], R), % we display the results maplist(writeln, R).  Output :  ?- first_class. 0.5 0.4999999999999999 0.5000000000000001 true.  ## Python  # Some built in functions and their inverses >>> from math import sin, cos, acos, asin >>> # Add a user defined function and its inverse >>> cube = lambda x: x * x * x >>> croot = lambda x: x ** (1/3.0) >>> # First class functions allow run-time creation of functions from functions >>> # return function compose(f,g)(x) == f(g(x)) >>> compose = lambda f1, f2: ( lambda x: f1(f2(x)) ) >>> # first class functions should be able to be members of collection types >>> funclist = [sin, cos, cube] >>> funclisti = [asin, acos, croot] >>> # Apply functions from lists as easily as integers >>> [compose(inversef, f)(.5) for f, inversef in zip(funclist, funclisti)] [0.5, 0.4999999999999999, 0.5] >>>  Or, equivalently: {{Works with|Python|3.7}} '''First-class functions''' from math import (acos, cos, asin, sin) from inspect import signature # main :: IO () def main(): '''Composition of several functions.''' pwr = flip(curry(pow)) fs = [sin, cos, pwr(3.0)] ifs = [asin, acos, pwr(1 / 3.0)] print([ f(0.5) for f in zipWith(compose)(fs)(ifs) ]) # GENERIC FUNCTIONS ------------------------------ # compose (<<<) :: (b -> c) -> (a -> b) -> a -> c def compose(g): '''Right to left function composition.''' return lambda f: lambda x: g(f(x)) # curry :: ((a, b) -> c) -> a -> b -> c def curry(f): '''A curried function derived from an uncurried function.''' return lambda a: lambda b: f(a, b) # flip :: (a -> b -> c) -> b -> a -> c def flip(f): '''The (curried or uncurried) function f with its two arguments reversed.''' if 1 < len(signature(f).parameters): return lambda a, b: f(b, a) else: return lambda a: lambda b: f(b)(a) # 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: [ f(a)(b) for (a, b) in zip(xs, ys) ] if __name__ == '__main__': main()  {{Out}} [0.49999999999999994, 0.5000000000000001, 0.5000000000000001]  ## R cube <- function(x) x^3 croot <- function(x) x^(1/3) compose <- function(f, g) function(x){f(g(x))} f1 <- c(sin, cos, cube) f2 <- c(asin, acos, croot) for(i in 1:3) { print(compose(f1[[i]], f2[[i]])(.5)) }  {{Out}} [1] 0.5 [1] 0.5 [1] 0.5  Alternatively: sapply(mapply(compose,f1,f2),do.call,list(.5))  {{Out}} [1] 0.5 0.5 0.5  ## Racket #lang racket (define (compose f g) (λ (x) (f (g x)))) (define (cube x) (expt x 3)) (define (cube-root x) (expt x (/ 1 3))) (define funlist (list sin cos cube)) (define ifunlist (list asin acos cube-root)) (for ([f funlist] [i ifunlist]) (displayln ((compose i f) 0.5)))  {{out}}  0.5 0.4999999999999999 0.5  ## REBOL {{incomplete|REBOL|Fails to demonstrate that the result of applying the composition of each function in A and its inverse in B to a value, is the original value}} REBOL [ Title: "First Class Functions" URL: http://rosettacode.org/wiki/First-class_functions ] ; 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]] cube: func [x][x * x * x] croot: func [x][power x 1 / 3] ; "compose" means something else in REBOL, so I "fashion" an alternative. fashion: func [f1 f2][ do compose/deep [func [x][(:f1) (:f2) x]]] A: [foo sine cosine cube] B: [bar arcsine arccosine croot] while [not tail? A][ fn: fashion get A/1 get B/1 source fn ; Prove that functions actually got composed. print [fn 0.5 crlf] A: next A B: next B ; Advance to next pair. ]  ## REXX The REXX language doesn't have any trigonometric functions built-in, nor the square root function, so several higher-math functions are included herein as RYO functions. The only REXX functions that have an inverse are: ::::* d2x ◄──► x2d ::::* d2c ◄──► c2d ::::* c2x ◄──► x2c These six functions (generally) only support non-negative integers, so a special test in the program below only supplies appropriate integers when testing the first function listed in the '''A''' collection. /*REXX program demonstrates first─class functions (as a list of the names of functions).*/ A = 'd2x square sin cos' /*a list of functions to demonstrate.*/ B = 'x2d sqrt Asin Acos' /*the inverse functions of above list. */ w=digits() /*W: width of numbers to be displayed.*/ /* [↓] collection of A & B functions*/ do j=1 for words(A); say; say /*step through the list; 2 blank lines*/ say center("number",w) center('function', 3*w+1) center("inverse", 4*w) say copies("─" ,w) copies("─", 3*w+1) copies("─", 4*w) if j<2 then call test j, 20 60 500 /*functions X2D, D2X: integers only. */ else call test j, 0 0.5 1 2 /*all other functions: floating point.*/ end /*j*/ exit /*stick a fork in it, we're all done. */ /*──────────────────────────────────────────────────────────────────────────────────────*/ Acos: procedure; parse arg x; if x<-1|x>1 then call AcosErr; return .5*pi()-Asin(x) r2r: return arg(1) // (pi()*2) /*normalize radians ──► 1 unit circle*/ square: return arg(1) ** 2 pi: pi=3.14159265358979323846264338327950288419716939937510582097494459230; return pi tellErr: say; say '*** error! ***'; say; say arg(1); say; exit 13 tanErr: call tellErr 'tan(' || x") causes division by zero, X=" || x AsinErr: call tellErr 'Asin(x), X must be in the range of -1 ──► +1, X=' || x AcosErr: call tellErr 'Acos(x), X must be in the range of -1 ──► +1, X=' || x /*──────────────────────────────────────────────────────────────────────────────────────*/ Asin: procedure; parse arg x; if x<-1 | x>1 then call AsinErr; s=x*x if abs(x)>=.7 then return sign(x)*Acos(sqrt(1-s)); z=x; o=x; p=z do j=2 by 2; o=o*s*(j-1)/j; z=z+o/(j+1); if z=p then leave; p=z; end return z /*──────────────────────────────────────────────────────────────────────────────────────*/ cos: procedure; parse arg x; x=r2r(x); a=abs(x); Hpi=pi*.5 numeric fuzz min(6,digits()-3); if a=pi() then return -1 if a=Hpi | a=Hpi*3 then return 0 ; if a=pi()/3 then return .5 if a=pi()*2/3 then return -.5; return .sinCos(1,1,-1) /*──────────────────────────────────────────────────────────────────────────────────────*/ sin: procedure; parse arg x; x=r2r(x); numeric fuzz min(5, digits()-3) if abs(x)=pi() then return 0; return .sinCos(x,x,1) /*──────────────────────────────────────────────────────────────────────────────────────*/ .sinCos: parse arg z 1 p,_,i; x=x*x do k=2 by 2; _=-_*x/(k*(k+i)); z=z+_; if z=p then leave; p=z; end; return z /*──────────────────────────────────────────────────────────────────────────────────────*/ invoke: parse arg fn,v; q='"'; if datatype(v,"N") then q= _=fn || '('q || v || q")"; interpret 'func='_; return func /*──────────────────────────────────────────────────────────────────────────────────────*/ sqrt: procedure; parse arg x; if x=0 then return 0; d=digits(); m.=9; numeric form numeric digits; parse value format(x,2,1,,0) 'E0' with g 'E' _ .; g=g*.5'e'_%2 h=d+6; do j=0 while h>9; m.j=h; h=h%2+1; end /*j*/ do k=j+5 to 0 by -1; numeric digits m.k; g=(g+x/g)*.5; end /*k*/ numeric digits d; return g/1 /*──────────────────────────────────────────────────────────────────────────────────────*/ test: procedure expose A B w; parse arg fu,xList; d=digits() /*xList: numbers. */ do k=1 for words(xList); x=word(xList, k) numeric digits d+5 /*higher precision.*/ fun=word(A, fu); funV=invoke(fun, x) ; fun@=_ inv=word(B, fu); invV=invoke(inv, funV); inv@=_ numeric digits d /*restore precision*/ if datatype(funV, 'N') then funV=funV/1 /*round to digits()*/ if datatype(invV, 'N') then invV=invV/1 /*round to digits()*/ say center(x, w) right(fun@, 2*w)'='left(left('', funV>=0)funV, w), right(inv@, 3*w)'='left(left('', invV>=0)invV, w) end /*k*/ return  '''output'''  number function inverse ───────── ──────────────────────────── ──────────────────────────────────── 20 d2x(20)= 14 x2d(14)= 20 60 d2x(60)= 3C x2d("3C")= 60 500 d2x(500)= 1F4 x2d("1F4")= 500 number function inverse ───────── ──────────────────────────── ──────────────────────────────────── 0 square(0)= 0 sqrt(0)= 0 0.5 square(0.5)= 0.25 sqrt(0.25)= 0.5 1 square(1)= 1 sqrt(1)= 1 2 square(2)= 4 sqrt(4)= 2 number function inverse ───────── ──────────────────────────── ──────────────────────────────────── 0 sin(0)= 0 Asin(0)= 0 0.5 sin(0.5)= 0.479425 Asin(0.47942553860419)= 0.5 1 sin(1)= 0.841470 Asin(0.84147098480862)= 1 2 sin(2)= 0.909297 Asin(0.90929742682567)= 1.141592 number function inverse ───────── ──────────────────────────── ──────────────────────────────────── 0 cos(0)= 1 Acos(1)= 0 0.5 cos(0.5)= 0.877582 Acos(0.87758256188987)= 0.5 1 cos(1)= 0.540302 Acos(0.54030230586810)= 1 2 cos(2)=-0.416146 Acos(-0.41614683650659)= 2  The reason why '''Asin[sin(n)]''' may not equal '''n''': Each of the trigonometric functions is periodic in the real part of its argument, running through all its values twice in each interval of 2$\pi$. '''Sine''' and '''cosecant''' begin their period at 2$\pi$k − $\pi$/2 (where k is an integer), finish it at 2$\pi$k + $\pi$/2, and then reverse themselves over 2$\pi$k + $\pi$/2 ───► 2$\pi$k + 3$\pi$/2. '''Cosine''' and '''secant''' begin their period at 2$\pi$k, finish it at 2$\pi$k + $\pi$, and then reverse themselves over 2$\pi$k + $\pi$ ───► 2$\pi$k + 2$\pi$. '''Tangent''' begins its period at 2$\pi$k − $\pi$/2, finishes it at 2$\pi$k + $\pi$/2, and then repeats it (forward) over 2$\pi$k + $\pi$/2 ───► 2$\pi$k + 3$\pi$/2. '''Cotangent''' begins its period at 2$\pi$k, finishes it at 2$\pi$k + $\pi$, and then repeats it (forward) over 2$\pi$k + $\pi$ ───► 2$\pi$k + 2$\pi$. The above text is from the Wikipedia webpage: http://en.wikipedia.org/wiki/Inverse_trigonometric_functions ## Ruby cube = proc{|x| x ** 3} croot = proc{|x| x ** (1.quo 3)} compose = proc {|f,g| proc {|x| f[g[x]]}} funclist = [Math.method(:sin), Math.method(:cos), cube] invlist = [Math.method(:asin), Math.method(:acos), croot] puts funclist.zip(invlist).map {|f, invf| compose[invf, f][0.5]}  {{out}}  0.5 0.4999999999999999 0.5  ## Rust This solution uses a feature of Nightly Rust that allows us to return a closure from a function without using the extra indirection of a pointer. Stable Rust can also accomplish this challenge -- the only difference being that compose would return a Box<Fn(T) -> V> which would result in an extra heap allocation. #![feature(conservative_impl_trait)] fn main() { let cube = |x: f64| x.powi(3); let cube_root = |x: f64| x.powf(1.0 / 3.0); let flist : [&Fn(f64) -> f64; 3] = [&cube , &f64::sin , &f64::cos ]; let invlist: [&Fn(f64) -> f64; 3] = [&cube_root, &f64::asin, &f64::acos]; let result = flist.iter() .zip(&invlist) .map(|(f,i)| compose(f,i)(0.5)) .collect::<Vec<_>>(); println!("{:?}", result); } fn compose<'a, F, G, T, U, V>(f: F, g: G) -> impl 'a + Fn(T) -> V where F: 'a + Fn(T) -> U, G: 'a + Fn(U) -> V, { move |x| g(f(x)) }  ## Scala import math._ // functions as values val cube = (x: Double) => x * x * x val cuberoot = (x: Double) => pow(x, 1 / 3d) // higher order function, as a method def compose[A,B,C](f: B => C, g: A => B) = (x: A) => f(g(x)) // partially applied functions in Lists val fun = List(sin _, cos _, cube) val inv = List(asin _, acos _, cuberoot) // composing functions from the above Lists val comp = (fun, inv).zipped map (_ compose _) // output results of applying the functions comp foreach {f => print(f(0.5) + " ")}  Output: 0.5 0.4999999999999999 0.5000000000000001  ## Scheme (define (compose f g) (lambda (x) (f (g x)))) (define (cube x) (expt x 3)) (define (cube-root x) (expt x (/ 1 3))) (define function (list sin cos cube)) (define inverse (list asin acos cube-root)) (define x 0.5) (define (go f g) (if (not (or (null? f) (null? g))) (begin (display ((compose (car f) (car g)) x)) (newline) (go (cdr f) (cdr g))))) (go function inverse)  Output: 0.5 0.5 0.5 ## Sidef {{trans|Perl}} func compose(f,g) { func (*args) { f(g(args...)) } } var cube = func(a) { a.pow(3) } var croot = func(a) { a.root(3) } var flist1 = [Num.method(:sin), Num.method(:cos), cube] var flist2 = [Num.method(:asin), Num.method(:acos), croot] for a,b (flist1 ~Z flist2) { say compose(a, b)(0.5) }  {{out}}  0.5 0.5 0.5  ## Slate {{incomplete|Slate|Fails to demonstrate that the result of applying the composition of each function in A and its inverse in B to a value, is the original value}} Compose is already defined in slate as (note the examples in the comment): m@(Method traits) ** n@(Method traits) "Answers a new Method whose effect is that of calling the first method on the results of the second method applied to whatever arguments are passed. This composition is associative, i.e. (a ** b) ** c = a ** (b ** c). When the second method, n, does not take a *rest option or the first takes more than one input, then the output is chunked into groups for its consumption. E.g.: #; er ** #; er applyTo: {'a'. 'b'. 'c'. 'd'} => 'abcd' #; er ** #name er applyTo: {#a. #/}. => 'a/'" [ n acceptsAdditionalArguments \/ [m arity = 1] ifTrue: [[| *args | m applyTo: {n applyTo: args}]] ifFalse: [[| *args | m applyTo: ([| :stream | args do: [| *each | stream nextPut: (n applyTo: each)] inGroupsOf: n arity] writingAs: {})]] ]. #**er asMethod: #compose: on: {Method traits. Method traits}.  used as: n@(Number traits) cubed [n raisedTo: 3]. n@(Number traits) cubeRoot [n raisedTo: 1 / 3]. define: #forward -> {#cos er. #sin er. #cube er}. define: #reverse -> {#arcCos er. #arcSin er. #cubeRoot er}. define: #composedMethods -> (forward with: reverse collect: #compose: er). composedMethods do: [| :m | inform: (m applyWith: 0.5)].  ## Smalltalk {{works with|GNU Smalltalk}} |forward reverse composer compounds| "commodities" Number extend [ cube [ ^self raisedTo: 3 ] ]. Number extend [ cubeRoot [ ^self raisedTo: (1 / 3) ] ]. forward := #( #cos #sin #cube ). reverse := #( #arcCos #arcSin #cubeRoot ). composer := [ :f :g | [ :x | f value: (g value: x) ] ]. "let us create composed funcs" compounds := OrderedCollection new. 1 to: 3 do: [ :i | compounds add: ([ :j | composer value: [ :x | x perform: (forward at: j) ] value: [ :x | x perform: (reverse at: j) ] ] value: i) ]. compounds do: [ :r | (r value: 0.5) displayNl ].  Output: 0.4999999999999999 0.5 0.5000000000000001  ## Standard ML - fun cube x = Math.pow(x, 3.0); val cube = fn : real -> real - fun croot x = Math.pow(x, 1.0 / 3.0); val croot = fn : real -> real - fun compose (f, g) = fn x => f (g x); (* this is already implemented in Standard ML as the "o" operator = we could have written "fun compose (f, g) x = f (g x)" but we show this for clarity *) val compose = fn : ('a -> 'b) * ('c -> 'a) -> 'c -> 'b - val funclist = [Math.sin, Math.cos, cube]; val funclist = [fn,fn,fn] : (real -> real) list - val funclisti = [Math.asin, Math.acos, croot]; val funclisti = [fn,fn,fn] : (real -> real) list - ListPair.map (fn (f, inversef) => (compose (inversef, f)) 0.5) (funclist, funclisti); val it = [0.5,0.5,0.500000000001] : real list  ## Stata In Mata it's not possible to get the address of a builtin function, so here we define user functions. function _sin(x) { return(sin(x)) } function _asin(x) { return(asin(x)) } function _cos(x) { return(cos(x)) } function _acos(x) { return(acos(x)) } function cube(x) { return(x*x*x) } function cuberoot(x) { return(sign(x)*abs(x)^(1/3)) } function compose(f,g,x) { return((*f)((*g)(x))) } a=&_sin(),&_cos(),&cube() b=&_asin(),&_acos(),&cuberoot() for(i=1;i<=length(a);i++) { printf("%10.5f\n",compose(a[i],b[i],0.5)) }  ## SuperCollider  a = [sin(_), cos(_), { |x| x ** 3 }]; b = [asin(_), acos(_), { |x| x ** (1/3) }]; c = a.collect { |x, i| x <> b[i] }; c.every { |x| x.(0.5) - 0.5 < 0.00001 }  ## Swift {{works with|Swift|1.2+}} import Darwin func compose<A,B,C>(f: (B) -> C, g: (A) -> B) -> (A) -> C { return { f(g($0)) }
}
let funclist = [ { (x: Double) in sin(x) }, { (x: Double) in cos(x) }, { (x: Double) in pow(x, 3) } ]
let funclisti = [ { (x: Double) in asin(x) }, { (x: Double) in acos(x) }, { (x: Double) in cbrt(x) } ]
println(map(zip(funclist, funclisti)) { f, inversef in compose(f, inversef)(0.5) })


{{out}}


[0.5, 0.5, 0.5]



## Tcl

The following is a transcript of an interactive session:

{{works with|tclsh|8.5}}

% namespace path tcl::mathfunc ;# to import functions like abs() etc.
% proc cube x {expr {$x**3}} % proc croot x {expr {$x**(1/3.)}}
% proc compose {f g} {list apply {{f g x} {{*}$f [{*}$g $x]}}$f $g} % compose abs cube ;# returns a partial command, without argument apply {{f g x} {{*}$f [{*}$g$x]}} abs cube

% {*}[compose abs cube] -3  ;# applies the partial command to argument -3
27

% set forward [compose [compose sin cos] cube] ;# omitting to print result
% set backward [compose croot [compose acos asin]]
% {*}$forward 0.5 0.8372297964617733 % {*}$backward [{*}\$forward 0.5]
0.5000000000000017


Obviously, the ([[C]]) library implementation of some of the trigonometric functions (on which Tcl depends for its implementation) on the platform used for testing is losing a little bit of accuracy somewhere.

See the comments at [[Function as an Argument#TI-89 BASIC]] for more information on first-class functions or the lack thereof in TI-89 BASIC. In particular, it is not possible to do proper function composition, because functions cannot be passed as values nor be closures.

Therefore, this example does everything but the composition.

(Note: The names of the inverse functions may not display as intended unless you have the “TI Uni” font.)

Prgm
Local funs,invs,composed,x,i

Define rc_cube(x) = x^3     © Cannot be local variables
Define rc_curt(x) = x^(1/3)

Define funs = {"sin","cos","rc_cube"}
Define invs = {"sin","cos","rc_curt"}

Define x = 0.5
Disp "x = " & string(x)
For i,1,3
Disp "f=" & invs[i] & " g=" & funs[i] & " f(g(x))=" & string(#(invs[i])(#(funs[i])(x)))
EndFor

DelVar rc_cube,rc_curt  © Clean up our globals
EndPrgm


## TXR

{{trans|Racket}}

Translation notes: we use op to create cube and inverse cube anonymously and succinctly. chain composes a variable number of functions, but unlike compose, from left to right, not right to left.

(defvar funlist [list sin
cos
(op expt @1 3)])

(defvar invlist [list asin
acos
(op expt @1 (/ 1 3))])

(each ((f funlist) (i invlist))
(prinl [(chain f i) 0.5]))


{{out}}

0.5
0.5
0.5
0.5


## Ursala

The algorithm is to zip two lists of functions into a list of pairs of functions, make that a list of functions by composing each pair, "gang" the list of functions into a single function returning a list, and apply it to the argument 0.5.

#import std
#import flo

functions = <sin,cos,times^/~& sqr>
inverses  = <asin,acos,math..cbrt>

#cast %eL

main = (gang (+)*p\functions inverses) 0.5


In more detail,

• (+)*p\functions inverses evaluates to (+)*p(inverses,functions) by definition of the reverse binary to unary combinator (</code>)
•  This expression evaluates to (+)*p(<asin,acos,math..cbrt>,<sin,cos,times^/~& sqr>) by substitution. The zipping is indicated by the p suffix on the map operator, (*) so that (+)p evaluates to (+) <(asin,sin),(acos,cos),(cbrt,times^/~& sqr)>. The composition ((+)) operator is then mapped over the resulting list of pairs of functions, to obtain the list of functions <asin+sin,acos+cos,cbrt+ times^/~& sqr>. gang<aisn+sin,acos+cos,cbrt+ times^/~& sqr> expresses a function returning a list in terms of a list of functions. 
 output: <5.000000e-01,5.000000e-01,5.000000e-01> zkl In zkl, methods bind their instance so something like x.sin is the sine method bound to x (whatever real number x is). eg var a=(30.0).toRad().sin; is a method and a() will always return 0.5 (ie basically a const in this case). Which means you can't just use the word "sin", it has to be used in conjunction with an instance. var a=T(fcn(x){ x.toRad().sin() }, fcn(x){ x.toRad().cos() }, fcn(x){ x*x*x} ); var b=T(fcn(x){ x.asin().toDeg() }, fcn(x){ x.acos().toDeg() }, fcn(x){ x.pow(1.0/3) }); var H=Utils.Helpers; var ab=b.zipWith(H.fcomp,a); //-->list of deferred calculations ab.run(True,5.0); //-->L(5.0,5.0,5.0) a.run(True,5.0) //-->L(0.0871557,0.996195,125) fcomp is the function composition function, fcomp(b,a) returns the function (x)-->b(a(x)). List.run(True,x) is inverse of List.apply/map, it returns a list of listi. The True is to return the result, False is just do it for the side effects. {{Omit From|AWK}} {{omit from|gnuplot}} {{omit from|LaTeX}} {{omit from|Make}} {{omit from|PlainTeX}} {{omit from|PureBasic}} {{omit from|TI-83 BASIC|Cannot define functions.}} [[Category:Functions and subroutines]] 
 
 Created by Adrian Sieber and contributors with Zola Licensed under the GFDL-1.3-or-later