Function composition

You are encouraged to You are encouraged to solve this task according to the task description, using any language you may know.

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.





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 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

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)



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





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), "

");



0;

}

Output:

6400

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 ) )

/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]}}

-- 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).

-- FUNCTIONS TO COMPOSE -------------------------------------------------------



on root ( x )

x ^ 0.5

end root



on succ ( x )

x + 1

end succ



on half ( x )

x / 2

end half



-- TEST -----------------------------------------------------------------------

on run



compose ( [ half, succ, root ] ) 's |λ| ( 5 )



--> 1.61803398875

end run



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



-- compose :: [(a -> a)] -> (a -> a)

on compose ( fs )

script

on |λ| ( x )

script

on |λ| ( a, f )

mReturn ( f ) 's |λ| ( a )

end |λ|

end script



foldr ( result , x, fs )

end |λ|

end script

end compose



-- 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

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

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

contributed by Laszlo on the ahk forum

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



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

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

}

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

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:

0.500000000

on Android phone:

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

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

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

" , CALL ( sin_asin , 0.5 ) ) ; /* prints "0.500000" */



free ( sin_asin ) ;

free ( my_sin ) ;

free ( my_asin ) ;



return 0 ;

}

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 ) ) ; } ;

}

}

}

#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

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 ;



return 0 ;

}

Works with: C++14

composing

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 ) << "

" ;

return 0 ;

}

This example is untested. Please check that it's correct, debug it as necessary, and remove this message.





Works with: GCC

#include <iostream>

#include <cmath>

#include <ext/functional>



int main ( ) {

std :: cout << __gnu_cxx :: compose1 ( std :: ptr_fun ( :: sin ) , std :: ptr_fun ( :: asin ) ) ( 0.5 ) << std :: endl ;



return 0 ;

}

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

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



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.

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>

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

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 .

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;



It is already defined in the standard library as $ .

compose f g:

labda:

f g

def compose ( f , g ) {

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

}



;; 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



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 4.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:

10

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

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

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

( eval-when-compile ( require 'cl ) ) ;; for `lexical-let' macro

( defun compose ( f g )

( lexical- let ( ( f f )

( g g ) )

( lambda ( x )

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



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

( funcall func 5 ) )

=>

7

- 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 > S in_asin_plus1 ( 0.5 ) .

1.5

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 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



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)}")

}

}



: compose ( xt1 xt2 -- xt3 )

>r >r :noname

r> compile,

r> compile,

postpone ;

;



' 2* ' 1+ compose ( xt )

3 swap execute . \ 7

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



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.

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

In this page you can see the solution of this task.

Fōrmulæ programs are not textual, visualization/edition of programs is done showing/manipulating structures but not text (more info). 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 transportation effects more than visualization and edition.

The option to show Fōrmulæ programs and their results is showing images. Unfortunately images cannot be uploaded in Rosetta Code.

Composition := function(f, g)

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

end;



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

h(5);

# 26

// 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

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

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

compose f g x = f ( g x )

Example use:

Prelude > let compose f g x = f ( g x )

Prelude > let sin _ asin = compose sin asin

Prelude > sin _ asin 0.5

0.5

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

( defn compose [ f g ]

( fn [ x ]

( f ( g x ) ) ) )

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 := ! [email protected]" , " 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

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:

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.

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 [ edit ]

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"

}

}

ES5 [ edit ]

Simple composition of two functions [ edit ]

function compose ( f , g ) {

return function ( x ) {

return f ( g ( x ) ) ;

} ;

}

Example:

var id = compose ( Math . sin , Math . asin ) ;

print ( id ( 0.5 ) ) ; // 0.5





Multiple composition [ edit ]

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 [ edit ]

( ( ) => {

'use strict' ;



// compose :: [(a -> a)] -> (a -> a)

const compose = ( ... fs ) =>

x => fs. reduceRight (

( a , f ) => f ( a ) ,

x

) ;



// Test a composition of 3 functions (right to left)

const

sqrt = Math . sqrt ,

succ = x => x + 1 ,

half = x => x / 2 ;



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



// --> 1.618033988749895

} ) ( ) ;

Output:

1.618033988749895

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

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.

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)

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

include ..\Utilitys.tlhy



:*2 2 * ;

:++ 1 + ;

:composite swap exec swap exec ;



@++ @*2 3 composite ? { result: 7 }



"End " input

// version 1.0.6



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



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



fun compose ( f : ( Int ) - > Int, g : ( Int ) - > Int ) : ( Int ) - > Int = { f ( g ( it ) ) }



fun main ( args : Array < String > ) {

val x = 10

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

}

Output:

144



{ 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





( 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 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 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

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



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



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:

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]

/* 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))));

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 *)

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:

80

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));

}

}



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

}



> ( 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



import future



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



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

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



var plusminustwo = compose(plustwo, minustwo)

echo plusminustwo(10)



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

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

" , [ g ( @ 2.0 ) doubleValue ] ) ;

printf ( "f(2.0) = %lf

" , [ f ( @ 2.0 ) doubleValue ] ) ;

printf ( "f(g(2.0)) = %lf

" , [ composed ( @ 2.0 ) doubleValue ] ) ;



}

return 0 ;

}

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

function r = compose ( f , g )

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

endfunction



r = compose ( @exp , @sin ) ;

r ( pi / 3 )

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]



( define ( compose f g )

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



;; or:



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



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.

declare

fun { Compose F G }

fun { $ X }

{ F { G X } }

end

end



SinAsin = { Compose Float . sin Float . asin }

in

{ Show { SinAsin 0 . 5 } }

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 )

See Delphi

sub compose {

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



sub {

$f -> ( $g -> ( @_ ) )

} ;

}



use Math :: Trig ;

print compose ( sub { sin $_ [ 0 ] } , \&asin ) -> ( 0.5 ) , "

" ;

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

def *2 2 * enddef

def ++ 1 + enddef

def composite swap exec swap exec enddef



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

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 ' ) , "

" ; // 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 ' ) , "

" ; // prints 4

?>

(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



/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



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:

8

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.

;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$,Body$ )



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



Simple composition of two functions [ edit ]

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 [ edit ]

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

Works with: Python version 3

from functools import reduce

from numbers import Number

import math





def main ( ) :

'''Test'''



f = composeList ( [

lambda x: x / 2 ,

succ ,

math . sqrt

] )



print (

f ( 5 )

)





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





# composeList :: [(a -> a)] -> (a -> a)

def composeList ( fs ) :

'''Composition, from right to left,

of a series of functions.'''

return lambda x: reduce (

lambda a , f: f ( a ) ,

fs [ ::- 1 ] ,

x

)





# succ :: Enum a => a -> a

def succ ( x ) :

'''The successor of a value. For numeric types, (1 +).'''

return 1 + x if isinstance ( x , Number ) else (

chr ( 1 + ord ( x ) )

)





if __name__ == '__main__' :

main ( )

Output:

1.618033988749895





composition via operator overloading [ edit ]

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 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) \



compose <- function(f,g) function(x) { f(g(x)) }

r <- compose(sin, cos)

print(r(.5))



(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.)

(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 [

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

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.*/



# 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:

11

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

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 [ edit ]

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 [ edit ]

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))

}

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

( 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

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

Function (method) composition is standard:

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

| 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.

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

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



f = { |x| x + 1 };

g = { |x| x * 2 };

h = g <> f;

h.(8); // returns 18



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

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



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



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.





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.

``s`ksk

Functional composition is a built in operation expressible as f+g for functions f and g, hence hardly worth defining. However, it could be defined without using the operator like this.

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

test program:

#import nat

#cast %n



test = compose(successor,double) 3

Output:

7

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

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

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

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:

8

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()); }

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