Function composition
You are encouraged to solve this task according to the task description, using any language you may know.
Create a function, compose, whose two arguments f and g, are both functions with one argument. The result of compose is to be a function of one argument, (lets call the argument x), which works like applying function f to the result of applying function g to x, i.e,
- compose(f, g) (x) = f(g(x))
Reference: Function composition
Hint: Implementing compose correctly requires creating a closure. If your language does not support closures directly, you will need to implement it yourself.
ActionScript
ActionScript supports closures, making function composition very straightforward. <lang ActionScript>function compose(f:Function, g:Function):Function { return function(x:Object) {return f(g(x));}; } function test() { trace(compose(Math.atan, Math.tan)(0.5)); }</lang>
Ada
The interface of a generic functions package. The package can be instantiated with any type that has value semantics. Functions are composed using the operation '*'. The same operation applied to an argument evaluates it there: f * x. Functions can be composed with pointers to Ada functions. (In Ada functions are not first-class): <lang ada>generic
type Argument is private;
package Functions is
type Primitive_Operation is not null
access function (Value : Argument) return Argument;
type Func (<>) is private;
function "*" (Left : Func; Right : Argument) return Argument;
function "*" (Left : Func; Right : Primitive_Operation) return Func;
function "*" (Left, Right : Primitive_Operation) return Func;
function "*" (Left, Right : Func) return Func;
private
type Func is array (Positive range <>) of Primitive_Operation;
end Functions;</lang> Here is an implementation; <lang ada>package body Functions is
function "*" (Left : Func; Right : Argument) return Argument is
Result : Argument := Right;
begin
for I in reverse Left'Range loop
Result := Left (I) (Result);
end loop;
return Result;
end "*";
function "*" (Left, Right : Func) return Func is
begin
return Left & Right;
end "*";
function "*" (Left : Func; Right : Primitive_Operation) return Func is
begin
return Left & (1 => Right);
end "*";
function "*" (Left, Right : Primitive_Operation) return Func is
begin
return (Left, Right);
end "*";
end Functions;</lang> The following is an example of use: <lang ada>with Ada.Numerics.Elementary_Functions; use Ada.Numerics.Elementary_Functions; with Ada.Text_IO; use Ada.Text_IO; with Functions;
procedure Test_Compose is
package Float_Functions is new Functions (Float); use Float_Functions;
Sin_Arcsin : Func := Sin'Access * Arcsin'Access;
begin
Put_Line (Float'Image (Sin_Arcsin * 0.5));
end Test_Compose;</lang> Sample output:
5.00000E-01
Aikido
<lang aikido> import math
function compose (f, g) {
return function (x) { return f(g(x)) }
}
var func = compose(Math.sin, Math.asin) println (func(0.5)) // 0.5
</lang>
ALGOL 68
Note: Returning PROC (REAL x)REAL: f1(f2(x)) from a function apparently
violates standard ALGOL 68's scoping rules. ALGOL 68G warns about this during
parsing, and then rejects during runtime.
<lang algol68>MODE F = PROC(REAL)REAL; # ALGOL 68 is strong typed #
- As a procedure for real to real functions #
PROC compose = (F f, g)F: (REAL x)REAL: f(g(x));
OP (F,F)F O = compose; # or an OPerator that can be overloaded #
- Example use: #
F sin arc sin = compose(sin, arc sin); print((sin arc sin(0.5), (sin O arc sin)(0.5), new line))</lang> Output:
+.500000000000000e +0 +.500000000000000e +0
ALGOL 68 is a stack based language, and the following apparently does not violate it's scoping rules.
<lang algol68>MODE F = PROC(REAL)REAL; # ALGOL 68 is strong typed #
- As a procedure for real to real functions #
PROC compose = (F f, g)F: ((F f2, g2, REAL x)REAL: f2(g2(x)))(f, g, ); # Curry #
PRIO O = 7; OP (F,F)F O = compose; # or an OPerator that can be overloaded #
- Example use: #
F sin arc sin = compose(sin, arc sin); print((sin arc sin(0.5), (sin O arc sin)(0.5), new line))</lang>
Argile
Only works for functions taking real and returning real (double precision, 64 bits)
<lang Argile>use std, math
let my_asin = new Function (.:<any,real x>:. -> real {asin x}) let my__sin = new Function (.:<any,real x>:. -> real { sin x}) let sinasin = my__sin o my_asin print sin asin 0.5 print *my__sin 0.0 print *sinasin 0.5 ~my_asin ~my__sin ~sinasin
=: <Function f> o <Function g> := -> Function {compose f g}
.:compose <Function f, Function g>:. -> Function
use array
let d = (new array of 2 Function)
(d[0]) = f ; (d[1]) = g
let c = new Function (.:<array of Function fg, real x>:. -> real {
*fg[0]( *fg[1](x) )
}) (d)
c.del = .:<any>:.{free any}
c
class Function
function(any)(real)->(real) func any data function(any) del
=: * <Function f> <real x> := -> real
Cgen "(*("(f.func)"))("(f.data)", "(x)")"
.: del Function <Function f> :.
unless f.del is nil
call f.del with f.data
free f
=: ~ <Function f> := {del Function f}
.: new Function <function(any)(real)-\>real func> (<any data>):. -> Function
let f = new Function f.func = func f.data = data f</lang>
AutoHotkey
contributed by Laszlo on the ahk forum <lang AutoHotkey>MsgBox % compose("sin","cos",1.5)
compose(f,g,x) { ; function composition
Return %f%(%g%(x))
}</lang>
Brat
<lang brat>compose = { f, g | { x | f g x } }
- Test
add1 = { x | x + 1 } double = { x | x * 2 } b = compose(->double ->add1) p b 1 #should print 4</lang>
C
Only works for functions taking a double and returning a double: <lang c>#include <stdlib.h>
/* generic interface for functors from double to double */ typedef struct double_to_double {
double (*fn)(struct double_to_double *, double);
} double_to_double;
- define CALL(f, x) f->fn(f, x)
/* functor returned by compose */
typedef struct compose_functor {
double (*fn)(struct compose_functor *, double); double_to_double *f; double_to_double *g;
} compose_functor; /* function to be used in "fn" in preceding functor */ double compose_call(compose_functor *this, double x) {
return CALL(this->f, CALL(this->g, x));
} /* returns functor that is the composition of functors
f & g. caller is responsible for deallocating memory */
double_to_double *compose(double_to_double *f,
double_to_double *g) {
compose_functor *result = malloc(sizeof(compose_functor));
result->fn = &compose_call;
result->f = f;
result->g = g;
return (double_to_double *)result;
}
- include <math.h>
/* we can make functors for sin and asin by using
the following as "fn" in a functor */
double sin_call(double_to_double *this, double x) {
return sin(x);
} double asin_call(double_to_double *this, double x) {
return asin(x);
}
- include <stdio.h>
int main() {
double_to_double *my_sin = malloc(sizeof(double_to_double)); my_sin->fn = &sin_call; double_to_double *my_asin = malloc(sizeof(double_to_double)); my_asin->fn = &asin_call;
double_to_double *sin_asin = compose(my_sin, my_asin);
printf("%f\n", CALL(sin_asin, 0.5)); /* prints "0.500000" */
free(sin_asin); free(my_sin); free(my_asin);
return 0;
}</lang>
C++
Note: this is already implemented as __gnu_cxx::compose1()
<lang cpp>#include <functional>
- include <cmath>
- include <iostream>
// functor class to be returned by compose function template <class Fun1, class Fun2> class compose_functor :
public std::unary_function<typename Fun2::argument_type,
typename Fun1::result_type>
{ protected:
Fun1 f; Fun2 g;
public:
compose_functor(const Fun1& _f, const Fun2& _g)
: f(_f), g(_g) { }
typename Fun1::result_type
operator()(const typename Fun2::argument_type& x) const
{ return f(g(x)); }
};
// we wrap it in a function so the compiler infers the template arguments // whereas if we used the class directly we would have to specify them explicitly template <class Fun1, class Fun2> inline compose_functor<Fun1, Fun2> compose(const Fun1& f, const Fun2& g) { return compose_functor<Fun1,Fun2>(f, g); }
int main() {
std::cout << compose(std::ptr_fun(::sin), std::ptr_fun(::asin))(0.5) << std::endl;
return 0;
}</lang>
C#
<lang csharp>using System; class Program {
static void Main(string[] args)
{
Func<int, int> outfunc = Composer<int, int, int>.Compose(functA, functB);
Console.WriteLine(outfunc(5)); //Prints 100
}
static int functA(int i) { return i * 10; }
static int functB(int i) { return i + 5; }
class Composer<A, B, C>
{
public static Func<C, A> Compose(Func<B, A> a, Func<C, B> b)
{
return delegate(C i) { return a(b(i)); };
}
}
}</lang>
Clojure
Function composition is built in to Clojure. Simply call the comp function.
A manual implementation could look like this: <lang clojure>(defn compose [f g]
(fn [x] (f (g x))))
- Example
(def inc2 (compose inc inc)) (println (inc2 5)) ; prints 7</lang>
Common Lisp
compose returns a function that closes on the lexical variables f and g.
<lang lisp>(defun compose (f g) (lambda (x) (funcall f (funcall g x))))</lang>
Example use: <lang lisp>>(defun compose (f g) (lambda (x) (funcall f (funcall g x)))) COMPOSE >(let ((sin-asin (compose #'sin #'asin))))
(funcall sin-asin 0.5))
0.5</lang>
This alternate solution, more ugly and more difficult, never closes on any lexical variables. Instead, it uses runtime evaluation to insert the values of f and g into new code. This is just a different way to create a closure.
<lang lisp>(defun compose (f g)
(eval `(lambda (x) (funcall ',f (funcall ',g x))))</lang>
D
D 2.0 version of compose function (template). <lang D>import std.stdio; import std.math;
T delegate(S) compose(T, U, S)(T delegate(U) f, U delegate(S) g) {
return (S s) { return f(g(s)); };
}</lang>
Compose working both in D 1.0 and 2.0: <lang D>T delegate(S) compose(T, U, S)(T delegate(U) f, U delegate(S) g) {
struct Wrapper {
typeof(f) fcp;
typeof(g) gcp;
T foobar(S s) { return fcp(gcp(s)); }
}
Wrapper* hold = new Wrapper;
hold.fcp = f;
hold.gcp = g;
return &hold.foobar;
}</lang>
Delphi
Anonymous methods were introduced in Delphi 2009, so next code works with Delphi 2009 and above:
<lang Delphi>program AnonCompose;
{$APPTYPE CONSOLE}
type
TFunc = reference to function(Value: Integer): Integer;
function Compose(F, G: TFunc): TFunc; begin
Result:= function(Value: Integer): Integer begin Result:= F(G(Value)); end
end;
var
Func1, Func2, Func3: TFunc;
begin
Func1:=
function(Value: Integer): Integer
begin
Result:= Value * 2;
end;
Func2:=
function(Value: Integer): Integer
begin
Result:= Value * 3;
end;
Func3:= Compose(Func1, Func2);
Writeln(Func3(6)); // 36 = 6 * 3 * 2 Readln;
end.</lang>
Dylan
<lang dylan>define method compose(f,g)
method(x) f(g(x)) end
end;</lang>
E
<lang e>def compose(f, g) {
return fn x { return f(g(x)) }
}</lang>
Erlang
<lang erlang>-module(fn). -export([compose/1, multicompose/2]).
compose(F,G) -> fun(X) -> F(G(X)) end.
multicompose(Fs) ->
lists:foldl(fun compose/2, fun(X) -> X end, Fs).</lang>
Using them: <lang erlang>1> (fn:compose(fun math:sin/1, fun math:asin/1))(0.5). 0.5 2> Sin_asin_plus1 = fn:multicompose([fun math:sin/1, fun math:asin/1, fun(X) -> X + 1 end]).
- Fun<tests.0.59446746>
82> Sin_asin_plus1(0.5). 1.5</lang>
F#
The most-used composition operator in F# is >>. It implements forward composition, i.e. f >> g is a function which calls f first and then calls g on the result.
The reverse composition operator <<, on the other hand, exactly fulfills the requirements of the compose function described in this task.
We can implement composition manually like this (F# Interactive session): <lang fsharp>> let compose f g x = f (g x);;
val compose : ('a -> 'b) -> ('c -> 'a) -> 'c -> 'b</lang> Usage: <lang fsharp>> let sin_asin = compose sin asin;;
val sin_asin : (float -> float)
> sin_asin 0.5;; val it : float = 0.5</lang>
Factor
When passing functions around and creating anonymous functions, Factor uses so called quotations. There is already a word (compose) that provides composition of quotations.
<lang factor>( scratchpad ) [ 2 * ] [ 1 + ] compose .
[ 2 * 1 + ]
( scratchpad ) 4 [ 2 * ] [ 1 + ] compose call .
9</lang>
Fantom
<lang fantom> class Compose {
static |Obj -> Obj| compose (|Obj -> Obj| fn1, |Obj -> Obj| fn2)
{
return |Obj x -> Obj| { fn2 (fn1 (x)) }
}
public static Void main ()
{
double := |Int x -> Int| { 2 * x }
|Int -> Int| quad := compose(double, double)
echo ("Double 3 = ${double(3)}")
echo ("Quadruple 3 = ${quad (3)}")
}
} </lang>
Forth
<lang forth>: compose ( xt1 xt2 -- xt3 )
>r >r :noname
r> compile,
r> compile,
postpone ;
' 2* ' 1+ compose ( xt ) 3 swap execute . \ 7</lang>
GAP
<lang gap>Composition := function(f, g)
return x -> f(g(x));
end;
h := Composition(x -> x+1, x -> x*x); h(5);
- 26</lang>
Go
Go doesn't have generics; this particular compose function just composes float functions <lang go>func compose(f, g func(float64) float64) func(float64) float64 {
return func(x float64) float64 {
return f(g(x))
}
}</lang> Example use: <lang go>package main import "math" import "fmt"
func compose(f, g func(float64) float64) func(float64) float64 {
return func(x float64) float64 {
return f(g(x))
}
}
func main() {
sin_asin := compose(math.Sin, math.Asin) fmt.Println(sin_asin(0.5))
}</lang>
Groovy
Solution: <lang groovy>def compose = { f, g -> { x -> f(g(x)) } }</lang>
Test program: <lang groovy>def sq = { it * it } def plus1 = { it + 1 } def minus1 = { it - 1 }
def plus1sqd = compose(sq,plus1) def sqminus1 = compose(minus1,sq) def identity = compose(plus1,minus1) def plus1sqdminus1 = compose(minus1,compose(sq,plus1)) def identity2 = compose(Math.&sin,Math.&asin)
println "(x+1)**2 = (0+1)**2 = " + plus1sqd(0) println "x**2-1 = 20**2-1 = " + sqminus1(20) println "(x+1)-1 = (12+1)-1 = " + identity(12) println "(x+1)**2-1 = (3+1)**2-1 = " + plus1sqdminus1(3) println "sin(asin(x)) = sin(asin(1)) = " + identity2(1)</lang>
Output:
(x+1)**2 = (0+1)**2 = 1 x**2-1 = 20**2-1 = 399 (x+1)-1 = (12+1)-1 = 12 (x+1)**2-1 = (3+1)**2-1 = 15 sin(asin(x)) = sin(asin(1)) = 1.0
Haskell
This is already defined as the . (dot) operator in Haskell. <lang haskell>compose f g x = f (g x)</lang> Example use: <lang haskell>Prelude> let compose f g x = f (g x) Prelude> let sin_asin = compose sin asin Prelude> sin_asin 0.5 0.5</lang>
Icon and Unicon
Icon and Unicon don't have a lambda function or native closure; however, they do have co-expressions which are extremely versatile and can be used to achieve the same effect. The list of functions to compose can be a 'procedure', 'co-expression", or an invocable string (i.e. procedure name or unary operator). It will correctly handle compose(compose(...),..).
There are a few limitations to be aware of:
- type(compose(f,g)) returns a co-expression not a procedure
- this construction only handles functions of 1 argument (a closure construct is better for the general case)
The solution below can be adapted to work in Icon by reverting to the old syntax for invoking co-expressions.
<lang Icon> x @ f # use this syntax in Icon instead of the Unicon f(x) to call co-expressions
every push(fL := [],!rfL) # use this instead of reverse(fL) as the Icon reverse applies only to strings</lang>
See Icon and Unicon Introduction:Minor Differences for more information
<lang Unicon>procedure main(arglist)
h := compose(sqrt,abs)
k := compose(integer,"sqrt",ord)
m := compose("-",k)
every write(i := -2 to 2, " h=(sqrt,abs)-> ", h(i))
every write(c := !"1@Q", " k=(integer,\"sqrt\",ord)-> ", k(c))
write(c := "1"," m=(\"-\",k) -> ",m(c))
end
invocable all # permit string invocations
procedure compose(fL[]) #: compose(f1,f2,...) returns the functional composition of f1,f2,... as a co-expression
local x,f,saveSource
every case type(x := !fL) of {
"procedure"|"co-expression": &null # procedures and co-expressions are fine
"string" : if not proc(x,1) then runnerr(123,fL) # as are invocable strings (unary operators, and procedures)
default: runerr(123,fL)
}
fL := reverse(fL) # reverse and isolate from mutable side-effects
cf := create { saveSource := &source # don't forget where we came from
repeat {
x := (x@saveSource)[1] # return result and resume here
saveSource := &source # ...
every f := !fL do x := f(x) # apply the list of 'functions'
}
}
return (@cf, cf) # 'prime' the co-expr before returning it
end</lang>
Sample Output:
-2 h=(sqrt,abs)-> 1.414213562373095
-1 h=(sqrt,abs)-> 1.0
0 h=(sqrt,abs)-> 0.0
1 h=(sqrt,abs)-> 1.0
2 h=(sqrt,abs)-> 1.414213562373095
1 k=(integer,"sqrt",ord)-> 7
@ k=(integer,"sqrt",ord)-> 8
Q k=(integer,"sqrt",ord)-> 9
1 m=("-",k) -> -7
J
Solution: <lang j>compose =: @</lang>
Example: <lang j>f compose g</lang>
Of course, given that @ is only one character long and is a built-in primitive, there is no need for the cover function compose. And @ is not the only composition primitive; composition is a very important concept in J. For more details, see the talk page.
Java
<lang java>public class Compose {
// Java doesn't have function type so we define an interface
// of function objects instead
public interface Fun<A,B> {
B call(A x);
}
public static <A,B,C> Fun<A,C> compose(final Fun<B,C> f, final Fun<A,B> g) {
return new Fun<A,C>() {
public C call(A x) {
return f.call(g.call(x));
}
};
}
public static void main(String[] args) {
Fun<Double,Double> sin = new Fun<Double,Double>() {
public Double call(Double x) {
return Math.sin(x);
}
};
Fun<Double,Double> asin = new Fun<Double,Double>() {
public Double call(Double x) {
return Math.asin(x);
}
};
Fun<Double,Double> sin_asin = compose(sin, asin);
System.out.println(sin_asin.call(0.5)); // prints "0.5" }
}</lang>
JavaScript
<lang javascript>function compose(f, g) {
return function(x) { return f(g(x)) }
}
var id = compose(Math.sin, Math.asin) print id(0.5) // 0.5</lang>
Joy
Composition is the default operation in Joy. The composition of two functions is the concatenation of those functions, in the order in which they are to be applied. <lang joy>g f</lang>
Lua
<lang lua>function compose(f, g) return function(...) return f(g(...)) end end</lang>
Mathematica
Built-in function that takes any amount of function-arguments: <lang Mathematica>Composition[f, g][x] Composition[f, g, h, i][x]</lang> gives back: <lang Mathematica>f[g[x]] f[g[h[i[x]]]]</lang> Custom function: <lang Mathematica>compose[f_, g_][x_] := f[g[x]] compose[Sin, Cos][r]</lang> gives back: <lang Mathematica>Sin[Cos[r]]</lang> Composition can be done in more than 1 way: <lang Mathematica>Composition[f,g,h][x] f@g@h@x x//h//g//f</lang> all give back: <lang Mathematica>f[g[h[x]]]</lang> The built-in function has a couple of automatic simplifications: <lang Mathematica>Composition[f, Identity, g] Composition[f, InverseFunction[f], h][x]</lang> becomes: <lang Mathematica>f[g[x]] h[x]</lang>
NewLISP
<lang NewLISP>> (define (compose f g) (expand (lambda (x) (f (g x))) 'f 'g)) (lambda (f g) (expand (lambda (x) (f (g x))) 'f 'g)) > ((compose sin asin) 0.5) 0.5 </lang>
Objective-C
The FunctionComposer is able to compose any object that conforms to the protocol FunctionCapsule (a selector/method accepting any object as argument and returning another object, i.e. computing a "function" of an object). A FunctionCaps class thought to encapsulate a function returning a double and with a double as argument is shown; anyway, as said, any object conforming to FunctionCapsule protocol can be composed with another object conforming to the same protocol. Argument passed and returned can be of any object type.
<lang objc>#include <Foundation/Foundation.h>
// the protocol of objects that can behave "like function" @protocol FunctionCapsule -(id)computeWith: (id)x; @end
// a commodity for "encapsulating" double f(double)
typedef double (*func_t)(double);
@interface FunctionCaps : NSObject <FunctionCapsule>
{
func_t function;
} +(id)capsuleFor: (func_t)f; -(id)initWithFunc: (func_t)f; @end
@implementation FunctionCaps -(id)initWithFunc: (func_t)f {
self = [self init]; function = f; return self;
} +(id)capsuleFor: (func_t)f {
return [[[self alloc] initWithFunc: f] autorelease];
} -(id)computeWith: (id)x {
return [NSNumber numberWithDouble: function([x doubleValue])];
} @end
// the "functions" composer
@interface FunctionComposer : NSObject <FunctionCapsule>
{
id funcA; id funcB;
} +(id) createCompositeFunctionWith: (id)A and: (id)B; -(id) initComposing: (id)A with: (id)B; -(id) init; -(id) dealloc; @end
@implementation FunctionComposer +(id) createCompositeFunctionWith: (id)A and: (id)B {
return [[[self alloc] initComposing: A with: B] autorelease];
}
-(id) init {
NSLog(@"FunctionComposer: init with initComposing!"); funcA = nil; funcB = nil; return self;
}
-(id) initComposing: (id)A with: (id)B {
self = [super init];
if ( ([A conformsToProtocol: @protocol(FunctionCapsule)] == YES) &&
([B conformsToProtocol: @protocol(FunctionCapsule)] == YES) ) {
[A retain]; [B retain];
funcA = A; funcB = B;
return self;
}
NSLog(@"FunctionComposer: cannot compose functions not responding to protocol FunctionCapsule!");
return nil;
}
-(id)computeWith: (id)x {
return [funcA computeWith: [funcB computeWith: x]];
} @end
-(void) dealloc {
[funcA release]; [funcB release]; [super dealloc];
}
// functions outside...
double my_f(double x)
{
return x+1.0;
}
double my_g(double x) {
return x*x;
}
int main()
{
NSAutoreleasePool *pool = [[NSAutoreleasePool alloc] init];
id funcf = [FunctionCaps capsuleFor: my_f]; id funcg = [FunctionCaps capsuleFor: my_g];
id composed = [FunctionComposer
createCompositeFunctionWith: funcf and: funcg];
printf("g(2.0) = %lf\n", [[funcg computeWith: [NSNumber numberWithDouble: 2.0]] doubleValue]);
printf("f(2.0) = %lf\n", [[funcf computeWith: [NSNumber numberWithDouble: 2.0]] doubleValue]);
printf("f(g(2.0)) = %lf\n", [[composed computeWith: [NSNumber numberWithDouble: 2.0]] doubleValue]);
[pool release]; return 0;
}</lang>
Objeck
<lang objeck> bundle Default {
class Test {
@f : static : (Int) ~ Int;
@g : static : (Int) ~ Int;
function : Main(args : String[]) ~ Nil {
compose := Composer(F(Int) ~ Int, G(Int) ~ Int);
compose(13)->PrintLine();
}
function : F(a : Int) ~ Int {
return a + 14;
}
function : G(a : Int) ~ Int {
return a + 15;
}
function : Compose(x : Int) ~ Int {
return @f(@g(x));
}
function : Composer(f : (Int) ~ Int, g : (Int) ~ Int) ~ (Int) ~ Int {
@f := f;
@g := g;
return Compose(Int) ~ Int;
}
}
} </lang> prints: 42
OCaml
<lang ocaml>let compose f g x = f (g x)</lang> Example use: <lang ocaml># let compose f g x = f (g x);; val compose : ('a -> 'b) -> ('c -> 'a) -> 'c -> 'b = <fun>
- let sin_asin = compose sin asin;;
val sin_asin : float -> float = <fun>
- sin_asin 0.5;;
- : float = 0.5</lang>
Octave
<lang octave>function r = compose(f, g)
r = @(x) f(g(x));
endfunction
r = compose(@exp, @sin); r(pi/3)</lang>
Oz
<lang oz>declare
fun {Compose F G}
fun {$ X}
{F {G X}}
end
end
SinAsin = {Compose Float.sin Float.asin}
in
{Show {SinAsin 0.5}}</lang>
PARI/GP
<lang parigp>compose(f, g)={
x -> f(g(x))
};
compose(x->sin(x),x->cos(x)(1)</lang>
Usage note: In Pari/GP 2.4.3, this can be expressed more succinctly: <lang parigp>compose(sin,cos)(1)</lang>
Perl
<lang perl>sub compose {
my ($f, $g) = @_;
sub {
$f -> ($g -> (@_))
};
}
use Math::Trig; print compose(sub {sin $_[0]}, \&asin)->(0.5), "\n";</lang>
Perl 6
<lang perl6>sub infix:<∘> (&f, &g --> Block) {
sub (*@args) { f g |@args };
}</lang>
Example of use:
<lang perl6>sub triple($n) { 3 * $n } my $f = &triple ∘ { $^x + 2 }; say $f(5); # Prints "21".</lang>
PHP
<lang php>function compose($f, $g) {
return create_function('$x', "return $f($g(\$x));");
}
$trim_strlen = compose('strlen', 'trim'); echo $result = $trim_strlen(' Test '); // prints 4</lang>
PicoLisp
<lang PicoLisp>(de compose (F G)
(curry (F G) (X)
(F (G X)) ) )</lang>
<lang PicoLisp>(def 'a (compose inc dec)) (def 'b (compose 'inc 'dec)) (def 'c (compose '((A) (inc A)) '((B) (dec B))))</lang> <lang PicoLisp>: (a 7) -> 7
- (b 7)
-> 7
- (c 7)
-> 7</lang>
PostScript
PostScript functions typically pops operand stack for argument, so calling two functions one after another naturally makes a compound function, and making a compound requires just defing them:<lang PostScript>/square { dup mul } def
/plus1 { 1 add } def
/sqPlus1{ square plus1 } def
% if the task really demands we make a function called "compose", well /compose { def } def % so now we can say: /sqPlus1 { square plus1 } compose</lang>
Prolog
Works with SWI-Prolog and module lambda, written by Ulrich Neumerkel found there http://www.complang.tuwien.ac.at/ulrich/Prolog-inedit/lambda.pl <lang Prolog>:- use_module(lambda).
compose(F,G, FG) :- FG = \X^Z^(call(G,X,Y), call(F,Y,Z)). </lang> Example of output :
?- compose(sin, asin, F), call(F, 0.5, Y). F = \_G4586^_G4589^ (call(asin,_G4586,_G4597),call(sin,_G4597,_G4589)), Y = 0.5.
PureBasic
<lang PureBasic>;Declare how our function looks like Prototype.i Func(Arg.i)
- Make a procedure that composes any functions of type "Func"
Procedure Compose(*a.Func,*b.Func, x)
ProcedureReturn *a(*b(x))
EndProcedure
- Just a procedure fitting "Func"
Procedure f(n)
ProcedureReturn 2*n
EndProcedure
- Yet another procedure fitting "Func"
Procedure g(n)
ProcedureReturn n+1
EndProcedure
- - Test it
X=Random(100) Title$="With x="+Str(x) Body$="Compose(f(),g(), x) ="+Str(Compose(@f(),@g(),X)) MessageRequester(Title$,Body$)</lang>
Purity
<lang Purity> data compose = f => g => $f . $g </lang>
Python
<lang python>compose = lambda f, g: lambda x: f( g(x) )</lang> Example use: <lang python>>>> compose = lambda f, g: lambda x: f( g(x) ) >>> from math import sin, asin >>> sin_asin = compose(sin, asin) >>> sin_asin(0.5) 0.5 >>></lang>
R
<lang R>compose <- function(f,g) function(x) { f(g(x)) } r <- compose(sin, cos) print(r(.5))</lang>
REBOL
<lang REBOL>REBOL [ Title: "Functional Composition" Author: oofoe Date: 2009-12-06 URL: http://rosettacode.org/wiki/Functional_Composition ]
- "compose" means something else in REBOL, therefore I use a 'compose-functions name.
compose-functions: func [
{compose the given functions F and G}
f [any-function!]
g [any-function!]
] [
func [x] compose [(:f) (:g) x]
]</lang>
Functions "foo" and "bar" are used to prove that composition actually took place by attaching their signatures to the result.
<lang REBOL>foo: func [x] [reform ["foo:" x]] bar: func [x] [reform ["bar:" x]]
foo-bar: compose-functions :foo :bar print ["Composition of foo and bar:" mold foo-bar "test"]
sin-asin: compose-functions :sine :arcsine print [crlf "Composition of sine and arcsine:" sin-asin 0.5]</lang>
Output:
Composition of foo and bar: "foo: bar: test" Composition of sine and arcsine: 0.5
REXX
<lang rexx> compose: procedure; parse arg f,g,x; interpret 'return' f"("g'(' x "))" exit /*control never gets here.*/ </lang>
Ruby
This compose method gets passed two Method objects <lang ruby>def compose(f,g)
lambda {|x| f.call(g.call(x))}
end s = compose(Math.method('sin'), Math.method('cos')) s.call(0.5) # => 0.769196354841008
- verify
Math.sin(Math.cos(0.5)) # => 0.769196354841008</lang>
With this method, you pass two symbols <lang ruby>include Math def compose(f,g)
lambda {|x| send(f, send(g, x))}
end s = compose(:sin, :cos) s.call(0.5) # => 0.769196354841008</lang>
Scala
<lang scala>def compose[A](f: A => A, g: A => A) = { x: A => f(g(x)) }
def add1(x: Int) = x+1 val add2 = compose(add1, add1)</lang>
We can achieve a more natural style by creating a container class for composable functions, which provides the compose method 'o':
<lang scala>class Composable[A](f: A => A) {
def o (g: A => A) = compose(f, g)
}
implicit def toComposable[A](f: A => A) = new Composable(f)
val add3 = (add1 _) o add2</lang>
> (add2 o add3)(37) res0: Int = 42
Scheme
<lang scheme>(define (compose f g) (lambda (x) (f (g x))))
- or
(define ((compose f g) x) (f (g x))) </lang> Example: <lang scheme> (display ((compose sin asin) 0.5)) (newline)</lang> Output: <lang>0.5</lang>
Slate
Function (method) composition is standard: <lang slate>[| :x | x + 1] ** [| :x | x squared] applyTo: {3}</lang>
Smalltalk
<lang smalltalk>| composer fg | composer := [ :f :g | [ :x | f value: (g value: x) ] ]. fg := composer value: [ :x | x + 1 ]
value: [ :x | x * x ].
(fg value:3) displayNl.</lang>
Standard ML
This is already defined as the o operator in Standard ML. <lang sml>fun compose (f, g) x = f (g x)</lang> Example use: <lang sml>- fun compose (f, g) x = f (g x); val compose = fn : ('a -> 'b) * ('c -> 'a) -> 'c -> 'b - val sin_asin = compose (Math.sin, Math.asin); val sin_asin = fn : real -> real - sin_asin 0.5; val it = 0.5 : real</lang>
Tcl
This creates a compose procedure that returns an anonymous function term that should be expanded as part of application to its argument.
<lang tcl>package require Tcl 8.5
namespace path {::tcl::mathfunc}
proc compose {f g} {
list apply [list {f g x} {{*}$f [{*}$g $x]}] $f $g]
}
set sin_asin [compose sin asin] {*}$sin_asin 0.5 ;# ==> 0.5 {*}[compose abs int] -3.14 ;# ==> 3</lang>
Unlambda
``s`ksk
Ursala
Functional composition is a built in operation expressible as f+g for functions f and g, hence hardly worth defining. However, it could be defined without using the operator like this. <lang Ursala>compose("f","g") "x" = "f" "g" "x"</lang> test program: <lang Ursala>#import nat
- cast %n
test = compose(successor,double) 3</lang> output:
7
VBScript
I'm not convinced that this is really a 'closure'. It looks to me more like a cute trick with Eval().
Implementation <lang vb> option explicit class closure
private composition
sub compose( f1, f2 ) composition = f2 & "(" & f1 & "(p1))" end sub
public default function apply( p1 ) apply = eval( composition ) end function
public property get formula formula = composition end property
end class </lang>
Invocation <lang vb> dim c set c = new closure
c.compose "ucase", "lcase" wscript.echo c.formula wscript.echo c("dog")
c.compose "log", "exp" wscript.echo c.formula wscript.echo c(12.3)
function inc( n ) inc = n + 1 end function
c.compose "inc", "inc" wscript.echo c.formula wscript.echo c(12.3)
function twice( n ) twice = n * 2 end function
c.compose "twice", "inc" wscript.echo c.formula wscript.echo c(12.3) </lang>
Output
lcase(ucase(p1)) dog exp(log(p1)) 12.3 inc(inc(p1)) 14.3 inc(twice(p1)) 25.6
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