Function composition
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.
11l
<lang 11l>V compose = (f, g) -> (x -> @f(@g(x))) V sin_asin = compose(x -> sin(x), x -> asin(x)) print(sin_asin(0.5))</lang>
- Output:
0.5
ActionScript
ActionScript supports closures, making function composition very straightforward. <lang ActionScript>function compose(f:Function, g:Function):Function { return function(x:Object) {return f(g(x));}; } function test() { trace(compose(Math.atan, Math.tan)(0.5)); }</lang>
Ada
The interface of a generic functions package. The package can be instantiated with any type that has value semantics. Functions are composed using the operation '*'. The same operation applied to an argument evaluates it there: f * x. Functions can be composed with pointers to Ada functions. (In Ada functions are not first-class): <lang ada>generic
type Argument is private;
package Functions is
type Primitive_Operation is not null
access function (Value : Argument) return Argument;
type Func (<>) is private;
function "*" (Left : Func; Right : Argument) return Argument;
function "*" (Left : Func; Right : Primitive_Operation) return Func;
function "*" (Left, Right : Primitive_Operation) return Func;
function "*" (Left, Right : Func) return Func;
private
type Func is array (Positive range <>) of Primitive_Operation;
end Functions;</lang> Here is an implementation; <lang ada>package body Functions is
function "*" (Left : Func; Right : Argument) return Argument is
Result : Argument := Right;
begin
for I in reverse Left'Range loop
Result := Left (I) (Result);
end loop;
return Result;
end "*";
function "*" (Left, Right : Func) return Func is
begin
return Left & Right;
end "*";
function "*" (Left : Func; Right : Primitive_Operation) return Func is
begin
return Left & (1 => Right);
end "*";
function "*" (Left, Right : Primitive_Operation) return Func is
begin
return (Left, Right);
end "*";
end Functions;</lang> The following is an example of use: <lang ada>with Ada.Numerics.Elementary_Functions; use Ada.Numerics.Elementary_Functions; with Ada.Text_IO; use Ada.Text_IO; with Functions;
procedure Test_Compose is
package Float_Functions is new Functions (Float); use Float_Functions;
Sin_Arcsin : Func := Sin'Access * Arcsin'Access;
begin
Put_Line (Float'Image (Sin_Arcsin * 0.5));
end Test_Compose;</lang>
- Output:
5.00000E-01
Agda
<lang Agda>compose : ∀ {a b c} {A : Set a} {B : Set b} {C : Set c}
→ (B → C)
→ (A → B)
→ A → C
compose f g x = f (g x)</lang>
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>
Aime
<lang aime>compose_i(,,) {
($0)(($1)($2));
}
compose(,) {
compose_i.apply($0, $1);
}
double(real a) {
2 * a;
}
square(real a) {
a * a;
}
main(void) {
o_(compose(square, double)(40), "\n");
0;
}</lang>
- Output:
6400
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>
AntLang
<lang AntLang>/Apply g to exactly one argument compose1: {f: x; g: y; {f[g[x]]}} /Extra: apply to multiple arguments compose: {f: x; g: y; {f[g apply args]}}</lang>
AppleScript
<lang applescript>-- Compose two functions where each function is -- a script object with a call(x) handler. on compose(f, g)
script
on call(x)
f's call(g's call(x))
end call
end script
end compose
script sqrt
on call(x)
x ^ 0.5
end call
end script
script twice
on call(x)
2 * x
end call
end script
compose(sqrt, twice)'s call(32) -- Result: 8.0</lang>
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).
<lang applescript>------------ COMPOSITION OF A LIST OF FUNCTIONS ----------
-- compose :: [(a -> a)] -> (a -> a) on compose(fs)
script
on |λ|(x)
script go
on |λ|(a, f)
mReturn(f)'s |λ|(a)
end |λ|
end script
foldr(go, x, fs)
end |λ|
end script
end compose
TEST -------------------------
on root(x)
x ^ 0.5
end root
on succ(x)
x + 1
end succ
on half(x)
x / 2
end half
on run
tell compose({half, succ, root})
|λ|(5)
end tell
--> 1.61803398875
end run
GENERIC FUNCTIONS -------------------
-- foldr :: (a -> b -> a) -> a -> [b] -> a on foldr(f, startValue, xs)
tell mReturn(f)
set v to startValue
set lng to length of xs
repeat with i from lng to 1 by -1
set v to |λ|(v, item i of xs, i, xs)
end repeat
return v
end tell
end foldr
-- Lift 2nd class handler function into 1st class script wrapper -- mReturn :: Handler -> Script on mReturn(f)
if class of f is script then
f
else
script
property |λ| : f
end script
end if
end mReturn</lang>
- Output:
1.61803398875
Applesoft BASIC
<lang ApplesoftBasic>10 F$ = "SIN" 20 DEF FN A(P) = ATN(P/SQR(-P*P+1)) 30 G$ = "FN A" 40 GOSUB 100"COMPOSE 50 SA$ = E$
60 X = .5 : E$ = SA$ 70 GOSUB 200"EXEC 80 PRINT R 90 END
100 E$ = F$ + "(" + G$ + "(X))" : RETURN : REMCOMPOSE F$ G$
200 D$ = CHR$(4) : FI$ = "TEMPORARY.EX" : M$ = CHR$(13) 210 PRINT D$"OPEN"FI$M$D$"CLOSE"FI$M$D$"DELETE"FI$ 220 PRINT D$"OPEN"FI$M$D$"WRITE"FI$ 230 PRINT "CALL-998:CALL-958:R="E$":CONT" 240 PRINT D$"CLOSE"FI$M$D$"EXEC"FI$:CALL-998:END:RETURN</lang>
Argile
Only works for functions taking real and returning real (double precision, 64 bits)
<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>
Arturo
<lang rebol>compose: function [f,g] ->
return function [x].import:[f,g][
call f @[call g @[x]]
]
splitupper: compose 'split 'upper
print call 'splitupper ["done"]</lang>
- Output:
D O N E
ATS
If I may state in greater detail what the task requires, it is this:
That compose should return a new function, which will exist independently of compose once created. A person should never have to call compose merely to get the result of the composed computation.
Thus it is probably impossible, for instance, to really satisfy the requirement in standard C, if the result of composition is to be called like an ordinary function. However, the C solution shows it is possible, if the notion of a function is expanded to include structures requiring more than just a plain C function call. Also, there is at least one platform-dependent library for creating a "true" closure in C.
In ATS we have closures, but of more than one kind.
<lang ats>(*
The task:
Create a function, compose, whose two arguments f and g, are
both functions with one argument.
The result of compose is to be a function of one argument,
(let's call the argument x), which works like applying function
f to the result of applying function g to x.
In ATS, we have to choose whether to use non-linear closures (cloref) or linear closures (cloptr). In the latter case, we also have to choose between closures allocated with malloc (or similar) and closures allocated on the stack.
For simplicity, we will use non-linear closures and assume there is a garbage collector, or that the memory allocated for the closures can be allowed to leak. (This is often the case in a program that does not run continuously.)
- )
- include "share/atspre_staload.hats"
(* The following is actually a *template function*, rather than a
function proper. It is expanded during template processing. *)
fn {t1, t2, t3 : t@ype} compose (f : t2 -<cloref1> t3,
g : t1 -<cloref1> t2) : t1 -<cloref1> t3 = lam x => f (g (x))
implement
main0 () =
let
val one_hundred = 100.0
val char_zero = '0'
val f = (lam y =<cloref1> add_double_int (one_hundred, y))
val g = (lam x =<cloref1> char2i x - char2i char_zero)
val z = compose (f, g) ('5')
val fg = compose (f, g)
val w = fg ('7')
in
println! (z : double);
println! (w : double)
end</lang>
- Output:
$ patscc -O2 -DATS_MEMALLOC_GCBDW function_composition.dats -lgc && ./a.out 105.000000 107.000000
Incidentally, it is possible to instantiate the template function and obtain a true function that does the composition. What the template does for us is give us compile-time type polymorphism. In the following, the template is instantiated as a true function for specific types:
<lang ats>#include "share/atspre_staload.hats"
fn {t1, t2, t3 : t@ype} compose (f : t2 -<cloref1> t3,
g : t1 -<cloref1> t2) : t1 -<cloref1> t3 = lam x => f (g (x))
fn compose_char2int2double
(f : int -<cloref1> double,
g : char -<cloref1> int) :
char -<cloref1> double =
compose<char, int, double> (f, g)
implement main0 () =
let
val one_hundred = 100.0
val char_zero = '0'
val f = (lam y =<cloref1> add_double_int (one_hundred, y))
val g = (lam x =<cloref1> char2i x - char2i char_zero)
val z = compose_char2int2double (f, g) ('5')
val fg = compose_char2int2double (f, g)
val w = fg ('7')
in
println! (z : double);
println! (w : double)
end</lang>
- Output:
$ patscc -O2 -DATS_MEMALLOC_GCBDW function_composition_2.dats -lgc && ./a.out 105.000000 107.000000
One could even make the composition procedures themselves be closures:
<lang ats>#include "share/atspre_staload.hats"
fn {t1, t2, t3 : t@ype} compose (f : t2 -<cloref1> t3,
g : t1 -<cloref1> t2) :<cloref1> t1 -<cloref1> t3 = lam x => f (g (x))
fn compose_char2int2double
(f : int -<cloref1> double,
g : char -<cloref1> int) :<cloref1>
char -<cloref1> double =
compose<char, int, double> (f, g)
implement main0 () =
let
val one_hundred = 100.0
val char_zero = '0'
val f = (lam y =<cloref1> add_double_int (one_hundred, y))
val g = (lam x =<cloref1> char2i x - char2i char_zero)
val z = compose_char2int2double (f, g) ('5')
val fg = compose_char2int2double (f, g)
val w = fg ('7')
in
println! (z : double);
println! (w : double)
end</lang>
- Output:
$ patscc -O2 -DATS_MEMALLOC_GCBDW function_composition_3.dats -lgc && ./a.out 105.000000 107.000000
AutoHotkey
contributed by Laszlo on the ahk forum <lang AutoHotkey>MsgBox % compose("sin","cos",1.5)
compose(f,g,x) { ; function composition
Return %f%(%g%(x))
}</lang>
BBC BASIC
<lang bbcbasic> REM Create some functions for testing:
DEF FNsqr(a) = SQR(a)
DEF FNabs(a) = ABS(a)
REM Create the function composition:
SqrAbs = FNcompose(FNsqr(), FNabs())
REM Test calling the composition:
x = -2 : PRINT ; x, FN(SqrAbs)(x)
END
DEF FNcompose(RETURN f%, RETURN g%)
LOCAL f$, p% : DIM p% 7 : p%!0 = f% : p%!4 = g%
f$ = "(x)=" + CHR$&A4 + "(&" + STR$~p% + ")(" + \
\ CHR$&A4 + "(&" + STR$~(p%+4) + ")(x))"
DIM p% LEN(f$) + 4 : $(p%+4) = f$ : !p% = p%+4
= p%</lang>
- Output:
-2 1.41421356
Bori
<lang bori>double sin (double v) { return Math.sin(v); } double asin (double v) { return Math.asin(v); } Var compose (Func f, Func g, double d) { return f(g(d)); }
void button1_onClick (Widget widget) { double d = compose(sin, asin, 0.5); label1.setText(d.toString(9)); }</lang>
- Output:
on Android phone
<lang bori>0.500000000</lang>
BQN
As a 2-modifier:
<lang bqn>_compose_ ← ∘</lang>
Or:
<lang bqn>_compose_ ← {𝔽𝔾𝕩}</lang>
As a dyadic function:
<lang bqn>Compose ← {𝕏∘𝕎}</lang>
This is how you can use it:
(Compose´ ⟨-,÷⟩) {𝕎𝕩} 2
¯0.5
Bracmat
This solution uses a macro in the body of the compose function.
Function composition is illustrated with a conversion from Fahrenheit to Celsius in two steps, followed by a conversion of the resulting rational number to a floating point expression. This shows that the returned value from the compose function indeed is a function and can be used as an argument to another call to compose.
<lang Bracmat>( ( 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 )</lang>
0 °F in °C = -1,78*10E1 100 °F in °C = 3,78*10E1
Brat
<lang brat>compose = { f, g | { x | f g x } }
- Test
add1 = { x | x + 1 } double = { x | x * 2 } b = compose(->double ->add1) p b 1 #should print 4</lang>
C
Only works for functions taking a double and returning a double: <lang c>#include <stdlib.h>
/* generic interface for functors from double to double */ typedef struct double_to_double {
double (*fn)(struct double_to_double *, double);
} double_to_double;
- define CALL(f, x) f->fn(f, x)
/* functor returned by compose */
typedef struct compose_functor {
double (*fn)(struct compose_functor *, double); double_to_double *f; double_to_double *g;
} compose_functor; /* function to be used in "fn" in preceding functor */ double compose_call(compose_functor *this, double x) {
return CALL(this->f, CALL(this->g, x));
} /* returns functor that is the composition of functors
f & g. caller is responsible for deallocating memory */
double_to_double *compose(double_to_double *f,
double_to_double *g) {
compose_functor *result = malloc(sizeof(compose_functor));
result->fn = &compose_call;
result->f = f;
result->g = g;
return (double_to_double *)result;
}
- include <math.h>
/* we can make functors for sin and asin by using
the following as "fn" in a functor */
double sin_call(double_to_double *this, double x) {
return sin(x);
} double asin_call(double_to_double *this, double x) {
return asin(x);
}
- include <stdio.h>
int main() {
double_to_double *my_sin = malloc(sizeof(double_to_double)); my_sin->fn = &sin_call; double_to_double *my_asin = malloc(sizeof(double_to_double)); my_asin->fn = &asin_call;
double_to_double *sin_asin = compose(my_sin, my_asin);
printf("%f\n", CALL(sin_asin, 0.5)); /* prints "0.500000" */
free(sin_asin); free(my_sin); free(my_asin);
return 0;
}</lang>
C#
<lang 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>
C++
<lang cpp>#include <functional>
- include <cmath>
- include <iostream>
// functor class to be returned by compose function template <class Fun1, class Fun2> class compose_functor :
public std::unary_function<typename Fun2::argument_type,
typename Fun1::result_type>
{ protected:
Fun1 f; Fun2 g;
public:
compose_functor(const Fun1& _f, const Fun2& _g)
: f(_f), g(_g) { }
typename Fun1::result_type
operator()(const typename Fun2::argument_type& x) const
{ return f(g(x)); }
};
// we wrap it in a function so the compiler infers the template arguments // whereas if we used the class directly we would have to specify them explicitly template <class Fun1, class Fun2> inline compose_functor<Fun1, Fun2> compose(const Fun1& f, const Fun2& g) { return compose_functor<Fun1,Fun2>(f, g); }
int main() {
std::cout << compose(std::ptr_fun(::sin), std::ptr_fun(::asin))(0.5) << std::endl;
return 0;
}</lang>
composing std::function
<lang cpp>#include <iostream>
- include <functional>
- include <cmath>
template <typename A, typename B, typename C> std::function<C(A)> compose(std::function<C(B)> f, std::function<B(A)> g) {
return [f,g](A x) { return f(g(x)); };
}
int main() {
std::function<double(double)> f = sin; std::function<double(double)> g = asin; std::cout << compose(f, g)(0.5) << std::endl;
return 0;
}</lang>
This much simpler version uses decltype(auto).
<lang cpp>#include <iostream>
- include <cmath>
template <class F, class G> decltype(auto) compose(F&& f, G&& g) {
return [=](auto x) { return f(g(x)); };
}
int main() {
std::cout << compose(sin, asin)(0.5) << "\n"; return 0;
}</lang>
GCC's C++ library has a built-in compose function
<lang cpp>#include <iostream>
- include <cmath>
- include <ext/functional>
int main() {
std::cout << __gnu_cxx::compose1(std::ptr_fun(::sin), std::ptr_fun(::asin))(0.5) << std::endl;
return 0;
}</lang>
Clojure
Function composition is built in to Clojure. Simply call the comp function.
A manual implementation could look like this: <lang clojure>(defn compose [f g]
(fn [x] (f (g x))))
- Example
(def inc2 (compose inc inc)) (println (inc2 5)) ; prints 7</lang>
CoffeeScript
<lang coffeescript> compose = ( f, g ) -> ( x ) -> f g x
- Example
add2 = ( x ) -> x + 2 mul2 = ( x ) -> x * 2
mulFirst = compose add2, mul2 addFirst = compose mul2, add2 multiple = compose mul2, compose add2, mul2
console.log "add2 2 #=> #{ add2 2 }" console.log "mul2 2 #=> #{ mul2 2 }" console.log "mulFirst 2 #=> #{ mulFirst 2 }" console.log "addFirst 2 #=> #{ addFirst 2 }" console.log "multiple 2 #=> #{ multiple 2 }" </lang>
- Output:
add2 2 #=> 4 mul2 2 #=> 4 mulFirst 2 #=> 6 addFirst 2 #=> 8 multiple 2 #=> 12
Or, extending the Function prototype.
<lang coffeescript> Function::of = (f) -> (args...) => @ f args...
- Example
add2 = (x) -> x + 2 mul2 = (x) -> x * 2
mulFirst = add2.of mul2 addFirst = mul2.of add2 multiple = mul2.of add2.of mul2
console.log "add2 2 #=> #{ add2 2 }" console.log "mul2 2 #=> #{ mul2 2 }" console.log "mulFirst 2 #=> #{ mulFirst 2 }" console.log "addFirst 2 #=> #{ addFirst 2 }" console.log "multiple 2 #=> #{ multiple 2 }" </lang>
Output is identical.
Common Lisp
compose returns a function that closes on the lexical variables f and g.
<lang lisp>(defun compose (f g) (lambda (x) (funcall f (funcall g x))))</lang>
Example use: <lang lisp>>(defun compose (f g) (lambda (x) (funcall f (funcall g x)))) COMPOSE >(let ((sin-asin (compose #'sin #'asin)))
(funcall sin-asin 0.5))
0.5</lang>
This alternate solution, more ugly and more difficult, never closes on any lexical variables. Instead, it uses runtime evaluation to insert the values of f and g into new code. This is just a different way to create a closure.
<lang lisp>(defun compose (f g)
(eval `(lambda (x) (funcall ',f (funcall ',g x)))))</lang>
In this last example, a macro is used to compose any number of single parameter functions. <lang lisp>CL-USER> (defmacro compose (fn-name &rest args) (labels ((rec1 (args) (if (= (length args) 1) `(funcall ,@args x) `(funcall ,(first args) ,(rec1 (rest args)))))) `(defun ,fn-name (x) ,(rec1 args))))</lang> Because this macro expands into a defun form, the function returned by compose is in the function namespace and the use of funcall is not necessary.
CL-USER> (compose f #'ceiling #'sin #'sqrt) F CL-USER> (compose g #'1+ #'abs #'cos) G CL-USER> (compose h #'f #'g) H CL-USER> (values (f pi) (g pi) (h pi)) 1 2.0L0 1 CL-USER>
Crystal
Crystal requires using closures for function composition. Since the only type the compiler can't infer for compose is the type of x, the type of the first argument to f has to be specified as the generic type T.
<lang ruby>require "math"
def compose(f : Proc(T, _), g : Proc(_, _)) forall T
return ->(x : T) { f.call(g.call(x)) }
end
compose(->Math.sin(Float64), ->Math.asin(Float64)).call(0.5) #=> 0.5</lang>
The types for f's output, g's input and output, and the result of compose can all be inferred, but could be specified verbosely with def compose(f : Proc(T, U), g : Proc(U, V)) : Proc(T, V) forall T, U, V
D
<lang d>import std.stdio;
T delegate(S) compose(T, U, S)(in T delegate(U) f,
in U delegate(S) g) {
return s => f(g(s));
}
void main() {
writeln(compose((int x) => x + 15, (int x) => x ^^ 2)(10)); writeln(compose((int x) => x ^^ 2, (int x) => x + 15)(10));
}</lang>
- Output:
115 625
Delphi
Anonymous methods were introduced in Delphi 2009, so next code works with Delphi 2009 and above:
<lang Delphi>program AnonCompose;
{$APPTYPE CONSOLE}
type
TFunc = reference to function(Value: Integer): Integer; // 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.</lang>
Diego
Function composition of two simple functions: <lang diego>set_namespace(rosettacode);
begin_funct(compose)_arg(f, g);
[]_ret(x)_calc([f]([g]([x])));
end_funct[];
me_msg()_funct(compose)_arg(f)_sin()_arg(g)_asin()_var(x)_value(0.5); // result: 0.5
reset_namespace[];</lang>
Function composition of two calculated functions: <lang diego>set_namespace(rosettacode);
with_funct(f)_arg({int}, x)_ret()_calc([x] * [x]); with_funct(g)_arg({int}, x)_ret()_calc([x] + 2);
begin_funct(compose)_arg(f, g);
[]_ret(x)_calc([f]([g]([x])));
end_funct[];
me_msg()_funct(compose)_arg(f)_funct(f)_arg(g)_funct(g)_var(x)_v(10); // result: 144 // or me_msg()_funct(compose)_arg({f}, f)_arg({g}, g)_var(x)_v(10);
reset_ns[];</lang>
Dylan
compose[1] is already part of the language standard, with a more complete definition than this.
<lang dylan> define method compose(f,g)
method(x) f(g(x)) end
end; </lang>
Déjà Vu
It is already defined in the standard library as $.
<lang dejavu>compose f g: labda: f g</lang>
E
<lang e>def compose(f, g) {
return fn x { return f(g(x)) }
}</lang>
EchoLisp
<lang lisp>
- 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))) </lang>
- Output:
<lang lisp> ((ucompose sin cos) 3) → -0.8360218615377305 ((compose sin cos) 3) → -0.8360218615377305 (sincos 3) → -0.8360218615377305 </lang>
Ela
It is already defined in standard prelude as (<<) operator.
<lang ela>let compose f g x = f (g x)</lang> ==Ela== It is already defined in standard prelude as (<<) operator.
<lang ela>compose f g x = f (g x)</lang>
Elena
ELENA 4.x : <lang elena>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))
}</lang>
- Output:
10
Elixir
<lang elixir>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)</lang>
- Output:
0.5 2.0 16.0
Emacs Lisp
Lexical binding is supported as of Emacs 24.1, allowing the use of a closure for function composition.
<lang Lisp>;; lexical-binding: t (defun compose (f g)
(lambda (x) (funcall f (funcall g x))))
(let ((func (compose '1+ '1+)))
(funcall func 5)) ;=> 7</lang>
Alternatively, a lambda form can be constructed with the desired f and g inserted. The result is simply a list. A list starting with lambda is a function.
<lang Lisp>(defun compose (f g)
`(lambda (x) (,f (,g x))))
(let ((func (compose '1+ '1+)))
(funcall func 5)) ;=> 7</lang>
A similar thing can be done with a macro like the following. It differs in that the arguments should be unquoted symbols, and if they're expressions then they're evaluated on every call to the resulting lambda.
<lang Lisp>(defmacro compose (f g)
`(lambda (x) (,f (,g x))))
(let ((func (compose 1+ 1+)))
(funcall func 5)) ;=> 7</lang>
Erlang
<lang erlang>-module(fn). -export([compose/2, multicompose/1]).
compose(F,G) -> fun(X) -> F(G(X)) end.
multicompose(Fs) ->
lists:foldl(fun compose/2, fun(X) -> X end, Fs).</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
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:
<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>
Fortran
Modern Fortran standard has (limited) kind of higher-order functions (as result, argument, and with one level of nested functions) and optional arguments, and this enables to compose the following function (it is impure because Fortran has no closures). For simple cases function calls may be just nested to achieve the effect of function composition, because in fortran nested calls f(g(d(x))) generate a hierarchic set of function calls and the result of each function is transmitted to its calling function in a standard way for all functions.
<lang fortran> 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 </lang>
Fortress
In Fortress, there are two ways that you can compose functions.
1. You can compose functions manually by writing your own composition function.
In this version, we allow any type of function to be used by defining our own types in the function definition and using those types to define how the composed function should behave. This version operates very similarly to the way that the COMPOSE operator, explained below, operates.
<lang fortress>
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)
</lang>
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. <lang fortress>
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)
</lang>
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.
<lang fortress>
opr_composed(i:Number): Number->RR64 = (sin COMPOSE cos)(i)
</lang>
Should you need to, you could also mix both methods by overloading the COMPOSE operator.
FreeBASIC
Illustrating with functions that take and return integers. <lang freebasic>function compose( f as function(as integer) as integer,_
g as function(as integer) as integer,_
n as integer ) as integer
return f(g(n))
end function</lang> If you have functions named, say, foo and bar you would call compose with
compose( @foo, @bar, n )
for some integer n.
FunL
<lang funl>import math.{sin, asin}
def compose( f, g ) = x -> f( g(x) )
sin_asin = compose( sin, asin )
println( sin_asin(0.5) )</lang>
- Output:
0.5
Fōrmulæ
Fōrmulæ programs are not textual, visualization/edition of programs is done showing/manipulating structures but not text. Moreover, there can be multiple visual representations of the same program. Even though it is possible to have textual representation —i.e. XML, JSON— they are intended for storage and transfer purposes more than visualization and edition.
Programs in Fōrmulæ are created/edited online in its website, However they run on execution servers. By default remote servers are used, but they are limited in memory and processing power, since they are intended for demonstration and casual use. A local server can be downloaded and installed, it has no limitations (it runs in your own computer). Because of that, example programs can be fully visualized and edited, but some of them will not run if they require a moderate or heavy computation/memory resources, and no local server is being used.
In this page you can see the program(s) related to this task and their results.
GAP
<lang gap>Composition := function(f, g)
return x -> f(g(x));
end;
h := Composition(x -> x+1, x -> x*x); h(5);
- 26</lang>
Go
<lang go>// Go doesn't have generics, but sometimes a type definition helps // readability and maintainability. This example is written to // the following function type, which uses float64. type ffType func(float64) float64
// compose function requested by task func compose(f, g ffType) ffType {
return func(x float64) float64 {
return f(g(x))
}
}</lang> Example use: <lang go>package main
import "math" import "fmt"
type ffType func(float64) float64
func compose(f, g ffType) ffType {
return func(x float64) float64 {
return f(g(x))
}
}
func main() {
sin_asin := compose(math.Sin, math.Asin) fmt.Println(sin_asin(.5))
}</lang>
- Output:
0.5
Groovy
Test program: <lang groovy>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</lang>
Haskell
This is already defined as the . (dot) operator in Haskell:
<lang haskell>Prelude> let sin_asin = sin . asin Prelude> sin_asin 0.5 0.49999999999999994</lang>
Ways to use directly: <lang haskell>(sin . asin) 0.5</lang> <lang haskell>sin . asin $ 0.5</lang>
Implementing compose function from scratch:
<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>
Right to left composition of a list of functions could be defined as flip (foldr id):
<lang haskell>composeList :: [a -> a] -> a -> a composeList = flip (foldr id)
main :: IO () main = print $ composeList [(/ 2), succ, sqrt] 5</lang>
- Output:
1.618033988749895
Hy
<lang clojure>(defn compose [f g]
(fn [x] (f (g x))))</lang>
Icon and Unicon
Icon and Unicon don't have a lambda function or native closure; however, they do have co-expressions which are extremely versatile and can be used to achieve the same effect. The list of functions to compose can be a 'procedure', 'co-expression", or an invocable string (i.e. procedure name or unary operator). It will correctly handle compose(compose(...),..).
There are a few limitations to be aware of:
- type(compose(f,g)) returns a co-expression not a procedure
- this construction only handles functions of 1 argument (a closure construct is better for the general case)
The solution below can be adapted to work in Icon by reverting to the old syntax for invoking co-expressions.
<lang Icon> x @ f # use this syntax in Icon instead of the Unicon f(x) to call co-expressions
every push(fL := [],!rfL) # use this instead of reverse(fL) as the Icon reverse applies only to strings</lang>
See Icon and Unicon Introduction:Minor Differences for more information
<lang Unicon>procedure main(arglist)
h := compose(sqrt,abs)
k := compose(integer,"sqrt",ord)
m := compose("-",k)
every write(i := -2 to 2, " h=(sqrt,abs)-> ", h(i))
every write(c := !"1@Q", " k=(integer,\"sqrt\",ord)-> ", k(c))
write(c := "1"," m=(\"-\",k) -> ",m(c))
end
invocable all # permit string invocations
procedure compose(fL[]) #: compose(f1,f2,...) returns the functional composition of f1,f2,... as a co-expression
local x,f,saveSource
every case type(x := !fL) of {
"procedure"|"co-expression": &null # procedures and co-expressions are fine
"string" : if not proc(x,1) then runnerr(123,fL) # as are invocable strings (unary operators, and procedures)
default: runerr(123,fL)
}
fL := reverse(fL) # reverse and isolate from mutable side-effects
cf := create { saveSource := &source # don't forget where we came from
repeat {
x := (x@saveSource)[1] # return result and resume here
saveSource := &source # ...
every f := !fL do x := f(x) # apply the list of 'functions'
}
}
return (@cf, cf) # 'prime' the co-expr before returning it
end</lang>
- Output:
-2 h=(sqrt,abs)-> 1.414213562373095
-1 h=(sqrt,abs)-> 1.0
0 h=(sqrt,abs)-> 0.0
1 h=(sqrt,abs)-> 1.0
2 h=(sqrt,abs)-> 1.414213562373095
1 k=(integer,"sqrt",ord)-> 7
@ k=(integer,"sqrt",ord)-> 8
Q k=(integer,"sqrt",ord)-> 9
1 m=("-",k) -> -7
J
Solution: <lang j>compose =: @</lang>
Example: <lang j>f compose g</lang>
Of course, given that @ is only one character long and is a built-in primitive, there is no need for the cover function compose. And @ is not the only composition primitive; composition is a very important concept in J. For more details, see the talk page.
Tentative new example:
<lang j>f=: >.@(1&o.)@%: g=: 1&+@|@(2&o.) h=: f@g</lang>
Example use: <lang j> (f, g, h) 1p1 1 2 1</lang>
Note: 1&o. is sine (mnemonic: sine is an odd circular function), 2&o. is cosine (cosine is an even circular function), %: is square root, >. is ceiling, | is absolute value and 1&+ adds 1.
Java
<lang java>public class Compose {
// Java doesn't have function type so we define an interface
// of function objects instead
public interface Fun<A,B> {
B call(A x);
}
public static <A,B,C> Fun<A,C> compose(final Fun<B,C> f, final Fun<A,B> g) {
return new Fun<A,C>() {
public C call(A x) {
return f.call(g.call(x));
}
};
}
public static void main(String[] args) {
Fun<Double,Double> sin = new Fun<Double,Double>() {
public Double call(Double x) {
return Math.sin(x);
}
};
Fun<Double,Double> asin = new Fun<Double,Double>() {
public Double call(Double x) {
return Math.asin(x);
}
};
Fun<Double,Double> sin_asin = compose(sin, asin);
System.out.println(sin_asin.call(0.5)); // prints "0.5" }
}</lang>
Java 8
Java 8's Function interface already has a .compose() default method:
<lang java>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" }
}</lang>
Implementing it yourself as a static method:
<lang java>import java.util.function.Function;
public class Compose {
public static <A,B,C> Function<A,C> compose(Function<B,C> f, Function<A,B> g) {
return x -> f.apply(g.apply(x));
}
public static void main(String[] args) {
Function<Double,Double> sin_asin = compose(Math::sin, Math::asin);
System.out.println(sin_asin.apply(0.5)); // prints "0.5" }
}</lang>
JavaScript
ES5
Simple composition of two functions
<lang javascript>function compose(f, g) {
return function(x) {
return f(g(x));
};
}</lang> Example: <lang javascript>var id = compose(Math.sin, Math.asin); console.log(id(0.5)); // 0.5</lang>
Multiple composition
Recursion apart, multiple composition can be written in at least two general ways in JS:
- Iteratively (faster to run, perhaps more fiddly to write)
- With a fold / reduction (see http://rosettacode.org/wiki/Catamorphism). The fold is arguably simpler to write and reason about, though not quite as fast to execute.
<lang JavaScript>(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);
});
})(); </lang>
- Output:
[1.618033988749895, 1.618033988749895]
ES6
Simple composition of two functions
<lang javascript>function compose(f, g) {
return x => f(g(x));
}</lang> or <lang javascript>var compose = (f, g) => x => f(g(x));</lang> Example: <lang javascript>var id = compose(Math.sin, Math.asin); console.log(id(0.5)); // 0.5</lang>
Multiple composition
<lang JavaScript>(() => {
'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
})();</lang>
- Output:
1.618033988749895
Joy
Composition is the default operation in Joy. The composition of two functions is the concatenation of those functions, in the order in which they are to be applied. <lang joy>g f</lang>
jq
The equivalent in jq of a function with one argument is a 0-arity filter. For example, in jq, exp is the exponential function and can be evaluated like so: 0.5 | exp.
We therefore illustrate here how a function that composes two 0-arity filters can be written: <lang jq>
- apply g first and then f
def compose(f; g): g | f; </lang> Example: 0.5 | compose(asin; sin)
In practice, "compose" is rarely used since, given two 0-arity filters, f and g, the expression "g|f" can be passed as an argument to other functions.
Julia
Built-in: <lang julia>@show (asin ∘ sin)(0.5)</lang>
Alternative: <lang julia>compose(f::Function, g::Function) = (x) -> g(f(x)) @show compose(sin, asin)(0.5)</lang>
K
The K syntax for APL tacit (point free) function composition is the dyadic form of apostrophe ('), here is a cover function <lang k>compose:{'[x;y]}</lang>
An equivalent explicit definition would be <lang k>compose:{x[y[z]]}</lang>
Example: <lang k> sin_asin:compose[sin;asin] // or compose . (sin;asin)
sin_asin 0.5
0.5</lang>
Klingphix
<lang Klingphix>include ..\Utilitys.tlhy
- 2 2 * ;
- ++ 1 + ;
- composite swap exec swap exec ;
@++ @*2 3 composite ? { result: 7 }
"End " input</lang>
Kotlin
<lang scala>// 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))
}</lang>
- Output:
144
Lambdatalk
<lang Scheme> {def compose
{lambda {:f :g :x}
{:f {:g :x}}}}
-> compose
{def funcA {lambda {:x} {* :x 10}}} -> funcA
{def funcB {lambda {:x} {+ :x 5}}} -> funcB
{def f {compose funcA funcB}} -> f
{{f} 3} -> 80 </lang>
LFE
<lang lisp> (defun compose (f g)
(lambda (x)
(funcall f
(funcall g x))))
(defun compose (funcs)
(lists:foldl #'compose/2
(lambda (x) x)
funcs))
(defun check ()
(let* ((sin-asin (compose #'math:sin/1 #'math:asin/1))
(expected (math:sin (math:asin 0.5)))
(compose-result (funcall sin-asin 0.5)))
(io:format '"Expected answer: ~p~n" (list expected))
(io:format '"Answer with compose: ~p~n" (list compose-result))))
</lang>
If you pasted those into the LFE REPL, you can do the following: <lang lisp> > (funcall (compose #'math:sin/1 #'math:asin/1)
0.5)
0.49999999999999994 > (funcall (compose `(,#'math:sin/1
,#'math:asin/1
,(lambda (x) (+ x 1))))
0.5)
1.5 > (check) Expected answer: 0.49999999999999994 Answer with compose: 0.49999999999999994 ok > </lang>
Lingo
Lingo does not support functions as first-class objects. However, there is a way to achieve something similar:
In Lingo global functions (i.e. either built-in functions or custom functions defined in movie scripts) are methods of the _movie object. There are 2 ways to call such functions:
- a) foo (1,2,3)
- b) call (#foo, _movie, 1, 2, 3)
If we ignore the standard way a) and only concentrate on b), we can define a "call-function" (arbitrary word coining) as:
- "Anything that supports the syntax 'call(<func>, _movie [, comma-separated arg list])' and might return a value."
As described above, this "call-function" definition includes all built-in and global user-defined functions.
For such "call-functions", function composition can be implemented using the following global (i.e. movie script) function compose() and the following parent script "Composer":
<lang lingo>-- 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</lang>
<lang lingo>-- 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</lang>
Usage: <lang lingo>-- 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</lang>
User-defined custom functions used in demo code above: <lang lingo>-- 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</lang>
LOLCODE
LOLCODE supports first-class functions only insofar as they may be stored in variables and returned from other functions. Alas, given the current lack of support for either lambdas or closures, function composition can only be reasonably simulated with the help of a few global variables. <lang LOLCODE>HAI 1.3
I HAS A fx, I HAS A gx
HOW IZ I composin YR f AN YR g
fx R f, gx R g
HOW IZ I composed YR x
FOUND YR I IZ fx YR I IZ gx YR x MKAY MKAY
IF U SAY SO
FOUND YR composed
IF U SAY SO
HOW IZ I incin YR num
FOUND YR SUM OF num AN 1
IF U SAY SO
HOW IZ I sqrin YR num
FOUND YR PRODUKT OF num AN num
IF U SAY SO
I HAS A incsqrin ITZ I IZ composin YR incin AN YR sqrin MKAY VISIBLE I IZ incsqrin YR 10 MKAY BTW, prints 101
I HAS A sqrincin ITZ I IZ composin YR sqrin AN YR incin MKAY VISIBLE I IZ sqrincin YR 10 MKAY BTW, prints 121
KTHXBYE</lang>
Lua
<lang lua>function compose(f, g) return function(...) return f(g(...)) end end</lang>
M2000 Interpreter
Using Lambda functions
<lang M2000 Interpreter> 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 </lang>
Using EVAL and EVAL$
<lang M2000 Interpreter> class Compose { private: composition$ public: function formula$ { =.composition$ } value (x){ =Eval(.composition$) } Class: module compose(a$, b$) { .composition$<=a$+"("+b$+"(x))" } } function Global Exp(x) { =round(2.7182818284590452**x) } class ComposeStr$ { private: composition$ public: function formula$ { =.composition$ } value (x$){ =Eval$(.composition$.) // NEED A DOT AFTER STRING VARIABLE } Class: module composeStr(a$, b$) { .composition$<=a$+"("+b$+"(x$))" } } ExpLog=Compose("Exp", "Ln") Print ExpLog(3) UcaseLcase$=ComposeStr$("Ucase$", "Lcase$") Print UcaseLcase$("GOOD") </lang>
Mathcad
Mathcad is a non-text-based programming environment. The expressions below are an approximations of the way that they are entered (and) displayed on a Mathcad worksheet. The worksheet is available at xxx_tbd_xxx
This particular version of Function Composition was created in Mathcad Prime Express 7.0, a free version of Mathcad Prime 7.0 with restrictions (such as no programming or symbolics). All Prime Express numbers are complex. There is a recursion depth limit of about 4,500.
compose(f,g,x):=f(g(x))
cube(x):=x3 cuberoot(x):=x1/3
funlist:=[sin cos cube]T invlist:=[asin acos cuberoot]T
invfunlist(x):= {vectorize}compose(invlist,funlist,x){/vectorize}
x:= 0.5
invfunlist(x)= {results of evaluation appears here) invfunlist([x √2 3]T)= {results)
apply(f,x):=f(x) apply(f,x):={vectorize}apply(f,x){/vectorize}
apply(funlist,x)= {results} + ... several more examples
Mathematica / Wolfram Language
Built-in function that takes any amount of function-arguments: <lang Mathematica>Composition[f, g][x] Composition[f, g, h, i][x]</lang> gives back: <lang Mathematica>f[g[x]] f[g[h[i[x]]]]</lang> Custom function: <lang Mathematica>compose[f_, g_][x_] := f[g[x]] compose[Sin, Cos][r]</lang> gives back: <lang Mathematica>Sin[Cos[r]]</lang> Composition can be done in more than 1 way: <lang Mathematica>Composition[f,g,h][x] f@g@h@x x//h//g//f</lang> all give back: <lang Mathematica>f[g[h[x]]]</lang> The built-in function has a couple of automatic simplifications: <lang Mathematica>Composition[f, Identity, g] Composition[f, InverseFunction[f], h][x]</lang> becomes: <lang Mathematica>f[g[x]] h[x]</lang>
Maxima
<lang maxima>/* built-in */ load(to_poly_solver);
compose_functions([sin, cos]); /* lambda([%g0],sin(cos(%g0)))*/
/* An implementation, to show a use of buildq */ compose(f, g) := buildq([f, g], lambda([x], f(g(x))));</lang>
min
Since min is both concatenative and homoiconic, function composition is equivalent to list concatenation. Example: <lang min>(1 +) (2 *) concat print</lang>
- Output:
(1 + 2 *)
MiniScript
<lang MiniScript>funcA = function(x)
return x * 10
end function
funcB = function(x)
return x + 5
end function
compose = function(f, g)
return function(x)
return f(g(x))
end function
end function
f = compose(@funcA, @funcB) print f(3) // should be equal to (3+5)*10</lang>
- Output:
80
Nemerle
<lang Nemerle>using System; using System.Console; using System.Math;
module Composition {
Compose[T](f : T -> T, g : T -> T, x : T) : T
{
f(g(x))
}
Main() : void
{
def SinAsin = Compose(Sin, Asin, _);
WriteLine(SinAsin(0.5));
}
}</lang>
Never
<lang Never> func compose(f(i : int) -> int, g(i : int) -> int) -> (int) -> int {
let func (i : int) -> int { f(g(i)) }
}
func dec(i : int) -> int { 10 * i }
func succ(i : int) -> int { i + 1 }
func main() -> int {
let h = compose(dec, succ);
print(h(1));
0
} </lang>
NewLISP
<lang NewLISP>> (define (compose f g) (expand (lambda (x) (f (g x))) 'f 'g)) (lambda (f g) (expand (lambda (x) (f (g x))) 'f 'g)) > ((compose sin asin) 0.5) 0.5 </lang>
Nim
<lang nim>import sugar
proc compose[A,B,C](f: A -> B, g: B -> C): A -> C = (x: A) => f(g(x))
proc plustwo(x: int): int = x + 2 proc minustwo(x: int): int = x - 2
var plusminustwo = compose(plustwo, minustwo) echo plusminustwo(10)</lang>
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
ObjectIcon
<lang objecticon># -*- ObjectIcon -*-
- The Rosetta Code function composition task, in Object Icon.
- Composition will result in a co-expression.
- Object Icon co-expressions are closures: they share the local
- variables of the context in which they are created. In Arizona Icon,
- co-expressions obtain only the *values* of those variables. However,
- this difference, despite its significance, is not really important
- to the notion of composition.
- This example is adapted from the Unicon implementation of the
- task. To simplify the example, I have removed support for string
- invocations.
import io
procedure main (arglist)
local f, g
# f gets a co-expression that is a composition of three procedures. f := compose(append_exclamation, string_repeat, double_it) write(123@f)
# g gets a co-expression that is a composition of a procedure and f. g := compose(string_repeat, f) write(123@g)
end
procedure double_it (n)
return n + n
end
procedure string_repeat (x)
return string(x) || string(x)
end
procedure append_exclamation (s)
return s || "!"
end
procedure compose (rfL[])
local x, f, saveSource, fL, cf
every push(fL := [], !rfL)
cf := create {
saveSource := &source
repeat {
x := x@saveSource
saveSource := &source
every f := !fL do {
case type(f) of {
"co-expression": x := x@f
default: x := f(x)
}
}
}
}
# Co-expressions often need to be "primed" before they can be # used. @cf
return cf
end</lang>
- Output:
$ oit -s function_composition-OI.icn && ./function_composition-OI 246246! 246246!246246!
Objective-C
We restrict ourselves to functions that take and return one object.
<lang objc>#include <Foundation/Foundation.h>
typedef id (^Function)(id);
// a commodity for "encapsulating" double f(double) typedef double (*func_t)(double); Function encapsulate(func_t f) {
return ^(id x) { return @(f([x doubleValue])); };
}
Function compose(Function a, Function b) {
return ^(id x) { return a(b(x)); };
}
// functions outside... double my_f(double x) {
return x+1.0;
}
double my_g(double x) {
return x*x;
}
int main()
{
@autoreleasepool {
Function f = encapsulate(my_f);
Function g = encapsulate(my_g);
Function composed = compose(f, g);
printf("g(2.0) = %lf\n", [g(@2.0) doubleValue]);
printf("f(2.0) = %lf\n", [f(@2.0) doubleValue]);
printf("f(g(2.0)) = %lf\n", [composed(@2.0) doubleValue]);
} return 0;
}</lang>
OCaml
<lang ocaml>let compose f g x = f (g x)</lang> Example use: <lang ocaml># let compose f g x = f (g x);; val compose : ('a -> 'b) -> ('c -> 'a) -> 'c -> 'b = <fun>
- let sin_asin = compose sin asin;;
val sin_asin : float -> float = <fun>
- sin_asin 0.5;;
- : float = 0.5</lang>
Octave
<lang octave>function r = compose(f, g)
r = @(x) f(g(x));
endfunction
r = compose(@exp, @sin); r(pi/3)</lang>
Oforth
Oforth uses RPN notation. Function composition of f and g is just calling : <lang Oforth>g f</lang> If a block is needed, a compose function can be implemented : <lang Oforth>: compose(f, g) #[ g perform f perform ] ;</lang> Usage : <lang Oforth>1.2 compose(#asin, #sin) perform [ 1, 2, 3, 4, 5 ] compose(#[ map(#sqrt) ], #[ filter(#isEven) ]) perform</lang> The last line returns : [1.4142135623731, 2]
Ol
<lang scheme> (define (compose f g)
(lambda (x) (f (g x))))
- or
(define ((compose f g) x) (f (g x))) </lang>
Order
Order supplies the built-in function 8compose for this purpose. However, a manual implementation might be:
<lang c>#include <order/interpreter.h>
- define ORDER_PP_DEF_8comp ORDER_PP_FN( \
8fn(8F, 8G, 8fn(8X, 8ap(8F, 8ap(8G, 8X)))) )</lang>
Interpreter limitations mean that local variables containing functions must be called with the 8ap operator, but the functions themselves are still first-class values.
Oz
<lang oz>declare
fun {Compose F G}
fun {$ X}
{F {G X}}
end
end
SinAsin = {Compose Float.sin Float.asin}
in
{Show {SinAsin 0.5}}</lang>
PARI/GP
<lang parigp>compose(f, g)={
x -> f(g(x))
};
compose(x->sin(x),x->cos(x)(1)</lang>
Usage note: In Pari/GP 2.4.3, this can be expressed more succinctly: <lang parigp>compose(sin,cos)(1)</lang>
Pascal
See Delphi
Perl
<lang perl>sub compose {
my ($f, $g) = @_;
sub {
$f -> ($g -> (@_))
};
}
use Math::Trig; print compose(sub {sin $_[0]}, \&asin)->(0.5), "\n";</lang>
Phix
There is not really any direct support for this sort of thing in Phix, but it is all pretty trivial to manage explicitly.
In the following, as it stands, you cannot use constant m in the same way as a routine_id, or pass a standard routine_id to call_composite(), but tagging the ctable entries so that you know precisely what to do with each entry does not sound the least bit difficult to me.
sequence ctable = {} function compose(integer f, integer g) ctable = append(ctable,{f,g}) return length(ctable) end function function call_composite(integer f, atom x) integer g {f,g} = ctable[f] return call_func(f,{call_func(g,{x})}) end function function plus1(atom x) return x+1 end function function halve(atom x) return x/2 end function constant m = compose(routine_id("halve"),routine_id("plus1")) ?call_composite(m,1) -- displays 1 ?call_composite(m,4) -- displays 2.5
Phixmonti
<lang Phixmonti>def *2 2 * enddef def ++ 1 + enddef def composite swap exec swap exec enddef
getid ++ getid *2 3 composite print /# result: 7 #/</lang>
PHP
<lang php><?php function compose($f, $g) {
return function($x) use ($f, $g) { return $f($g($x)); };
}
$trim_strlen = compose('strlen', 'trim'); echo $result = $trim_strlen(' Test '), "\n"; // prints 4 ?></lang>
works with regular functions as well as functions created by create_function() <lang php><?php function compose($f, $g) {
return create_function('$x', 'return '.var_export($f,true).'('.var_export($g,true).'($x));');
}
$trim_strlen = compose('strlen', 'trim'); echo $result = $trim_strlen(' Test '), "\n"; // prints 4 ?></lang>
PicoLisp
<lang PicoLisp>(de compose (F G)
(curry (F G) (X)
(F (G X)) ) )</lang>
<lang PicoLisp>(def 'a (compose inc dec)) (def 'b (compose 'inc 'dec)) (def 'c (compose '((A) (inc A)) '((B) (dec B))))</lang> <lang PicoLisp>: (a 7) -> 7
- (b 7)
-> 7
- (c 7)
-> 7</lang>
PostScript
<lang PostScript> /compose { % f g -> { g f }
[ 3 1 roll exch
% procedures are not executed when encountered directly
% insert an 'exec' after procedures, but not after operators
1 index type /operatortype ne { /exec cvx exch } if
dup type /operatortype ne { /exec cvx } if
] cvx
} def
/square { dup mul } def /plus1 { 1 add } def /sqPlus1 /square load /plus1 load compose def </lang>
PowerShell
You can simply call g inside f like this: <lang PowerShell> function g ($x) {
$x + $x
} function f ($x) {
$x*$x*$x
} f (g 1) </lang>
Or g and f can become paramaters of a new function fg
<lang PowerShell> function fg (${function:f}, ${function:g}, $x) {
f (g $x)
} fg f g 1 </lang>
In both cases the answer is:
8
Prolog
Works with SWI-Prolog and module lambda, written by Ulrich Neumerkel found there http://www.complang.tuwien.ac.at/ulrich/Prolog-inedit/lambda.pl <lang Prolog>:- use_module(lambda).
compose(F,G, FG) :- FG = \X^Z^(call(G,X,Y), call(F,Y,Z)). </lang>
- Output:
?- compose(sin, asin, F), call(F, 0.5, Y). F = \_G4586^_G4589^ (call(asin,_G4586,_G4597),call(sin,_G4597,_G4589)), Y = 0.5.
PureBasic
<lang PureBasic>;Declare how our function looks like Prototype.i Func(Arg.i)
- Make a procedure that composes any functions of type "Func"
Procedure Compose(*a.Func,*b.Func, x)
ProcedureReturn *a(*b(x))
EndProcedure
- Just a procedure fitting "Func"
Procedure f(n)
ProcedureReturn 2*n
EndProcedure
- Yet another procedure fitting "Func"
Procedure g(n)
ProcedureReturn n+1
EndProcedure
- - Test it
X=Random(100) Title$="With x="+Str(x) Body$="Compose(f(),g(), x) ="+Str(Compose(@f(),@g(),X)) MessageRequester(Title$,Body$)</lang>
Purity
<lang Purity> data compose = f => g => $f . $g </lang>
Python
Simple composition of two functions
<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>
Or, expanding slightly:
<lang python>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()</lang>
- Output:
[0.49999999999999994, 0.5000000000000001, 0.5000000000000001]
Multiple composition
Nested composition of several functions can be streamlined by using functools.reduce.
<lang python>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()</lang>
- Output:
1.618033988749895
composition via operator overloading
Here need composition of several functions is reduced with classes.
<lang python>
- 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))</lang>
Qi
Qi supports partial applications, but only when calling a function with one argument. <lang qi> (define compose
F G -> (/. X
(F (G X))))
((compose (+ 1) (+ 2)) 3) \ (Outputs 6) \ </lang>
Alternatively, it can be done like this:
<lang qi> (define compose F G X -> (F (G X)))
(((compose (+ 1)) (+ 2)) 3) \ (Outputs 6) \ </lang>
Quackery
<lang Quackery> [ nested swap
nested swap join ] is compose ( g f --> [ )
( ----- demonstration ----- )
( create a named nest -- equivalent to a function )
[ 2 * ] is double ( n --> n )
( "[ 4 + ]" is an unnamed nest
-- equivalent to a lambda function. )
( "quoting" a nest with ' puts it on the stack rather than it being evaluated. "do" evaluates the top of stack. )
19 ' double ' [ 4 + ] compose do echo
</lang>
- Output:
42
R
<lang R>compose <- function(f,g) function(x) { f(g(x)) } r <- compose(sin, cos) print(r(.5))</lang>
Racket
<lang racket> (define (compose f g)
(lambda (x) (f (g x))))
</lang>
Also available as a compose1 builtin, and a more general compose where one function can produce multiple arguments that are sent the the next function in the chain. (Note however that this is rarely desired.)
Raku
(formerly Perl 6)
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: <lang perl6>sub triple($n) { 3 * $n } my &f = &triple ∘ &prefix:<-> ∘ { $^n + 2 }; say &f(5); # prints "-21".</lang>
REBOL
<lang REBOL>REBOL [ Title: "Functional Composition" URL: http://rosettacode.org/wiki/Functional_Composition ]
- "compose" means something else in REBOL, therefore I use a 'compose-functions name.
compose-functions: func [
{compose the given functions F and G}
f [any-function!]
g [any-function!]
] [
func [x] compose [(:f) (:g) x]
]</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 should never gets here, but this was added just in case.*/</lang>
Ring
<lang ring>
- Project : Function composition
sumprod = func1(:func2,2,3) see sumprod + nl
func func1(func2,x,y)
temp = call func2(x,y)
res = temp + x + y
return res
func func2(x,y)
res = x * y
return res
</lang> Output:
11
Ruby
This compose method gets passed two Method objects or Proc objects <lang ruby>def compose(f,g)
lambda {|x| f[g[x]]}
end s = compose(Math.method(:sin), Math.method(:cos)) p s[0.5] # => 0.769196354841008
- verify
p Math.sin(Math.cos(0.5)) # => 0.769196354841008</lang>
Rust
In order to return a closure (anonymous function) in Stable Rust, it must be wrapped in a layer of indirection via a heap allocation. However, there is a feature coming down the pipeline (currently available in Nightly) which makes this possible. Both of the versions below are in the most general form i.e. their arguments may be functions or closures with the only restriction being that the output of g is the same type as the input of f.
Stable
Function is allocated on the heap and is called via dynamic dispatch <lang rust>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)))
}</lang>
Nightly
Function is returned on the stack and is called via static dispatch (monomorphized) <lang rust>#![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))
}</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)))
- 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)))))))
</lang> Example: <lang scheme> (display ((compose sin asin) 0.5)) (newline)</lang>
- Output:
<lang>0.5</lang>
Sidef
<lang ruby>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</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>
SuperCollider
has a function composition operator (the message `<>`): <lang SuperCollider> f = { |x| x + 1 }; g = { |x| x * 2 }; h = g <> f; h.(8); // returns 18 </lang>
Swift
<lang swift>func compose<A,B,C>(f: (B) -> C, g: (A) -> B) -> (A) -> C {
return { f(g($0)) }
}
let sin_asin = compose(sin, asin) println(sin_asin(0.5))</lang>
- Output:
0.5
Tcl
This creates a compose procedure that returns an anonymous function term that should be expanded as part of application to its argument.
<lang tcl>package require Tcl 8.5
namespace path {::tcl::mathfunc}
proc compose {f g} {
list apply [list {f g x} {{*}$f [{*}$g $x]}] $f $g]
}
set sin_asin [compose sin asin] {*}$sin_asin 0.5 ;# ==> 0.5 {*}[compose abs int] -3.14 ;# ==> 3</lang>
TypeScript
<lang TypeScript> function compose<T, U, V> (fn1: (input: T) => U, fn2: (input: U) => V){
return function(value: T) {
return fn2(fn1(value))
}
}
function size (s: string): number { return s.length; }
function isEven(x: number): boolean { return x % 2 === 0; }
const evenSize = compose(size, isEven);
console.log(evenSize("ABCD")) // true console.log(evenSize("ABC")) // false </lang>
uBasic/4tH
<lang>Print FUNC(_Compose (_f, _g, 3)) End
_Compose Param (3) : Return (FUNC(a@(FUNC(b@(c@))))) _f Param (1) : Return (a@ + 1) _g Param (1) : Return (a@ * 2)</lang>
UNIX Shell
Each function takes its argument from standard input,
and puts its result to standard output.
Then the composition of f and g is a shell pipeline, c() { g | f; }.
<lang bash>compose() { eval "$1() { $3 | $2; }" }
downvowel() { tr AEIOU aeiou; } upcase() { tr a-z A-Z; } compose c downvowel upcase echo 'Cozy lummox gives smart squid who asks for job pen.' | c
- => CoZY LuMMoX GiVeS SMaRT SQuiD WHo aSKS FoR JoB PeN.</lang>
This solution uses no external tools, just Bash itself.
<lang bash>
- compose a new function consisting of the application of 2 unary functions
compose () { f="$1"; g="$2"; x="$3"; "$f" "$("$g" "$x")";}
chartolowervowel()
- Usage: chartolowervowel "A" --> "a"
- Based on a to_upper script in Chris F. A. Johnson's book Pro Bash Programming Ch7. String Manipulation
- (with minor tweaks to use local variables and return the value of the converted character
- http://cfajohnson.com/books/cfajohnson/pbp/
- highly recommended I have a copy and have bought another for a friend
{
local LWR="";
case $1 in
A*) _LWR=a ;;
- B*) _LWR=b ;;
- C*) _LWR=c ;;
- D*) _LWR=d ;;
E*) _LWR=e ;;
- F*) _LWR=f ;;
- G*) _LWR=g ;;
- H*) _LWR=h ;;
I*) _LWR=i ;;
- J*) _LWR=j ;;
- K*) _LWR=k ;;
- L*) _LWR=L ;;
- M*) _LWR=m ;;
- N*) _LWR=n ;;
O*) _LWR=o ;;
- P*) _LWR=p ;;
- Q*) _LWR=q ;;
- R*) _LWR=r ;;
- S*) _LWR=s ;;
- T*) _LWR=t ;;
U*) _LWR=u ;;
- V*) _LWR=v ;;
- W*) _LWR=w ;;
- X*) _LWR=x ;;
- Y*) _LWR=y ;;
- Z*) _LWR=z ;;
*) _LWR=${1%${1#?}} ;; esac; echo "$_LWR";
}
strdownvowel()
- Usage: strdownvowel "STRING" --> "STRiNG"
- Based on an upword script in Chris F. A. Johnson's book Pro Bash Programming Ch7. String Manipulation
- (with minor tweaks to use local variables and return the value of the converted string
- http://cfajohnson.com/books/cfajohnson/pbp/
- highly recommended I have a copy and have bought another for a friend
{
local _DWNWORD=""
local word="$1"
while [ -n "$word" ] ## loop until nothing is left in $word
do
chartolowervowel "$word" >> /dev/null
_DWNWORD=$_DWNWORD$_LWR
word=${word#?} ## remove the first character from $word
done Echo "$_DWNWORD"
}
chartoupper()
- Usage: chartoupper "s" --> "S"
- From Chris F. A. Johnson's book Pro Bash Programming Ch7. String Manipulation
- (with minor tweaks to use local variables and return the value of the converted character
- http://cfajohnson.com/books/cfajohnson/pbp/
- highly recommended I have a copy and have bought another for a friend
{
local UPR="";
case $1 in
a*) _UPR=A ;;
b*) _UPR=B ;;
c*) _UPR=C ;; d*) _UPR=D ;; e*) _UPR=E ;; f*) _UPR=F ;; g*) _UPR=G ;; h*) _UPR=H ;; i*) _UPR=I ;; j*) _UPR=J ;; k*) _UPR=K ;; l*) _UPR=L ;; m*) _UPR=M ;; n*) _UPR=N ;; o*) _UPR=O ;; p*) _UPR=P ;; q*) _UPR=Q ;; r*) _UPR=R ;; s*) _UPR=S ;; t*) _UPR=T ;; u*) _UPR=U ;; v*) _UPR=V ;; w*) _UPR=W ;; x*) _UPR=X ;; y*) _UPR=Y ;; z*) _UPR=Z ;; *) _UPR=${1%${1#?}} ;; esac; echo "$_UPR"; }
strupcase()
- Usage: strupcase "string" --> "STRING"
- Based on an upword script in Chris F. A. Johnson's book Pro Bash Programming Ch7. String Manipulation
- (with minor tweaks to use local variables and return the value of the converted string
- http://cfajohnson.com/books/cfajohnson/pbp/
- highly recommended I have a copy and have bought another for a friend
{
local _UPWORD=""
local word="$1"
while [ -n "$word" ] ## loop until nothing is left in $word
do
chartoupper "$word" >> /dev/null
_UPWORD=$_UPWORD$_UPR
word=${word#?} ## remove the first character from $word
done Echo "$_UPWORD"
}
compose strdownvowel strupcase "Cozy lummox gives smart squid who asks for job pen."
- --> CoZY LuMMoX GiVeS SMaRT SQuiD WHo aSKS FoR JoB PeN.</lang>
es
With shell pipelines:
<lang es>fn compose f g { result @ {$g | $f} }
fn downvowel {tr AEIOU aeiou} fn upcase {tr a-z A-Z} fn-c = <={compose $fn-downvowel $fn-upcase} echo 'Cozy lummox gives smart squid who asks for job pen.' | c
- => CoZY LuMMoX GiVeS SMaRT SQuiD WHo aSKS FoR JoB PeN.</lang>
With function arguments:
<lang es>fn compose f g { result @ x {result <={$f <={$g $x}}} }
fn downvowel x {result `` {tr AEIOU aeiou <<< $x}} fn upcase x {result `` {tr a-z A-Z <<< $x}} fn-c = <={compose $fn-downvowel $fn-upcase} echo <={c 'Cozy lummox gives smart squid who asks for job pen.'}
- => CoZY LuMMoX GiVeS SMaRT SQuiD WHo aSKS FoR JoB PeN.</lang>
Unlambda
``s`ksk
Ursala
Functional composition is a built in operation expressible as f+g for functions f and g, hence hardly worth defining. However, it could be defined without using the operator like this. <lang Ursala>compose("f","g") "x" = "f" "g" "x"</lang> test program: <lang Ursala>#import nat
- cast %n
test = compose(successor,double) 3</lang>
- Output:
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
WDTE
The simplest way is with a lambda:
<lang WDTE>let compose f g => (@ c x => g x -> f);</lang>
Alternatively, you can take advantage of partial function calls:
<lang WDTE>let compose f g x => g x -> f;</lang>
Both can be used as follows:
<lang WDTE>(compose (io.writeln io.stdout) !) true;</lang>
Output:
<lang WDTE>false</lang>
Wortel
The @ operator applied to a array literal will compose the functions in the array and ^ with a group literal will do the same, but also quotes operators.
<lang wortel>! @[f g] x ; f(g(x))</lang>
<lang wortel>! ^(f g) x ; f(g(x))</lang>
Defining the compose function
<lang wortel>@var compose &[f g] &x !f!g x</lang>
Wren
<lang ecmascript>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))</lang>
- Output:
8
zkl
<lang zkl>Utils.Helpers.fcomp('+(1),'*(2))(5) //-->11</lang> Which is implemented with a closure (.fp1), which fixes the second paramter <lang zkl>fcn fcomp(f,g,h,etc){
{ fcn(x,hgf){ T(x).pump(Void,hgf.xplode()) }.fp1(vm.arglist.reverse()); }</lang>
ZX Spectrum Basic
DEF FN commands can be nested, making this appear trivial: <lang zxbasic>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)</lang> 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: <lang zxbasic>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)</lang>
- Output:
2 A Invalid argument, 50:1
- Programming Tasks
- Higher-order functions
- 11l
- ActionScript
- Ada
- Agda
- Aikido
- Aime
- ALGOL 68
- AntLang
- AppleScript
- Applesoft BASIC
- Argile
- Arturo
- ATS
- AutoHotkey
- BBC BASIC
- Bori
- BQN
- Bracmat
- Brat
- C
- C sharp
- C++
- Cpp examples needing attention
- Examples needing attention
- Clojure
- CoffeeScript
- Common Lisp
- Crystal
- D
- Delphi
- Diego
- Dylan
- Déjà Vu
- E
- EchoLisp
- Ela
- Elena
- Elixir
- Emacs Lisp
- Erlang
- Euphoria/Omit
- F Sharp
- Factor
- Fantom
- Forth
- Fortran
- Fortress
- FreeBASIC
- FunL
- Fōrmulæ
- GAP
- Go
- Groovy
- Haskell
- Hy
- Icon
- Unicon
- J
- Java
- JavaScript
- Joy
- Jq
- Julia
- K
- Klingphix
- Kotlin
- Lambdatalk
- LFE
- Lingo
- LOLCODE
- Lua
- M2000 Interpreter
- Mathcad
- Mathematica
- Wolfram Language
- Maxima
- Min
- MiniScript
- Nemerle
- Never
- NewLISP
- Nim
- Objeck
- ObjectIcon
- Objective-C
- OCaml
- Octave
- Oforth
- Ol
- Order
- Oz
- PARI/GP
- Pascal
- Perl
- Phix
- Phixmonti
- PHP
- PicoLisp
- PostScript
- PowerShell
- Prolog
- PureBasic
- Purity
- Python
- Qi
- Quackery
- R
- Racket
- Raku
- REBOL
- REXX
- Ring
- Ruby
- Rust
- Scala
- Scheme
- Sidef
- Slate
- Smalltalk
- Standard ML
- SuperCollider
- Swift
- Tcl
- TypeScript
- UBasic/4tH
- UNIX Shell
- Es
- Unlambda
- Ursala
- TI-83 BASIC/Omit
- TI-89 BASIC/Omit
- Fortran/Omit
- VBScript
- WDTE
- Wortel
- Wren
- Zkl
- ZX Spectrum Basic