Higher-order functions

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

Pass a function as an argument to another function.

ActionScript

<lang actionscript>package {

   public class MyClass {

       public function first(func:Function):String {
           return func.call();
       }
    
       public function second():String {
           return "second";
       }
       
       public static function main():void {
           var result:String = first(second);
           trace(result);
           result = first(function() { return "third"; });
           trace(result);
       }
   }

}</lang>

Ada

Simple Example

<lang ada>with Ada.Text_Io; use Ada.Text_Io;

procedure Subprogram_As_Argument is

  type Proc_Access is access procedure;
  
  procedure Second is
  begin
     Put_Line("Second Procedure");
  end Second;
 
  procedure First(Proc : Proc_Access) is
  begin
     Proc.all;
  end First;

begin

  First(Second'Access);

end Subprogram_As_Argument;</lang>

Complex Example

<lang ada>with Ada.Text_Io; use Ada.Text_Io;

procedure Subprogram_As_Argument_2 is

  -- Definition of an access to long_float

  type Lf_Access is access Long_Float;
  
  -- Definition of a function returning Lf_Access taking an
  -- integer as a parameter

  function Func_To_Be_Passed(Item : Integer) return Lf_Access is
     Result : Lf_Access := new Long_Float;
  begin
     Result.All := 3.14159 * Long_Float(Item);
     return Result;
  end Func_To_Be_Passed;
  
  -- Definition of an access to function type matching the function
  -- signature above

  type Func_Access is access function(Item : Integer) return Lf_Access;
  
  -- Definition of an integer access type

  type Int_Access is access Integer;
  
  -- Define a function taking an instance of Func_Access as its
  -- parameter and returning an integer access type

  function Complex_Func(Item : Func_Access; Parm2 : Integer) return Int_Access is
     Result : Int_Access := new Integer;
  begin
     Result.All := Integer(Item(Parm2).all / 3.14149);
     return Result;
  end Complex_Func;
  
  -- Declare an access variable to hold the access to the function

  F_Ptr : Func_Access := Func_To_Be_Passed'access;
  
  -- Declare an access to integer variable to hold the result

  Int_Ptr : Int_Access;

begin

  -- Call the function using the access variable

  Int_Ptr := Complex_Func(F_Ptr, 3);
  Put_Line(Integer'Image(Int_Ptr.All));

end Subprogram_As_Argument_2;</lang>

ALGOL 68

<lang algol68>PROC first = (PROC(LONG REAL)LONG REAL f) LONG REAL: (

 f(1) + 2

);

PROC second = (LONG REAL x)LONG REAL: (

 x/2

);

main: (

 printf(($xg(5,2)l$,first(second)))

)</lang> Output: <lang algol68>+2.50</lang>

AmigaE

The {} takes the pointer to an object (code/functions, variables and so on); Amiga E does not distinguish nor check anything, so it is up to the programmer to use the pointer properly. For this reason, a warning is always raised when a variable (func, holding a pointer to a real function in our case) is used like a function. <lang amigae>PROC compute(func, val)

 DEF s[10] : STRING
 WriteF('\s\n', RealF(s,func(val),4))

ENDPROC

PROC sin_wrap(val) IS Fsin(val) PROC cos_wrap(val) IS Fcos(val)

PROC main()

 compute({sin_wrap}, 0.0)
 compute({cos_wrap}, 3.1415)

ENDPROC</lang>

AutoHotkey

<lang AutoHotkey>func = round msgbox % %func%(4.5)</lang>

C

Simple example

The pointer to the function to be passed as an argument is the only involved pointer.

Definition of a function whose only parameter is a pointer to a function with no parameters and no return value:

<lang c>void myFuncSimple( void (*funcParameter)(void) ) {

   /* ... */
  
   (*funcParameter)();  /* Call the passed function. */
   funcParameter();     /* Same as above with slight different syntax. */

   /* ... */

}</lang>

Note that you can't call the passed function by " *funcParameter() ", since that would mean "call funcParameter and than apply the * operator on the returned value".

Call:

<lang c>void funcToBePassed(void);

/* ... */

myFuncSimple(&funcToBePassed);</lang>

Complex example

Definition of a function whose return value is a pointer to int and whose only parameter is a pointer to a function, whose (in turn) return value is a pointer to double and whose only parameter is a pointer to long.

<lang c>int* myFuncComplex( double* (*funcParameter)(long* parameter) ) {

    long inLong;
    double* outDouble;
    long *inLong2 = &inLong;

    /* ... */

    outDouble = (*funcParameter)(&inLong);  /* Call the passed function and store returned pointer. */
    outDouble = funcParameter(inLong2);     /* Same as above with slight different syntax. */

    /* ... */

}</lang> Call:

<lang c>double* funcToBePassed(long* parameter);

/* ... */

int* outInt;

outInt = myFuncComplex(&funcToBePassed);</lang>

Pointer

Finally, declaration of a pointer variable of the proper type to hold such a function as myFunc:

<lang c>int* (*funcPointer)( double* (*funcParameter)(long* parameter) );

/* ... */

funcPointer = &myFuncComplex;</lang>

Of course, in a real project you shouldn't write such a convoluted code, but use some typedef instead, in order to break complexity into steps.

C++

Function Pointer

Works with: g++ version 3.4.2 (mingw-special)

Same as C.

Template

Works with: Visual C++ version 2005

<lang cpp>#include <iostream>

template<class Func> void first(Func func) {

 func();

}

void second() {

 std::cout << "second" << std::endl;

}

int main() {

 first(second);
 return 0;

}</lang>

Template and Inheritance

Works with: Visual C++ version 2005

<lang cpp>#include <iostream>

1. include <functional>

template<class Func> typename Func::result_type first(Func func, typename Func::argument_type arg) {

 return func(arg);

}

class second : public std::unary_function<int, int> { public:

 result_type operator()(argument_type arg)
 {
   return arg * arg;
 }

};

int main() {

 std::cout << first(second(), 2) << std::endl;
 return 0;

}</lang>

Clean

Take a function as an argument and apply it to all elements in a list: <lang clean>map f [x:xs] = [f x:map f xs] map f [] = []</lang> Pass a function as an argument: <lang clean>incr x = x + 1

Start = map incr [1..10]</lang> Do the same using a anonymous function: <lang clean>Start = map (\x -> x + 1) [1..10]</lang> Do the same using currying: <lang clean>Start = map ((+) 1) [1..10]</lang>

Groovy

As closures: <lang groovy>first = { func -> func() } second = { println "second" }

first(second)</lang>

As functions: <lang groovy>def first(func) { func() } def second() { println "second" }

first(this.&second)</lang>

Clojure

<lang lisp> (defn append-hello [s]

 (str "Hello " s))

(defn modify-string [f s]

 (f s))

(println (modify-string append-hello "World!")) </lang>

Common Lisp

In Common Lisp, functions are first class objects, so you can pass function objects as arguments to other functions:

<lang lisp>CL-USER> (defun add (a b) (+ a b)) ADD CL-USER> (add 1 2) 3 CL-USER> (defun call-it (fn x y)

           (funcall fn x y))

CALL-IT CL-USER> (call-it #'add 1 2) 3</lang>

D

D's function/delegate will be investigated by passing each type of function/delegate to _test_ as argument. <lang d>module functest ; import std.stdio ;

// test the function argument string test(U)(string scopes, U func) {

 string typeStr = typeid(typeof(func)).toString ;
 string isFunc = (typeStr[$-1] == '*') ? "function" : "delegate" ;
 writefln("Hi, %-13s : scope: %-8s (%s) : %s", func(), scopes, isFunc, typeStr ) ; 
 return scopes ;

}

// normal module level function string aFunction(){ return "Function" ; }

// Implicit-Function-Template-Instantiation(IFTI) Function T tmpFunc(T)() { return "IFTI.function" ; }

// Member in a template template tmpGroup(T) {

 T t0(){ return "Tmp.member.0" ; } 
 T t1(){ return "Tmp.member.1" ; } 
 T t2(){ return "Tmp.member.2" ; } 

}

// used for implementing member function at class & struct template Impl() {

 static string aStatic() { return "Static Method" ;  }
 string aMethod(){ return "Method" ; }

} class C { mixin Impl!() ; } struct S { mixin Impl!() ; }

void main() {

 // nested function
 string aNested(){
   return "Nested" ;
 } 

 // bind to a variable
 auto variableF = function string() { return "variable.F"; } ;
 auto variableD = delegate string() { return "variable.D"; } ;

 C c = new C ;
 S s ;

   "Global".test(&aFunction) ;
   "Nested".test(&aNested) ; 
    "Class".test(&C.aStatic) 
           .test(&c.aMethod) ; 
   "Struct".test(&S.aStatic) 
           .test(&s.aMethod) ; 
 "Template".test(&tmpFunc!(string))
           .test(&tmpGroup!(string).t2) ;
  "Binding".test(variableF)
           .test(variableD) ;  
 // leteral function/delegate
  "Literal".test(function string() { return "literal.F"; })
           .test(delegate string() { return "literal.D"; }) ;  

}</lang>

E

<lang e>def map(f, list) {

 var out := []
 for x in list {
   out with= f(x)
 }
 return out

}

? map(fn x { x + x }, [1, "two"])

1. value: [2, "twotwo"]

? map(1.add, [5, 10, 20])

1. value: [6, 11, 21]

? def foo(x) { return -(x.size()) } > map(foo, ["", "a", "bc"])

1. value: [0, -1, -2]</lang>

Erlang

Erlang functions are atoms, and they're considered different functions if their arity (the number of arguments they take) is different. As such, an Erlang function must be passed as fun Function/Arity, but can be used as any other variable: <lang erlang>-module(test). -export([first/1, second/0]).

first(F) -> F(). second() -> hello.</lang> Testing it: <lang erlang>1> c(tests). {ok, tests} 2> tests:first(fun tests:second/0). hello 3> tests:first(fun() -> anonymous_function end). anonymous_function</lang>

FALSE

Anonymous code blocks are the basis of FALSE control flow and function definition. These blocks may be passed on the stack as with any other parameter. <lang false>[f:[$0>][@@\f;!\1-]#%]r: { reduce n stack items using the given basis and binary function }

1 2 3 4 0 4[+]r;!." " { 10 } 1 2 3 4 1 4[*]r;!." " { 24 } 1 2 3 4 0 4[$*+]r;!. { 30 }</lang>

Forth

Forth words can be referenced on the stack via their execution token or XT. An XT is obtained from a word via the quote operator, and invoked via EXECUTE. Anonymous functions may be defined via :NONAME (returning an XT) instead of a standard colon definition.

<lang forth>: square dup * ;

cube dup dup * * ;

map. ( xt addr len -- )

 0 do  2dup i cells + @ swap execute .  loop 2drop ;

create array 1 , 2 , 3 , 4 , 5 , ' square array 5 map. cr \ 1 4 9 16 25 ' cube array 5 map. cr \ 1 8 27 64 125

noname 2* 1+ ; array 5 map. cr \ 3 5 7 9 11</lang>

Fortran

Works with: Fortran version 90 and later

use the EXTERNAL attribute to show the dummy argument is another function rather than a data object. i.e. <lang fortran>FUNCTION FUNC3(FUNC1, FUNC2, x, y)

 REAL, EXTERNAL :: FUNC1, FUNC2 
 REAL :: FUNC3
 REAL :: x, y

 FUNC3 = FUNC1(x) * FUNC2(y)

END FUNCTION FUNC3</lang>

Another way is to put the functions you want to pass in a module:

<lang fortran>module FuncContainer

 implicit none

contains

 function func1(x)
   real :: func1
   real, intent(in) :: x

   func1 = x**2.0
 end function func1

 function func2(x)
   real :: func2
   real, intent(in) :: x

   func2 = x**2.05
 end function func2

end module FuncContainer

program FuncArg

 use FuncContainer
 implicit none

 print *, "Func1"
 call asubroutine(func1)

 print *, "Func2"
 call asubroutine(func2)

contains

 subroutine asubroutine(f)
   ! the following interface is redundant: can be omitted
   interface
      function f(x)
        real, intent(in) :: x
        real :: f
      end function f
   end interface
   real :: px

   px = 0.0
   do while( px < 10.0 )
      print *, px, f(px)
      px = px + 1.0
   end do
 end subroutine asubroutine

end program FuncArg</lang>

Haskell

Works with: GHCi version 6.6

A function is just a value that wants arguments: <lang haskell>func1 f = f "a string" func2 s = "func2 called with " ++ s

main = putStrLn $ func1 func2</lang> Or, with an anonymous function: <lang haskell>func f = f 1 2

main = print $ func (\x y -> x+y) -- output: 3</lang> Note that func (\x y -> x+y) is equivalent to func (+). (Operators are functions too.)

Icon

<lang icon> procedure main()

  local lst
  lst := [10, 20, 30, 40]
  myfun(callback, lst)

end

procedure myfun(fun, lst)

  every fun(!lst)

end

procedure callback(arg)

  write("->", arg)

end</lang>

J

Adverbs take a single verb or noun argument and conjunctions take two. For example, / (insert) \ (prefix) and \. (suffix) are adverbs and ^: (power) is a conjunction. The following expressions illustrate their workings.

<lang j> + / 3 1 4 1 5 9 NB. sum 23

  >./ 3 1 4 1 5 9   NB. max

9

  *./ 3 1 4 1 5 9   NB. lcm

180

  +/\ 3 1 4 1 5 9   NB. sum prefix (partial sums)

3 4 8 9 14 23

  +/\. 3 1 4 1 5 9  NB. sum suffix

23 20 19 15 14 9

  f=: -:@(+ 2&%)    NB. one Newton iteration
  f 1

1.5

  f f 1

1.41667

  f^:(i.5) 1        NB. first 5 Newton iterations

1 1.5 1.41667 1.41422 1.41421

  f^:(i.5) 1x       NB. rational approximations to sqrt 2

1 3r2 17r12 577r408 665857r470832</lang>

Java

There is no real callback in Java like in C or C++, but we can do the same as swing does for executing an event. We need to create an interface that has the method we want to call or create one that will call the method we want to call. The following example uses the second way.

<lang java>public class NewClass {

  public NewClass() {
      first(new AnEventOrCallback() {
          public void call() {
              second();
          }
      });
  }
  
  public void first(AnEventOrCallback obj) {
      obj.call();
  }
  
  public void second() {
      System.out.println("Second");
  }
  
  public static void main(String[] args) {
      new NewClass();
  }

}

interface AnEventOrCallback {

  public void call();

}</lang>

JavaScript

<lang javascript>function first (func) {

 return func();

}

function second () {

 return "second";

}

var result = first(second); result = first(function () { return "third"; });</lang>

An example with anonymous functions and uses in the core library

Works with: Firefox version 1.5

for methods filter and map.

<lang javascript>>>> var array = [2, 4, 5, 13, 18, 24, 34, 97]; >>> array [2, 4, 5, 13, 18, 24, 34, 97]

// return all elements less than 10 >>> array.filter(function (x) { return x < 10 }); [2, 4, 5]

// return all elements less than 30 >>> array.filter(function (x) { return x < 30 }); [2, 4, 5, 13, 18, 24]

// return all elements less than 100 >>> array.filter(function (x) { return x < 100 }); [2, 4, 5, 13, 18, 24, 34, 97]

// multiply each element by 2 and return the new array >>> array.map(function (x) { return x * 2 }); [4, 8, 10, 26, 36, 48, 68, 194]

// sort the array from smallest to largest >>> array.sort(function (a, b) { return a > b }); [2, 4, 5, 13, 18, 24, 34, 97]

// sort the array from largest to smallest >>> array.sort(function (a, b) { return a < b }); [97, 34, 24, 18, 13, 5, 4, 2]</lang>

Joy

This example is taken from V. Define first as multiplying two numbers on the stack. <lang joy>DEFINE first == *.</lang> There will be a warning about overwriting builtin first. Define second as interpreting the passed quotation on the stack. <lang joy>DEFINE second == i.</lang> Pass first enclosed in quotes to second which applies it on the stack. <lang joy>2 3 [first] second.</lang> The program prints 6.

Logo

You can pass the quoted symbol for the function and invoke it with RUN. <lang logo>to printstuff

 print "stuff

end to runstuff :proc

 run :proc

end runstuff "printstuff  ; stuff runstuff [print [also stuff]]  ; also stuff</lang>

Mathematica

Passing 3 arguments and a value (could be a number, variable, graphic or a function as well, actually it could be anything), and composing them in an unusual way: <lang Mathematica>PassFunc[f_, g_, h_, x_] := f[g[x]*h[x]] PassFunc[Tan, Cos, Sin, x] % /. x -> 0.12 PassFunc[Tan, Cos, Sin, 0.12]</lang> gives back: <lang Mathematica>Tan[Cos[x] Sin[x]] 0.119414 0.119414</lang>

MAXScript

<lang maxscript>fn second = (

   print "Second"

)

fn first func = (

   func()

)

first second</lang>

Metafont

We can simulate this by using scantokens, which digests a string as if it would be a source input.

<lang metafont>def calcit(expr v, s) = scantokens(s & decimal v) enddef;

t := calcit(100.4, "sind"); show t; end</lang>

Modula-3

<lang modula3>MODULE Proc EXPORTS Main;

IMPORT IO;

TYPE Proc = PROCEDURE();

PROCEDURE Second() =

 BEGIN
   IO.Put("Second procedure.\n");
 END Second;

PROCEDURE First(proc: Proc) =

 BEGIN
   proc();
 END First;

BEGIN

 First(Second);

END Proc.</lang>

OCaml

A function is just a value that wants arguments: <lang ocaml># let func1 f = f "a string";; val func1 : (string -> 'a) -> 'a = <fun>

1. let func2 s = "func2 called with " ^ s;;

val func2 : string -> string = <fun>

1. print_endline (func1 func2);;

func2 called with a string - : unit = ()</lang>

Or, with an anonymous function: <lang ocaml># let func f = f 1 2;; val func : (int -> int -> 'a) -> 'a = <fun>

1. Printf.printf "%d\n" (func (fun x y -> x + y));;

3 - : unit = ()</lang> Note that func (fun x y -> x + y) is equivalent to func (+). (Operators are functions too.)

Octave

We can pass a function handle (@function_name)

<lang octave>function r = computeit(f, g, v)

 r = f(g(v));

endfunction

computeit(@exp, @sin, pi/3) computeit(@log, @cos, pi/6)</lang>

Or pass the string name of the function and use the feval primitive.

<lang octave>function r = computeit2(f, g, v)

 r = f(feval(g, v));

endfunction

computeit2(@exp, "sin", pi/3)</lang>

Pascal

Standard Pascal (will not work with Turbo Pascal): <lang pascal>program example(output);

function first(function f(x: real): real): real;

begin
 first := f(1.0) + 2.0;
end;

function second(x: real): real;

begin
 second := x/2.0;
end;

begin

writeln(first(second));

end.</lang>

Turbo Pascal (will not work with Standard Pascal):

<lang pascal>program example;

type

FnType = function(x: real): real;

function first(f: FnType): real;

begin
 first := f(1.0) + 2.0;
end;

function second(x: real): real;

begin
 second := x/2.0;
end;

begin

writeln(first(second));

end.</lang>

Perl

<lang perl>sub another {

   # take a function and a value
   my $func = shift;
   my $val  = shift;

   # call the function with the value as argument
   return $func->($val);

};

sub reverser {

   return scalar reverse shift;

};

1. pass named coderef

print another \&reverser, 'data';

1. pass anonymous coderef

print another sub {return scalar reverse shift}, 'data';

1. if all you have is a string and you want to act on that,
2. set up a dispatch table

my %dispatch = (

   square => sub {return shift() ** 2},
   cube   => sub {return shift() ** 3},
   rev    => \&reverser,

);

print another $dispatch{$_}, 123 for qw(square cube rev);</lang>

<lang perl>sub apply (&@) { # use & as the first item in a prototype to take bare blocks like map and grep

   my ($sub, @ret) = @_;   # this function applies a function that is expected to modify $_ to a list
   $sub->() for @ret;      # it allows for simple inline application of the s/// and tr/// constructs
   @ret

}

print join ", " => apply {tr/aeiou/AEIOU/} qw/one two three four/;

1. OnE, twO, thrEE, fOUr</lang>

<lang perl>sub first {shift->()}

sub second {'second'}

print first \&second;

print first sub{'sub'};</lang>

Perl 6

The best type to use for the parameter of a higher-order function is Callable, a role common to all function-like objects. For an example of defining and calling a second-order function, see Functional Composition.

PHP

<lang php>function first($func) {

 return $func();

}

function second() {

 return 'second';

}

$result = first('second');</lang>

Pop11

<lang pop11>;;; Define a function define x_times_three_minus_1(x);

 return(3*x-1);

enddefine;

Pass it as argument to built-in function map and print the result

mapdata({0 1 2 3 4}, x_times_three_minus_1) =></lang>

Python

Works with: Python version 2.5

<lang python>def first(function):

   return function()

def second():

   return "second"

result = first(second)</lang>

or

<lang python> result = first(lambda: "second")</lang>

Functions are first class objects in Python. They can be bound to names ("assigned" to "variables"), associated with keys in dictionaries, and passed around like any other object references. Classes are also first class objects and every class in Python is, implicitly, a "factory" for creating (instantiating) objects of that class. The use of class references support metaprogramming.

R

<lang R>f <- function(f0) f0(pi) # calc. the function in pi tf <- function(x) x^pi # a func. just to test

print(f(sin)) print(f(cos)) print(f(tf))</lang>

Ruby

With a proc (procedure): <lang ruby>succ = proc{|x| x+1} def to2(&f)

 f[2]

end

to2(&succ) #=> 3 to2{|x| x+1} #=> 3</lang>

With a method: <lang ruby>def succ(n)

 n+1

end def to2(m)

 m[2]

end

meth = method(:succ) to2(meth) #=> 3</lang>

Scala

<lang scala>def functionWithAFunctionArgument(x : int, y : int, f : (int, int) => int) = f(x,y)</lang> Call: <lang scala>functionWithAFunctionArgument(3, 5, {(x, y) => x + y}) // returns 8</lang>

Scheme

A function is just a value that wants arguments: <lang scheme>> (define (func1 f) (f "a string")) > (define (func2 s) (string-append "func2 called with " s)) > (begin (display (func1 func2)) (newline)) func2 called with a string</lang>

Or, with an anonymous function: <lang scheme>> (define (func f) (f 1 2)) > (begin (display (func (lambda (x y) (+ x y)))) (newline)) 3</lang> Note that (func (lambda (x y) (+ x y))) is equivalent to (func +). (Operators are functions too.)

Slate

Methods and blocks can both be passed as arguments to functions (other methods and blocks): <lang slate>define: #function -> [| :x | x * 3 - 1].

1. (1 1 2 3 5 8) collect: function.</lang>

Standard ML

<lang sml>- fun func1 f = f "a string"; val func1 = fn : (string -> 'a) -> 'a - fun func2 s = "func2 called with " ^ s; val func2 = fn : string -> string

- print (func1 func2 ^ "\n"); func2 called with a string val it = () : unit</lang>

Or, with an anonymous function: <lang sml>- fun func f = f (1, 2); val func = fn : (int * int -> 'a) -> 'a

- print (Int.toString (func (fn (x, y) => x + y)) ^ "\n"); 3 val it = () : unit</lang> Note that func (fn (x, y) => x + y) is equivalent to func op+. (Operators are functions too.)

Tcl

<lang tcl># this procedure executes its argument: proc demo {function} {

   $function 

}

1. for example:

demo bell</lang> It is more common to pass not just a function, but a command fragment or entire script. When used with the built-in list command (which introduces a very useful degree of quoting) this makes for a very common set of techniques when doing advanced Tcl programming. <lang tcl># This procedure executes its argument with an extra argument of "2" proc demoFrag {fragment} {

   {*}$fragment 2

}

1. This procedure executes its argument in the context of its caller, which is
2. useful for scripts so they get the right variable resolution context

proc demoScript {script} {

   uplevel 1 $script

}

1. Examples...

set chan stderr demoFrag [list puts $chan] demoFrag {

   apply {x {puts [string repeat ? $x]}}

} demoScript {

   parray tcl_platform

}</lang>

TI-89 BASIC

TI-89 BASIC does not have first-class functions; while function definitions as stored in variables are fully dynamic, it is not possible to extract a function value from a variable rather than calling it. In this case, we use the indirection operator #, which takes a string and returns the value of the named variable, to use the name of the function as something to be passed.

The function name passed cannot be that of a local function, because the local function map does not see the local variables of the enclosing function.

<lang ti89b>Local map Define map(f,l)=Func

 Return seq(#f(l[i]),i,1,dim(l))

EndFunc Disp map("sin", {0, π/6, π/4, π/3, π/2})</lang>

Toka

Toka allows obtaining a function pointer via the ` (backtick) word. The pointers are passed on the stack, just like all other data.

<lang toka>[ ." First\n" ] is first [ invoke ] is second ` first second</lang>

Ursala

Autocomposition is a user defined function that takes a function as an argument, and returns a function equivalent to the given functon composed with itself.

<lang Ursala>(autocomposition "f") "x" = "f" "f" "x"</lang> test program: <lang Ursala>#import flo

1. cast %e

example = autocomposition(sqrt) 16.0</lang> output:

2.000000e+00

V

Define first as multiplying two numbers on stack <lang v>[first *].</lang> Define second as applying the passed quote on stack <lang v>[second i].</lang> Pass the first enclosed in quote to second which applies it on stack. <lang v>2 3 [first] second</lang>

=6