Partial function application: Difference between revisions

From Rosetta Code
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m (→‎{{header|AppleScript}}: (edited a name, slightly rearranged the test))
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on run
on run
set fs to curry(map)
tell curry(map)
set fsf1 to |λ|(f1)
⚫
set fsf1 to fs's lambda(f1)
set fsf2 to |λ|(f2)
end tell
set fsf2 to fs's lambda(f2)
{fsf1's lambda({0, 1, 2, 3}), fsf2's lambda({0, 1, 2, 3}), ¬
{fsf1's |λ|({0, 1, 2, 3}), ¬
fsf1's lambda({2, 4, 6, 8}), fsf2's lambda({2, 4, 6, 8})}
fsf2's |λ|({0, 1, 2, 3}), ¬
⚫
fsf1's |λ|({2, 4, 6, 8}), ¬
fsf2's |λ|({2, 4, 6, 8})}
end run
end run


Line 166: Line 169:
on curry(f)
on curry(f)
script
script
on lambda(a)
on |λ|(a)
script
script
on lambda(b)
on |λ|(b)
lambda(a, b) of mReturn(f)
|λ|(a, b) of mReturn(f)
end lambda
end |λ|
end script
end script
end lambda
end |λ|
end script
end script
end curry
end curry
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set lst to {}
set lst to {}
repeat with i from 1 to lng
repeat with i from 1 to lng
set end of lst to lambda(item i of xs, i, xs)
set end of lst to |λ|(item i of xs, i, xs)
end repeat
end repeat
return lst
return lst
Line 195: Line 198:
else
else
script
script
property lambda : f
property |λ| : f
end script
end script
end if
end if

Revision as of 02:16, 9 May 2017

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

Partial function application   is the ability to take a function of many parameters and apply arguments to some of the parameters to create a new function that needs only the application of the remaining arguments to produce the equivalent of applying all arguments to the original function.

E.g:

Given values v1, v2
Given f(param1, param2)
Then partial(f, param1=v1) returns f'(param2)
And f(param1=v1, param2=v2) == f'(param2=v2) (for any value v2)


Note that in the partial application of a parameter, (in the above case param1), other parameters are not explicitly mentioned. This is a recurring feature of partial function application.


Task
  • Create a function fs( f, s ) that takes a function, f( n ), of one value and a sequence of values s.
    Function fs should return an ordered sequence of the result of applying function f to every value of s in turn.
  • Create function f1 that takes a value and returns it multiplied by 2.
  • Create function f2 that takes a value and returns it squared.
  • Partially apply f1 to fs to form function fsf1( s )
  • Partially apply f2 to fs to form function fsf2( s )
  • Test fsf1 and fsf2 by evaluating them with s being the sequence of integers from 0 to 3 inclusive and then the sequence of even integers from 2 to 8 inclusive.


Notes
  • In partially applying the functions f1 or f2 to fs, there should be no explicit mention of any other parameters to fs, although introspection of fs within the partial applicator to find its parameters is allowed.
  • This task is more about how results are generated rather than just getting results.



Ada

Ada allows to define generic functions with generic parameters, which are partially applicable.

<lang Ada>with Ada.Text_IO;

procedure Partial_Function_Application is 

  type Sequence is array(Positive range <>) of Integer;

  -- declare a function FS with a generic parameter F and a normal parameter S
  generic
     with function F(I: Integer) return Integer; -- generic parameter
  function FS (S: Sequence) return Sequence;

  -- define FS
  function FS (S: Sequence) return Sequence is
     Result: Sequence(S'First .. S'Last);
  begin
     for Idx in S'Range loop
        Result(Idx) := F(S(Idx));
     end loop;
     return Result;
  end FS;

  -- define functions F1 and F2
  function F1(I: Integer) return Integer is
  begin
     return 2*I;
  end F1;

  function F2(I: Integer) return Integer is
  begin
     return I**2;
  end F2;

  -- instantiate the function FS by F1 and F2 (partially apply F1 and F2 to FS)
  function FSF1 is new FS(F1);
  function FSF2 is new FS(F2);

  procedure Print(S: Sequence) is
  begin
     for Idx in S'Range loop
        Ada.Text_IO.Put(Integer'Image(S(Idx)));
     end loop;
     Ada.Text_IO.New_Line;
  end Print;

begin 

  Print(FSF1((0,1,2,3)));
  Print(FSF2((0,1,2,3)));
  Print(FSF1((2,4,6,8)));
  Print(FSF2((2,4,6,8)));

end Partial_Function_Application;</lang>

Output: 

 0 2 4 6
 0 1 4 9
 4 8 12 16
 4 16 36 64

ALGOL 68

Translation of: Python
Works with: ALGOL 68 version Revision 1 - Requires Currying extensions to language.
Works with: ALGOL 68G version Any - tested with release 1.18.0-9h.tiny.

<lang algol68>MODE SET = FLEX[0]INT;

MODE F = PROC(INT)INT, 

    FS = PROC(SET)SET;

PROC fs = (F f, SET set)SET: ( 

 [LWB set:UPB set]INT out;
 FOR i FROM LWB set TO UPB set DO out[i]:=f(set[i]) OD;
 out

);

PROC f1 = (INT value)INT: value * 2, 

    f2 = (INT value)INT: value ** 2;

FS fsf1 = fs(f1,), 

  fsf2 = fs(f2,);

[4]INT set; FORMAT set fmt = $"("n(UPB set-LWB set)(g(0)", ")g(0)")"l$;

set := (0, 1, 2, 3); 

 printf((set fmt, fsf1((0, 1, 2, 3)))); # prints (0, 2, 4, 6) #
 printf((set fmt, fsf2((0, 1, 2, 3)))); # prints (0, 1, 4, 9) #

set := (2, 4, 6, 8); 

 printf((set fmt, fsf1((2, 4, 6, 8)))); # prints (4, 8, 12, 16) #
 printf((set fmt, fsf2((2, 4, 6, 8))))  # prints (4, 16, 36, 64) #

</lang> Output: 

(0, 2, 4, 6)
(0, 1, 4, 9)
(4, 8, 12, 16)
(4, 16, 36, 64)

AppleScript

To derive first class functions in AppleScript, we have to lift ordinary handlers into script objects with lambda handlers.

<lang AppleScript>-- PARTIAL APPLICATION --------------------------------------------

on f1(x) 

   x * 2

end f1

on f2(x) 

   x * x

end f2

on run 

   tell curry(map)
       set fsf1 to |λ|(f1)
       set fsf2 to |λ|(f2)
   end tell
   
   {fsf1's |λ|({0, 1, 2, 3}), ¬
       fsf2's |λ|({0, 1, 2, 3}), ¬
       
       fsf1's |λ|({2, 4, 6, 8}), ¬
       fsf2's |λ|({2, 4, 6, 8})}

end run


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

-- curry :: (Script|Handler) -> Script on curry(f) 

   script
       on |λ|(a)
           script
               on |λ|(b)
                   |λ|(a, b) of mReturn(f)
               end |λ|
           end script
       end |λ|
   end script

end curry

-- map :: (a -> b) -> [a] -> [b] on map(f, xs) 

   tell mReturn(f)
       set lng to length of xs
       set lst to {}
       repeat with i from 1 to lng
           set end of lst to |λ|(item i of xs, i, xs)
       end repeat
       return lst
   end tell

end map

-- Lift 2nd class handler function into 1st class script wrapper -- mReturn :: Handler -> Script on mReturn(f) 

   if class of f is script then
       f
   else
       script
           property |λ| : f
       end script
   end if

end mReturn</lang>

Output:
{{0, 2, 4, 6}, {0, 1, 4, 9}, {4, 8, 12, 16}, {4, 16, 36, 64}}

BBC BASIC

Works with: BBC BASIC for Windows

<lang bbcbasic> fsf1 = FNpartial(PROCfs(), FNf1()) 

     fsf2 = FNpartial(PROCfs(), FNf2())
     
     DIM seq(3)
     PRINT "Calling function fsf1 with sequence 1:"
     seq() = 0, 1, 2, 3 : PROC(fsf1)(seq())
     FOR i% = 0 TO 3 : PRINT seq(i%); : NEXT : PRINT
     PRINT "Calling function fsf1 with sequence 2:"
     seq() = 2, 4, 6, 8 : PROC(fsf1)(seq())
     FOR i% = 0 TO 3 : PRINT seq(i%); : NEXT : PRINT
     PRINT "Calling function fsf2 with sequence 1:"
     seq() = 0, 1, 2, 3 : PROC(fsf2)(seq())
     FOR i% = 0 TO 3 : PRINT seq(i%); : NEXT : PRINT
     PRINT "Calling function fsf2 with sequence 2:"
     seq() = 2, 4, 6, 8 : PROC(fsf2)(seq())
     FOR i% = 0 TO 3 : PRINT seq(i%); : NEXT : PRINT
     END
     
     REM Create a partial function:
     DEF FNpartial(RETURN f1%, RETURN f2%)
     LOCAL f$, p%
     DIM p% 7 : p%!0 = f1% : p%!4 = f2%
     f$ = "(s())" + CHR$&F2 + "(&" + STR$~p% + ")(" + \
     \              CHR$&A4 + "(&" + STR$~(p%+4) + ")(),s()):" + CHR$&E1
     DIM p% LEN(f$) + 4
     $(p%+4) = f$ : !p% = p%+4
     = p%
     
     REM Replaces the input sequence with the output sequence:
     DEF PROCfs(RETURN f%, seq())
     LOCAL i%
     FOR i% = 0 TO DIM(seq(),1)
       seq(i%) = FN(^f%)(seq(i%))
     NEXT
     ENDPROC
     
     DEF FNf1(n) = n * 2
     
     DEF FNf2(n) = n ^ 2</lang>

Output: 

Calling function fsf1 with sequence 1:
         0         2         4         6
Calling function fsf1 with sequence 2:
         4         8        12        16
Calling function fsf2 with sequence 1:
         0         1         4         9
Calling function fsf2 with sequence 2:
         4        16        36        64

Bracmat

The body of the function fs consists of two macros. The first macro merely optimizes the second one by replacing the name of the argument function by the definition of the function. The second macro inserts this function in a function body that implements an iteration over a list. The function called partial uses a lambda abstraction to construct a new functions from two functions. <lang bracmat>( ( fs 

 =   
   .   '$!arg:?arg
     &   
       ' ( first r
         .   :?r
           &   whl
             ' ( !arg:%?first ?arg
               & !r ($arg)$!first:?r
               )
           & !r
         )
 )

& ( partial 

 =   
   .   !arg:(?f.?g)
     & /('(x./('(y.($x)$($y)))$!g))$!f
 )

& (f1=.2*!arg) & (f2=.!arg^2) & partial$(fs.f1):(=?fsf1) & partial$(fs.f2):(=?fsf2) & out$(fsf1$(0 1 2 3)) & out$(fsf2$(0 1 2 3)) & out$(fsf1$(2 4 6 8)) & out$(fsf2$(2 4 6 8)) );</lang> Output: 

0 2 4 6
0 1 4 9
4 8 12 16
4 16 36 64

Clojure

<lang Clojure>(defn fs [f s] (map f s)) (defn f1 [x] (* 2 x)) (defn f2 [x] (* x x)) (def fsf1 (partial fs f1)) (def fsf2 (partial fs f2))

(doseq [s [(range 4) (range 2 9 2)]] 

 (println "seq: " s)
 (println "  fsf1: " (fsf1 s))
 (println "  fsf2: " (fsf2 s)))</lang>

Output: 

seq:  (0 1 2 3)
  fsf1:  (0 2 4 6)
  fsf2:  (0 1 4 9)
seq:  (2 4 6 8)
  fsf1:  (4 8 12 16)
  fsf2:  (4 16 36 64)

Common Lisp

<lang lisp>(defun fs (f s) 

 (mapcar f s))

(defun f1 (i) 

 (* i 2))

(defun f2 (i) 

 (expt i 2))

(defun partial (func &rest args1) 

 (lambda (&rest args2)
   (apply func (append args1 args2))))

(setf (symbol-function 'fsf1) (partial #'fs #'f1)) (setf (symbol-function 'fsf2) (partial #'fs #'f2))

(dolist (seq '((0 1 2 3) (2 4 6 8))) 

 (format t
         "~%seq: ~A~%  fsf1 seq: ~A~%  fsf2 seq: ~A"

seq 

         (fsf1 seq)
         (fsf2 seq)))

</lang>

Output: 

seq: (0 1 2 3)
  fsf1 seq: (0 2 4 6)
  fsf2 seq: (0 1 4 9)
seq: (2 4 6 8)
  fsf1 seq: (4 8 12 16)
  fsf2 seq: (4 16 36 64)

C

Nasty hack, but the partial does return a true C function pointer, which is otherwise hard to achieve. (In case you are wondering, no, this is not a good or serious solution.) Compiled with gcc -Wall -ldl. <lang C>#include <stdio.h>

  1. include <unistd.h>
  2. include <stdlib.h>
  3. include <dlfcn.h>
  4. include <sys/wait.h>
  5. include <err.h>

typedef int (*intfunc)(int); typedef void (*pfunc)(int*, int);

pfunc partial(intfunc fin) { pfunc f; static int idx = 0; char cc[256], lib[256]; FILE *fp; sprintf(lib, "/tmp/stuff%d.so", ++idx); sprintf(cc, "cc -pipe -x c -shared -o %s -", lib);

fp = popen(cc, "w"); fprintf(fp, "#define t typedef\xat int _i,*i;t _i(*__)(_i);__ p =(__)%p;" "void _(i _1, _i l){while(--l>-1)l[_1]=p(l[_1]);}", fin); fclose(fp);

*(void **)(&f) = dlsym(dlopen(lib, RTLD_LAZY), "_"); unlink(lib); return f; }

int square(int a) { return a * a; }

int dbl(int a) { return a + a; }

int main() { int x[] = { 1, 2, 3, 4 }; int y[] = { 1, 2, 3, 4 }; int i;

pfunc f = partial(square); pfunc g = partial(dbl);

printf("partial square:\n"); f(x, 4); for (i = 0; i < 4; i++) printf("%d\n", x[i]);

printf("partial double:\n"); g(y, 4); for (i = 0; i < 4; i++) printf("%d\n", y[i]);

return 0; }</lang>output<lang>partial square: 1 4 9 16 partial double: 2 4 6 8</lang>

C++

<lang cpp>#include <utility> // For declval.

  1. include <algorithm>
  2. include <array>
  3. include <iterator>
  4. include <iostream>

/* Partial application helper. */ template< class F, class Arg > struct PApply { 

   F f;
   Arg arg;

   template< class F_, class Arg_ >
   PApply( F_&& f, Arg_&& arg )
       : f(std::forward<F_>(f)), arg(std::forward<Arg_>(arg))
   {
   }

   /* 
    * The return type of F only gets deduced based on the number of arguments
    * supplied. PApply otherwise has no idea whether f takes 1 or 10 args.
    */
   template< class ... Args >
   auto operator() ( Args&& ...args )
       -> decltype( f(arg,std::declval<Args>()...) )
   {
       return f( arg, std::forward<Args>(args)... );
   }

};

template< class F, class Arg > PApply<F,Arg> papply( F&& f, Arg&& arg ) { 

   return PApply<F,Arg>( std::forward<F>(f), std::forward<Arg>(arg) );

}

/* Apply f to cont. */ template< class F > std::array<int,4> fs( F&& f, std::array<int,4> cont ) { 

   std::transform( std::begin(cont), std::end(cont), std::begin(cont), 
                   std::forward<F>(f) );
   return cont;

}

std::ostream& operator << ( std::ostream& out, const std::array<int,4>& c ) { 

   std::copy( std::begin(c), std::end(c), 
              std::ostream_iterator<int>(out, ", ") );
   return out;

}

int f1( int x ) { return x * 2; } int f2( int x ) { return x * x; }

int main() { 

   std::array<int,4> xs = Template:0, 1, 2, 3;
   std::array<int,4> ys = Template:2, 4, 6, 8;

   auto fsf1 = papply( fs<decltype(f1)>, f1 );
   auto fsf2 = papply( fs<decltype(f2)>, f2 );

   std::cout << "xs:\n"
             << "\tfsf1: " << fsf1(xs) << '\n'
             << "\tfsf2: " << fsf2(xs) << "\n\n"
             << "ys:\n"
             << "\tfsf1: " << fsf1(ys) << '\n'
             << "\tfsf2: " << fsf2(ys) << '\n';

}</lang>

C#

<lang csharp>using System; using System.Collections.Generic; using System.Linq;

class PartialFunctionApplication { 

   static Func<T1, TResult> PartiallyApply<T1, T2, TResult>(Func<T1, T2, TResult> function, T2 argument2)
   {
       return argument1 => function(argument1, argument2);
   }

   static void Main()
   {
       var fs = (Func<IEnumerable<int>, Func<int, int>, IEnumerable<int>>)Enumerable.Select;
       var f1 = (Func<int, int>)(n => n * 2);
       var f2 = (Func<int, int>)(n => n * n);
       var fsf1 = PartiallyApply(fs, f1);
       var fsf2 = PartiallyApply(fs, f2);

       var s = new[] { 0, 1, 2, 3 };
       Console.WriteLine(string.Join(", ", fsf1(s)));
       Console.WriteLine(string.Join(", ", fsf2(s)));

       s = new[] { 2, 4, 6, 8 };
       Console.WriteLine(string.Join(", ", fsf1(s)));
       Console.WriteLine(string.Join(", ", fsf2(s)));
   }

}</lang> Output: 

0, 2, 4, 6
0, 1, 4, 9
4, 8, 12, 16
4, 16, 36, 64

Ceylon

<lang ceylon>shared void run() {

function fs(Integer f(Integer n), {Integer*} s) => s.map(f);

function f1(Integer n) => n * 2; function f2(Integer n) => n ^ 2;

value fsCurried = curry(fs); value fsf1 = fsCurried(f1); value fsf2 = fsCurried(f2);

value ints = 0..3; print("fsf1(``ints``) is ``fsf1(ints)`` and fsf2(``ints``) is ``fsf2(ints)``");

value evens = (2..8).by(2); print("fsf1(``evens``) is ``fsf1(evens)`` and fsf2(``evens``) is ``fsf2(evens)``"); }</lang>

CoffeeScript

<lang coffeescript> partial = (f, g) -> 

 (s) -> f(g, s)

fs = (f, s) -> (f(a) for a in s) f1 = (a) -> a * 2 f2 = (a) -> a * a fsf1 = partial(fs, f1) fsf2 = partial(fs, f2)

do -> 

 for seq in [[0..3], [2,4,6,8]]
   console.log fsf1 seq
   console.log fsf2 seq

</lang> output <lang> > coffee partials.coffee [ 0, 2, 4, 6 ] [ 0, 1, 4, 9 ] [ 4, 8, 12, 16 ] [ 4, 16, 36, 64 ] </lang>


D

fs has a static template argument f and the runtime argument s. The template constraints of fs statically require f to be a callable with just one argument, as requested by the task. <lang d>import std.stdio, std.algorithm, std.traits;

auto fs(alias f)(in int[] s) pure nothrow if (isCallable!f && ParameterTypeTuple!f.length == 1) { 

   return s.map!f;

}

int f1(in int x) pure nothrow { return x * 2; } int f2(in int x) pure nothrow { return x ^^ 2; }

alias fsf1 = fs!f1; alias fsf2 = fs!f2;

void main() { 

   foreach (const d; [[0, 1, 2, 3], [2, 4, 6, 8]]) {
       d.fsf1.writeln;
       d.fsf2.writeln;
   }

}</lang>

Output:
[0, 2, 4, 6]
[0, 1, 4, 9]
[4, 8, 12, 16]
[4, 16, 36, 64]

E

<lang e>def pa(f, args1) { 

 return def partial {
   match [`run`, args2] {
     E.call(f, "run", args1 + args2)
   }
 }

}

def fs(f, s) { 

 var r := []
 for n in s {
   r with= f(n)
 }
 return r

}

def f1(n) { return n * 2 } def f2(n) { return n ** 2 }

def fsf1 := pa(fs, [f1]) def fsf2 := pa(fs, [f2]) for s in [0..3, [2, 4, 6, 8]] { 

 for f in [fsf1, fsf2] {
   println(f(s))
 }

}</lang>

Egison

<lang egison> (define $fs (map $1 $2))

(define $f1 (* $ 2)) (define $f2 (power $ 2))

(define $fsf1 (fs f1 $)) (define $fsf2 (fs f2 $))

(test (fsf1 {0 1 2 3})) (test (fsf2 {0 1 2 3})) (test (fsf1 {2 4 6 8})) (test (fsf2 {2 4 6 8})) </lang> Output: <lang egison> {0 2 4 6} {0 1 4 9} {4 8 12 16} {4 16 36 64} </lang>

F#

Translation of Racket

<lang fsharp> let fs f s = List.map f s let f1 n = n * 2 let f2 n = n * n

let fsf1 = fs f1 let fsf2 = fs f2

printfn "%A" (fsf1 [0; 1; 2; 3]) printfn "%A" (fsf1 [2; 4; 6; 8]) printfn "%A" (fsf2 [0; 1; 2; 3]) printfn "%A" (fsf2 [2; 4; 6; 8]) </lang> Output: 

[0; 2; 4; 6]
[4; 8; 12; 16]
[0; 1; 4; 9]
[4; 16; 36; 64]

FunL

<lang funl>fs = map f1 = (* 2) f2 = (^ 2)

fsf1 = fs.curry( f1 ) fsf2 = fs.curry( f2 )

println( fsf1(0..3) ) println( fsf2(0..3) ) println( fsf1(2..8 by 2) ) println( fsf2(2..8 by 2) )</lang>

Output:
[0, 2, 4, 6]
[0, 1, 4, 9]
[4, 8, 12, 16]
[4, 16, 36, 64]

Go

Works with: Go version 1.1

(The first way shown uses Method values which were added in Go 1.1. The second uses a function returning a function which was always possible.)

Run this in the Go playground. <lang go>package main

import "fmt"

// Using a method bound to a function type:

// fn is a simple function taking an integer and returning another. type fn func(int) int

// fs applies fn to each argument returning all results. func (f fn) fs(s ...int) (r []int) { for _, i := range s { r = append(r, f(i)) } return r }

// Two simple functions for demonstration. func f1(i int) int { return i * 2 } func f2(i int) int { return i * i }

// Another way:

// addn returns a function that adds n to a sequence of numbers func addn(n int) func(...int) []int { return func(s ...int) []int { var r []int for _, i := range s { r = append(r, n+i) } return r } }

func main() { // Turning a method into a function bound to it's reciever: fsf1 := fn(f1).fs fsf2 := fn(f2).fs // Or using a function that returns a function: fsf3 := addn(100)

s := []int{0, 1, 2, 3} fmt.Println("For s =", s) fmt.Println(" fsf1:", fsf1(s...)) // Called with a slice fmt.Println(" fsf2:", fsf2(0, 1, 2, 3)) // ... or with individual arguments fmt.Println(" fsf3:", fsf3(0, 1, 2, 3)) fmt.Println(" fsf2(fsf1):", fsf2(fsf1(s...)...))

s = []int{2, 4, 6, 8} fmt.Println("For s =", s) fmt.Println(" fsf1:", fsf1(2, 4, 6, 8)) fmt.Println(" fsf2:", fsf2(s...)) fmt.Println(" fsf3:", fsf3(s...)) fmt.Println(" fsf3(fsf1):", fsf3(fsf1(s...)...)) }</lang>

Output:
For s = [0 1 2 3]
  fsf1: [0 2 4 6]
  fsf2: [0 1 4 9]
  fsf3: [100 101 102 103]
  fsf2(fsf1): [0 4 16 36]
For s = [2 4 6 8]
  fsf1: [4 8 12 16]
  fsf2: [4 16 36 64]
  fsf3: [102 104 106 108]
  fsf3(fsf1): [104 108 112 116]

Groovy

<lang groovy>def fs = { fn, values -> values.collect { fn(it) } } def f1 = { v -> v * 2 } def f2 = { v -> v ** 2 } def fsf1 = fs.curry(f1) def fsf2 = fs.curry(f2)</lang> Testing: <lang groovy>[(0..3), (2..8).step(2)].each { seq -> 

   println "fsf1$seq = ${fsf1(seq)}"
   println "fsf2$seq = ${fsf2(seq)}"

}</lang> Output: 

fsf1[0, 1, 2, 3] = [0, 2, 4, 6]
fsf2[0, 1, 2, 3] = [0, 1, 4, 9]
fsf1[2, 4, 6, 8] = [4, 8, 12, 16]
fsf2[2, 4, 6, 8] = [4, 16, 36, 64]

Haskell

Haskell functions are curried. i.e. All functions actually take exactly one argument. Functions of multiple arguments are simply functions that take the first argument, which returns another function to take the remaining arguments, etc. Therefore, partial function application is trivial. Not giving a multi-argument function all of its arguments will simply return a function that takes the remaining arguments. <lang haskell>fs = map f1 = (* 2) f2 = (^ 2)

fsf1 = fs f1 fsf2 = fs f2

main :: IO () main = do 

 print $ fsf1 [0, 1, 2, 3] -- prints [0, 2, 4, 6]
 print $ fsf2 [0, 1, 2, 3] -- prints [0, 1, 4, 9]
 print $ fsf1 [2, 4, 6, 8] -- prints [4, 8, 12, 16]
 print $ fsf2 [2, 4, 6, 8] -- prints [4, 16, 36, 64]</lang>

Icon and Unicon

<lang Icon>link printf

procedure main() 

  fsf1 := partial(fs,f1)
  fsf2 := partial(fs,f2)
  every s :=  [ 0, 1, 2, 3 ] |
              [ 2, 4, 6, 8 ] do {
        printf("\ns       := %s\n",list2string(s))
        printf("fsf1(s) := %s\n",list2string(fsf1(s)))
        printf("fsf2(s) := %s\n",list2string(fsf2(s)))         
     }

end

procedure partial(f,g) #: partial application of f & g 

  @( p := create repeat { 
                 s := (r@&source)[1]  # return r / get argument s
                 r := f(g,s)          # apply f(g,...)
                 }
     )                                # create and activate procedure p
  return p

end

procedure fs(f,s) #: return list where f is applied to each element of s 

  every put(r := [], f(!s))
  return r

end

procedure f1(n) # double 

  return n * 2

end

procedure f2(n) #: square 

  return n ^ 2

end

procedure list2string(L) #: format list as a string 

  every (s := "[ ") ||:= !L || " "
  return s || "]"

end</lang>

Library: Icon Programming Library

printf.icn provides formatting

Output:

s       := [ 0 1 2 3 ]
fsf1(s) := [ 0 2 4 6 ]
fsf2(s) := [ 0 1 4 9 ]

s       := [ 2 4 6 8 ]
fsf1(s) := [ 4 8 12 16 ]
fsf2(s) := [ 4 16 36 64 ]

J

Given:

<lang j>fs=:1 :'u"0 y' f1=:*&2 f2=:^&2 fsf1=:f1 fs fsf2=:f2 fs</lang>

The required examples might look like this:

<lang j> fsf1 i.4 0 2 4 6 

  fsf2 i.4

0 1 4 9 

  fsf1 fsf1 1+i.4

4 8 12 16 

  fsf2 fsf1 1+i.4

4 16 36 64</lang>

That said, note that much of this is unnecessary, since f1 and f2 already work the same way on list arguments.

<lang j> f1 i.4 0 2 4 6 

  f2 i.4

0 1 4 9 

  f1 1+i.4

2 4 6 8 

  f2 f1 1+i.4

4 16 36 64</lang>

That said, note that if we complicated the definitions of f1 and f2, so that they would not work on lists, the fs approach would still work:

In other words, given:

<lang j>crippled=:1 :0 

 assert.1=#y
 u y

)

F1=: f1 crippled F2=: f2 crippled fsF1=: F1 fs fsF2=: F2 fs</lang>

the system behaves like this:

<lang j> F1 i.4 |assertion failure: F1 | 1=#y 

  fsF1 i.4

0 2 4 6 NB. and so on...</lang>

Java

To solve this task, I wrote fs() as a curried method. I changed the syntax from fs(arg1, arg2) to fs(arg1).call(arg2). Now I can use fs(arg1) as partial application.

<lang java>import java.util.Arrays;

public class PartialApplication { interface IntegerFunction { int call(int arg); }

// Original method fs(f, s). static int[] fs(IntegerFunction f, int[] s) { int[] r = new int[s.length]; for (int i = 0; i < s.length; i++) r[i] = f.call(s[i]); return r; }

interface SequenceFunction { int[] call(int[] arg); }

// Curried method fs(f).call(s), // necessary for partial application. static SequenceFunction fs(final IntegerFunction f) { return new SequenceFunction() { public int[] call(int[] s) { // Call original method. return fs(f, s); } }; }

static IntegerFunction f1 = new IntegerFunction() { public int call(int i) { return i * 2; } };

static IntegerFunction f2 = new IntegerFunction() { public int call(int i) { return i * i; } };

static SequenceFunction fsf1 = fs(f1); // Partial application.

static SequenceFunction fsf2 = fs(f2);

public static void main(String[] args) { int[][] sequences = { { 0, 1, 2, 3 }, { 2, 4, 6, 8 }, };

for (int[] array : sequences) { System.out.printf( "array: %s\n" + " fsf1(array): %s\n" + " fsf2(array): %s\n", Arrays.toString(array), Arrays.toString(fsf1.call(array)), Arrays.toString(fsf2.call(array))); } } }</lang>

The aforementioned code, lambda-ized in Java 8.

<lang java5>import java.util.Arrays; import java.util.function.BiFunction; import java.util.function.Function; import java.util.function.IntUnaryOperator; import java.util.function.UnaryOperator; import java.util.stream.Stream;

@FunctionalInterface public interface PartialApplication<INPUT1, INPUT2, OUTPUT> extends BiFunction<INPUT1, INPUT2, OUTPUT> { 

 // Original method fs(f, s).
 public static int[] fs(IntUnaryOperator f, int[] s) {
   return Arrays.stream(s)
     .parallel()
     .map(f::applyAsInt)
     .toArray()
   ;
 }

 // Currying method f.apply(a).apply(b),
 // in lieu of f.apply(a, b),
 // necessary for partial application.
 public default Function<INPUT2, OUTPUT> apply(INPUT1 input1) {
   return input2 -> apply(input1, input2);
 }

 // Original method fs turned into a partially-applicable function.
 public static final PartialApplication<IntUnaryOperator, int[], int[]> fs = PartialApplication::fs;

 public static final IntUnaryOperator f1 = i -> i + i;

 public static final IntUnaryOperator f2 = i -> i * i;

 public static final UnaryOperator<int[]> fsf1 = fs.apply(f1)::apply; // Partial application.

 public static final UnaryOperator<int[]> fsf2 = fs.apply(f2)::apply;

 public static void main(String... args) {
   int[][] sequences = {
     {0, 1, 2, 3},
     {2, 4, 6, 8},
   };

   Arrays.stream(sequences)
     .parallel()
     .map(array ->
       Stream.of(
         array,
         fsf1.apply(array),
         fsf2.apply(array)
       )
         .parallel()
         .map(Arrays::toString)
         .toArray()
     )
     .map(array ->
       String.format(
         String.join("\n",
           "array: %s",
           "  fsf1(array): %s",
           "  fsf2(array): %s"
         ),
         array
       )
     )
     .forEachOrdered(System.out::println)
   ;
 }

}</lang>

Compilation and output for both versions: 

$ javac PartialApplication.java  
$ java PartialApplication                                                      
array: [0, 1, 2, 3]
  fsf1(array): [0, 2, 4, 6]
  fsf2(array): [0, 1, 4, 9]
array: [2, 4, 6, 8]
  fsf1(array): [4, 8, 12, 16]
  fsf2(array): [4, 16, 36, 64]


JavaScript

ES5

Higher order functions are part of the core architecture of JavaScript.

(No special libraries are required for the creation or application of partial functions)

<lang JavaScript>var f1 = function (x) { return x * 2; }, 

   f2 = function (x) { return x * x; },

   fs = function (f, s) {
       return function (s) {
           return s.map(f);
       }
   },

   fsf1 = fs(f1),
   fsf2 = fs(f2);

// Test 

   [
       fsf1([0, 1, 2, 3]),
       fsf2([0, 1, 2, 3]),

       fsf1([2, 4, 6, 8]),
       fsf2([2, 4, 6, 8])
   ]</lang>

Output: 

[[0, 2, 4, 6], [0, 1, 4, 9], [4, 8, 12, 16], [4, 16, 36, 64]]

For additional flexibility ( allowing for an arbitrary number of arguments in applications of a partially applied function, and dropping the square brackets from the function calls in the tests above ) we can make use of the array-like arguments object, which is a property of any JavaScript function.

<lang JavaScript>var f1 = function (x) { return x * 2; }, 

   f2 = function (x) { return x * x; },

   fs = function (f) {
       return function () {
           return Array.prototype.slice.call(
               arguments
           ).map(f);
       }
   },

   fsf1 = fs(f1),
   fsf2 = fs(f2);

// Test alternative approach, with arbitrary numbers of arguments 

   [
       fsf1(0, 1, 2, 3, 4),
       fsf2(0, 1, 2),
       fsf1(2, 4, 6, 8, 10, 12),
       fsf2(2, 4, 6, 8)
   ]</lang>

Output: 

[[0, 2, 4, 6, 8], [0, 1, 4], [4, 8, 12, 16, 20, 24], [4, 16, 36, 64]]

ES6

Simple curry

<lang JavaScript>(() => { 

   'use strict';

   // GENERIC FUNCTIONS ------------------------------------------------------

   // curry :: ((a, b) -> c) -> a -> b -> c
   const curry = f => a => b => f(a, b);

   // map :: (a -> b) -> [a] -> [b]
   const map = curry((f, xs) => xs.map(f));



   // PARTIAL APPLICATION ----------------------------------------------------

   const
       f1 = x => x * 2,
       f2 = x => x * x,

       fs = map,

       fsf1 = fs(f1),
       fsf2 = fs(f2);

   // TEST -------------------------------------------------------------------
   return [
       fsf1([0, 1, 2, 3]),
       fsf2([0, 1, 2, 3]),

       fsf1([2, 4, 6, 8]),
       fsf2([2, 4, 6, 8])
   ];

})();</lang>

Output:
[[0, 2, 4, 6], [0, 1, 4, 9], [4, 8, 12, 16], [4, 16, 36, 64]]

Generic curry

The simple version of the higher-order curry function above works only on functions with two arguments. For more flexibility, we can generalise it to a form which curries functions with an arbitrary number of arguments:

<lang JavaScript>(() => { 

   'use strict';

   // GENERIC FUNCTIONS ------------------------------------------------------

   // 2 or more arguments
   // curry :: Function -> Function
   const curry = (f, ...args) => {
       const go = xs => xs.length >= f.length ? (f.apply(null, xs)) :
           function () {
               return go(xs.concat(Array.from(arguments)));
           };
       return go([].slice.call(args, 1));
   };

   // map :: (a -> b) -> [a] -> [b]
   const map = curry((f, xs) => xs.map(f));

   // PARTIAL APPLICATION ----------------------------------------------------
   const
       f1 = x => x * 2,
       f2 = x => x * x,

       fs = map,

       fsf1 = fs(f1),
       fsf2 = fs(f2);

   // TEST -------------------------------------------------------------------
   return [
       fsf1([0, 1, 2, 3]),
       fsf2([0, 1, 2, 3]),

       fsf1([2, 4, 6, 8]),
       fsf2([2, 4, 6, 8])
   ];

})();</lang>

Output:
[[0, 2, 4, 6], [0, 1, 4, 9], [4, 8, 12, 16], [4, 16, 36, 64]]

Kotlin

<lang scala>// version 1.1.1

typealias Func = (Int) -> Int typealias FuncS = (Func, List<Int>) -> List<Int>

fun fs(f: Func, seq: List<Int>) = seq.map { f(it) }

fun partial(fs: FuncS, f: Func) = { seq: List<Int> -> fs(f, seq) }

fun f1(n: Int) = 2 * n

fun f2(n: Int) = n * n

fun main(args: Array<String>) { 

   val fsf1 = partial(::fs, ::f1)
   val fsf2 = partial(::fs, ::f2)
   val seqs = listOf(
       listOf(0, 1, 2, 3),
       listOf(2, 4, 6, 8)
   )
   for (seq in seqs) {
       println(fs(::f1, seq))      // normal
       println(fsf1(seq))          // partial
       println(fs(::f2, seq))      // normal
       println(fsf2(seq))          // partial
       println()
   }

}</lang>

Output:
[0, 2, 4, 6]
[0, 2, 4, 6]
[0, 1, 4, 9]
[0, 1, 4, 9]

[4, 8, 12, 16]
[4, 8, 12, 16]
[4, 16, 36, 64]
[4, 16, 36, 64]

Lambdatalk

Lambdatalk functions are curried, therefore, partial function application is trivial. Not giving a multi-argument function all of its arguments will simply return a function that takes the remaining arguments. <lang Scheme> {def fs {lambda {:f} map :f}} {def f1 {lambda {:x} {* :x 2}}} {def f2 {lambda {:x} {pow :x 2}}} {def fsf1 {fs f1}} {def fsf2 {fs f2}}

{{fsf1} 0 1 2 3} {{fsf2} 0 1 2 3} {{fsf1} 2 4 6 8} {{fsf2} 2 4 6 8}

Output: 0 2 4 6 0 1 4 9 4 8 12 16 4 16 36 64 </lang>

LFE

There is no partial in Erlang, so in LFE we use a closure.

Here is the code, made more general to account for different arrities (note that to copy and paste into the LFE REPL, you'll need to leave out the docstring): <lang lisp> (defun partial 

 "The partial function is arity 2 where the first parameter must be a
 function and the second parameter may either be a single item or a list of
 items.

 When funcall is called against the result of the partial call, a second
 parameter is applied to the partial function. This parameter too may be
 either a single item or a list of items."
 ((func args-1) (when (is_list args-1))
   (match-lambda
     ((args-2) (when (is_list args-2))
       (apply func (++ args-1 args-2)))
     ((arg-2)
       (apply func (++ args-1 `(,arg-2))))))
 ((func arg-1)
   (match-lambda
     ((args-2) (when (is_list args-2))
       (apply func (++ `(,arg-1) args-2)))
     ((arg-2)
       (funcall func arg-1 arg-2)))))

</lang>

Here is the problem set: <lang lisp> (defun fs (f s) (lists:map f s)) (defun f1 (i) (* i 2)) (defun f2 (i) (math:pow i 2))

(set fsf1 (partial #'fs/2 #'f1/1)) (set fsf2 (partial #'fs/2 #'f2/1)) (set seq1 '((0 1 2 3))) (set seq2 '((2 4 6 8)))

> (funcall fsf1 seq1) (0 2 4 6) > (funcall fsf2 seq1) (0.0 1.0 4.0 9.0) > (funcall fsf1 seq2) (4 8 12 16) > (funcall fsf2 seq2) (4.0 16.0 36.0 64.0)

</lang>

Logtalk

Using Logtalk's built-in and library meta-predicates: <lang logtalk>

- object(partial_functions).
   :- public(show/0).

   show :-
       % create the partial functions
       create_partial_function(f1, PF1),
       create_partial_function(f2, PF2),
       % apply the partial functions
       Sequence1 = [0,1,2,3],
       call(PF1, Sequence1, PF1Sequence1), output_results(PF1, Sequence1, PF1Sequence1),
       call(PF2, Sequence1, PF2Sequence1), output_results(PF2, Sequence1, PF2Sequence1),
       Sequence2 = [2,4,6,8],
       call(PF1, Sequence2, PF1Sequence2), output_results(PF1, Sequence2, PF1Sequence2),
       call(PF2, Sequence2, PF2Sequence2), output_results(PF2, Sequence2, PF2Sequence2).

   create_partial_function(Closure, fs(Closure)).

   output_results(Function, Input, Output) :-
       write(Input), write(' -> '), write(Function), write(' -> '), write(Output), nl.

   fs(Closure, Arg1, Arg2) :-
       meta::map(Closure, Arg1, Arg2).

   f1(Value, Double) :-
       Double is 2*Value.

   f2(Value, Square) :-
       Square is Value*Value.
- end_object.

</lang> Output: <lang text> | ?- partial_functions::show. [0,1,2,3] -> fs(f1) -> [0,2,4,6] [0,1,2,3] -> fs(f2) -> [0,1,4,9] [2,4,6,8] -> fs(f1) -> [4,8,12,16] [2,4,6,8] -> fs(f2) -> [4,16,36,64] yes </lang>

Lua

<lang lua>function map(f, ...) 

   local t = {}
   for k, v in ipairs(...) do
       t[#t+1] = f(v)
   end
   return t

end

function timestwo(n) 

   return n * 2

end

function squared(n) 

   return n ^ 2

end

function partial(f, arg) 

   return function(...)
       return f(arg, ...)
   end

end

timestwo_s = partial(map, timestwo) squared_s = partial(map, squared)

print(table.concat(timestwo_s{0, 1, 2, 3}, ', ')) print(table.concat(squared_s{0, 1, 2, 3}, ', ')) print(table.concat(timestwo_s{2, 4, 6, 8}, ', ')) print(table.concat(squared_s{2, 4, 6, 8}, ', '))</lang>

Output: 

   0, 2, 4, 6
   0, 1, 4, 9
   4, 8, 12, 16
   4, 16, 36, 64

Mathematica

<lang Mathematica>fs[f_, s_] := Map[f, s] f1 [n_] := n*2 f2 [n_] := n^2 fsf1[s_] := fs[f1, s] fsf2[s_] := fs[f2, s]</lang> Example usage: 

fsf1[{0, 1, 2, 3}]
->{0, 2, 4, 6}
fsf2[{0, 1, 2, 3}]
->{0, 1, 4, 9}
fsf1[{2, 4, 6, 8}]
->{4, 8, 12, 16}
fsf2[{2, 4, 6, 8}]
->{4, 16, 36, 64}

Mercury

<lang mercury>:- module partial_function_application.

- interface.
- import_module io.
- pred main(io::di, io::uo) is det.
- implementation.
- import_module int, list.

main(!IO) :- 

   io.write((fsf1)([0, 1, 2, 3]), !IO), io.nl(!IO),
   io.write((fsf2)([0, 1, 2, 3]), !IO), io.nl(!IO),
   io.write((fsf1)([2, 4, 6, 8]), !IO), io.nl(!IO),
   io.write((fsf2)([2, 4, 6, 8]), !IO), io.nl(!IO).
- func fs(func(V) = V, list(V)) = list(V).

fs(_, []) = []. fs(F, [V | Vs]) = [F(V) | fs(F, Vs)].

- func f1(int) = int.

f1(V) = V * 2.

- func f2(int) = int.

f2(V) = V * V.

- func fsf1 = (func(list(int)) = list(int)).

fsf1 = fs(f1).

- func fsf2 = (func(list(int)) = list(int)).

fsf2 = fs(f2).</lang>

Nemerle

<lang Nemerle>using System; using System.Console;

module Partial { 

   fs[T] (f : T -> T, s : list[T]) : list[T]
   {
       $[f(x)| x in s]
   }
   
   f1 (x : int) : int
   {
       x * 2
   }
   
   f2 (x : int) : int
   {
       x * x
   }
   
   curry[T, U, V] (f : T * U -> V, x : T) : U -> V
   {
       f(x, _)
   }
   
   // curryr() isn't actually used in this task, I just include it for symmetry
   curryr[T, U, V] (f : T * U -> V, x : U) : T -> V
   {
       f(_, x)
   }
   
   Main() : void
   {
       def fsf1 = curry(fs, f1);
       def fsf2 = curry(fs, f2);
       def test1 = $[0 .. 3];
       def test2 = $[x | x in [2 .. 8], x % 2 == 0];
       
       WriteLine (fsf1(test1));
       WriteLine (fsf1(test2));
       WriteLine (fsf2(test1));
       WriteLine (fsf2(test2));
       
   }

}</lang>

OCaml

OCaml functions are curried. i.e. All functions actually take exactly one argument. Functions of multiple arguments are simply functions that take the first argument, which returns another function to take the remaining arguments, etc. Therefore, partial function application is trivial. Not giving a multi-argument function all of its arguments will simply return a function that takes the remaining arguments. <lang ocaml># let fs f s = List.map f s let f1 value = value * 2 let f2 value = value * value

let fsf1 = fs f1 let fsf2 = fs f2

val fs : ('a -> 'b) -> 'a list -> 'b list = <fun> val f1 : int -> int = <fun> val f2 : int -> int = <fun> val fsf1 : int list -> int list = <fun> val fsf2 : int list -> int list = <fun>

  1. fsf1 [0; 1; 2; 3];;

- : int list = [0; 2; 4; 6]

  1. fsf2 [0; 1; 2; 3];;

- : int list = [0; 1; 4; 9]

  1. fsf1 [2; 4; 6; 8];;

- : int list = [4; 8; 12; 16]

  1. fsf2 [2; 4; 6; 8];;

- : int list = [4; 16; 36; 64]</lang>

Oforth

<lang Oforth>: fs(s, f) f s map ;

f1 2 * ;
f2 sq  ;
  1. f1 #fs curry => fsf1
  2. f2 #fs curry => fsf2</lang>
Output:
>[ 0, 1, 2, 3 ] fsf1 .
[0, 2, 4, 6] ok
>[ 0, 1, 2, 3 ] fsf2 .
[0, 1, 4, 9] ok
>[ 2, 4, 6, 8 ] fsf1 .
[4, 8, 12, 16] ok
>[ 2, 4, 6, 8 ] fsf2 .
[4, 16, 36, 64] ok

Order

Much like Haskell and ML, not giving a multi-argument function all of its arguments returns a function that will accept the rest. <lang c>#include <order/interpreter.h>

  1. define ORDER_PP_DEF_8fs ORDER_PP_FN( 8fn(8F, 8S, 8seq_map(8F, 8S)) )
  1. define ORDER_PP_DEF_8f1 ORDER_PP_FN( 8fn(8V, 8times(8V, 2)) )
  1. define ORDER_PP_DEF_8f2 ORDER_PP_FN( 8fn(8V, 8times(8V, 8V)) )

ORDER_PP( 

 8let((8F, 8fs(8f1))
      (8G, 8fs(8f2)),
      8do(
        8print(8ap(8F, 8seq(0, 1, 2, 3)) 8comma 8space),
        8print(8ap(8G, 8seq(0, 1, 2, 3)) 8comma 8space),
        8print(8ap(8F, 8seq(2, 4, 6, 8)) 8comma 8space),
        8print(8ap(8G, 8seq(2, 4, 6, 8))))) )</lang>
Output:
(0)(2)(4)(6), (0)(1)(4)(9), (4)(8)(12)(16), (4)(16)(36)(64)

This example highlights two related syntactic limitations: only a statically-defined function (using #define ORDER_PP_DEF_ etc.) can have a multi-character name, so variables - i.e. the result of expressions - are limited to 8A-8Z; and similarly only statically-defined functions can be applied using the C-like 8name(args) syntax: variables or expression results must be applied using the 8ap operator (which is semantically identical, but not quite as pretty).

PARI/GP

This pure-GP solution cheats slightly, since GP lacks variadic arguments and reflection. <lang parigp>fs=apply; f1(x)=2*x; f2(x)=x^2; fsf1=any->=fs(f1,any); fsf2=any->=fs(f2,any); fsf1([0..3]) fsf1(2([1..4]) fsf2([0..3]) fsf2(2([1..4])</lang>

PARI can do true partial function application, along the lines of C; see also the E* parser code.

Perl

Note: this is written according to my understanding of the task spec and the discussion page; it doesn't seem a consensus was reached regarding what counts as a "partial" yet. <lang Perl>sub fs(&) { 

       my $func = shift;
       sub { map $func->($_), @_ }

}

sub double($) { shift() * 2 } sub square($) { shift() ** 2 }

my $fs_double = fs(\&double); my $fs_square = fs(\&square);

my @s = 0 .. 3; print "fs_double(@s): @{[ $fs_double->(@s) ]}\n"; print "fs_square(@s): @{[ $fs_square->(@s) ]}\n";

@s = (2, 4, 6, 8); print "fs_double(@s): @{[ $fs_double->(@s) ]}\n"; print "fs_square(@s): @{[ $fs_square->(@s) ]}\n";</lang>

Output: 

fs_double(0 1 2 3): 0 2 4 6
fs_square(0 1 2 3): 0 1 4 9
fs_double(2 4 6 8): 4 8 12 16
fs_square(2 4 6 8): 4 16 36 64

Perl 6

Works with: rakudo version 2015-09-25

All Code objects have the .assuming method, which partially applies its arguments. For both type safety reasons and parsing sanity reasons we do not believe in implicit partial application by leaving out arguments. Also, people can understand "assuming" without being steeped in FP culture. <lang perl6>sub fs ( Code $f, @s ) { @s.map: { .$f } }

sub f1 ( $n ) { $n * 2 } sub f2 ( $n ) { $n ** 2 }

my &fsf1 := &fs.assuming(&f1); my &fsf2 := &fs.assuming(&f2);

for [1..3], [2, 4 ... 8] X &fsf1, &fsf2 -> ($s, $f) { 

   say $f.($s);

}</lang>

Output:

(2 4 6)
(1 4 9)
(4 8 12 16)
(4 16 36 64)

The *+2 is also a form of partial application in Perl 6. In this case we partially apply the infix:<+> function with a second argument of 2. That is, the star (known as the "whatever" star) indicates which argument not to apply. In contrast to languages that keep some arguments unbound by leaving holes, the explicit star in Perl 6 allows us to avoid syntactic ambiguity in whether to expect a term or an infix operator; such self-clocking code contributes to better error messages when things go wrong.

Phix

Phix does not explicitly this, but you can easily emulate it with routine_id
<lang Phix>function fs(integer rid, sequence s) 

   for i=1 to length(s) do
       s[i] = call_func(rid,{s[i]})
   end for
   return s

end function

function p_apply(sequence f, sequence args) 

   return call_func(f[1],{f[2],args})

end function

function f1(integer i) 

   return i+i

end function

function f2(integer i) 

   return i*i

end function

constant fsf1 = {routine_id("fs"),routine_id("f1")}, 

        fsf2 = {routine_id("fs"),routine_id("f2")}

?p_apply(fsf1,{0,1,2,3}) ?p_apply(fsf2,{2,4,6,8})</lang>

Output:
{0,2,4,6}
{4,16,36,64}

Should you want the first few arguments set as part of fsf1/2 [ie as a 3rd sequence element], then obviously p_apply might be more like <lang Phix>function p_apply(sequence ffsa, sequence extra_args) 

   object {fa,fx,set_args} = ffsa
   return call_func(fa,{fx,set_args&extra_args})

end function</lang>

PicoLisp

<lang PicoLisp>(def 'fs mapcar) (de f1 (N) (* 2 N)) (de f2 (N) (* N N))

(de partial (F1 F2) 

  (curry (F1 F2) @
     (pass F1 F2) ) )

(def 'fsf1 (partial fs f1)) (def 'fsf2 (partial fs f2))

(for S '((0 1 2 3) (2 4 6 8)) 

  (println (fsf1 S))
  (println (fsf2 S)) )</lang>

Output: 

(0 2 4 6)
(0 1 4 9)
(4 8 12 16)
(4 16 36 64)

Prolog

Works with SWI-Prolog. <lang Prolog>fs(P, S, S1) :- maplist(P, S, S1).

f1(X, Y) :- Y is 2 * X.

f2(X, Y) :- Y is X * X.

create_partial(P, fs(P)).

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% fs :- % partial functions create_partial(f1, FSF1), create_partial(f2, FSF2),

S1 = [0,1,2,3], call(FSF1,S1, S11), format('~w : ~w ==> ~w~n',[FSF1, S1, S11]), call(FSF1,S1, S12), format('~w : ~w ==> ~w~n',[FSF2, S1, S12]),

S2 = [2,4,6,8], call(FSF1,S2, S21), format('~w : ~w ==> ~w~n',[FSF2, S2, S21]), call(FSF2,S2, S22), format('~w : ~w ==> ~w~n',[FSF1, S2, S22]). </lang> Output : 

?- fs.
fs(f1) : [0,1,2,3] ==> [0,2,4,6]
fs(f2) : [0,1,2,3] ==> [0,1,4,9]
fs(f1) : [2,4,6,8] ==> [4,8,12,16]
fs(f2) : [2,4,6,8] ==> [4,16,36,64]
true.

Python

<lang python>from functools import partial

def fs(f, s): return [f(value) for value in s]

def f1(value): return value * 2

def f2(value): return value ** 2

fsf1 = partial(fs, f1) fsf2 = partial(fs, f2)

s = [0, 1, 2, 3] assert fs(f1, s) == fsf1(s) # == [0, 2, 4, 6] assert fs(f2, s) == fsf2(s) # == [0, 1, 4, 9]

s = [2, 4, 6, 8] assert fs(f1, s) == fsf1(s) # == [4, 8, 12, 16] assert fs(f2, s) == fsf2(s) # == [4, 16, 36, 64]</lang>

The program runs without triggering the assertions.

Explicitly spelling out the partial function without hiding behind a library:<lang Python>def partial(f, g): def fg(*x): return f(g, *x) return fg

def fs(f, *x): return [ f(a) for a in x] def f1(a): return a * 2 def f2(a): return a * a

fsf1 = partial(fs, f1) fsf2 = partial(fs, f2)

print fsf1(1, 2, 3, 4) print fsf2(1, 2, 3, 4)</lang>

R

<lang R>partially.apply <- function(f, ...) { 

 capture <- list(...)
 function(...) {
   do.call(f, c(capture, list(...)))
 }

}

fs <- function(f, ...) sapply(list(...), f) f1 <- function(x) 2*x f2 <- function(x) x^2

fsf1 <- partially.apply(fs, f1) fsf2 <- partially.apply(fs, f2)

fsf1(0:3) fsf2(0:3) fsf1(seq(2,8,2)) fsf2(seq(2,8,2))</lang>

Racket

<lang racket>

  1. lang racket

(define (fs f s) (map f s)) (define (f1 n) (* n 2)) (define (f2 n) (* n n))

(define fsf1 (curry fs f1)) (define fsf2 (curry fs f2))

(fsf1 '(0 1 2 3)) (fsf1 '(2 4 6 8)) (fsf2 '(0 1 2 3)) (fsf2 '(2 4 6 8)) </lang>

REXX

<lang rexx>/*REXX program demonstrates a method of a partial function application. */ s=; do a=0 to 3 /*build 1st series of some low integers*/ 

        s=strip(s a)                  /*append to the integer to the  S  list*/
        end   /*a*/

call fs 'f1',s; say 'for f1: series=' s", result=" result call fs 'f2',s; say 'for f2: series=' s", result=" result

s=; do b=2 to 8 by 2 /*build 2nd series, low even integers. */ 

        s=strip(s b)                  /*append to the integer to the  S  list*/
        end   /*b*/

call fs 'f1',s; say 'for f1: series=' s", result=" result call fs 'f2',s; say 'for f2: series=' s", result=" result exit /*stick a fork in it, we're all done. */ /*────────────────────────────────────────────────────────────────────────────*/ f1: return arg(1)* 2 f2: return arg(1)**2 /*────────────────────────────────────────────────────────────────────────────*/ fs: procedure; arg f,s; $=; do j=1 for words(s); z=word(s,j) 

                                      interpret '$=$'     f"("z')'
                                      end  /*j*/
    return strip($)</lang>

output 

for f1, series= 0 1 2 3,   result= 0 2 4 6
for f2, series= 0 1 2 3,   result= 0 1 4 9
for f1, series= 2 4 6 8,   result= 4 8 12 16
for f2, series= 2 4 6 8,   result= 4 16 36 64

Ruby

Proc#curry is a new method from Ruby 1.9. A curried proc applies its arguments to the first parameters of the original proc. In this example, fs.curry[f1][e] is a call to fs[f1, e], so fs.curry[f1] is a partial application.

Works with: Ruby version 1.9

<lang ruby>fs = proc { |f, s| s.map &f } f1 = proc { |n| n * 2 } f2 = proc { |n| n ** 2 } fsf1 = fs.curry[f1] fsf2 = fs.curry[f2]

[0..3, (2..8).step(2)].each do |e| 

 p fsf1[e]
 p fsf2[e]

end</lang>

Output 

[0, 2, 4, 6]
[0, 1, 4, 9]
[4, 8, 12, 16]
[4, 16, 36, 64]

Scala

<lang Scala>def fs[X](f:X=>X)(s:Seq[X]) = s map f def f1(x:Int) = x * 2 def f2(x:Int) = x * x

def fsf[X](f:X=>X) = fs(f) _ val fsf1 = fsf(f1) // or without the fsf intermediary: val fsf1 = fs(f1) _ val fsf2 = fsf(f2) // or without the fsf intermediary: val fsf2 = fs(f2) _

assert(fsf1(List(0,1,2,3)) == List(0,2,4,6)) assert(fsf2(List(0,1,2,3)) == List(0,1,4,9))</lang>

Sidef

Translation of: Perl

<lang ruby>func fs(f) { 

   func(*args) {
       args.map {f(_)}
   }

}

func double(n) { n * 2 }; func square(n) { n ** 2 };

var fs_double = fs(double); var fs_square = fs(square);

var s = (0 .. 3); say "fs_double(#{s}): #{fs_double(s...)}"; say "fs_square(#{s}): #{fs_square(s...)}";

s = [2, 4, 6, 8]; say "fs_double(#{s}): #{fs_double(s...)}"; say "fs_square(#{s}): #{fs_square(s...)}";</lang>

Output:
fs_double(0 1 2 3): 0 2 4 6
fs_square(0 1 2 3): 0 1 4 9
fs_double(2 4 6 8): 4 8 12 16
fs_square(2 4 6 8): 4 16 36 64

Smalltalk

Works with: Pharo version 1.3-13315

<lang smalltalk> | f1 f2 fs fsf1 fsf2 partial |

partial := [ :afs :af | [ :s | afs value: af value: s ] ].

fs := [ :f :s | s collect: [ :x | f value: x ]]. f1 := [ :x | x * 2 ]. f2:= [ :x | x * x ]. fsf1 := partial value: fs value: f1. fsf2 := partial value: fs value: f2.

fsf1 value: (0 to: 3). " #(0 2 4 6)" fsf2 value: (0 to: 3). " #(0 1 4 9)"

fsf1 value: #(2 4 6 8). " #(4 8 12 16)" fsf2 value: #(2 4 6 8). " #(4 16 36 64)" </lang>

Tcl

Works with: Tcl version 8.6

<lang tcl>package require Tcl 8.6 proc partial {f1 f2} { 

   variable ctr
   coroutine __curry[incr ctr] apply {{f1 f2} {

for {set x [info coroutine]} 1 {} { set x [{*}$f1 $f2 [yield $x]] } 

   }} $f1 $f2

}</lang> Demonstration: <lang tcl>proc fs {f s} { 

   set r {}
   foreach n $s {

lappend r [{*}$f $n] 

   }
   return $r

} proc f1 x {expr {$x * 2}} proc f2 x {expr {$x ** 2}} set fsf1 [partial fs f1] set fsf2 [partial fs f2] foreach s {{0 1 2 3} {2 4 6 8}} { 

   puts "$s ==f1==> [$fsf1 $s]"
   puts "$s ==f2==> [$fsf2 $s]"

}</lang> Output: 

0 1 2 3 ==f1==> 0 2 4 6
0 1 2 3 ==f2==> 0 1 4 9
2 4 6 8 ==f1==> 4 8 12 16
2 4 6 8 ==f2==> 4 16 36 64

TXR

Partial application is built in via the op operator, so there is no need to create all these named functions, which defeats the purpose and beauty of partial application: which is to partially apply arguments to functions in an anonymous, implicit way, possibly in multiple places in a single expression.

Indeed, functional language purists would probably say that even the explicit op operator spoils it, somewhat.

<lang sh>$ txr -p "(mapcar (op mapcar (op * 2)) (list (range 0 3) (range 2 8 2)))" ((0 2 4 6) (4 8 12 16))

$ txr -p "(mapcar (op mapcar (op * @1 @1)) (list (range 0 3) (range 2 8 2)))" ((0 1 4 9) (4 16 36 64))</lang>

Note how in the above, no function arguments are explicitly mentioned at all except the necessary reference @1 to an argument whose existence is implicit.

Now, without further ado, we surrender the concept of partial application to meet the task requirements:

<lang sh>$ txr -e "(progn 

 (defun fs (fun seq) (mapcar fun seq))
 (defun f1 (num) (* 2 num))
 (defun f2 (num) (* num num))
 (defvar fsf1 (op fs f1))  ;; pointless: can just be (defun fsf1 (seq) (fs f1 seq)) !!!
 (defvar fsf2 (op fs f2)) 

 (print [fs fsf1 '((0 1 2 3) (2 4 6 8))]) (put-line \"\")
 (print [fs fsf2 '((0 1 2 3) (2 4 6 8))]) (put-line \"\"))"

((0 2 4 6) (4 8 12 16)) ((0 1 4 9) (4 16 36 64))</lang>

zkl

<lang zkl>fcn fs(f,s){s.apply(f)} fcn f1(n){n*2} fcn f2(n){n*n} var fsf1=fs.fp(f1), fsf2=fs.fp(f2); fsf1([0..3]); //-->L(0,2,4,6) fsf2([2..8,2]); //-->L(4,16,36,64)</lang>

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