Currying

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

This page uses content from Wikipedia. The original article was at Currying. The list of authors can be seen in the page history. As with Rosetta Code, the text of Wikipedia is available under the GNU FDL. (See links for details on variance)

Create a simple demonstrative example of Currying in the specific language.

Add any historic details as to how the feature made its way into the language.

ALGOL 68

In 1968 C.H. Lindsey proposed for partial parametrisation for ALGOL 68, this is implemented as an extension in wp:ALGOL 68G. <lang algol68># Raising a function to a power #

MODE FUN = PROC (REAL) REAL; PROC pow = (FUN f, INT n, REAL x) REAL: f(x) ** n; OP ** = (FUN f, INT n) FUN: pow (f, n, );

1. Example: sin (3 x) = 3 sin (x) - 4 sin^3 (x) (follows from DeMoivre's theorem) #

REAL x = read real; print ((new line, sin (3 * x), 3 * sin (x) - 4 * (sin ** 3) (x)))</lang>

AppleScript

The nearest thing to a first-class function in AppleScript is a 'script' in which a 'handler' (with some default or vanilla name like 'call' or 'lambda' is embedded). First class use of an ordinary 2nd class 'handler' function requires 'lifting' it into an enclosing script – a process which can be abstracted to a general mReturn function.

<lang AppleScript> -- curry :: (Script|Handler) -> Script on curry(f)

   set mf to mReturn(f)
   script
       on lambda(a)
           script
               on lambda(b)
                   mf's lambda(a, b)
               end lambda
           end script
       end lambda
   end script

end curry

-- TESTS

-- add :: Num -> Num -> Num on add(a, b)

   a + b

end add

-- product :: Num -> Num -> Num on product(a, b)

   a * b

end product

-- Test 1. curry(add)

--> «script»

-- Test 2. curry(add)'s lambda(2)

--> «script»

-- Test 3. curry(add)'s lambda(2)'s lambda(3)

--> 5

-- Test 4. map(curry(product)'s lambda(7), range(1, 10))

--> {7, 14, 21, 28, 35, 42, 49, 56, 63, 70}

-- Combined: {curry(add), ¬

   curry(add)'s lambda(2), ¬
   curry(add)'s lambda(2)'s lambda(3), ¬
   map(curry(product)'s lambda(7), range(1, 10))}

--> {«script», «script», 5, {7, 14, 21, 28, 35, 42, 49, 56, 63, 70}}

-- GENERIC FUNCTIONS

-- 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 lambda : f
       end script
   end if

end mReturn

-- 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 lambda(item i of xs, i, xs)
       end repeat
       return lst
   end tell

end map

-- range :: Int -> Int -> [Int] on range(m, n)

   if n < m then
       set d to -1
   else
       set d to 1
   end if
   set lst to {}
   repeat with i from m to n by d
       set end of lst to i
   end repeat
   return lst

end range </lang>

Output:

{«script», «script», 5, {7, 14, 21, 28, 35, 42, 49, 56, 63, 70}}

C#

This shows how to create syntactically natural currying functions in C#. <lang csharp>public delegate int Plus(int y); public delegate Plus CurriedPlus(int x); public static CurriedPlus plus =

     delegate(int x) {return delegate(int y) {return x + y;};};

static void Main() {

   int sum = plus(3)(4); // sum = 7
   int sum2= plus(2)(plus(3)(4)) // sum2 = 9

}</lang>

C++

Currying may be achieved in C++ using the Standard Template Library function object adapters (binder1st and binder2nd), and more generically using the Boost bind mechanism.

Clojure

<lang clojure>(def plus-a-hundred (partial + 100)) (assert (=

          (plus-a-hundred 1)
          101))

</lang>

Common Lisp

<lang lisp>(defun curry (function &rest args-1)

 (lambda (&rest args-2)
   (apply function (append args-1 args-2))))

</lang>

Usage: <lang lisp> (funcall (curry #'+ 10) 10)

20 </lang>

D

<lang d>void main() {

   import std.stdio, std.functional;

   int add(int a, int b) {
       return a + b;
   }

   alias add2 = curry!(add, 2);
   writeln("Add 2 to 3: ", add(2, 3));
   writeln("Add 2 to 3 (curried): ", add2(3));

}</lang>

Output:

Add 2 to 3: 5
Add 2 to 3 (curried): 5

EchoLisp

EchoLisp has native support for curry, which is implemented thru closures, as shown in CommonLisp . <lang>

curry functional definition

(define (curry proc . left-args) (lambda right-args (apply proc (append left-args right-args))))

right-curry

(define (rcurry proc . right-args) (lambda left-args (apply proc (append left-args right-args))))

(define add42 (curry + 42)) (add42 666) → 708

(map (curry cons 'simon) '( gallubert garfunkel et-merveilles))

  →   ((simon . gallubert) (simon . garfunkel) (simon . et-merveilles))

(map (rcurry cons 'simon) '( gallubert garfunkel et-merveilles))

  →   ((gallubert . simon) (garfunkel . simon) (et-merveilles . simon))

Implementation

result of currying :

(curry * 2 3 (+ 2 2))

   → (λ _#:g1004 (#apply-curry #* (2 3 4)  _#:g1004))

</lang>

Eero

<lang objc>#import <stdio.h>

int main()

 addN := (int n)
   int adder(int x)
     return x + n
   return adder

 add2 := addN(2)

 printf( "Result = %d\n", add2(7) )

 return 0

</lang> Alternative implementation (there are a few ways to express blocks/lambdas): <lang objc>#import <stdio.h>

int main()

 addN := (int n)
   return (int x | return x + n)

 add2 := addN(2)

 printf( "Result = %d\n", add2(7) )

 return 0

</lang>

Eiffel

Eiffel has direct support for lambda expressions and hence currying through "inline agents". If f is a function with two arguments, of signature (X × Y) → Z then its curried version is obtained by simply writing

   g (x: X): FUNCTION [ANY, TUPLE [Y], Z]
       do
           Result := agent (closed_x: X; y: Y): Z 
              do 
                 Result := f (closed_x, y) 
              end (x, ?)
       end

where FUNCTION [ANY, TUPLE [Y], Z] denotes the type Y → Z (agents taking as argument a tuple with a single argument of type Y and returning a result of type Z), which is indeed the type of the agent expression used on the next-to-last line to define the "Result" of g.

Erlang

There are three solutions provided for this problem. The simple version is using anonymous functions as other examples of other languages do. The second solution corresponds to the definition of currying. It takes a function of a arity n and applies a given argument, returning then a function of arity n-1. The solution provided uses metaprogramming facilities to create the new function. Finally, the third solution is a generalization that allows to curry any number of parameters and in a given order.

<lang erlang> -module(currying).

-compile(export_all).

% Function that curry the first or the second argument of a given function of arity 2

curry_first(F,X) ->

   fun(Y) -> F(X,Y) end.

curry_second(F,Y) ->

   fun(X) -> F(X,Y) end.

% Usual curry

curry(Fun,Arg) -> case erlang:fun_info(Fun,arity) of {arity,0} -> erlang:error(badarg); {arity,ArityFun} -> create_ano_fun(ArityFun,Fun,Arg); _ -> erlang:error(badarg) end.

create_ano_fun(Arity,Fun,Arg) -> Pars = [{var,1,list_to_atom(lists:flatten(io_lib:format("X~p", [N])))} || N <- lists:seq(2,Arity)], Ano = {'fun',1, {clauses,[{clause,1,Pars,[], [{call,1,{var,1,'Fun'},[{var,1,'Arg'}] ++ Pars}]}]}}, {_,Result,_} = erl_eval:expr(Ano, [{'Arg',Arg},{'Fun',Fun}]), Result.

% Generalization of the currying

curry_gen(Fun,GivenArgs,PosGivenArgs,PosParArgs) ->

   Pos = PosGivenArgs ++ PosParArgs,
   case erlang:fun_info(Fun,arity) of
       {arity,ArityFun} -> 
           case ((length(GivenArgs) + length(PosParArgs)) == ArityFun) and 
                (length(GivenArgs) == length(PosGivenArgs)) and 
                (length(Pos) == sets:size(sets:from_list(Pos))) of 
               true -> 
                   fun(ParArgs) -> 
                       case length(ParArgs) == length(PosParArgs) of 
                           true -> 
                               Given = lists:zip(PosGivenArgs,GivenArgs),
                               Pars = lists:zip(PosParArgs,ParArgs),
                               {_,Args} = lists:unzip(lists:sort(Given ++ Pars)),
                               erlang:apply(Fun,Args);
                           false -> 
                               erlang:error(badarg)
                       end
                   end;
               false -> 
                   erlang:error(badarg)
           end;
       _ -> 
           erlang:error(badarg)
   end.

</lang>

Output (simple version):

> (currying:curry_first(fun(X,Y) -> X + Y end,3))(2).
5
> (currying:curry_first(fun(X,Y) -> X - Y end,3))(2). 
1
> (currying:curry_second(fun(X,Y) -> X - Y end,3))(2).
-1

Output (usual curry):

> G = fun(A,B,C)-> (A + B) * C end.
#Fun<erl_eval.18.90072148>
> (currying:curry(G,3))(2,1).
5
> (currying:curry(currying:curry(G,3),2))(1).
5
> (currying:curry(currying:curry(currying:curry(G,3),2),1))().
5

Output (generalized version):

> (currying:curry_gen(fun(A,B,C,D) -> (A + B) * (C - D) end,[1.0,0.0],[1,2],[3,4]))([2.0,5.0]).
-3.0
> (currying:curry_gen(fun(A,B,C,D) -> (A + B) * (C - D) end,[1.0,0.0],[4,2],[1,3]))([2.0,5.0]).
8.0
> (currying:curry_gen(fun(A,B,C) -> (A + B) * C end,[1.0,0.0],[3,2],[1]))([5.0]).  
5.0

F#

Translation of: Python

<lang fsharp>let addN n = (+) n</lang>

<lang fsharp>> let add2 = addN 2;;

val add2 : (int -> int)

> add2;; val it : (int -> int) = <fun:addN@1> > add2 7;; val it : int = 9</lang>

Forth

Translation of: Common Lisp

<lang forth>: curry ( x xt1 -- xt2 )

 swap 2>r :noname r> postpone literal r> compile, postpone ; ;

5 ' + curry constant +5 5 +5 execute . 7 +5 execute .</lang>

Output:

10 12

Go

Go has had function literals and method expressions since before Go 1.0. Method values were added in Go 1.1. <lang go>package main

import (

       "fmt"
       "math"

)

func PowN(b float64) func(float64) float64 {

       return func(e float64) float64 { return math.Pow(b, e) }

}

func PowE(e float64) func(float64) float64 {

       return func(b float64) float64 { return math.Pow(b, e) }

}

type Foo int

func (f Foo) Method(b int) int {

       return int(f) + b

}

func main() {

       pow2 := PowN(2)
       cube := PowE(3)

       fmt.Println("2^8 =", pow2(8))
       fmt.Println("4³ =", cube(4))

       var a Foo = 2
       fn1 := a.Method   // A "method value", like currying 'a'
       fn2 := Foo.Method // A "method expression", like uncurrying

       fmt.Println("2 + 2 =", a.Method(2)) // regular method call
       fmt.Println("2 + 3 =", fn1(3))
       fmt.Println("2 + 4 =", fn2(a, 4))
       fmt.Println("3 + 5 =", fn2(Foo(3), 5))

}</lang> Run on the Go Playground.

Groovy

curry()

This method can be applied to any Groovy closure or method reference (demonstrated here with closures). The arguments given to the curry() method are applied to the original (invoking) method/closure. The "curry()" method returns a closure as it's result. The arguments on the "curry()" method are passed, in their specified order, as the first (left-most) arguments of the original method/closure. The remaining, as yet unspecified arguments of the original method/closure, form the argument list of the resulting closure.

Example: <lang groovy>def divide = { Number x, Number y ->

 x / y

}

def partsOf120 = divide.curry(120)

println "120: half: ${partsOf120(2)}, third: ${partsOf120(3)}, quarter: ${partsOf120(4)}"</lang>

Results:

120: half: 60, third: 40, quarter: 30

rcurry()

This method can be applied to any Groovy closure or method reference. The arguments given to the rcurry() method are applied to the original (invoking) method/closure. The "rcurry()" method returns a closure as it's result. The arguments on the "rcurry()" method are passed, in their specified order, as the last (right-most) arguments of the original method/closure. The remaining, as yet unspecified arguments of the original method/closure, form the argument list of the resulting closure.

Example (using the same "divide()" closure as before): <lang groovy>def half = divide.rcurry(2) def third = divide.rcurry(3) def quarter = divide.rcurry(4)

println "30: half: ${half(30)}; third: ${third(30)}, quarter: ${quarter(30)}"</lang>

Results:

30: half: 15; third: 10, quarter: 7.5

History

I invite any expert on the history of the Groovy language to correct this if necessary. Groovy is a relatively recent language, with alphas and betas first appearing on the scene in 2003 and a 1.0 release in 2007. To the best of my understanding currying has been a part of the language from the outset.

Haskell

Likewise in Haskell, function type signatures show the currying-based structure of functions (note: "<lang haskell>\ -></lang>" is Haskell's syntax for anonymous functions, in which the sign <lang haskell>\</lang> has been chosen for its resemblance to the Greek letter λ (lambda); it is followed by a list of space-separated arguments, and the arrow <lang haskell>-></lang> separates the arguments list from the function body)

   Prelude> let plus = \x y -> x + y
   Prelude> :type plus
   plus :: Integer -> Integer -> Integer
   Prelude> plus 3 5
   8

and currying functions is trivial

   Prelude> let plus5 = plus 5
   Prelude> :type plus5
   plus5 :: Integer -> Integer
   Prelude> plus5 3
   8

In fact, the Haskell definition <lang haskell>\x y -> x + y</lang> is merely syntactic sugar for <lang haskell>\x -> \y -> x + y</lang>, which has exactly the same type signature:

   Prelude> let nested_plus = \x -> \y -> x + y
   Prelude> :type nested_plus
   nested_plus :: Integer -> Integer -> Integer

Icon and Unicon

This version only works in Unicon because of the coexpression calling syntax used.

<lang unicon>procedure main(A)

   add2 := addN(2)
   write("add2(7) = ",add2(7))
   write("add2(1) = ",add2(1))

end

procedure addN(n)

   return makeProc{ repeat { (x := (x@&source)[1], x +:= n) } }

end

procedure makeProc(A)

   return (@A[1], A[1])

end</lang>

Output:

->curry
add2(7) = 9
add2(1) = 3
->

Io

A general currying function written in the Io programming language: <lang io>curry := method(fn, a := call evalArgs slice(1) block( b := a clone appendSeq(call evalArgs) performWithArgList("fn", b) ) )

// example: increment := curry( method(a,b,a+b), 1 ) increment call(5) // result => 6</lang>

J

Solution:Use & (bond). This primitive conjunction accepts two arguments: a function (verb) and an object (noun) and binds the object to the function, deriving a new function. Example:<lang j> threePlus=: 3&+

  threePlus 7

10

  halve =: %&2  NB.  % means divide 
  halve 20

10

  someParabola =: _2 3 1 &p. NB. x^2 + 3x - 2</lang>

Note: The final example (someParabola) shows the single currying primitive (&) combined with J's array oriented nature, permits partial application of a function of any number of arguments.

Java

<lang java5> public class Currier<ARG1, ARG2, RET> {

       public interface CurriableFunctor<ARG1, ARG2, RET> {
           RET evaluate(ARG1 arg1, ARG2 arg2);
       }
   
       public interface CurriedFunctor<ARG2, RET> {
           RET evaluate(ARG2 arg);
       }
   
       final CurriableFunctor<ARG1, ARG2, RET> functor;
   
       public Currier(CurriableFunctor<ARG1, ARG2, RET> fn) { functor = fn; }
       
       public CurriedFunctor<ARG2, RET> curry(final ARG1 arg1) {
           return new CurriedFunctor<ARG2, RET>() {
               public RET evaluate(ARG2 arg2) {
                   return functor.evaluate(arg1, arg2);
               }
           };
       }
   
       public static void main(String[] args) {
           Currier.CurriableFunctor<Integer, Integer, Integer> add
               = new Currier.CurriableFunctor<Integer, Integer, Integer>() {
                   public Integer evaluate(Integer arg1, Integer arg2) {
                       return new Integer(arg1.intValue() + arg2.intValue());
                   }
           };
           
           Currier<Integer, Integer, Integer> currier
               = new Currier<Integer, Integer, Integer>(add);
           
           Currier.CurriedFunctor<Integer, Integer> add5
               = currier.curry(new Integer(5));
           
           System.out.println(add5.evaluate(new Integer(2)));
       }
   }</lang>

JavaScript

ES5

Partial application

<lang javascript> function addN(n) {

   var curry = function(x) {
       return x + n;
   };
   return curry;
}

add2 = addN(2);
alert(add2);
alert(add2(7));</lang>

Generic currying

Basic case - returning a curried version of a function of two arguments

<lang JavaScript>(function () {

   // curry :: ((a, b) -> c) -> a -> b -> c
   function curry(f) {
       return function (a) {
           return function (b) {
               return f(a, b);
           };
       };
   }

   // TESTS

   // product :: Num -> Num -> Num
   function product(a, b) {
       return a * b;
   }

   // return typeof curry(product);
   // --> function

   // return typeof curry(product)(7)
   // --> function

   //return typeof curry(product)(7)(9)
   // --> number

   return [1, 2, 3, 4, 5, 6, 7, 8, 9, 10]
       .map(curry(product)(7))

   // [7, 14, 21, 28, 35, 42, 49, 56, 63, 70]

})(); </lang>

Output:

<lang JavaScript>[7, 14, 21, 28, 35, 42, 49, 56, 63, 70]</lang>

Functions of arbitrary arity can also be curried:

<lang JavaScript>(function () {

   // (arbitrary arity to fully curried)
   // extraCurry :: Function -> Function
   function extraCurry(f) {

       // Recursive currying
       function _curry(xs) {
           return xs.length >= f.length ? (
               f.apply(null, xs)
           ) : function () {
               return _curry(xs.concat([].slice.apply(arguments)));
           };
       }

       return _curry([].slice.call(arguments, 1));
   }

   // TEST

   // product3:: Num -> Num -> Num -> Num
   function product3(a, b, c) {
       return a * b * c;
   }

   return [1, 2, 3, 4, 5, 6, 7, 8, 9, 10]
       .map(extraCurry(product3)(7)(2))

   // [14, 28, 42, 56, 70, 84, 98, 112, 126, 140]

})();</lang>

Output:

<lang JavaScript>[14, 28, 42, 56, 70, 84, 98, 112, 126, 140]</lang>

Y combinator

Using a definition of currying that does not imply partial application, only conversion of a function of multiple arguments, e.g.: <lang javascript>(a,b) => expr_using_a_and_b</lang>into a function that takes a series of as many function applications as that function took arguments, e.g.:<lang javascript>a => b => expr_using_a_and_b</lang>

One version for functions of a set amount of arguments that takes no rest arguments, and one version for functions with rest argument. The caveat being that if the rest argument would be empty, it still requires a separate application, and multiple rest arguments cannot be curried into multiple applications, since we have to figure out the number of applications from the function signature, not the amount of arguments the user might want to send it. <lang javascript>let

 fix = // This is a variant of the Applicative order Y combinator
   f => (f => f(f))(g => f((...a) => g(g)(...a))),
 curry =
   f => (
     fix(
       z => (n,...a) => (
         n>0
         ?b => z(n-1,...a,b)
         :f(...a)))
     (f.length)),
 curryrest =
   f => (
     fix(
       z => (n,...a) => (
         n>0
         ?b => z(n-1,...a,b)
         :(...b) => f(...a,...b)))
     (f.length)),
 curriedmax=curry(Math.max),
 curryrestedmax=curryrest(Math.max);

print(curriedmax(8)(4),curryrestedmax(8)(4)(),curryrestedmax(8)(4)(9,7,2)); // 8,8,9 </lang> Neither of these handle propagation of the this value for methods, as ECMAScript 2015 (ES6) fat arrow syntax doesn't allow for this value propagation. Versions could easily be written for those cases using an outer regular function expression and use of Function.prototype.call or Function.prototype.apply. Use of Y combinator could also be removed through use of an inner named function expression instead of the anonymous fat arrow function syntax.

Simple 2 and N argument versions

In the most rudimentary form, for example for mapping two-argument functions over an array:

<lang JavaScript>(() => {

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

   // TEST

   // product :: Num -> Num -> Num
   let product = (a, b) => a * b,

       // Int -> Int -> Maybe Int -> [Int]
       range = (m, n, step) => {
           let d = (step || 1) * (n >= m ? 1 : -1);

           return Array.from({
               length: Math.floor((n - m) / d) + 1
           }, (_, i) => m + (i * d));
       }

   return range(1, 10)
       .map(curry(product)(7))

   // [7, 14, 21, 28, 35, 42, 49, 56, 63, 70]

})();</lang>

Output:

<lang JavaScript>[7, 14, 21, 28, 35, 42, 49, 56, 63, 70]</lang>

Or, recursively currying functions of arbitrary arity:

<lang JavaScript>( () => {

   // (arbitrary arity to fully curried)
   // extraCurry :: Function -> Function
   let extraCurry =  (f, ...args) => {

       // Recursive currying
       let _curry = (xs, ...arguments) => {
           return xs.length >= f.length ? (
               f.apply(null, xs)
           ) : function () {
               return _curry(xs.concat([].slice.apply(arguments)));
           };
       };

       return _curry([].slice.call(args, 1));
   };

   // TEST

   // product3:: Num -> Num -> Num -> Num
   let product3 = (a, b, c) => a * b * c;

   return [1, 2, 3, 4, 5, 6, 7, 8, 9, 10]
       .map(extraCurry(product3)(7)(2))

   // [14, 28, 42, 56, 70, 84, 98, 112, 126, 140]

})();</lang>

Output:

<lang JavaScript>[14, 28, 42, 56, 70, 84, 98, 112, 126, 140]</lang>

jq

In jq, functions are filters. Accordingly, we illustrate currying by defining plus(x) to be a filter that adds x to its input, and then define plus5 as plus(5): <lang jq> def plus(x): . + x;

def plus5: plus(5); </lang>

We can now use plus5 as a filter, e.g.<lang jq>3 | plus5</lang> produces 8.

LFE

<lang lisp>(defun curry (f arg)

 (lambda (x)
   (apply f
     (list arg x))))

</lang> Usage: <lang lisp> (funcall (curry #'+/2 10) 10) </lang>

Logtalk

<lang logtalk> | ?- logtalk << call([Z]>>(call([X,Y]>>(Y is X*X), 5, R), Z is R*R), T). T = 625 yes </lang>

Logtalk support for lambda expressions and currying was introduced in version 2.38.0, released in December 2009.

Lua

<lang lua> function curry2(f)

  return function(x)
     return function(y)
        return f(x,y)
     end
  end

end

function add(x,y)

  return x+y

end

local adder = curry2(add) assert(adder(3)(4) == 3+4) local add2 = adder(2) assert(add2(3) == 2+3) assert(add2(5) == 2+5) </lang>

Mathematica / Wolfram Language

Currying can be implemented by nesting the Function function. The following method curries the Plus function.

   In[1]:=   plusFC = Function[{x},Function[{y},Plus[x,y]]];

A higher currying function can be implemented straightforwardly.

   In[2]:=   curry = Function[{x}, Function[{y}, Function[{z}, x[y, z]]]];

Output:

    In[3]:=   Plus[2,3]
    Out[3]:=  5

    In[4]:=   plusFC[2][3]
    Out[4]:=  5

    In[5]:=   curry[Plus][2][3]
    Out[5]:=  5

Nemerle

Currying isn't built in to Nemerle, but is relatively straightforward to define. <lang Nemerle>using System; using System.Console;

module Curry {

   Curry[T, U, R](f : T * U -> R) : T -> U -> R
   {
       fun (x) { fun (y) { f(x, y) } }
   }

   Main() : void
   {
       def f(x, y) { x + y }

def g = Curry(f); def h = Curry(f)(12); // partial application WriteLine($"$(Curry(f)(20)(22))"); WriteLine($"$(g(21)(21))"); WriteLine($"$(h(30))")

   }

}</lang>

Nim

<lang nim>proc addN[T](n: T): auto = (proc(x: T): T = x + n)

let add2 = addN(2) echo add2(7)</lang> Alternative syntax: <lang nim>import future

proc addM[T](n: T): auto = (x: T) => x + n

let add3 = addM(3) echo add3(7)</lang>

OCaml

OCaml has a built-in natural method of defining functions that are curried: <lang ocaml>let addnums x y = x+y (* declare a curried function *)

let add1 = addnums 1 (* bind the first argument to get another function *) add1 42 (* apply to actually compute a result, 43 *)</lang> The type of addnums above will be int -> int -> int.

Note that fun addnums x y = ..., or, equivalently, let addnums = fun x y -> ..., is really just syntactic sugar for let addnums = function x -> function y -> ....

You can also define a general currying higher-ordered function: <lang ocaml>let curry f x y = f (x,y) (* Type signature: ('a * 'b -> 'c) -> 'a -> 'b -> 'c *)</lang> This is a function that takes a function as a parameter and returns a function that takes one of the parameters and returns another function that takes the other parameter and returns the result of applying the parameter function to the pair of arguments.

Oforth

<lang Oforth>2 #+ curry => 2+ 5 2+ . 7 ok</lang>

PARI/GP

Simple currying example with closures. <lang parigp>curriedPlus(x)=y->x+y; curriedPlus(1)(2)</lang>

Output:

3

Perl

This is a Perl 5 example of a general curry function and curried plus using closures: <lang perl>sub curry{

 my ($func, @args) = @_;

 sub {
   #This @_ is later
   &$func(@args, @_);
 }

}

sub plusXY{

 $_[0] + $_[1];

}

my $plusXOne = curry(\&plusXY, 1); print &$plusXOne(3), "\n";</lang>

Perl 6

All callable objects have an "assuming" method that can do partial application of either positional or named arguments. Here we curry the built-in subtraction operator. <lang perl6>my &negative = &infix:<->.assuming(0); say negative 1;</lang>

Output:

-1

PicoLisp

: (de multiplier (@X)
   (curry (@X) (N) (* @X N)) )
-> multiplier
: (multiplier 7)
-> ((N) (* 7 N))
: ((multiplier 7) 3)
-> 21

PowerShell

<lang PowerShell> function Add($x) { return { param($y) return $y + $x }.GetNewClosure() } </lang> <lang PowerShell> & (Add 1) 2 </lang>

Output:

3

Add each number in list to its square root: <lang PowerShell> (4,9,16,25 | ForEach-Object { & (add $_) ([Math]::Sqrt($_)) }) -join ", " </lang>

Output:

6, 12, 20, 30

Prolog

Works with SWI-Prolog and module lambda.pl
Module lambda.pl can be found at http://www.complang.tuwien.ac.at/ulrich/Prolog-inedit/lambda.pl .

 ?- [library('lambda.pl')].
% library(lambda.pl) compiled into lambda 0,00 sec, 28 clauses
true.

 ?- N = 5, F = \X^Y^(Y is X+N), maplist(F, [1,2,3], L).
N = 5,
F = \X^Y^ (Y is X+5),
L = [6,7,8].

Python

<lang python> def addN(n):

    def adder(x):
        return x + n
    return adder</lang>

<lang python> >>> add2 = addN(2)

>>> add2
<function adder at 0x009F1E30>
>>> add2(7)
9</lang>

Racket

The simplest way to make a curried functions is to use curry:

<lang racket>

1. lang racket

(((curry +) 3) 2) ; =>5 </lang>

As an alternative, one can use the following syntax: <lang racket>

1. lang racket

(define ((curried+ a) b)

 (+ a b))

((curried+ 3) 2)  ; => 5 </lang>

REXX

This example is modeled after the   D   example.

specific version

<lang ress>/*REXX program demonstrates a REXX currying method to perform addition. */ say 'add 2 to 3: ' add(2 ,3) say 'add 2 to 3 (curried):' add2(3) exit /*stick a fork in it, we're done.*/ /*──────────────────────────────────subroutines─────────────────────────*/ add: procedure; $=arg(1); do j=2 to arg(); $=$+arg(j); end; return $ add2: procedure; return add(arg(1), 2)</lang>

Output:

add 2 to 3:           5
add 2 to 3 (curried): 5

generic version

<lang rexx>/*REXX program demonstrates a REXX currying method to perform addition. */ say 'add 2 to 3: ' add(2 ,3) say 'add 2 to 3 (curried):' add2(3) exit /*stick a fork in it, we're done.*/ /*──────────────────────────────────ADD subroutine──────────────────────*/ add: procedure; $=0; do j=1 for arg()

                           do k=1  for words(arg(j));  $=$+word(arg(j),k)
                           end   /*k*/
                        end      /*j*/

return $ /*──────────────────────────────────ADD2 subroutine─────────────────────*/ add2: procedure; return add(arg(1), 2)</lang> output is the same as the 1^st version.

Ruby

The curry method was added in Ruby 1.9.1. It takes an optional arity argument, which determines the number of arguments to be passed to the proc. If that number is not reached, the curry method returns a new curried method for the rest of the arguments. (Examples taken from the documentation). <lang ruby> b = proc {|x, y, z| (x||0) + (y||0) + (z||0) } p b.curry[1][2][3] #=> 6 p b.curry[1, 2][3, 4] #=> 6 p b.curry(5)[1][2][3][4][5] #=> 6 p b.curry(5)[1, 2][3, 4][5] #=> 6 p b.curry(1)[1] #=> 1

b = proc {|x, y, z, *w| (x||0) + (y||0) + (z||0) + w.inject(0, &:+) } p b.curry[1][2][3] #=> 6 p b.curry[1, 2][3, 4] #=> 10 p b.curry(5)[1][2][3][4][5] #=> 15 p b.curry(5)[1, 2][3, 4][5] #=> 15 p b.curry(1)[1] #=> 1 </lang>

Rust

This is a simple currying function written in Rust: <lang rust>#![feature(box_syntax)] fn add_n(n : i32) -> Box<Fn(i32) -> i32 + 'static> {

   box move |&: x| n + x

}

fn main() {

   let adder = add_n(40);
   println!("The answer to life is {}.", adder(2));

}</lang>

Note that once "unboxed, abstract return types" are supported it can be done without the heap allocation/trait object indirection.

Scala

<lang Scala> def add(a: Int)(b: Int) = a + b val add5 = add(5) _ add5(2) </lang>

Sidef

This can be done by using lazy methods: <lang ruby>var adder = 1.method(:add); say adder(3); #=> 4</lang>

Or by using a generic curry function: <lang ruby>func curry(f, *args1) {

   func (*args2) {
       f(args1..., args2...);
   }

}

func add(a, b) {

   a + b

}

var adder = curry(add, 1); say adder(3); #=>4</lang>

Swift

You can return a closure (or nested function): <lang Swift>func addN(n:Int)->Int->Int { return {$0 + n} }

var add2 = addN(2) println(add2) // (Function) println(add2(7)) // 9</lang>

Prior to Swift 3, there was a curried function definition syntax: <lang Swift>func addN(n:Int)(x:Int) -> Int { return x + n }

var add2 = addN(2) println(add2) // (Function) println(add2(x:7)) // 9</lang> However, there was a bug in the above syntax which forces the second parameter to always be labeled. As of Swift 1.2, you could explicitly make the second parameter not labeled: <lang Swift>func addN(n:Int)(_ x:Int) -> Int { return x + n }

var add2 = addN(2) println(add2) // (Function) println(add2(7)) // 9</lang>

Standard ML

Standard ML has a built-in natural method of defining functions that are curried: <lang sml>fun addnums (x:int) y = x+y (* declare a curried function *)

val add1 = addnums 1 (* bind the first argument to get another function *) add1 42 (* apply to actually compute a result, 43 *)</lang> The type of addnums above will be int -> int -> int (the type constraint in the declaration only being necessary because of the polymorphic nature of the + operator).

Note that fun addnums x y = ... is really just syntactic sugar for val addnums = fn x => fn y => ....

You can also define a general currying higher-ordered function: <lang sml>fun curry f x y = f(x,y) (* Type signature: ('a * 'b -> 'c) -> 'a -> 'b -> 'c *)</lang> This is a function that takes a function as a parameter and returns a function that takes one of the parameters and returns another function that takes the other parameter and returns the result of applying the parameter function to the pair of arguments.

Tcl

The simplest way to do currying in Tcl is via an interpreter alias: <lang tcl>interp alias {} addone {} ::tcl::mathop::+ 1 puts [addone 6]; # => 7</lang> Tcl doesn't support automatic creation of curried functions though; the general variadic nature of a large proportion of Tcl commands makes that impractical.

History

The type of aliases used here are a simple restriction of general inter-interpreter aliases to the case where both the source and target interpreter are the current one; these aliases are a key component of the secure interpreter mechanism introduced in Tcl 7.6, and are the mechanism used to allow access to otherwise-insecure behavior from a secure context (e.g., to write to a particular file, but not any old file).

TXR

TXR Lisp has an operator called op for currying. Of course, currying is done with lambdas under the hood; the operator generates lambdas. Its name is inspired by the same-named operators featured in the Goo language, and in the Common Lisp library cl-op.

References: Goo op: [1] cl-op: [2]

TXR's op is quite different in that it uses numbered arguments, has some additional features, and is accompanied by a "zoo" of related operators which share its currying syntax, providing various useful derived behaviors.

A two-argument function which subtracts is arguments from 10, and then subtracts five:

<lang txrlisp>(op - 10 @1 @2 5)</lang>

Wortel

The \ operator takes a function and an argument and partial applies the argument to the function. The &\ works like the \ operator but can also take an array literal and partial applies all the arguments in the array. <lang wortel>@let {

 addOne \+ 1
 subtractFrom1 \- 1
 subtract1 \~- 1
 
 subtract1_2 &\- [. 1]

 add ^+
 ; partial apply to named functions
 addOne_2 \add 1

 ; testing
 [[
   !addOne 5 ; returns 6
   !subtractFrom1 5 ; returns -4
   !subtract1 5 ; returns 4
   !subtract1_2 5 ; returns 4
   !addOne_2 5 ; returns 6
 ]]

}</lang>

zkl

zkl doesn't support currying per se (recompilation of f with fixed input to create a new function), it does support partial application, for all objects, for any [number of] positional parameters to create an object of reduced arity. <lang zkl>addOne:= Op("+").fp(1); addOne(5) //-->6 minusOne:=Op("-").fp1(1); minusOne(5) //-->4, note that this fixed 1 as the second parameter

  // fix first and third parameters:

foo:=String.fpM("101","<foo>","</foo>"); foo("zkl"); //-->"<foo>zkl</foo>" fcn g(x){x+1} f:=fcn(f,x){f(x)+x}.fp(g); f(5); //-->11 f:=fcn(f,x){f(x)+x}.fp(fcn(x){x+1}); // above with lambdas all the way down</lang>