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)

Task

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

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

11l

Translation of: Python

F addN(n)
   F adder(x)
      R x + @=n
   R adder

V add2 = addN(2)
V add3 = addN(3)
print(add2(7))
print(add3(7))

Output:

9
10

Ada

Ada lacks explicit support for currying, or indeed just about any form of functional programming at all. However if one views generic subprograms as approximately equivalent to higher order functions, and generic packages as approximately equivalent to closures, then the desired functionality can still be achieved. The chief limitation is that separate generic support packages must exist for each arity that is to be curried.

Support package spec:

generic
    type Argument_1 (<>) is limited private;
    type Argument_2 (<>) is limited private;
    type Argument_3 (<>) is limited private;
    type Return_Value (<>) is limited private;

    with function Func
           (A : in Argument_1;
            B : in Argument_2;
            C : in Argument_3)
        return Return_Value;
package Curry_3 is

    generic
        First : in Argument_1;
    package Apply_1 is

        generic
            Second : in Argument_2;
        package Apply_2 is

            function Apply_3
                   (Third : in Argument_3)
                return Return_Value;

        end Apply_2;

    end Apply_1;

end Curry_3;

Support package body:

package body Curry_3 is

    package body Apply_1 is

        package body Apply_2 is

            function Apply_3
                   (Third : in Argument_3)
                return Return_Value is
            begin
                return Func (First, Second, Third);
            end Apply_3;

        end Apply_2;

    end Apply_1;

end Curry_3;

Currying a function:

with Curry_3, Ada.Text_IO;

procedure Curry_Test is

    function Sum
           (X, Y, Z : in Integer)
        return Integer is
    begin
        return X + Y + Z;
    end Sum;

    package Curried is new Curry_3
       (Argument_1   => Integer,
        Argument_2   => Integer,
        Argument_3   => Integer,
        Return_Value => Integer,
        Func         => Sum);

    package Sum_5 is new Curried.Apply_1 (5);
    package Sum_5_7 is new Sum_5.Apply_2 (7);
    Result : Integer := Sum_5_7.Apply_3 (3);

begin

    Ada.Text_IO.Put_Line ("Five plus seven plus three is" & Integer'Image (Result));

end Curry_Test;

Output:

Five plus seven plus three is 15

Aime

Curry a function printing an integer, on a given number of characters, with commas inserted every given number of digits, with a given number of digits, in a given base:

ri(list l)
{
    l[0] = apply.apply(l[0]);
}
curry(object o)
{
    (o.__count - 1).times(ri, list(o));
}
main(void)
{
    o_wbfxinteger.curry()(16)(3)(12)(16)(1 << 30);
    0;
}

Output:

 000,040,000,000

ALGOL 68

In 1968 C.H. Lindsey proposed for partial parametrisation for ALGOL 68, this is implemented as an extension in wp:ALGOL 68G.

# 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, );

# 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)))

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.

-- 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


-- 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 |λ|(2)

--> «script»


-- Test 3.
curry(add)'s |λ|(2)'s |λ|(3)

--> 5


-- Test 4. 
map(curry(product)'s |λ|(7), enumFromTo(1, 10))

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


-- Combined:
{curry(add), ¬
    curry(add)'s |λ|(2), ¬
    curry(add)'s |λ|(2)'s |λ|(3), ¬
    map(curry(product)'s |λ|(7), enumFromTo(1, 10))}

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


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

-- enumFromTo :: Int -> Int -> [Int]
on enumFromTo(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 enumFromTo

-- 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

Output:

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

Arturo

addN: function [n][
    return function [x] with 'n [
        return x + n
    ]
]

add2: addN 2
add3: addN 3

do [
    print add2 7
    print add3 7
]

Output:

9
10

BASIC

FreeBASIC

FreeBASIC is not a functional language and does not support either currying or nested functions/lambdas which are typically used by otherwise imperative languages to implement the former. The nearest I could get to currying using the features which the language does support is the following:

' FB 1.05.0 Win64

Type CurriedAdd
  As Integer i 
  Declare Function add(As Integer) As Integer
End Type

Function CurriedAdd.add(j As Integer) As Integer
  Return i + j
End Function

Function add (i As Integer) as CurriedAdd
   Return Type<CurriedAdd>(i)
End Function

Print "3 + 4 ="; add(3).add(4)
Print "2 + 6 ="; add(2).add(6)
Sleep

Output:

3 + 4 = 7
2 + 6 = 8

Visual Basic .NET

Compiler: Roslyn Visual Basic (language version >=15.3)

Functions are not curried in VB.NET, so this entry details functions that take a function and return functions that act as if the original function were curried (i.e. each takes one parameter and returns another function that takes one parameter, with the function for which all parameters of the original function are supplied calling the original function with those arguments.

Fixed-arity approach

Uses generics and lambdas returning lambdas.

Option Explicit On
Option Infer On
Option Strict On

Module Currying
    ' The trivial curry.
    Function Curry(Of T1, TResult)(func As Func(Of T1, TResult)) As Func(Of T1, TResult)
        ' At least satisfy the implicit contract that the result isn't reference-equal to the original function.
        Return Function(a) func(a)
    End Function

    Function Curry(Of T1, T2, TResult)(func As Func(Of T1, T2, TResult)) As Func(Of T1, Func(Of T2, TResult))
        Return Function(a) Function(b) func(a, b)
    End Function

    Function Curry(Of T1, T2, T3, TResult)(func As Func(Of T1, T2, T3, TResult)) As Func(Of T1, Func(Of T2, Func(Of T3, TResult)))
        Return Function(a) Function(b) Function(c) func(a, b, c)
    End Function

    ' And so on.
End Module

Test code:

Module Main
    ' An example binary function.
    Function Add(a As Integer, b As Integer) As Integer
        Return a + b
    End Function

    Sub Main()
        Dim curriedAdd = Curry(Of Integer, Integer, Integer)(AddressOf Add)
        Dim add2To = curriedAdd(2)

        Console.WriteLine(Add(2, 3))
        Console.WriteLine(add2To(3))
        Console.WriteLine(curriedAdd(2)(3))

        ' An example ternary function.
        Dim substring = Function(s As String, startIndex As Integer, length As Integer) s.Substring(startIndex, length)
        Dim curriedSubstring = Curry(substring)

        Console.WriteLine(substring("abcdefg", 2, 3))
        Console.WriteLine(curriedSubstring("abcdefg")(2)(3))

        ' The above is just syntax sugar for this (a call to the Invoke() method of System.Delegate):
        Console.WriteLine(curriedSubstring.Invoke("abcdefg").Invoke(2).Invoke(3))

        Dim substringStartingAt1 = curriedSubstring("abcdefg")(1)
        Console.WriteLine(substringStartingAt1(2))
        Console.WriteLine(substringStartingAt1(4))
    End Sub
End Module

Late-binding approach

Library: .NET Core version >=1.0

or both

Library: .NET Framework version >=4.5

and

Library: System.Collections.Immutable version 1.5.0

Due to VB's syntax, with indexers using parentheses, late-bound invocation expressions are compiled as invocations of the default property of the receiver. Thus, it is not possible to perform a late-bound delegate invocation. This limitation can, however, be circumvented, by declaring a type that wraps a delegate and defines a default property that invokes the delegate. Furthermore, by making this type what is essentially a discriminated union of a delegate and a result and guaranteeing that all invocations return another instance of this type, it is possible for the entire system to work with Option Strict on.

Option Explicit On
Option Infer On
Option Strict On

Module CurryingDynamic
    ' Cheat visual basic's syntax by defining a type that can be the receiver of what appears to be a method call.
    ' Needless to say, this is not idiomatic VB.
    Class CurryDelegate
        ReadOnly Property Value As Object
        ReadOnly Property Target As [Delegate]

        Sub New(value As Object)
            Dim curry = TryCast(value, CurryDelegate)
            If curry IsNot Nothing Then
                Me.Value = curry.Value
                Me.Target = curry.Target
            ElseIf TypeOf value Is [Delegate] Then
                Me.Target = DirectCast(value, [Delegate])
            Else
                Me.Value = value
            End If
        End Sub

        ' CurryDelegate could also work as a dynamic n-ary function delegate, if an additional ParamArray argument were to be added.
        Default ReadOnly Property Invoke(arg As Object) As CurryDelegate
            Get
                If Me.Target Is Nothing Then Throw New InvalidOperationException("All curried parameters have already been supplied")

                Return New CurryDelegate(Me.Target.DynamicInvoke({arg}))
            End Get
        End Property

        ' A syntactically natural way to assert that the currying is complete and that the result is of the specified type.
        Function Unwrap(Of T)() As T
            If Me.Target IsNot Nothing Then Throw New InvalidOperationException("Some curried parameters have not yet been supplied.")
            Return DirectCast(Me.Value, T)
        End Function
    End Class

    Function DynamicCurry(func As [Delegate]) As CurryDelegate
        Return DynamicCurry(func, ImmutableList(Of Object).Empty)
    End Function

    ' Use ImmutableList to create a new list every time any curried subfunction is called avoiding multiple or repeated
    ' calls interfering with each other.
    Private Function DynamicCurry(func As [Delegate], collectedArgs As ImmutableList(Of Object)) As CurryDelegate
        Return If(collectedArgs.Count = func.Method.GetParameters().Length,
            New CurryDelegate(func.DynamicInvoke(collectedArgs.ToArray())),
            New CurryDelegate(Function(arg As Object) DynamicCurry(func, collectedArgs.Add(arg))))
    End Function
End Module

Test code:

Module Program
    Function Add(a As Integer, b As Integer) As Integer
        Return a + b
    End Function

    Sub Main()
        ' A delegate for the function must be created in order to eagerly perform overload resolution.
        Dim curriedAdd = DynamicCurry(New Func(Of Integer, Integer, Integer)(AddressOf Add))
        Dim add2To = curriedAdd(2)

        Console.WriteLine(add2To(3).Unwrap(Of Integer))
        Console.WriteLine(curriedAdd(2)(3).Unwrap(Of Integer))

        Dim substring = Function(s As String, i1 As Integer, i2 As Integer) s.Substring(i1, i2)
        Dim curriedSubstring = DynamicCurry(substring)

        Console.WriteLine(substring("abcdefg", 2, 3))
        Console.WriteLine(curriedSubstring("abcdefg")(2)(3).Unwrap(Of String))

        ' The trickery of using a parameterized default property also makes it appear that the "delegate" has an Invoke() method.
        Console.WriteLine(curriedSubstring.Invoke("abcdefg").Invoke(2).Invoke(3).Unwrap(Of String))

        Dim substringStartingAt1 = curriedSubstring("abcdefg")(1)
        Console.WriteLine(substringStartingAt1(2).Unwrap(Of String))
        Console.WriteLine(substringStartingAt1(4).Unwrap(Of String))
    End Sub
End Module

Output (for both versions):

5
5
5
cde
cde
cde
bc
bcde

Binary Lambda Calculus

In BLC, all multi argument functions are necessarily achieved by currying, since lambda calculus functions (lambdas) are single argument. A good example is the Church numeral 2, which given a function f and an argument x, applies f twice on x: C2 = \f. (\x. f (f x)). This is written in BLC as

00 00 01 110 01 110 01

where 00 denotes lambda, 01 denotes application, and 1^n0 denotes the variable bound by the n'th enclosing lambda. Which is all there is to BCL!

BQN

All BQN functions can only take 2 arguments, signified by 𝕨 and 𝕩 in block definitions. Hence, currying is largely done with the help of combinators like Before(⊸) and After(⟜).

Adapted from J.

Plus3 ← 3⊸+
Plus3_1 ← +⟜3

•Show Plus3 1
•Show Plus3_1 1

4
4

C

#include<stdarg.h>
#include<stdio.h>

long int factorial(int n){
	if(n>1)
		return n*factorial(n-1);
	return 1;
}

long int sumOfFactorials(int num,...){
	va_list vaList;
	long int sum = 0;
	
	va_start(vaList,num);
	
	while(num--)
		sum += factorial(va_arg(vaList,int));
	
	va_end(vaList);
	
	return sum;
}

int main()
{
	printf("\nSum of factorials of [1,5] : %ld",sumOfFactorials(5,1,2,3,4,5));
	printf("\nSum of factorials of [3,5] : %ld",sumOfFactorials(3,3,4,5));
	printf("\nSum of factorials of [1,3] : %ld",sumOfFactorials(3,1,2,3));
	
	return 0;
}

Output:

C:\rosettaCode>curry.exe

Sum of factorials of [1,5] : 153
Sum of factorials of [3,5] : 150
Sum of factorials of [1,3] : 9

C#

This shows how to create syntactically natural currying functions in C#.

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
}

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.

Ceylon

Translation of: Groovy

shared void run() {
    
    function divide(Integer x, Integer y) => x / y;
    
    value partsOf120 = curry(divide)(120);
    
    print("half of 120 is ``partsOf120(2)``
           a third is ``partsOf120(3)``
           and a quarter is ``partsOf120(4)``");
}

Clojure

(def plus-a-hundred (partial + 100))
(assert (= 
           (plus-a-hundred 1)
           101))

Common Lisp

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

Usage:

(funcall (curry #'+ 10) 10)

20

Crystal

Crystal allows currying procs with either Proc#partial or by manually creating closures:

add_things = ->(x1 : Int32, x2 : Int32, x3 : Int32) { x1 + x2 + x3 }
add_curried = add_things.partial(2, 3)
add_curried.call(4)  #=> 9

def add_two_things(x1)
  return ->(x2 : Int32) {
    ->(x3 : Int32) { x1 + x2 + x3 }
  }
end
add13 = add_two_things(3).call(10)
add13.call(5)  #=> 18

D

void main() {
    import std.stdio, std.functional;

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

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

Output:

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

Delphi

Library: System.SysUtils

Translation of: C#

program Currying;

{$APPTYPE CONSOLE}
{$R *.res}

uses
  System.SysUtils;

var
  Plus: TFunc<Integer, TFunc<Integer, Integer>>;

begin
  Plus :=
    function(x: Integer): TFunc<Integer, Integer>
    begin
      result :=
        function(y: Integer): Integer
        begin
          result := x + y;
        end;
    end;

  Writeln(Plus(3)(4));
  Writeln(Plus(2)(Plus(3)(4)));
  readln;
end.

Output:

7
9

EchoLisp

EchoLisp has native support for curry, which is implemented thru closures, as shown in Common Lisp .

;;
;; 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))

Ecstasy

module CurryPower {
    @Inject Console console;
    void run() {
        function Int(Int, Int) divide     = (x,y) -> x / y;
        function Int(Int)      half       = divide(_, 2);
        function Int(Int)      partsOf120 = divide(120, _);

        console.print($|half of a dozen is {half(12)}
                       |half of 120 is {partsOf120(2)}
                       |a third is {partsOf120(3)}
                       |and a quarter is {partsOf120(4)}
                     );
    }
}

Output:

half of a dozen is 6
half of 120 is 60
a third is 40
and a quarter is 30

Eero

#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

Alternative implementation (there are a few ways to express blocks/lambdas):

#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

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.

Elixir

iex(1)> plus = fn x, y -> x + y end
#Function<41.125776118/2 in :erl_eval.expr/6>
iex(2)> plus.(3, 5)
8
iex(3)> plus5 = &plus.(5, &1)
#Function<42.125776118/1 in :erl_eval.expr/6>
iex(4)> plus5.(3)
8

EMal

Translation of: C#

fun plus = fun by int y
  return int by int x do return x + y end
end
int sum0 = plus(3)(4)
int sum1 = plus(2)(plus(3)(4))
writeLine(sum0)
writeLine(sum1)

Output:

7
9

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.

-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.

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

F# is largely based on ML and has a built-in natural method of defining functions that are curried:

let addN n = (+) n

> let add2 = addN 2;;

val add2 : (int -> int)

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

Factor

IN: scratchpad 2 [ 3 + ] curry

--- Data stack:
[ 2 3 + ]
IN: scratchpad call

--- Data stack:
5

Currying doesn't need to be an atomic operation. compose lets you combine quotations.

IN: scratchpad [ 3 4 ] [ 5 + ] compose

--- Data stack:
[ 3 4 5 + ]
IN: scratchpad call

--- Data stack:
3
9

You can even treat quotations as sequences.

IN: scratchpad { 1 2 3 4 5 } [ 1 + ] { 2 / } append map

--- Data stack:
{ 1 1+1/2 2 2+1/2 3 }

Finally, fried quotations are often clearer than using curry and compose. Use _ to take objects from the stack and slot them into the quotation.

USE: fry
IN: scratchpad 2 3 '[ _ _ + ]

--- Data stack:
[ 2 3 + ]

Use @ to insert the contents of a quotation into another quotation.

IN: scratchpad { 1 2 3 4 5 } [ 1 + ] '[ 2 + @ ] map

--- Data stack:
{ 4 5 6 7 8 }

Forth

Translation of: Common Lisp

: curry ( x xt1 -- xt2 )
  swap 2>r :noname r> postpone literal r> compile, postpone ; ;

5 ' + curry constant +5
5 +5 execute .
7 +5 execute .

Output:

10 12

Fōrmulæ

Fōrmulæ programs are not textual, visualization/edition of programs is done showing/manipulating structures but not text. Moreover, there can be multiple visual representations of the same program. Even though it is possible to have textual representation —i.e. XML, JSON— they are intended for storage and transfer purposes more than visualization and edition.

Programs in Fōrmulæ are created/edited online in its website.

In this page you can see and run the program(s) related to this task and their results. You can also change either the programs or the parameters they are called with, for experimentation, but remember that these programs were created with the main purpose of showing a clear solution of the task, and they generally lack any kind of validation.

Solution

In Fōrmulæ, a function is just a named lambda expression, and a function call is just a lambda application.

The following is a simple definition of a lambda expression:

When a lambda application is called with the same number of arguments, the result is the habitual:

However, if a less number of parameters is applied, currying is performed. Notice that the result is another lambda expression.

Because the result is a lambda expression, it can be used in a lambda application, so we must get the same result:

Using functions:

GDScript

Translation of: Python

Uses Godot 4's lambdas. This runs as a script attached to a node.

extends Node

func addN(n: int) -> Callable:
	return func(x):
		return n + x

func _ready():
	# Test currying
	var add2 := addN(2)
	print(add2.call(7))

	get_tree().quit() # Exit

Go

Go has had function literals and method expressions since before Go 1.0. Method values were added in Go 1.1.

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))
}

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:

def divide = { Number x, Number y ->
  x / y
}

def partsOf120 = divide.curry(120)

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

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):

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)}"

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: "

\ ->

" is Haskell's syntax for anonymous functions, in which the sign

\

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

->

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

\x y -> x + y

is merely syntactic sugar for

\x -> \y -> x + y

, which has exactly the same type signature:

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

Hy

(defn addN [n]
  (fn [x]
    (+ x n)))

=> (setv add2 (addN 2))
=> (add2 7)
9

=> ((addN 3) 4)
7

Icon and Unicon

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

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

Output:

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

Io

A general currying function written in the Io programming language:

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

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:

   threePlus=: 3&+
   threePlus 7
10
   halve =: %&2  NB.  % means divide 
   halve 20
10
   someParabola =: _2 3 1 &p. NB. x^2 + 3x - 2

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.

Note: J's adverbs and conjunctions (such as &) will curry themselves when necessary. Thus, for example:

   with2=: &2
   +with2 3
5

Java

    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)));
        }
    }

Java 8

import java.util.function.BiFunction;
import java.util.function.Function;

public class Curry {
	
	//Curry a method
	public static <T, U, R> Function<T, Function<U, R>> curry(BiFunction<T, U, R> biFunction) {
		return t -> u -> biFunction.apply(t, u);
	}
	
	public static int add(int x, int y) {
		return x + y;
	}
	
	public static void curryMethod() {
		BiFunction<Integer, Integer, Integer> bif = Curry::add;
		Function<Integer, Function<Integer, Integer>> add = curry(bif);
		Function<Integer, Integer> add5 = add.apply(5);
		System.out.println(add5.apply(2));
	}

	//Or declare the curried function in one line
	public static void curryDirectly() {
		Function<Integer, Function<Integer, Integer>> add = x -> y -> x + y;
		Function<Integer, Integer> add5 = add.apply(5);
		System.out.println(add5.apply(2));
	}
	
	//prints 7 and 7
	public static void main(String[] args) {
		curryMethod();
		curryDirectly();
	}
}

JavaScript

ES5

Partial application

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

 add2 = addN(2);
 alert(add2);
 alert(add2(7));

Generic currying

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

(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]

})();

Output:

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

Functions of arbitrary arity can also be curried:

(function () {

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

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

        var intArgs = f.length;

        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]

})();

Output:

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

ES6

Y combinator

Using a definition of currying that does not imply partial application, only conversion of a function of multiple arguments, e.g.:

(a,b) => expr_using_a_and_b

into a function that takes a series of as many function applications as that function took arguments, e.g.:

a => b => expr_using_a_and_b

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.

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

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 a two-argument function over an array:

(() => {

    // 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]

})();

Output:

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

Or, recursively currying functions of arbitrary arity:

(() => {

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

        // Recursive currying
        let _curry = (xs, ...arguments) =>
            xs.length >= intArgs ? (
                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]

})();

Output:

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

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):

 
def plus(x): . + x;

def plus5: plus(5);

We can now use plus5 as a filter, e.g.

3 | plus5

produces 8.

Julia

function addN(n::Number)::Function
  adder(x::Number) = n + x
  return adder
end

Output:

julia> add2 = addN(2)
(::adder) (generic function with 1 method)

julia> add2(1)
3

A shorter form of the above function, also without type specification:

addN(n) = x -> n + x

Kotlin

// version 1.1.2

fun curriedAdd(x: Int) = { y: Int -> x + y }

fun main(args: Array<String>) {
    val a = 2
    val b = 3
    val sum = curriedAdd(a)(b)
    println("$a + $b = $sum")
}

Output:

2 + 3 = 5

Lambdatalk

Called with a number of values lesser than the number of arguments a function memorizes the given values and returns a function waiting for the missing ones.

1) just define function a binary function:
{def power {lambda {:a :b} {pow :a :b}}} 
-> power
 
2) and use it:
{power 2 8}                            // power is a function waiting for two numbers
-> 256

{{power 2} 8}                          // {power 2} is a function waiting for the missing number
-> 256

{S.map {power 2} {S.serie 1 10}}       // S.map applies the {power 2} unary function
-> 2 4 8 16 32 64 128 256 512 1024     // to a sequence of numbers from 1 to 10

Latitude

addN := {
  takes '[n].
  {
    $1 + n.
  }.
}.

add3 := addN 3.
add3 (4). ;; 7

Note that, because of the syntax of the language, it is not possible to call addN in one line the naive way.

;; addN (3) (4). ;; Syntax error!
;; (addN (3)) (4). ;; Syntax error!
addN (3) call (4). ;; Works as expected.

As a consequence, it is more common in Latitude to return new objects whose methods have meaningful names, rather than returning a curried function.

addN := {
  takes '[n].
  Object clone tap {
    self do := {
      $1 + n.
    }.
  }.
}.

addN 3 do 4. ;; 7

LFE

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

Usage:

(funcall (curry #'+/2 10) 10)

Logtalk

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

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

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)

another implementation

Proper currying, tail call without array packing/unpack.

local curry do
  local call,env = function(fn,...)return fn(...)end
  local fmt,cat,rawset,rawget,floor = string.format,table.concat,rawset,rawget,math.floor
  local curryHelper = setmetatable({},{
    __call = function(me, n, m, ...)return me[n*256+m](...)end,
    __index = function(me,k)
      local n,m = floor(k / 256), k % 256
      local r,s = {},{} for i=1,m do r[i],s[i]='_'..i,'_'..i end s[1+#s]='...'
      r,s=cat(r,','),cat(s,',')
      s = n<m and fmt('CALL(%s)',r) or fmt('function(...)return ME(%d,%d+select("#",...),%s)end',n,m,s)
      local sc = fmt('local %s=... return %s',r,s)
      rawset(me,k,(loadstring or load)(sc,'_',nil,env) )
      return rawget(me,k)
    end})
  env = {CALL=call,ME=curryHelper,select=select} 
  function curry(...)
    local pn,n,fn = select('#',...),...
    if pn==1 then n,fn = debug.getinfo(n, 'u'),n ; n = n and n.nparams end
    if type(n)~='number' or n~=floor(n)then return nil,'invalid curry' 
    elseif n<=0 then return fn -- edge case
    else return curryHelper(n,1,fn)
    end
  end
end

-- test
function add(x,y)
   return x+y
end
 
local adder = curry(add) -- get params count from debug.getinfo
assert(adder(3)(4) == 3+4)
local add2 = adder(2)
assert(add2(3) == 2+3)
assert(add2(5) == 2+5)

M2000 Interpreter

Module LikeGroovy {
      divide=lambda (x, y)->x/y
      partsof120=lambda divide ->divide(120, ![])
      Print "half of 120 is ";partsof120(2)
      Print "a third is ";partsof120(3)
      Print "and a quarter is ";partsof120(4)
}
LikeGroovy

Module Joke {
      \\ we can call F1(),  with any number of arguments, and always read one and then
      \\ call itself passing the remain arguments
      \\ ![] take stack of values and place it in the next call.
      F1=lambda -> {
            if empty then exit
            Read x
            =x+lambda(![])
      }
      
      Print F1(F1(2),2,F1(-4))=0
      Print F1(-4,F1(2),2)=0
      Print F1(2, F1(F1(2),2))=F1(F1(F1(2),2),2)
      Print F1(F1(F1(2),2),2)=6
      Print F1(2, F1(2, F1(2),2))=F1(F1(F1(2),2, F1(2)),2)
      Print F1(F1(F1(2),2, F1(2)),2)=8
      Print F1(2, F1(10, F1(2, F1(2),2)))=F1(F1(F1(2),2, F1(2)),2, 10)
      Print F1(F1(F1(2),2, F1(2)),2, 10)=18
      Print F1(2,2,2,2,10)=18
      Print F1()=0

      Group F2 {
            Sum=0
            Function Add  (x){
                  .Sum+=x
                  =x
            }
      }
      Link F2.Add() to F2()
      Print F1(F1(F1(F2(2)),F2(2), F1(F2(2))),F2(2))=8
      Print F2.Sum=8
}
Joke

Without joke, can anyone answer this puzzle?

Module Puzzle {
            Global Group F2 {
                  Sum=0
                  Sum2=0
                  Function Add  (x){
                        .Sum+=x
                        =x
                  }
            }
            F1=lambda -> {
                  if empty then exit
                  Read x
                  Print ">>>", F2.Sum
                  F2.Sum2++   ' add one each time we read x
                  =x+lambda(![])
            }
            Link F2.Add() to F2()
            P=F1(F1(F1(F2(2)),F2(2), F1(F2(2))),F2(2))=8
            Print F2.Sum=8
            Print F2.Sum2=7  
            \\  We read 7 times x, but we get 8, 2+2+2+2
            \\  So 3 times x was zero, or not?
            \\  but where we pass zero?
            \\  zero return from F1 if no argument pass, so how x  get zero??
} 
Puzzle

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

MiniScript

Translation of: Rust

addN = function(n)
  f = function(x)
    return n + x
  end function
  return @f
end function

adder = addN(40)
print "The answer to life is " + adder(2) + "."

Output:

The answer to life is 42.

Nemerle

Currying isn't built in to Nemerle, but is relatively straightforward to define.

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))")
    }
}

Nim

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

let add2 = addN(2)
echo add2(7)

Alternative syntax:

import sugar

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

let add3 = addM(3)
echo add3(7)

OCaml

OCaml has a built-in natural method of defining functions that are curried:

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 *)

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:

let curry f x y = f (x,y)
(* Type signature: ('a * 'b -> 'c) -> 'a -> 'b -> 'c *)

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

2 #+ curry => 2+
5 2+ .
7 ok

Ol

(define (addN n)
   (lambda (x) (+ x n)))

(let ((add10 (addN 10))
      (add20 (addN 20)))
   (print "(add10 4) ==> " (add10 4))
   (print "(add20 4) ==> " (add20 4)))

Output:

(add10 4) ==> 14
(add20 4) ==> 24

PARI/GP

Simple currying example with closures.

curriedPlus(x)=y->x+y;
curriedPlus(1)(2)

Output:

3

Perl

This is a Perl 5 example of a general curry function and curried plus using closures:

sub curry{
  my ($func, @args) = @_;

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

sub plusXY{
  $_[0] + $_[1];
}

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

Phix

Phix does not support currying. The closest I can manage is very similar to my solution for closures

with javascript_semantics
sequence curries = {}
function create_curried(integer rid, sequence partial_args)
    curries = append(curries,{rid,partial_args})
    return length(curries) -- (return an integer id)
end function
 
function call_curried(integer id, sequence args)
    {integer rid, sequence partial_args} = curries[id]
    return call_func(rid,partial_args&args)
end function
 
function add(atom a, b)
    return a+b
end function
 
integer curried = create_curried(routine_id("add"),{2})
printf(1,"2+5=%d\n",call_curried(curried,{5}))

Output:

2+5=7

(Of course you would probably not have to try too much harder to make it say 2+2=5 instead.)

PHP

<?php

function curry($callable)
{
    if (_number_of_required_params($callable) === 0) {
        return _make_function($callable);
    }
    if (_number_of_required_params($callable) === 1) {
        return _curry_array_args($callable, _rest(func_get_args()));
    }
    return _curry_array_args($callable, _rest(func_get_args()));
}

function _curry_array_args($callable, $args, $left = true)
{
    return function () use ($callable, $args, $left) {
        if (_is_fullfilled($callable, $args)) {
            return _execute($callable, $args, $left);
        }
        $newArgs = array_merge($args, func_get_args());
        if (_is_fullfilled($callable, $newArgs)) {
            return _execute($callable, $newArgs, $left);
        }
        return _curry_array_args($callable, $newArgs, $left);
    };
}

function _number_of_required_params($callable)
{
    if (is_array($callable)) {
        $refl = new \ReflectionClass($callable[0]);
        $method = $refl->getMethod($callable[1]);
        return $method->getNumberOfRequiredParameters();
    }
    $refl = new \ReflectionFunction($callable);
    return $refl->getNumberOfRequiredParameters();
}

function _make_function($callable)
{
    if (is_array($callable))
        return function() use($callable) {
            return call_user_func_array($callable, func_get_args());
        };
    return $callable;
}

function _execute($callable, $args, $left)
{
    if (! $left) {
        $args = array_reverse($args);
    }
    $placeholders = _placeholder_positions($args);
    if (0 < count($placeholders)) {
        $n = _number_of_required_params($callable);
        if ($n <= _last($placeholders[count($placeholders) - 1])) {
            throw new \Exception('Argument Placeholder found on unexpected position!');
        }
        foreach ($placeholders as $i) {
            $args[$i] = $args[$n];
            array_splice($args, $n, 1);
        }
    }
    return call_user_func_array($callable, $args);
}

function _placeholder_positions($args)
{
    return array_keys(array_filter($args, '_is_placeholder'));
}

function _is_fullfilled($callable, $args)
{
    $args = array_filter($args, function($arg) {
        return ! _is_placeholder($arg);
    });
    return count($args) >= _number_of_required_params($callable);
}

function _is_placeholder($arg)
{
    return $arg instanceof Placeholder;
}

function _rest(array $args)
{
    return array_slice($args, 1);
}

function product($a, $b)
{
    return $a * $b;
}

echo json_encode(array_map(curry('product', 7), [1, 2, 3, 4, 5, 6, 7, 8, 9, 10]));

Output:

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

PicoLisp

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

PowerShell

function Add($x) { return { param($y) return $y + $x }.GetNewClosure() }

& (Add 1) 2

Output:

3

Add each number in list to its square root:

(4,9,16,25 | ForEach-Object { & (add $_) ([Math]::Sqrt($_)) }) -join ", "

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

Nested defs and functools.partial

Since Python has had local functions with closures since around 1.0, it's always been possible to create curried functions manually:

 def addN(n):
     def adder(x):
         return x + n
     return adder

 >>> add2 = addN(2)
 >>> add2
 <function adder at 0x009F1E30>
 >>> add2(7)
 9

But Python also comes with a function to build partial functions (with any number of positional or keyword arguments bound in) for you. This was originally in a third-party model called functional, but was added to the stdlib functools module in 2.5. Every year or so, someone suggests either moving it into builtins because it's so useful or removing it from the stdlib entirely because it's so easy to write yourself, but it's been in the functools module since 2.5 and will probably always be there.

>>> from functools import partial
>>> from operator import add
>>> add2 = partial(add, 2)
>>> add2
functools.partial(<built-in function add>, 2)
>>> add2(7)
9
>>> double = partial(map, lambda x: x*2)
>>> print(*double(range(5)))
0 2 4 6 8

But for a true curried function that can take arguments one at a time via normal function calls, you have to do a bit of wrapper work to build a callable object that defers to partial until all of the arguments are available. Because of the Python's dynamic nature and flexible calling syntax, there's no way to do this in a way that works for every conceivable valid function, but there are a variety of ways that work for different large subsets. Or just use a third-party library like toolz that's already done it for you:

>>> from toolz import curry
>>> import operator
>>> add = curry(operator.add)
>>> add2 = add(2)
>>> add2
<built-in function add>
>>> add2(7)
9
>>> # Toolz also has pre-curried versions of most HOFs from builtins, stdlib, and toolz
>>>from toolz.curried import map
>>> double = map(lambda x: x*2)
>>> print(*double(range(5)))
0 2 4 6 8

Automatic curry and uncurry functions using lambdas

As an alternative to nesting defs, we can also define curried functions, perhaps more directly, in terms of lambdas. We can also write a general curry function, and a corresponding uncurry function, for automatic derivation of curried and uncurried functions at run-time, without needing to import functools.partial:

# AUTOMATIC CURRYING AND UNCURRYING OF EXISTING FUNCTIONS


# curry :: ((a, b) -> c) -> a -> b -> c
def curry(f):
    return lambda a: lambda b: f(a, b)


# uncurry :: (a -> b -> c) -> ((a, b) -> c)
def uncurry(f):
    return lambda x, y: f(x)(y)


# EXAMPLES --------------------------------------

# A plain uncurried function with 2 arguments,

# justifyLeft :: Int -> String -> String
def justifyLeft(n, s):
    return (s + (n * ' '))[:n]


# and a similar, but manually curried, function.

# justifyRight :: Int -> String -> String
def justifyRight(n):
    return lambda s: (
        ((n * ' ') + s)[-n:]
    )


# CURRYING and UNCURRYING at run-time:

def main():
    for s in [
        'Manually curried using a lambda:',
        '\n'.join(map(
            justifyRight(5),
            ['1', '9', '10', '99', '100', '1000']
        )),

        '\nAutomatically uncurried:',
        uncurry(justifyRight)(5, '10000'),

        '\nAutomatically curried',
        '\n'.join(map(
            curry(justifyLeft)(10),
            ['1', '9', '10', '99', '100', '1000']
        ))
    ]:
        print (s)


main()

Output:

Manually curried using a lambda:
    1
    9
   10
   99
  100
 1000

Automatically uncurried:
10000

Automatically curried
1         
9         
10        
99        
100       
1000      

Quackery

Quackery does not have a currying function, but one is easily defined.

The word curried in the definition below curries the word following it, (which should act on two arguments on the stack), with the argument on the top of the stack. In the shell dialogue in the output: section the word + is combined with the number 5 on the top of stack to create the curried lambda nest [ ' 5 + ] which will add 5 the number on the top of stack when it is evaluated with do.

In the second example we drop the 8 from the previous example from the stack and then use currying to join "lamb" to "balti".

  [ ' [ ' ] swap nested join
    ]'[ nested join ]        is curried ( x --> [ )

Output:

/O> 5 curried +
... 

Stack: [ ' 5 + ] 

/O> 3 swap do 
... 

Stack: 8

/O> drop
... $ "balti" curried join    
... $ "lamb " swap do echo$
... 
lamb balti
Stack empty.

R

Works with: R version 4.1.0

We can easily define currying and uncurrying for two-argument functions as follows:

curry   <- \(f) \(x) \(y) f(x, y)
uncurry <- \(f) \(x, y) f(x)(y)

Here are some examples

add_curry <- curry(`+`)
add2 <- add_curry(2)
add2(40)
uncurry(add_curry)(40, 2)

Output:

> curry   <- \(f) \(x) \(y) f(x, y)
> uncurry <- \(f) \(x, y) f(x)(y)
> 
> add_curry <- curry(`+`)
> add2 <- add_curry(2)
> add2(40)
[1] 42
> uncurry(add_curry)(40, 2)
[1] 42

Racket

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

#lang racket
(((curry +) 3) 2) ; =>5

As an alternative, one can use the following syntax:

#lang racket

(define ((curried+ a) b)
  (+ a b))

((curried+ 3) 2)  ; => 5

Raku

(formerly 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.

my &negative = &infix:<->.assuming(0);
say negative 1;

Output:

-1

REXX

This example is modeled after the   D   example.

specific version

/*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 all done. */
/*──────────────────────────────────────────────────────────────────────────────────────*/
add:  procedure;  $= arg(1);       do j=2  to arg();   $= $ + arg(j);   end;      return $
add2: procedure;  return add( arg(1), 2)

output   when using the defaults:

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

generic version

/*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 all done. */
/*──────────────────────────────────────────────────────────────────────────────────────*/
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: procedure;  return add( arg(1), 2)

output   is identical to the 1^st REXX version.

RPL

RPL has not been designed as a functional programming language, but appropriate words can be created so that it becomes almost one. For RPL, all programs are functions that can take arguments (or not) from the stack. Programs can easily be converted into strings: it is then possible to have a program rewrite another one, in order to insert the desired argument in the code, thus avoiding to pick it in the stack.

Works with: Halcyon Calc version 4.2.7

RPL code

Comment

≪ 2 OVER SIZE 1 - SUB ≫ 'SHAVE' STO ≪ →STR SHAVE "≪" ROT →STR IF LAST TYPE 6 == THEN SHAVE END + " SWAP " + SWAP + STR→ ≫ 'CURRX' STO ≪ →STR SHAVE "≪" ROT →STR IF LAST TYPE 6 == THEN SHAVE END + SWAP + STR→ ≫ 'CURRY' STO

SHAVE ( "abcde" -- "bcd" ) CURRX ( a ≪( x y -- z )≫ -- ≪( a y -- z )≫ ) convert function to string and remove delimiters rewrite the program beginning if a is an object name, remove its delimiters add a SWAP instruction to put a at stack level 2 CURRY ( a ≪( x y -- z )≫ -- ≪( x a -- z )≫ ) convert function to string and remove delimiters rewrite the program beginning if a is an object name, remove its delimiters put the call to a at level 1

Let's demonstrate the curryfication on the following function :

≪ SQ SWAP SQ SWAP - ≫

which calculates x² - y² on x and y passed as arguments resp. in levels 2 and 1 of the stack. The following sequence of instructions:

5 ≪ SQ SWAP SQ SWAP - ≫ CURRX 'D2SQY' STO

returns a curryfied program stored as the word D2SQY. We can then check it works as planned:

'Y' D2SQY

will return

1: '25-SQ(Y)'

Similarly:

5 ≪ SQ SWAP SQ SWAP - ≫ CURRY 'D2SQX' STO

will return a new program named D2SQX, which effect on the 'X' argument at stack level 1 will be:

1: 'SQ(X)-25'

It is also possible to pass the reference to the function to be curryfied, rather than the function itself. if ≪ SQ SWAP SQ SWAP - ≫ is stored as D2SQ, the following command line will have the same effect as above:

5 'D2SQ' CURRY 'D2SQX' STO

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).

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

Rust

This is a simple currying function written in Rust:

fn add_n(n : i32) -> impl Fn(i32) -> i32 {
    move |x| n + x
}

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

Scala

def add(a: Int)(b: Int) = a + b
val add5 = add(5) _
add5(2)

Sidef

This can be done by using lazy methods:

var adder = 1.method(:add);
say adder(3);                #=> 4

Or by using a generic curry function:

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

func add(a, b) {
    a + b
}

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

Standard ML

Standard ML has a built-in natural method of defining functions that are curried:

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 *)

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:

fun curry f x y = f(x,y)
(* Type signature: ('a * 'b -> 'c) -> 'a -> 'b -> 'c *)

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.

Swift

You can return a closure (or nested function):

func addN(n:Int)->Int->Int { return {$0 + n} }

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

Prior to Swift 3, there was a curried function definition syntax:

func addN(n:Int)(x:Int) -> Int { return x + n }

var add2 = addN(2)
println(add2) // (Function)
println(add2(x:7)) // 9

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:

func addN(n:Int)(_ x:Int) -> Int { return x + n }

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

Tcl

The simplest way to do currying in Tcl is via an interpreter alias:

interp alias {} addone {} ::tcl::mathop::+ 1
puts [addone 6]; # => 7

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

Note: many solutions for this task are conflating currying with partial application. Currying converts an N-argument function into a cascade of one-argument functions. The curry operator doesn't itself bind any arguments; no application is going on. The relationship between currying and partial application is that partial application occurs when the cascade is unraveled as arguments are applied to it: each successive one-argument call in the cascade binds an argument, and when all the arguments are bound, the value of the original function over those arguments is computed.

TXR Lisp has an operator called op for partial application. Of course, partial application 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 partial application syntax, providing various useful derived behaviors.

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

(op - 10 @1 @2 5)

TXR Lisp doesn't have a predefined function or operator for currying. A function can be manually curried. For instance, the three-argument named function: (defun f (x y z) (* (+ x y) z)) can be curried by hand to produce a function g like this:

(defun g (x)
  (lambda (y)
    (lambda (z)
       (* (+ x y) z))))

Or, by referring to the definition of f:

(defun g (x)
  (lambda (y)
    (lambda (z)
       (f x y z))))

Since a three-argument function can be defined directly, and has advantages like diagnosing incorrect calls which pass fewer than three or more than three arguments, currying is not useful in this language. Similar reasoning applies as given in the "Why not real currying/uncurrying?" paragraph under the Design Rationale of Scheme's SRFI 26.

Vala

delegate double Dbl_Op(double d);

Dbl_Op curried_add(double a) {
  return (b) => a + b;
}

void main() { 
  print(@"$(curried_add(3.0)(4.0))\n");
  double sum2 = curried_add(2.0) (curried_add(3.0)(4.0)); //sum2 = 9
  print(@"$sum2\n");
}

Output:

7
9

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.

@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
  ]]
}

Wren

Translation of: Rust

var addN = Fn.new { |n| Fn.new { |x| n + x } }

var adder = addN.call(40)
System.print("The answer to life is %(adder.call(2)).")

Output:

The answer to life is 42.

Z80 Assembly

Works with: Amstrad CPC

The BIOS call &BB75 takes HL as input (as if it were an x,y coordinate pair) and outputs a video memory address into HL. Using a fixed input of HL=0x0101 we can effectively reset the drawing cursor to the top left corner of the screen.

macro ResetCursors
ld hl,&0101
call &BB75
endm

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.

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