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
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
or both
and
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
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
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
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#
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
: 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
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))
}
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 | plus5produces 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. ;; 7LFE
(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
}
JokeWithout 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??
}
PuzzleMathematica / 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
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($"$(Curry(f)(20)(22))");
WriteLine($"$(g(21)(21))");
WriteLine($"$(h(30))")
}
}
Nim
proc addN[T](n: T): auto = (proc(x: T): T = x + n)
let add2 = addN(2)
echo add2(7)
Alternative syntax:
import sugar
proc addM[T](n: T): auto = (x: T) => x + n
let add3 = addM(3)
echo add3(7)
OCaml
OCaml has a built-in natural method of defining functions that are curried:
let addnums x y = x+y (* declare a curried function *)
let add1 = addnums 1 (* bind the first argument to get another function *)
add1 42 (* apply to actually compute a result, 43 *)
The type of addnums above will be int -> int -> int.
Note that fun addnums x y = ..., or, equivalently, let addnums = fun x y -> ..., is really just syntactic sugar for let addnums = function x -> function y -> ....
You can also define a general currying higher-ordered function:
let curry f x y = f (x,y)
(* Type signature: ('a * 'b -> 'c) -> 'a -> 'b -> 'c *)
This is a function that takes a function as a parameter and returns a function that takes one of the parameters and returns another function that takes the other parameter and returns the result of applying the parameter function to the pair of arguments.
Oforth
2 #+ curry => 2+
5 2+ .
7 okOl
(define (addN n)
(lambda (x) (+ x n)))
(let ((add10 (addN 10))
(add20 (addN 20)))
(print "(add10 4) ==> " (add10 4))
(print "(add20 4) ==> " (add20 4)))
- Output:
(add10 4) ==> 14 (add20 4) ==> 24
PARI/GP
Simple currying example with closures.
curriedPlus(x)=y->x+y;
curriedPlus(1)(2)- Output:
3
Perl
This is a Perl 5 example of a general curry function and curried plus using closures:
sub curry{
my ($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
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 1st 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.
| 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); #=> 4Or 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); #=>4Standard 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)) // 9Prior 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)) // 9However, 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)) // 9Tcl
The simplest way to do currying in Tcl is via an interpreter alias:
interp alias {} addone {} ::tcl::mathop::+ 1
puts [addone 6]; # => 7Tcl 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
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
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
endmzkl
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- Programming Tasks
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