Currying: Difference between revisions
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> add2 7;; |
> add2 7;; |
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val it : int = 9</lang> |
val it : int = 9</lang> |
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=={{header|Go}}== |
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Go has had [http://golang.org/ref/spec#Function_literals function literals] |
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and [http://golang.org/ref/spec#Method_expressions method expressions] |
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since before Go 1.0. |
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[http://golang.org/ref/spec#Method_values Method values] were added |
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in [http://golang.org/doc/go1.1#method_values Go 1.1]. |
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<lang go>package main |
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import ( |
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"fmt" |
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"math" |
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) |
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func PowN(b float64) func(float64) float64 { |
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return func(e float64) float64 { return math.Pow(b, e) } |
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} |
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func PowE(e float64) func(float64) float64 { |
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return func(b float64) float64 { return math.Pow(b, e) } |
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} |
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type Foo int |
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func (f Foo) Method(b int) int { |
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return int(f) + b |
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} |
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func main() { |
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pow2 := PowN(2) |
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cube := PowE(3) |
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fmt.Println("2^8 =", pow2(8)) |
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fmt.Println("4³ =", cube(4)) |
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var a Foo = 2 |
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fn1 := a.Method // A "method value", like currying 'a' |
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fn2 := Foo.Method // A "method expression", like uncurrying |
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fmt.Println("2 + 2 =", a.Method(2)) // regular method call |
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fmt.Println("2 + 3 =", fn1(3)) |
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fmt.Println("2 + 4 =", fn2(a, 4)) |
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fmt.Println("3 + 5 =", fn2(Foo(3), 5)) |
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}</lang> |
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[http://play.golang.org/p/0YL9YTe-9V Run on the Go Playground.] |
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=={{header|Haskell}}== |
=={{header|Haskell}}== |
Revision as of 17:33, 6 August 2014
![Task](http://static.miraheze.org/rosettacodewiki/thumb/b/ba/Rcode-button-task-crushed.png/64px-Rcode-button-task-crushed.png)
You are encouraged to solve this task according to the task description, using any language you may know.
This page uses content from Wikipedia. The original article was at Currying. The list of authors can be seen in the page history. As with Rosetta Code, the text of Wikipedia is available under the GNU FDL. (See links for details on variance) |
Create a simple demonstrative example of Currying in the specific language.
Add any historic details as to how the feature made its way into the language.
ALGOL 68
In 1968 C.H. Lindsey proposed for partial parametrisation for ALGOL 68, this is implemented as an extension in wp:ALGOL 68G. <lang algol68># Raising a function to a power #
MODE FUN = PROC (REAL) REAL; PROC pow = (FUN f, INT n, REAL x) REAL: f(x) ** n; OP ** = (FUN f, INT n) FUN: pow (f, n, );
- Example: sin (3 x) = 3 sin (x) - 4 sin^3 (x) (follows from DeMoivre's theorem) #
REAL x = read real; print ((new line, sin (3 * x), 3 * sin (x) - 4 * (sin ** 3) (x)))</lang>
C#
This shows how to create syntactically natural currying functions in C#. <lang csharp>public delegate int Plus(int y); public delegate Plus CurriedPlus(int x); public static CurriedPlus plus =
delegate(int x) {return delegate(int y) {return x + y;};};
static void Main() {
int sum = plus(3)(4); // sum = 7 int sum2= plus(2)(plus(3)(4)) // sum2 = 9
}</lang>
C++
Currying may be achieved in C++ using the Standard Template Library function object adapters (binder1st
and binder2nd
), and more generically using the Boost bind
mechanism.
Common Lisp
<lang lisp>(defun curry (function &rest args-1)
(lambda (&rest args-2) (apply function (append args-1 args-2))))
</lang>
Usage: <lang lisp> (funcall (curry #'+ 10) 10)
20 </lang>
D
<lang d>void main() {
import std.stdio, std.functional;
int add(int a, int b) { return a + b; }
alias add2 = curry!(add, 2); writeln("Add 2 to 3: ", add(2, 3)); writeln("Add 2 to 3 (curried): ", add2(3));
}</lang>
- Output:
Add 2 to 3: 5 Add 2 to 3 (curried): 5
Eero
<lang objc>#import <stdio.h>
int main()
addN := (int n) int adder(int x) return x + n return adder
add2 := addN(2)
printf( "Result = %d\n", add2(7) )
return 0
</lang> Alternative implementation (there are a few ways to express blocks/lambdas): <lang objc>#import <stdio.h>
int main()
addN := (int n) return (int x | return x + n)
add2 := addN(2)
printf( "Result = %d\n", add2(7) )
return 0
</lang>
Eiffel
Eiffel has direct support for lambda expressions and hence currying through "inline agents". If f is a function with two arguments, of signature (X × Y) → Z then its curried version is obtained by simply writing
g (x: X): FUNCTION [ANY, TUPLE [Y], Z] do Result := agent (closed_x: X; y: Y): Z do Result := f (closed_x, y) end (x, ?) end
where FUNCTION [ANY, TUPLE [Y], Z] denotes the type Y → Z (agents taking as argument a tuple with a single argument of type Y and returning a result of type Z), which is indeed the type of the agent expression used on the next-to-last line to define the "Result" of g.
F#
<lang fsharp>let addN n = (+) n</lang>
<lang fsharp>> let add2 = addN 2;;
val add2 : (int -> int)
> add2;; val it : (int -> int) = <fun:addN@1> > add2 7;; val it : int = 9</lang>
Go
Go has had function literals and method expressions since before Go 1.0. Method values were added in Go 1.1. <lang go>package main
import (
"fmt" "math"
)
func PowN(b float64) func(float64) float64 {
return func(e float64) float64 { return math.Pow(b, e) }
}
func PowE(e float64) func(float64) float64 {
return func(b float64) float64 { return math.Pow(b, e) }
}
type Foo int
func (f Foo) Method(b int) int {
return int(f) + b
}
func main() {
pow2 := PowN(2) cube := PowE(3)
fmt.Println("2^8 =", pow2(8)) fmt.Println("4³ =", cube(4))
var a Foo = 2 fn1 := a.Method // A "method value", like currying 'a' fn2 := Foo.Method // A "method expression", like uncurrying
fmt.Println("2 + 2 =", a.Method(2)) // regular method call fmt.Println("2 + 3 =", fn1(3)) fmt.Println("2 + 4 =", fn2(a, 4)) fmt.Println("3 + 5 =", fn2(Foo(3), 5))
}</lang> Run on the Go Playground.
Haskell
Likewise in Haskell, function type signatures show the currying-based structure of functions (note: "<lang haskell>\ -></lang>" is Haskell's syntax for anonymous functions, in which the sign <lang haskell>\</lang> has been chosen for its resemblance to the Greek letter λ (lambda); it is followed by a list of space-separated arguments, and the arrow <lang haskell>-></lang> separates the arguments list from the function body)
Prelude> let plus = \x y -> x + y Prelude> :type plus plus :: Integer -> Integer -> Integer Prelude> plus 3 5 8
and currying functions is trivial
Prelude> let plus5 = plus 5 Prelude> :type plus5 plus5 :: Integer -> Integer Prelude> plus5 3 8
In fact, the Haskell definition <lang haskell>\x y -> x + y</lang> is merely syntactic sugar for <lang haskell>\x -> \y -> x + y</lang>, which has exactly the same type signature:
Prelude> let nested_plus = \x -> \y -> x + y Prelude> :type nested_plus nested_plus :: Integer -> Integer -> Integer
Icon and Unicon
This version only works in Unicon because of the coexpression calling syntax used.
<lang unicon>procedure main(A)
add2 := addN(2) write("add2(7) = ",add2(7)) write("add2(1) = ",add2(1))
end
procedure addN(n)
return makeProc{ repeat { (x := (x@&source)[1], x +:= n) } }
end
procedure makeProc(A)
return (@A[1], A[1])
end</lang>
Output:
->curry add2(7) = 9 add2(1) = 3 ->
Io
A general currying function written in the Io programming language: <lang io>curry := method(fn, a := call evalArgs slice(1) block( b := a clone appendSeq(call evalArgs) performWithArgList("fn", b) ) )
// example: increment := curry( method(a,b,a+b), 1 ) increment call(5) // result => 6</lang>
J
Solution:Use & (bond). This primitive conjunction accepts two arguments: a function (verb) and an object (noun) and binds the object to the function, deriving a new function. Example:<lang j> threePlus=: 3&+
threePlus 7
10
halve =: %&2 NB. % means divide halve 20
10
someParabola =: _2 3 1 &p. NB. x^2 + 3x - 2</lang>
Note: The final example (someParabola) shows the single currying primitive (&) combined with J's array oriented nature, permits partial application of a function of any number of arguments.
Java
<lang java5> public class Currier<ARG1, ARG2, RET> {
public interface CurriableFunctor<ARG1, ARG2, RET> { RET evaluate(ARG1 arg1, ARG2 arg2); } public interface CurriedFunctor<ARG2, RET> { RET evaluate(ARG2 arg); } final CurriableFunctor<ARG1, ARG2, RET> functor; public Currier(CurriableFunctor<ARG1, ARG2, RET> fn) { functor = fn; } public CurriedFunctor<ARG2, RET> curry(final ARG1 arg1) { return new CurriedFunctor<ARG2, RET>() { public RET evaluate(ARG2 arg2) { return functor.evaluate(arg1, arg2); } }; } public static void main(String[] args) { Currier.CurriableFunctor<Integer, Integer, Integer> add = new Currier.CurriableFunctor<Integer, Integer, Integer>() { public Integer evaluate(Integer arg1, Integer arg2) { return new Integer(arg1.intValue() + arg2.intValue()); } }; Currier<Integer, Integer, Integer> currier = new Currier<Integer, Integer, Integer>(add); Currier.CurriedFunctor<Integer, Integer> add5 = currier.curry(new Integer(5)); System.out.println(add5.evaluate(new Integer(2))); } }</lang>
JavaScript
<lang javascript> function addN(n) {
var curry = function(x) { return x + n; }; return curry; }
add2 = addN(2); alert(add2); alert(add2(7));</lang>
jq
In jq, functions are filters. Accordingly, we illustrate currying by defining plus(x) to be a filter that adds x to its input, and then define plus5 as plus(5): <lang jq> def plus(x): . + x;
def plus5: plus(5); </lang>
We can now use plus5 as a filter, e.g.<lang jq>3 | plus5</lang> produces 8.
LFE
<lang lisp>(defun curry (f arg)
(lambda (x) (apply f (list arg x))))
</lang> Usage: <lang lisp> (funcall (curry #'+/2 10) 10) </lang>
Mathematica
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
ML
Suppose that plus
is a function taking two arguments x
and y
and returning x + y
. In the ML programming language we would define it as follows:
plus = fn(x, y) => x + y
and plus(1, 2)
returns 3
as we expect.
The curried version of plus
takes a single argument x
and returns a new function which takes a single argument y
and returns x + y
. In ML we would define it as follows:
curried_plus = fn(x) => fn(y) => x + y
and now when we call curried_plus(1)
we get a new function that adds 1 to its argument:
plus_one = curried_plus(1)
and now plus_one(2)
returns 3
and plus_one(7)
returns 8
.
When declaring functions in the strictly-typed OCaml programming language, the type returned by a function shows the Curried form of the function. Typing the function into the OCaml interpreter displays the type immediately:
# let plus x y = x + y ;; val plus : int -> int -> int = <fun>
Nemerle
Currying isn't built in to Nemerle, but is relatively straightforward to define. <lang Nemerle>using System; using System.Console;
module Curry {
Curry[T, U, R](f : T * U -> R) : T -> U -> R { fun (x) { fun (y) { f(x, y) } } } Main() : void { def f(x, y) { x + y }
def g = Curry(f); def h = Curry(f)(12); // partial application WriteLine($"$(Curry(f)(20)(22))"); WriteLine($"$(g(21)(21))"); WriteLine($"$(h(30))")
}
}</lang>
Nimrod
<lang nimrod>proc addN[T](n: T): auto = (proc(x: T): T = x + n)
let add2 = addN(2) echo add2(7)</lang> Alternative syntax: <lang nimrod>import future
proc addM[T](n: T): auto = (x: T) => x + n
let add3 = addM(3) echo add3(7)</lang>
PARI/GP
Simple currying example with closures. <lang parigp>curriedPlus(x)=y->x+y; curriedPlus(1)(2)</lang>
- Output:
3
Perl
This is a Perl 5 example of a general curry function and curried plus using closures: <lang perl>sub curry{
my ($func, @args) = @_;
sub { #This @_ is later &$func(@args, @_); }
}
sub plusXY{
$_[0] + $_[1];
}
my $plusXOne = curry(\&plusXY, 1); print &$plusXOne(3), "\n";</lang>
Perl 6
All callable objects have an "assuming" method that can do partial application of either positional or named arguments. Here we curry the built-in subtraction operator. <lang perl6>my &negative = &infix:<->.assuming(0); say negative 1;</lang>
- Output:
-1
Prolog
Works with SWI-Prolog and module lambda.pl
Module lambda.pl can be found at http://www.complang.tuwien.ac.at/ulrich/Prolog-inedit/lambda.pl .
?- [library('lambda.pl')]. % library(lambda.pl) compiled into lambda 0,00 sec, 28 clauses true. ?- N = 5, F = \X^Y^(Y is X+N), maplist(F, [1,2,3], L). N = 5, F = \X^Y^ (Y is X+5), L = [6,7,8].
Python
<lang python> def addN(n):
def adder(x): return x + n return adder</lang>
<lang python> >>> add2 = addN(2)
>>> add2 <function adder at 0x009F1E30> >>> add2(7) 9</lang>
Racket
The simplest way to make a curried functions is to use curry:
<lang racket>
- lang racket
(((curry +) 3) 2) ; =>5 </lang>
As an alternative, one can use the following syntax: <lang racket>
- lang racket
(define ((curried+ a) b)
(+ a b))
((curried+ 3) 2) ; => 5 </lang>
REXX
This example is modeled after the D example.
specific version
<lang ress>/*REXX program demonstrates a REXX currying method to perform addition. */ say 'add 2 to 3: ' add(2 ,3) say 'add 2 to 3 (curried):' add2(3) exit /*stick a fork in it, we're done.*/ /*──────────────────────────────────subroutines─────────────────────────*/ add: procedure; $=arg(1); do j=2 to arg(); $=$+arg(j); end; return $ add2: procedure; return add(arg(1), 2)</lang> output
add 2 to 3: 5 add 2 to 3 (curried): 5
generic version
<lang rexx>/*REXX program demonstrates a REXX currying method to perform addition. */ say 'add 2 to 3: ' add(2 ,3) say 'add 2 to 3 (curried):' add2(3) exit /*stick a fork in it, we're done.*/ /*──────────────────────────────────ADD subroutine──────────────────────*/ add: procedure; $=0; do j=1 for arg()
do k=1 for words(arg(j)); $=$+word(arg(j),k) end /*k*/ end /*j*/
return $
/*──────────────────────────────────ADD2 subroutine─────────────────────*/
add2: procedure; return add(arg(1), 2)</lang>
output is the same as the 1st version.
Ruby
The curry method was added in Ruby 1.9.1. It takes an optional arity argument, which determines the number of arguments to be passed to the proc. If that number is not reached, the curry method returns a new curried method for the rest of the arguments. (Examples taken from the documentation). <lang ruby> b = proc {|x, y, z| (x||0) + (y||0) + (z||0) } p b.curry[1][2][3] #=> 6 p b.curry[1, 2][3, 4] #=> 6 p b.curry(5)[1][2][3][4][5] #=> 6 p b.curry(5)[1, 2][3, 4][5] #=> 6 p b.curry(1)[1] #=> 1
b = proc {|x, y, z, *w| (x||0) + (y||0) + (z||0) + w.inject(0, &:+) } p b.curry[1][2][3] #=> 6 p b.curry[1, 2][3, 4] #=> 10 p b.curry(5)[1][2][3][4][5] #=> 15 p b.curry(5)[1, 2][3, 4][5] #=> 15 p b.curry(1)[1] #=> 1 </lang>
Scheme
This is a simple general currying function written in Scheme: <lang scheme>;curry:function,args->(function)
- Adding using currying
(define (curry f . args) (lambda x (apply f (append args x))))</lang> This is an example of applying a curried function: <lang scheme>>((curry + 10) 10) 20</lang>
Standard ML
Standard ML has a built-in natural method of defining functions that are curryable: <lang sml>fun addnums x:int y = x+y (* declare a curryable function *)
val add1 = addnums 1 (* bind the first argument to get another function *)
addnums 42 (* apply to actually compute a result, 43 *)</lang>
The type of addnums
above will be int -> int -> int (the type constraint in the declaration only being necessary because of the polymorphic nature of the +
operator).
You can also define a general currying functor: <lang sml>fun curry f x y = f(x,y) (* Type signature: ('a * 'b -> 'c) -> 'a -> 'b -> 'c *)</lang> This is a function that takes a function as a parameter and returns a function that takes one of the parameters and returns another function that takes the other parameter and returns the result of applying the parameter function to the pair of arguments.
Tcl
The simplest way to do currying in Tcl is via an interpreter alias: <lang tcl>interp alias {} addone {} ::tcl::mathop::+ 1 puts [addone 6]; # => 7</lang> Tcl doesn't support automatic creation of curried functions though; the general variadic nature of a large proportion of Tcl commands makes that impractical.
History
The type of aliases used here are a simple restriction of general inter-interpreter aliases to the case where both the source and target interpreter are the current one; these aliases are a key component of the secure interpreter mechanism introduced in Tcl 7.6, and are the mechanism used to allow access to otherwise-insecure behavior from a secure context (e.g., to write to a particular file, but not any old file).
Wortel
The \
operator takes a function and an argument and partial applies the argument to the function. The &\
works like the \
operator but can also take an array literal and partial applies all the arguments in the array.
<lang wortel>@let {
addOne \+ 1 subtractFrom1 \- 1 subtract1 \~- 1 subtract1_2 &\- [. 1]
add ^+ ; partial apply to named functions addOne_2 \add 1
; testing [[ !addOne 5 ; returns 6 !subtractFrom1 5 ; returns -4 !subtract1 5 ; returns 4 !subtract1_2 5 ; returns 4 !addOne_2 5 ; returns 6 ]]
}</lang>
zkl
zkl doesn't support currying per se (recompilation of f with fixed input to create a new function), it does support partial application, for all objects, for any [number of] positional parameters to create an object of reduced arity. <lang zkl>addOne:= Op("+").fp(1); addOne(5) //-->6 minusOne:=Op("-").fp1(1); minusOne(5) //-->4, note that this fixed 1 as the second parameter
// fix first and third parameters:
foo:=String.fpM("101","<foo>","</foo>"); foo("zkl"); //-->"<foo>zkl</foo>" fcn g(x){x+1} f:=fcn(f,x){f(x)+x}.fp(g); f(5); //-->11 f:=fcn(f,x){f(x)+x}.fp(fcn(x){x+1}); // above with lambdas all the way down</lang>