Closures/Value capture

Closures/Value capture is a draft programming task. It is not yet considered ready to be promoted as a complete task, for reasons that should be found in its talk page.

Task: Create a list of 10 functions, in the simplest manner possible (anonymous functions are encouraged), such that the function at index i (you may choose to start i from either 0 or 1), when run, should return the square of the index, that is, i². Display the result of running any but the last function, to demonstrate that the function indeed remembers its value.

Goal: To demonstrate how to create a series of independent closures based on the same template but maintain separate copies of the variable closed over. In imperative languages, one would generally use a loop with a mutable counter variable. For each function to maintain the correct number, it has to capture the value of the variable at the time it was created, rather than just a reference to the variable, which would have a different value by the time the function was run.

Axiom

Using the Spad compiler:

)abbrev package TESTP TestPackage
TestPackage() : with
     test: () -> List((()->Integer))
   == add
     test() == [(() +-> i^2) for i in 1..10]

This can be called from the interpreter using:

[x() for x in test()]

With output:

[1,4,9,16,25,36,49,64,81,100]
                                     Type: List(Integer)

C

Function image copying approach

Non-portable. Copying a function body depends on implementation-specific semantics of volatile, if the replacement target still exists after optimization, if the dest memory is suitably aligned, if the memory is executable, if it makes any function calls to a relative offset, if it refers to any memory location with an absolute address, etc. It only very occasionally works.

#include <stdio.h>
#include <string.h>
#include <stdlib.h>
#include <sys/mman.h>
 
typedef int (*f_int)();
 
#define TAG 0xdeadbeef
int _tmpl() { 
	volatile int x = TAG;
	return x * x;
}
 
#define PROT (PROT_EXEC | PROT_WRITE)
#define FLAGS (MAP_PRIVATE | MAP_ANONYMOUS) 
f_int dupf(int v)
{
	size_t len = (void*)dupf - (void*)_tmpl;
	f_int ret = mmap(NULL, len, PROT, FLAGS, 0, 0);
	char *p;
	if(ret == MAP_FAILED) {
		perror("mmap");
		exit(-1);
	}
	memcpy(ret, _tmpl, len);
	for (p = (char*)ret; p < (char*)ret + len - sizeof(int); p++)
		if (*(int *)p == TAG) *(int *)p = v;
	return ret;
}
 
int main()
{
	f_int funcs[10];
	int i;
	for (i = 0; i < 10; i++) funcs[i] = dupf(i);
 
	for (i = 0; i < 9; i++)
		printf("func[%d]: %d\n", i, funcs[i]());
 
	return 0;
}

output

func[0]: 0
func[1]: 1
func[2]: 4
func[3]: 9
func[4]: 16
func[5]: 25
func[6]: 36
func[7]: 49
func[8]: 64

Greenspunned mini Lisp dialect

See Closures/Variable_capture/C for complete code. The relevant excerpt is:

void init(void)
{
  t = intern(lit("t"));
  x = intern(lit("x"));
}
 
val square(val env)
{
  val xbind = assoc(env, x); /* look up binding of variable x in env */
  val xval = cdr(xbind);     /* value is the cdr of the binding cell */
  return num(cnum(xval) * cnum(xval));
}
 
int main(void)
{
  int i;
  val funlist = nil, iter;
 
  init();
 
  for (i = 0; i < 10; i++) {
    val closure_env = cons(cons(x, num(i)), nil);
    funlist = cons(func_f0(closure_env, square), funlist);
  }
 
  for (iter = funlist; iter != nil; iter = cdr(iter)) {
    val fun = car(iter);
    val square = funcall(fun, nao);
 
    printf("%d\n", cnum(square));
  }
  return 0;
}

Here, we create an environment explicitly as an association list which we can search with the assoc function. The environment contains a binding for the symbol x. The square function retrieves the value and returns its square.

Output:

$ ./a.out
81
64
49
36
25
16
9
4
1
0

C++

Works with: C++11

#include <iostream>
#include <functional>
#include <vector>
 
int main() {
  std::vector<std::function<int()> > funcs;
  for (int i = 0; i < 10; i++)
    funcs.push_back([=]() { return i * i; });
  std::cout << funcs[3]() << std::endl;
 
  return 0;
}

Output:

9

C#

Using Linq

using System;
using System.Linq;
 
class Program
{
    static void Main()
    {
        var captor = (Func<int, Func<int>>)(number => () => number * number);
        var functions = Enumerable.Range(0, 10).Select(captor);
        foreach (var function in functions.Take(9))
        {
            Console.WriteLine(function());
        }
    }
}

Output:

0
1
4
9
16
25
36
49
64

Using delegates only

 
using System;
using System.Collections.Generic;
 
class Program
{
    static void Main( string[] args )
    {
        List<Func<int>> l = new List<Func<int>>();
        for ( int i = 0; i < 10; ++i )
        {
            // This is key to avoiding the closure trap, because
            // the anonymous delegate captures a reference to 
            // outer variables, not their value.  So we create 10
            // variables, and each created anonymous delegate 
            // has references to that variable, not the loop variable
            var captured_val = i;
            l.Add( delegate() { return captured_val * captured_val; } );
        }
 
        l.ForEach( delegate( Func<int> f ) { Console.WriteLine( f() ); } );
    }
}
 

Output:

0
1
4
9
16
25
36
49
64

Common Lisp

CL-USER> (defparameter alist
	   (loop for i from 1 to 10
	      collect (cons i (let ((i i))
				(lambda () (* i i))))))
ALIST
CL-USER> (funcall (cdr (assoc 2 alist)))
4
CL-USER> (funcall (cdr (assoc 8 alist)))
64

The loop mutates its binding i. The purpose of (let ((i i)) ...) is to create a different binding i for each lambda to capture. Otherwise, all 10 lambdas would capture the same binding and return 100.

D

Less Functional Version

import std.stdio;
 
void main() {
    int delegate()[] funcs;
 
    foreach (i; 0 .. 10)
        funcs ~= (i => () => i ^^ 2)(i);
 
    writeln(funcs[3]());
}

Output:

9

More Functional Version

import std.stdio, std.range, std.algorithm;
 
void main() {
    auto funcs = iota(10).map!(i => () => i*i)();
    funcs.map!q{ a() }().writeln();
}

Output:

[0, 1, 4, 9, 16, 25, 36, 49, 64, 81]

Emacs Lisp

Emacs Lisp now has lexical-let, which allows for the capture of variables.

 
(require 'cl)
(mapcar 'funcall
	(mapcar (lambda (x)
		  (lexical-let ((x x))
		    (lambda () (* x x)))) [1 2 3 4 5 6 7 8 9 10]))
;; => (1 4 9 16 25 36 49 64 81 100)
 

Erlang

Erlang uses lexical scoping and has anonymous functions.

 
-module(capture_demo).
-export([demo/0]).
 
demo() ->
    Funs = lists:map(fun (X) ->
                             fun () ->
                                     X * X
                             end
                     end,
                     lists:seq(1,10)),
    lists:foreach(fun (F) ->
                    io:fwrite("~B~n",[F()])
            end, Funs).
 

1> capture_demo:demo().
1
4
9
16
25
36
49
64
81
100
ok

Factor

Using lexical variables

USING: io kernel locals math prettyprint sequences ;
 
[let
    ! Create a sequence of 10 quotations
    10 iota [
        :> i            ! Bind lexical variable i
        [ i i * ]       ! Push a quotation to calculate i squared
    ] map :> seq
 
    { 3 8 } [
        dup pprint " squared is " write
        seq nth call .
    ] each
]

$ ./factor script.factor
3 squared is 9
8 squared is 64

The code :> i always binds a new variable. This happens inside a loop, so this program creates 10 different bindings. Each closure [ i i * ] captures a different binding, and remembers a different value.

The wrong way would use f :> i! 10 iota [ i! [ i i * ] ] map :> seq to mutate a single binding. Then the program would print, "3 squared is 81", "8 squared is 81".

Using fried quotations

Forget the variable! Each fried quotation captures some values by pulling them from the stack.

USING: fry io kernel math prettyprint sequences ;
 
! Push a sequence of 10 quotations
10 iota [
    '[ _ dup * ]        ! Push a quotation ( i -- i*i )
] map
 
{ 3 8 } [
    dup pprint " squared is " write
    over nth call .
] each
drop

Fantom

 
class Closures
{
  Void main ()
  {
    // define a list of functions, which take no arguments and return an Int
    |->Int|[] functions := [,]
 
    // create and store a function which returns i*i for i in 0 to 10
    (0..10).each |Int i|
    {
      functions.add (|->Int| { i*i })
    }
 
    // show result of calling function at index position 7
    echo ("Function at index: " + 7 + " outputs " + functions[7].call)
  }
}
 

Output:

Function at index: 7 outputs 49

Go

package main
 
import "fmt"
 
func main() {
    fs := make([]func() int, 10)
    for i := range fs {
        i := i
        fs[i] = func() int {
            return i * i
        }
    }
    fmt.Println("func #0:", fs[0]())
    fmt.Println("func #3:", fs[3]())
}

Output:

func #0: 0
func #3: 9

Groovy

Solution:

def closures = (0..9).collect{ i -> { -> i*i } }

Test:

assert closures instanceof List
assert closures.size() == 10
closures.each { assert it instanceof Closure }
println closures[7]()

Output:

49

Haskell

Using map:

fs = map (\i _ -> i * i) [1 .. 10]

Using list comprehensions:

fs = [const $ i * i | i <- [1 .. 10]]

Using infinite lists:

fs = take 10 coFs where coFs = [const $ i * i | i <- [1 ..]]

Testing:

> :t fs
fs :: [b -> Integer]
> map ($ ()) fs
[1,4,9,16,25,36,49,64,81,100]
> fs !! 9 $ ()
100
> fs !! 8 $ undefined
81

Icon and Unicon

This uses Unicon specific calling sequences for co-expressions. It can be made to run under Icon by modifying the calling syntax.

procedure main(args)                                      # Closure/Variable Capture
    every put(L := [], vcapture(1 to 10))                 # build list of index closures
    write("Randomly selecting L[",i := ?*L,"] = ",L[i]()) # L[i]() calls the closure
end
 
# The anonymous 'function', as a co-expression.  Most of the code is standard 
# boilerplate needed to use a co-expression as an anonymous function.
 
procedure vcapture(x)             # vcapture closes over its argument 
   return makeProc { repeat { x[1]^2 @ &source } }  
end
 
procedure makeProc(A)             # the makeProc PDCO from the UniLib Utils package
    return (@A[1], A[1])
end

Library: Unicon Code Library

package Utils provides makeProc Summary of Anonymous Functions in Unicon

Sample Output:

Randomly selecting L[8] = 64

J

The natural way of implementing this in J is to define a function which produces a gerund of a constant function.

constF=:3 :0
  {.''`(y "_)
)

Thus, a list of 10 functions each producing a value in 0..9, and another with their squares:

flist=: constF"0 i.10
slist=: constF"0 *:i.10

Referencing a function:

   flist @.3
3"_
   slist @.3
9"_

Using a function:

   flist @.4''
4
   slist @.4''
16

Running a randomly picked function which is not the last one:

   flist@.(?9) ''
7
   slist@.(?9) ''
25

Java

Works with: Java version 8+

import java.util.function.Supplier;
import java.util.ArrayList;
 
public class ValueCapture {
    public static void main(String[] args) {
	ArrayList<Supplier<Integer>> funcs = new ArrayList<>();
	for (int i = 0; i < 10; i++) {
	    int j = i;
	    funcs.add(() -> j * j);
	}
 
	Supplier<Integer> foo = funcs.get(3);
	System.out.println(foo.get()); // prints "9"
    }
}

JavaScript

var funcs = [];
for (var i = 0; i < 10; i++) {
    funcs.push( (function(i) {
                     return function() { return i * i; }
                })(i) );
}
window.alert(funcs[3]()); // alerts "9"

Works with: JavaScript version 1.7+

(Firefox 2+)

<script type="application/javascript;version=1.7">
var funcs = [];
for (var i = 0; i < 10; i++) {
    let (i = i) {
        funcs.push( function() { return i * i; } );
    }
}
window.alert(funcs[3]()); // alerts "9"
</script>

Maple

> L := map( i -> (() -> i^2), [seq](1..10) ):
> seq( L[i](),i=1..10);                      
                  1, 4, 9, 16, 25, 36, 49, 64, 81, 100
> L[4]();
                                   16
 

Mathematica

Function[i, i^2 &] /@ Range@10
->{1^2 &, 2^2 &, 3^2 &, 4^2 &, 5^2 &, 6^2 &, 7^2 &, 8^2 &, 9^2 &, 10^2 &}
 
%[[2]][]
->4

Objective-C

Works with: Cocoa version Mac OS X 10.6+

NSMutableArray *funcs = [[NSMutableArray alloc] init];
for (int i = 0; i < 10; i++) {
  [funcs addObject:[[^() { return i * i; } copy] autorelease]];
}
 
int (^foo)() = [funcs objectAtIndex:3];
NSLog(@"%d", foo()); // logs "9"
[funcs release];
 

OCaml

All functions in OCaml are closures.

let () =
  let cls = Array.init 10 (fun i -> (function () -> i * i)) in
  Random.self_init ();
  for i = 1 to 6 do
    let x = Random.int 9 in
    Printf.printf " fun.(%d) = %d\n" x (cls.(x) ());
  done

Output:

 fun.(4) = 16
 fun.(1) = 1
 fun.(4) = 16
 fun.(7) = 49
 fun.(3) = 9
 fun.(6) = 36

PARI/GP

Works with: PARI/GP version 2.4.2 and above

vector(10,i,()->i^2)[5]()

Output:

%1 = 25

Perl

my @f = map(sub { $_ * $_ }, 0 .. 9);   # @f is an array of subs
print $f[$_](), "\n" for (0 .. 8); # call and print all but last

output

0
1
4
9
16
25
36
49
64

Perl 6

All blocks are anonymous closures in Perl 6, and parameters are lexicals, so it's easy to generate a list of them. We'll use a gather/take generator loop, and call the closures in random order, just to keep things interesting.

my @c = gather for ^10 -> $i {
    take { $i * $i }
}
 
.().say for @c.pick(*);  # call them in random order

Output:

36
64
25
1
16
0
4
9
81
49

Or equivalently, using a more functional notation:

say .() for pick *, map -> $i { -> {$i * $i} }, ^10

PHP

Works with: PHP version 5.3+

<?php
$funcs = array();
for ($i = 0; $i < 10; $i++) {
    $funcs[] = function () use ($i) { return $i * $i; };
}
echo $funcs[3](), "\n"; // prints 9
?>

Works with: PHP version pre-5.3

This method can capture value types like numbers, strings, arrays, etc., but not objects.

<?php
$funcs = array();
for ($i = 0; $i < 10; $i++) {
    $funcs[] = create_function('', '$i = ' . var_export($i, true) . '; return $i * $i;');
}
echo $funcs[3](), "\n"; // prints 9
?>

PicoLisp

(setq FunList
   (make
      (for @N 10
         (link (curry (@N) () (* @N @N))) ) ) )

Test:

: ((get FunList 2))
-> 4

: ((get FunList 8))
-> 64

Pike

array funcs = ({});
foreach(enumerate(10);; int i)
{ 
  funcs+= ({ 
              lambda(int j)
              {
                  return lambda()
                         { 
                             return j*j; 
                         }; 
              }(i) 
          }); 
}

Prolog

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

:-use_module(library(lambda)).
 
 
closure :-
	numlist(1,10, Lnum),
	maplist(make_func, Lnum, Lfunc),
	maplist(call_func, Lnum, Lfunc).
 
 
make_func(I, \X^(X is I*I)).
 
call_func(N, F) :-
	call(F, R),
	format('Func ~w : ~w~n', [N, R]).
 

Output :

 ?- closure.
Func 1 : 1
Func 2 : 4
Func 3 : 9
Func 4 : 16
Func 5 : 25
Func 6 : 36
Func 7 : 49
Func 8 : 64
Func 9 : 81
Func 10 : 100
true.

Python

The naive way does not work:

funcs = []
for i in range(10):
    funcs.append(lambda: i * i)
print funcs[3]() # prints 81

The simplest solution is to add optional parameters with default arguments at the end of the parameter list, to create a local copy of the variable, and evaluate the variable at the time the function is created. (The optional parameter is not expected to ever be passed.) Often, the optional parameter will be named the same as the variable to be closed over (leading to odd-looking code of the form foo=foo in the arguments), so that the code inside the function need not be changed, but this might lead to confusion. This technique does not work for functions with a variable number of arguments.

funcs = []
for i in range(10):
    funcs.append(lambda i=i: i * i)
print funcs[3]() # prints 9

or equivalently the list comprehension:

funcs = [lambda i=i: i * i for i in range(10)]
print funcs[3]() # prints 9

Another solution is to wrap an immediately-executed function around our function. The wrapping function creates a new scope, and its execution forces the evaluation of the variable to be closed over.

funcs = []
for i in range(10):
    funcs.append((lambda i: lambda: i * i)(i))
print funcs[3]() # prints 9

or equivalently the list comprehension:

funcs = [(lambda i: lambda: i)(i * i) for i in range(10)]
print funcs[3]() # prints 9

In this case it is also possible to use map() since the function passed to it creates a new scope

funcs = map(lambda i: lambda: i * i, range(10))
print funcs[3]() # prints 9

It is also possible to use eval.

funcs=[eval("lambda:%s"%i**2)for i in range(10)]
print funcs[3]() # prints 9

R

R is a natural language for this task, but you need to understand the nuances of delayed evaluation. Arguments in R are referred to as promises because they aren't evaluated until first use. If you're not careful, you can bind to a promise that hasn't yet been evaluated, and you won't get what you expect.

 
# assign 's' a list of ten functions 
s <- sapply (1:10,  # integers 1..10 become argument 'x' below 
    function (x) {
        x  # force evaluation of promise x
	function (i=x) i*i   # this *function* is the return value
    })
 
s[[5]]()  # call the fifth function in the list of returned functions 
[1] 25    # returns vector of length 1 with the value 25
 

Note that I bound the captured variable as the default argument on a unary function. If you supply your own argument, as below, it squares the supplied argument and ignores the default argument.

 
s[[5]](10) 
[1] 100 
 

As a further technicality, note that you need some extra voodoo to modify the bound argument with persistence across calls. This example increments the bound variable after each call.

 
s <- sapply (1:10,  
    function (x) {
        x  # force evaluation of promise x
	function () {   
            R <- x*x 
            # evaluate the language expression "x <- x + 1" in the persistent parent environment 
            evalq (x <- x + 1, parent.env(environment()))
            R  # return squared value 
    }})
 
s[[5]]() 
[1] 25     # 5^2
s[[5]]() 
[1] 36     # now 6^2
s[[1]]()
[1] 1      # 1^2
s[[1]]()
[1] 4      # now 2^2
 

As shown, each instance increments separately.

Racket

 
#lang racket
(map (λ(f) (f)) 
     (for/list ([i 10]) (λ () (* i i))))
 

Output:

 
'(0 1 4 9 16 25 36 49 64 81)
 

REXX

/*REXX pgm has a list of 10 functions, each returns its invocation(idx)²*/
 
     do j=1  for 9                    /*invoke random functions 9 times.*/
     interpret 'CALL .'random(0,9)    /*invoke a randomly selected func.*/
     end   /*j*/                      /* [↑] the random func has no args*/
 
say 'The tenth invocation of  .0  ───► ' .0()
exit                                   /*stick a fork in it, we're done.*/
/*─────────────────────────────────list of 10 functions─────────────────*/
/*[Below is the closest thing to anonymous functions in the REXX lang.] */
 .0:return .(); .1:return .(); .2:return .(); .3:return .(); .4:return .()
 .5:return .(); .6:return .(); .7:return .(); .8:return .(); .9:return .()
/*─────────────────────────────────. function───────────────────────────*/
.: if symbol('@')=='LIT' then @=0 /*handle 1st invoke*/; @=@+1; return @*@

output

The tenth invocation of  .0  ───►  100

Ruby

irb(main):001:0> list = {}; (1..10).each {|i| list[i] = proc {i * i}}
=> 1..10
irb(main):002:0> list[3].call
=> 9
irb(main):003:0> list[7][]
=> 49

This works because i in (1..10).each {|i| ...} is local to its block. The loop calls the block 10 times, so there are 10 different variables to capture.

With Ruby 1.9, i is always local to its block. With Ruby 1.8, i is local unless there is another i in the outer scope. If i is not local, all 10 procs will return 100.

However, (on both Ruby 1.8 and 1.9) when using a for loop, the loop variable is shared and not local to each iteration:

irb(main):001:0> list = {}; for i in 1..10; list[i] = proc {i * i}; end
=> 1..10
irb(main):002:0> list[3][]
=> 100

Scheme

;;; Collecting lambdas in a tail-recursive function.
(define (build-list-of-functions n i list)
  (if (< i n)
      (build-list-of-functions n (+ i 1) (cons (lambda () (* (- n i) (- n i))) list))
      list))
 
(define list-of-functions (build-list-of-functions 11 1 '()))
 
(map (lambda (f) (f)) list-of-functions)
 
((list-ref list-of-functions 8))

Output:

(1 4 9 16 25 36 49 64 81 100)
81

Scala

val closures=for(i <- 0 to 9) yield (()=>i*i)
0 to 8 foreach (i=> println(closures(i)()))
println("---\n"+closures(7)())

Output:

0
1
4
9
16
25
36
49
64
---
49

Smalltalk

funcs := (1 to: 10) collect: [ :i | [ i * i ] ] .
(funcs at: 3) value displayNl .

Output:

9

Tcl

Tcl does not support closures (either value-capturing or variable-capturing) by default, but value-capturing closures are easy to emulate.

package require Tcl 8.6; # Just for tailcall command
# Builds a value-capturing closure; does NOT couple variables
proc closure {script} {
    set valuemap {}
    foreach v [uplevel 1 {info vars}] {
	lappend valuemap [list $v [uplevel 1 [list set $v]]]
    }
    set body [list $valuemap $script [uplevel 1 {namespace current}]]
    # Wrap, to stop untoward argument passing
    return [list apply [list {} [list tailcall apply $body]]]
    # A version of the previous line compatible with Tcl 8.5 would be this
    # code, but the closure generated is more fragile:
    ### return [list apply $body]
}
 
# Simple helper, to avoid capturing unwanted variable
proc collectFor {var from to body} {
    upvar 1 $var v
    set result {}
    for {set v $from} {$v < $to} {incr v} {lappend result [uplevel 1 $body]}
    return $result
}
# Build a list of closures
proc buildList {} {
    collectFor i 0 10 {
	closure {
	    # This is the body of the closure
	    return [expr $i*$i]
	}
    }
}
set theClosures [buildList]
foreach i {a b c d e} {# Do 5 times; demonstrates no variable leakage
    set idx [expr {int(rand()*9)}]; # pick random int from [0..9)
    puts $idx=>[{*}[lindex $theClosures $idx]]
}

Sample output:

5=>25
0=>0
8=>64
1=>1
8=>64