Accumulator factory

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

A problem posed by Paul Graham is that of creating a function that takes a single (numeric) argument and which returns another function that is an accumulator. The returned accumulator function in turn also takes a single numeric argument, and returns the sum of all the numeric values passed in so far to that accumulator (including the initial value passed when the accumulator was created).

The detailed rules are at http://paulgraham.com/accgensub.html and are reproduced here for simplicity (with additions in small italic text).

Before you submit an example, make sure the function

1. Takes, and returns functions that take, exactly one argument.
2. Works for any numeric type-- i.e. can take both ints and floats and returns functions that can take both ints and floats. (It is not enough simply to convert all input to floats. An accumulator that has only seen integers must return integers.) (i.e., if the language doesn't allow for numeric polymorphism, you have to use overloading or something like that)
3. Generates functions that return the sum of every number ever passed to them, not just the most recent. (This requires a piece of state to hold the accumulated value, which in turn means that pure functional languages can't be used for this task.)
4. Returns a real function, meaning something that you can use wherever you could use a function you had defined in the ordinary way in the text of your program. (Follow your language's conventions here.)
5. Doesn't store the accumulated value or the returned functions in a way that could cause them to be inadvertantly modified by other code. (No global variables or other such things.)

E.g. if after the example, you added the following code (in a made-up language) where the factory function is called foo:

<lang pseudocode>x = foo(1);

x(5); foo(3); print x(2.3);</lang>

It should print 8.3. (There is no need to print the form of the accumulator function returned by foo(3); it's not part of the task at all.)

The purpose of this task is to create a function that implements the described rules. It need not handle any special error cases not described above. The simplest way to implement the task as described is typically to use a closure, providing the language supports them.

Where it is not possible to hold exactly to the constraints above, describe the deviations.

C++

Deviation: The return type is wrong when the accumulator is called with an integer argument after is has been called with a float argument.

<lang cpp>class Acc { public:

   Acc(int init)
       : _type(intType)
       , _intVal(init)
   {}

   Acc(float init)
       : _type(floatType)
       , _floatVal(init)
   {}

   int operator()(int x)
   {
       if( _type == intType )
       {
           _intVal += x;
           return _intVal;
       }
       else
       {
           _floatVal += x;
           return static_cast<int>(_floatVal);
       }
   }

   float operator()(float x)
   {
       if( _type == intType )
       {
           _floatVal = _intVal + x;
           _type = floatType;
           return _floatVal;
       }
       else
       {
           _floatVal += x;
           return _floatVal;
       }
   }

private:

   enum {floatType, intType} _type;
   float _floatVal;
   int _intVal;

};

int main(int argc, char* argv[]) {

   Acc a(1);
   a(5);
   Acc(3);
   std::cout << a(2.3f);
   return 0;

}</lang>

Clojure

The atom function creates an atomically updatable identity holding a value. The swap! function atomically updates the atom's value, returning the new value. The function returned from an accum call satisfies all the requirements. <lang lisp>(defn accum [n]

 (let [acc (atom n)]
   (fn [m] (swap! acc + m))))</lang>

Common Lisp

<lang lisp>(defun accumulator (sum)

 (lambda (n)
   (setf sum (+ sum n))))</lang>

Example usage: <lang lisp>(defvar x (accumulator 1)) (funcall x 5) (accumulator 3) (funcall x 2.3)</lang> This prints:

X
6
#<CLOSURE :LAMBDA (N) (SETF SUM (+ SUM N))>
8.3

E

<lang e>def foo(var x) {

 return fn y { x += y }

}</lang>

Factor

<lang factor>:: accumulator ( n! -- quot ) [ n + dup n! ] ;

1 accumulator [ 5 swap call drop ] [ drop 3 accumulator drop ] [ 2.3 swap call ] tri .</lang>

Haskell

Translation of: Ruby

<lang haskell>import Control.Monad.ST import Data.STRef

accumulator :: (Num a) => a -> ST s (a -> ST s a) accumulator sum0 = do

 sum <- newSTRef sum0
 return $ \n -> do
   modifySTRef sum (+ n)
   readSTRef sum

main :: IO () main = print foo

   where foo = runST $ do
                 x <- accumulator 1
                 x 5
                 accumulator 3
                 x 2.3</lang>

outputs

8.3

J

See http://www.jsoftware.com/jwiki/Guides/Lexical%20Closure

<lang J>oleg=:1 :0

 a=. cocreate
 n__a=: m
 a&(4 : 'n__x=: n__x + y')

)</lang>

Example use:

   F=: 10 oleg
   F 11
21
   F 12
33

Java

Java has no first-class functions; the standard syntactic workaround is to use a standard method name. Java uses objects to maintain state. <lang java>public class Accumulator {

   private double sum;
   public Accumulator(double sum0) {
       sum = sum0;
   }
   public double call(double n) {
       return sum += n;
   }

   public static void main(String[] args) {
       Accumulator x = new Accumulator(1);
       x.call(5);
       System.out.println(new Accumulator(3));
       System.out.println(x.call(2.3));
   }

}</lang> outputs

Accumulator@42e816
8.3

To do a full version that sums with integers as long as possible before switching to double-precision floats requires a little more work and the use of the Number class...

Works with: Java version 5.0

<lang java5>public class Accumulator {

   private Long sumA; // non-null if we're working in the integer domain
   private double sumB;
   public Accumulator(Number sum0) {

if (sum0 instanceof Double) { sumB = sum0.doubleValue(); } else { sumA = sum0.longValue(); }

   }
   public Number call(Number n) {
       if (sumA != null) {

if (n instanceof Double) { sumB = n.doubleValue() + sumA; sumA = null; return sumB; }

           return sumA += n.longValue();
       }
       return sumB += n.doubleValue();
   }

   public static void main(String[] args) {
       Accumulator x = new Accumulator(1);
       x.call(5);
       Accumulator y = new Accumulator(3);
       System.out.println(y+" has value "+y.call(0));
       System.out.println(x.call(2.3));
   }

}</lang> Producing this sample output:

Accumulator@6100ab23 has value 3
8.3

JavaScript

Translation of: Ruby

Works with: SpiderMonkey

<lang javascript>function accumulator(sum) {

   return function(n) {return sum += n}

}

x = accumulator(1); x(5); print(accumulator(3)); print(x(2.3));</lang>

output

function (n) {
    return sum += n;
}
8.3

OCaml

Translation of: Ruby

<lang ocaml>let accumulator sum0 =

 let sum = ref sum0 in
 fun n ->
   sum := !sum +. n;
   !sum

let () =

 let x = accumulator 1.0 in
 x 5.0;
 accumulator 3.0; (* generates a warning because we are discarding a non-unit value *)
 Printf.printf "%g\n" (x 2.3)

</lang>

outputs

8.3

Oz

A bit unwieldy because the '+' operator does not allow mixed type operands. The implementation is thread-safe (atomic Exchange operation). <lang oz>declare

 fun {Acc Init}
    State = {NewCell Init}
 in
    fun {$ X}
       OldState
    in
       {Exchange State OldState} = {Sum OldState X}
    end
 end

 fun {Sum A B}
    if {All [A B] Int.is} then A+B
    else {ToFloat A}+{ToFloat B}
    end
 end

 fun {ToFloat X}
    if {Float.is X} then X
    elseif {Int.is X} then {Int.toFloat X}
    end
 end

 X = {Acc 1}

in

 {X 5 _}
 {Acc 3 _}
 {Show {X 2.3}}</lang>

Perl

Translation of: Ruby

<lang perl>sub accumulator {

 my $sum = shift;
 sub { $sum += shift }

}

my $x = accumulator(1); $x->(5); print accumulator(3), "\n"; print $x->(2.3), "\n";</lang> outputs

CODE(0x91131f0)
8.3

Perl 6

Works with: Rakudo version #23 "Lisbon"

<lang perl6>sub accum ($n is copy) { sub { $n += $^x } }</lang>

Example use:

<lang perl6>my $a = accum 5; $a(4.5); say $a(.5); # Prints "10".</lang>

Python

Translation of: Ruby

Works with: Python version 3.x

<lang python>def accumulator(sum):

 def f(n):
   nonlocal sum
   sum += n
   return sum
 return f

x = accumulator(1) x(5) print(accumulator(3)) print(x(2.3))</lang> outputs

<function f at 0xb7c2d0ac>
8.3

Ruby

Add some output to the 2nd call to "accumulator" to show what it returns <lang ruby>def accumulator(sum)

 lambda {|n| sum += n}

end

x = accumulator(1) x.call(5) p accumulator(3) puts x.call(2.3)</lang> outputs

#<Proc:0x1002f14c@accumulator.rb:5>
8.3

Scala

The type of a function can't change in Scala, and there is no "numeric" type that is a supertype of all such types. So, if the accumulator is declared as integer, it can only receive and return integers, and so on.

<lang scala>def AccumulatorFactory[N](n: N)(implicit num: Numeric[N]) = {

 import num._
 var acc = n
 (inc: N) => {
   acc = acc + inc
   acc
 }

}</lang>

Sample:

scala> val x = AccumulatorFactory(1.0)
x: (Double) => Double = <function1>

scala> x(5.0)
res7: Double = 6.0

scala> AccumulatorFactory(3.0)
res8: (Double) => Double = <function1>

scala> println(x(2.3))
8.3

Scheme

Translation of: Ruby

<lang scheme>(define (accumulator sum)

 (lambda (n)
   (set! sum (+ sum n))
   sum))

or

(define ((accumulator sum) n)

 (set! sum (+ sum n))
 sum)

(define x (accumulator 1)) (x 5) (display (accumulator 3)) (newline) (display (x 2.3)) (newline)</lang> outputs

#<procedure>
8.3

Tcl

Works with: Tcl version 8.6

This uses nested coroutines to manage the state, which for the outer coroutine is a counter used to generate unique instances of the inner coroutine, and for the inner coroutine it is the actual accumulator variable. Note that Tcl commands (including coroutines) are never nameless, but it is trivial to synthesize a name for them. It's possible to guarantee uniqueness of names, but just using a simple sequence generator gets 90% of the effect for 10% of the effort. <lang tcl>package require Tcl 8.6

1. make the creation of coroutines without procedures simpler

proc coro {name arguments body args} {

   coroutine $name apply [list $arguments $body] {*}$args

}

1. Wrap the feeding of values in and out of a generator

proc coloop {var body} {

   set val [info coroutine]
   upvar 1 $var v
   while 1 {

set v [yield $val]

       if {$v eq "stop"} break

set val [uplevel 1 $body]

   }

}

1. The outer coroutine is the accumulator factory
2. The inner coroutine is the particular accumulator

coro accumulator {} {

   coloop n {

coro accumulator.[incr counter] n { coloop i { set n [expr {$n + $i}] } } $n

   }

}</lang> Sample usage (extra characters over Paul's example to show more clearly what is going on): <lang tcl>% set x [accumulator 1]

accumulator.1

% $x 5 6 % accumulator 3

accumulator.2

% puts ">>[$x 2.3]<<" >>8.3<<</lang>