Problem Statement

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).

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.

Let's start with the solution:

fun accumulator (sum0:real) : real -> real = let
  val sum = ref sum0
  in
    fn n => (
      sum := !sum + n;
      !sum)
  end;

let
  val x = accumulator 1.0
  val _ = x 5.0
  val _ = accumulator 3.0
in
  print (Real.toString (x 2.3) ^ "\n")
end;