Sorting in Standard ML

(* Standard ML's List module provides sorting functionality for lists.
   We'll look at sorting for built-in types first. *)

(* The `sort` function in the List module is polymorphic and works
   for any type that has an ordering. *)

val strs = ["c", "a", "b"]
val sortedStrs = List.sort String.compare strs
val _ = print("Strings: " ^ String.concatWith " " sortedStrs ^ "\n")

(* An example of sorting integers *)
val ints = [7, 2, 4]
val sortedInts = List.sort Int.compare ints
val _ = print("Ints:    " ^ String.concatWith " " (List.map Int.toString sortedInts) ^ "\n")

(* We can also check if a list is already in sorted order *)
fun isSorted compare [] = true
  | isSorted compare [_] = true
  | isSorted compare (x::y::rest) = 
    compare(x, y) <= EQUAL andalso isSorted compare (y::rest)

val s = isSorted Int.compare sortedInts
val _ = print("Sorted:  " ^ Bool.toString s ^ "\n")

This Standard ML code demonstrates sorting functionality similar to the original example. Here’s an explanation of the key points:

1. Standard ML uses the List module for list operations, including sorting.

2. The List.sort function is polymorphic and works with any comparable type. It takes a comparison function as its first argument.

3. For strings, we use String.compare as the comparison function. For integers, we use Int.compare.

4. To print the results, we use String.concatWith to join the list elements into a string.

5. The isSorted function is a custom implementation to check if a list is sorted. It’s defined recursively and uses the provided comparison function.

6. Standard ML doesn’t have a built-in boolean type name, so we use Bool.toString to convert the boolean result to a string for printing.

To run this program, you would typically save it to a file (e.g., sorting.sml) and then use an Standard ML interpreter or compiler. For example, with the Standard ML of New Jersey (SML/NJ) system:

$ sml sorting.sml
Strings: a b c
Ints:    2 4 7
Sorted:  true

This example demonstrates how to perform sorting operations in Standard ML, showcasing its functional programming features and the use of the standard library modules.