How to create and use my own structure/signature in SML/NJ?

Question

I'm new to functional programming and I want to create my own structure/signature called Dictionary. So far I have this in file called dictionary-en.sml:

(* The signature DICTIONARY defines a type and a programming interface for
   the dictionary data structure. The data structure allows us to store
   data in the form of (key, value) pairs and to query the data using a key. *)
signature DICTIONARY =
sig

    (* The structure has to implement a dictionary type. It defines key type,
       which has to support equality checking, and a value type for the data
       stored in the dictionary. *)
    type (''key, 'value) dict

    (* Creates an empty dictionary. *)
    val empty: (''key, 'value) dict

    (* Returns true if a key exists in the dictionary. *)
    val exists: (''key, 'value) dict -> ''key -> bool

end

And I have this in file solution.sml:

structure Dictionary :> DICTIONARY =
struct
    type (''key, 'value) dict = (''key * 'value) list

    val empty = []

    fun exists dict key =
        case dict of
            [] => false
          | (k, _ )::rep => if k = key
                            then true
                            else exists rep key
end

But I don't how to use this. When I wrote in REPL:

- Dictionary.exists [(3,"c"), (5, "e"), (7, "g")] 3;

I got this error:

stdIn:1.2-3.7 Error: operator and operand do not agree [tycon mismatch]
  operator domain: (''Z,'Y) Dictionary.dict
  operand:         ([int ty] * string) list
  in expression:
    Dictionary.exists ((3,"c") :: (5,"e") :: (<exp>,<exp>) :: nil)

Can someone please help me? I don't know what I did wrong.

Answer 1

In the function

fun exists dict key =
    case dict of
        [] => []
      | (k, _ )::rep => if k = key
                        then true
                        else exists rep key

I spot two issues:

• You can't return [] in one place and true in another.
• Instead of if P then true else Q, write P orelse Q.

You're using :> which means that the module is opaque, so you can only access the things specified in the signature. The internal list representation is not mentioned in the signature, so you can't refer to a dict as a list, even though you may know that that's how it's implemented. This is a feature.

I would probably call exists for member, since List.exists is a higher-order predicate, e.g. List.exists (fn x => x > 5) [3, 6, 9]. You could also deviate from any standard library naming and say containsKey and containsValue, or something like that.

Besides the insert function that molbdnilo suggested, you may like to have a fromList function.

Here's a refactored version (comments omitted for brevity, but I think your comments are good!):

signature DICTIONARY =
sig
    type (''key, 'value) dict

    val empty: (''key, 'value) dict
    val member: ''key -> (''key, 'value) dict -> bool
    val insert: (''key * 'value) -> (''key, 'value) dict -> (''key, 'value) dict
    val fromList: (''key * 'value) list -> (''key, 'value) dict
end

structure Dictionary :> DICTIONARY =
struct
    type (''key, 'value) dict = (''key * 'value) list

    val empty = []

    fun member key [] = false
      | member key ((key2, _)::dict) =
          key = key2 orelse member key dict

    fun insert (key, value) [] = [(key, value)]
      | insert (key, value) ((key2, value2)::dict) =
          if key = key2
          then (key, value) :: dict
          else (key2, value2) :: insert (key, value) dict

    fun fromList pairs = foldl (fn (pair, dict) => insert pair dict) empty pairs
end

---

But since you're building a dictionary module, there are two things you want to consider:

1. Make it possible to use some kind of binary tree as internal representation, requiring that the keys can be ordered rather than compared for equality.
2. Since Standard ML doesn't have special syntax like ''key to express that something can be ordered (Haskell generalises this as type classes, but Standard ML has only the special syntax ''key), this is a good case for using functors, which is the name given to higher-order modules, aka parameterised modules.

Here's an example signature, functor and structure that you can fill out:

signature ORD = sig
  type t
  val compare : t * t -> order
end

signature DICT = sig
  type key
  type 'value dict

  val empty: 'value dict
  val member: key -> 'value dict -> bool
  val insert: key * 'value -> 'value dict -> 'value dict
  val fromList: (key * 'value) list -> 'value dict
end

functor Dict (Ord : ORD) :> DICT = struct
  type key = Ord.t
  type 'value dict = (key * 'value) list

  val empty = ...
  fun member _ _ = raise Fail "not implemented"
  fun insert _ _ = raise Fail "not implemented"
  fun fromList _ = raise Fail "not implemented"
end

At this point you can change type 'value dict into using a binary tree, and when you need to decide whether to go left or right in this binary tree, you can write:

case Ord.compare (key1, key2) of
     LESS => ...
   | EQUAL => ...
   | GREATER => ...

And when you need a dictionary where the key is some particular orderable type, you can create a module using this functor:

structure IntDict = Dict(struct
                           type t = int
                           val compare = Int.compare
                         end)

structure StringDict = Dict(struct
                              type t = string
                              val compare = String.compare
                            end)

See also Standard ML functor examples for more examples.

Answer 2

You can't access the internal representation; the entire interface is given by the signature.
You need to add to the signature some way to create a dictionary without depending on the representation used in a particular structure.

For instance,

val insert : (''key * 'value) -> (''key, 'value) dict -> (''key, 'value) dict

would let you write

Dictionary.exists (Dictionary.insert (3,"c") Dictionary.empty) 3;

Implementation left as an exercise.