Re: A datatype that is, and is not, an equality type?

On 09/01/2013 08:27 AM, Phil Clayton wrote:
> However, none of them accept
>
>     signature S =
>       sig
>         eqtype 'a t
>         val eq : 'a t * 'b t ->  bool
>       end
>
>     structure S :>  S =
>       struct
>         datatype 'a t = A of int
>         fun eq (a, b) = a = b
>       end
>
> on the grounds that 'a t is _not_ an equality type!
>    

That's not what I see from SML/NJ, and not what I'd expect from my 
understanding of SML.  Rather, the issue with [eq] is that equality only 
works on two operands of the _same_ type, whereas here you are trying to 
apply it on values of _different_ types ['a t] and ['b t].  This notion 
of "different" comes from SML's basic semantics of datatype declarations.

As we would expect from that explanation, the following module 
definition works fine:

    structure S :> S =
      struct
        datatype t' = A of int
        type 'a t = t'
        fun eq (a, b) = a = b
      end

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