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

01/09/13 13:42, Adam Chlipala wrote:
> 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.

Good point.  That was a mistake in the example and not actually the 
issue I was intending to ask about.  Sorry.  I should have said that 
none of them accept

    signature S =
      sig
        eqtype 'a t
        val eq : 'a t * 'a 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 (even though it is 
accepted as an equality type as shown in my previous message).


> 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

That's a better work-around when the type parameter is not referenced in 
the datatype.  For the actual example, I have

     datatype 'a t = A of 'a ref

Phil

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