[Ur] Ur record types as sets of fields

[Anthony Clayden]

> On 4/11/2017, at 12:57 AM, Adam Chlipala <adamc at csail.mit.edu> wrote:
> 
>> On 11/02/2017 09:51 PM, Anthony Clayden wrote:
>> I'm curious what the full signature would look like. Here's my guess:
>> 
>>     fun natJoin [ t1' :: {Type} ] [ t1_2 :: {Type} ] [ t2' :: {Type} ]
>>                     [ t1' ~ t1_2 ] [ t1' ~ t2' ] [ t1_2 ~ t2' ]
>>                     ( t1 : $( t1' ++ t1_2 ) )  ( t2 : $( t1_2 ++ t2' ) )
>>                     = ??
> 
> One possibility is:
>     t1 ++ (t2 --- t1_2)

IIUC that's merely projecting away the t1_2 attributes from t2; then cross-multiplying with t1(?) What it needs is matching records type t1 with records type t2 that have the same values in the fields in common -- i.e. in their t1_2 fields. That's typically implemented as a record-by-record fold over one argument.

> It's not clear to me what result type you expect, though.
> 
Oh, that was in the earlier message: [ t1' ++ t1_2 ++ t2' ]

Perhaps that should be $( t1' ++ t1_2 ++ t2' )

What I gave was based on the `fun proj ...` definition in the 'Ur by example' section of your paper, which doesn't give the type of the result.


>> And how would I invoke it? With those three `~` constraints, does that need
>> 
>>     natJoin ! ! ! r1 r2
>> 
>> And can Ur figure out the rest?
> 
> Disjointness proofs are implicit by default, so just
>     natJoin r1 r2
> 
cool. thanks 

AntC