[Ur] Ur record types as sets of fields

[Anthony Clayden]

Hi citizens of Ur,

A long while back, Adam responded in a discussion about Ur's record system  http://blog.ezyang.com/2012/04/how-urweb-records-work-and-what-it-might-mean-for-haskell/#comment-3705

I'm wondering whether Ur's disjointness constraint might be used to build a record merge operator -- as needed for Relational Algebra Natural Join.

(I'm finding it a bit weird using `~` for disjointness: I'm so used to it being a type equality constraint in Haskell. So apologies if I stuff up. Also in the Ur materials I looked at, I don't see how to express type equality? For equality of record types I mean same set of field names, and same type of each corresponding field.)

Given two records of type t1, t2 with (some) fields in common, some private; let's chop their fields into projections:
t1' -- fields private to t1
t1_2 -- fields in common
t2' -- fields private to t2

Then we can say (treating `++` as union of fields): 
t1 is [ t1' ++ t1_2 ]; 
t2 is [ t1_2 ++ t2' ]; 
the result of Natural Join is [ t1' ++ t1_2 ++ t2' ].

We also require those projections to be disjoint: 
[ t1' ~ t1_2 ], [ t1' ~ t2' ], [ t1_2 ~ t2' ]

Those constraints uniquely 'fix' all those record types modulo ordering of names/fields in the records. Is that going to work?

It also feels weird using `++` for record union: again it strongly suggests Haskell's list concatenation, which is non-commutative. Perhaps Ur's `++` is non-commutative(?) It's the inbuilt semantics for `$( )`, `!` that make `++` commutative in effect(?)

Thank you
AntC
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