[pattern-switch] Totality

[Brian Goetz]

>
>> We can easily generalize the definition of totality to a set of 
>> patterns.  In this case, we can handle sealed types and enums:
>>
>>  - Let E be an enum type.  The set of patterns { C1 .. Cn } is total 
>> on E with remainder { null, E e } if C1 .. Cn contains all the 
>> constants of E.
>>
>> Observation: that `E e` pattern is pretty broad!  But that's OK; it 
>> captures all novel constant values, and, because the explicit cases 
>> cover all the known values, captures only the novel values.  Same for 
>> sealed types:
>>
>>  - Let S be a sealed abstract type or interface, with permitted 
>> direct subtypes C*, and P* be a set of patterns applicable to S.  If 
>> for each C in C*, there exists a subset Pc of P* that is total on C 
>> with remainder Rc, then P* is total on S with remainder { null } 
>> union \forall{c \in C}{ Rc }.
>
> I think there should not be set braces around that last occurrence of 
> “Rc”.

Right.

> I assume that this use of syntax “T = U | V” is meant to imply that T 
> is a sealed type that permits U and V.

Right.

>
>> { Circle, Rect } total on Shape with remainder { Shape, null }
>>
>> -> { Box(Circle), Box(Rect) total on Box<Shape> with remainder { 
>> Box(Shape), Box(null), null }
>>
>> -> { Bag(Circle), Bag(Rect) total on Bag<Shape> with remainder { 
>> Bag(Shape), Bag(null), null }
>>
>> -> P* total on Container<Shape> with remainder { 
>> Container(Box(Shape)), Container(Box(null)), Container(Bag(Shape)), 
>> Container(Box(Shape)), Container(null), null }
>
> I believe that, in this last remainder, the second occurrence of 
> `Container(Box(Shape))` was intended to be `Container(Bag(null))`.

Yes, cut and paste bug.  This IDE needs better inspection helpers!

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