HaloO,
Ruud H.G. van Tol wrote:
TSa schreef:
A(|)B produces a subtype of A and B, and that A(&)B
produces a supertype
Are you sure?
Very sure ;)
In record subtyping a record is a mapping of labels to types.
In Perl 6 speak this is what a package does. One record type
is a subytpe if it has a superset of the label set and the
types of the common labels are subtypes. This record is the
intension set of types. When it grows the "number" of objects
in the extension set decreases. The limiting cases are the
universal set Any that has the empty intension set and Undef
or Whatever with the universal intension set but no defined
instances.
I see "&" as "limiting; sub" and "|" as "enlarging;
super".
To me, "&" is connected to multiplication (and inproduct, statistics,
fuzzy logic), and "|" to addition (and outproduct).
As I just wrote elsewhere this is the extensional view of the
sets underlying types. The extension of Bool e.g. is {0,1} and
that of Int is {...,-2,-1,0,1,2,...} from which one argues that
Bool is a subtype of Int and that Bool(&)Int (=) Bool. On the
interface side of things Bool has to support all methods that
Int has, e.g. +, -, *, and /. Note that both types are not closed
under these operations: 1 + 1 == 2, 5/4 == 1.25. Bool adds logical
operators like && and || to the intension set.
Regards, TSa.
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