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[Bug 24569] Least common types and lattices

From: <bugzilla@jessica.w3.org>
Date: Fri, 07 Feb 2014 10:06:24 +0000
To: public-qt-comments@w3.org
Message-ID: <bug-24569-523-sZQyhFtwRf@http.www.w3.org/Bugs/Public/>
https://www.w3.org/Bugs/Public/show_bug.cgi?id=24569

--- Comment #5 from Michael Kay <mike@saxonica.com> ---
Perhaps there is a line of reasoning as follows. The subset relation defines a
lattice (see http://www.proofwiki.org/wiki/Power_Set_is_Complete_Lattice).
Every type has a value space S(T), and if T is a subtype of U then S(T) is a
subset of S(U) (However, the converse does not follow). 

This means that if we consider the value spaces defined by our types, then the
value spaces define a lattice under the subset relation. The types themselves
do not necessarily form a lattice, because two different types may have the
same value space.

When we do type inference for streamability, we are only interested in the
value space, and not in any other properties of the type. So we can regard two
types that have the same value space as equivalent for the purpose. If
equivalent types in this sense are regarded as a single type, then the types
(hopefully) form a lattice.

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