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*To*: "Peter H. Froehlich" <address@hidden>*Subject*: Re: Any and Every... (was Re: Eval)*From*: address@hidden*Date*: 09 Jan 2002 11:02:42 -0500*Cc*: address@hidden*In-reply-to*: <376F243A-048F-11D6-B058-003065F6D8BE@ics.uci.edu>*References*: <376F243A-048F-11D6-B058-003065F6D8BE@ics.uci.edu>*Sender*: address@hidden*User-agent*: Gnus/5.0808 (Gnus v5.8.8) XEmacs/21.4 (Civil Service (Windows))

"Peter H. Froehlich" <pfroehli@ics.uci.edu> writes: > Hi there! > > I think now the terminology gets completely out of hand. :-) > > Let's say my language L has the simple types INTEGER and BOOLEAN as > well as the compound types (well, type-constructors) ARRAY and > RECORD. The "set of types in L" is {INTEGER, BOOLEAN, ARRAY, RECORD} > where ARRAY and RECORD stand for "all declared ARRAY and RECORD types" > (so there are lots). > > > The subset of simple types of L is {INTEGER, BOOLEAN} and the subset > of compound types of L is {ARRAY, RECORD}. Now why would I *not* be > able to talk about the intersection of these to subsets being empty? Well, you could talk about the types themselves, but you probably are more interested in talking about the *elements* within them. So let's say my language has simple types `positive-integer', `negative-integer', and `boolean'. Sure I could make a set of some of these types {`positive-integer', `boolean'}, but what of it? It is a set with two elements. So is {`positive-integer', `negative-integer'}. These sets aren't even representable in my language! What is much more interesting is talking about the *elements* of the types. `positive-integer' is a set {1, 2, 3, ...} and `negative-integer' is a set {-1, -2, -3}. The union of these is {1, -1, 2, -2, 3, -3, ....} and the intersection is {}.

**References**:**Re: Any and Every... (was Re: Eval)***From:*"Peter H. Froehlich" <pfroehli@ics.uci.edu>

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