Re: It don't mean a thing ...

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"Brian Inglis" <Brian.Inglis_at_SystematicSw.Invalid> wrote in message news:9la8c05mod79mgocfogfpeia654oh5i9bk_at_4ax.com...
> On Sun, 06 Jun 2004 12:01:59 +0200 in comp.databases.theory, mAsterdam
> <mAsterdam_at_vrijdag.org> wrote:
>

> >Using type in the 'valid set of values' way:
>
> Types as 'valid sets of values' can only be tested for existence and
> membership and have limited usefulness mainly for validity checking.
> Without even those meagre existence and membership predicate
> operations which depend on some comparison operation, the type would
> be a uselessly abstract concept, not even an idea.
>
> But types as 'valid sets of values' in the sense of equivalence
> classes with properties and possibly associated or value dependent
> operations are much more interesting and useful objects.

Why "equivalence classes" ?
Why not "closed sets" ?

> >The defining operators affect meaning,
> >the others, though they do affect use,
> >do not affect meaning.
>
> You are claiming that the operations which may be used on a type do
> not affect the meaning of the type.
> But you also state that operations affect use, so you must admit that
> types without operations may be useless.
> Would you not agree that the change of the type from useless to useful
> certainly gives the type additional meaning in changing that use
> property, plus those additional operations adds information not
> originally available from the type and so affects the type semantics?
>
> ISTM the operations which may be used on what you call a type are both
> an enhancement and a tightening of the definition and meaning of the
> type, making it a different type, and so the operations allowed on
> types are an integral part of the type semantics.

The question is if *ALL* operations allowed on a type are integral part of the type *semantics* and if *ALL* operations allowed on a type are integral part of the type *definition*.

This is a chicken and egg situation.
A type has a 'valid set of values' and a 'set of operations' associated. The problem is that one can define the 'valid set of values' as domain or codomain of 'set of operations' and the definition of a 'valid set of values' is a prerequisite for defining some 'set of operations'.

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