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

On Sun, 06 Jun 2004 12:01:59 +0200 in comp.databases.theory, mAsterdam <mAsterdam_at_vrijdag.org> wrote:

>Brian Inglis wrote:
>> mAsterdam wrote:
>>>Brian Inglis wrote:
>>>>mAsterdam wrote:
>>>>><quote>
>>>>> Data on its own has no meaning, only
>>>>> when interpreted by some kind of data
>>>>> processing system does it take on
>>>>> meaning and become information.
>>>>></quote>
>>>>ISTM it's just the very old statement that a string of bits or bytes
>>>>by itself has no semantic content, but it gains semantics when it is
>>>>interpreted as a type: characters, an integer, or an FP number.
>>>
>>>(Type as 'valid set of values' - please correct me
>>>if you use another definition) The only semantics
>>>it gains by being interpreted as a type is
>>>being member of a set.
>>
>> Type or Class also allowing certain operations.
>
>(http://en.wikipedia.org/wiki/Peano_axioms)
>
>The Peano axioms define natural numbers
>by means of the 'successor' operator.
>But, say, addition - while surely possible
>on natural numbers does not define them.

The operations on numbers are an important part of the semantics of numeric data types and are part of the type definition IMHO.

>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.

>Some operators (help) define a type, other operators,
>though possible do not. I would think
>that all the possible operators would be part
>of the class definition, not the type.

I don't really see or make much distinction between type, domain, class, object, assuming the latter does not have the meaning of instance.

>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.

Types with operations as part of their semantic definition are much more interesting in that they can be combined in various ways to generate useful information not already available.

Sets as types would have limited usefulness by themselves alone, without any of the more interesting set operations and the associated semantics defined on them.

>> data has no meaning at the machine bits, bytes, words level;
>> data gains meaning at higher levels of abstraction, as it gains
>> tighter and tighter definitions of type.

-- 
Thanks. Take care, Brian Inglis 	Calgary, Alberta, Canada

Brian.Inglis_at_CSi.com 	(Brian dot Inglis at SystematicSw dot ab dot ca)
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