# Re: Function

From: Bob Badour <bbadour_at_pei.sympatico.ca>

Date: Tue, 15 Jan 2008 14:22:50 -0400

Message-ID: <478cf9fc$0$4077$9a566e8b_at_news.aliant.net>

> This is not good enough. It is possible that a value exists in the

> This seems right. A domain is just a set of values. In relational

> On the other hand, mathematics does not require a domain to be non-empty.

> No, there is always just one meaning of function in database.

> Essentially correct, although to be rigorous you need to define how such

> Yea. It's really an abused use of the term in software design.

> Fair.

Date: Tue, 15 Jan 2008 14:22:50 -0400

Message-ID: <478cf9fc$0$4077$9a566e8b_at_news.aliant.net>

Kira Yamato wrote:

> On 2008-01-15 09:26:01 -0500, mAsterdam <mAsterdam_at_vrijdag.org> said:

*>
*

>> vldm10 wrote: >> >>> I think it will be good to have two definitions for the functions in >>> your glossary. >>> Definition1 A function from A to B is a rule that assigns, to each >>> member of set A, exactly one member of set B. >>> >>> And second definition is similar to Jan's suggestion, but slightly >>> changed: >>> Definition2 >>> A function from A to B is a relation between A and B that associates >>> each element of A with exactly one element of B. >>> >>> First definition says that a function do something. You can call it >>> intutive definition of a function. Here the function in fact is a >>> procedure as you mentioned. >>> Second definition is set theoretic. >> >> Another difference I see with Jan's is a sense of direction. >> >> How about this: >> cdt glossary proposal: >> >>>> [Codomain] >>>> See function, math context. >>>> >>>> [Domain] >>>> 1. Given a relation R, a domain is a set Sn such >>>> that for each tuple (A1, A2, ...An, ...Am) in R, >>>> An is an element of Sn.

*>*> This is not good enough. It is possible that a value exists in the

*> domain Sn yet the relation has no corresponding tuple which holds that**> value for An.**>*>>>> >>>> 2. A domain is a set of values: for example >>>> "integers between 0 and 255", >>>> "character strings less than 10 characters long", >>>> "dates". >>>> Sometimes used synonymously with type.

*>**>*> This seems right. A domain is just a set of values. In relational

*> algebra, this set is required to be non-empty since attributes are**> non-null.*Theoretically, the universal subtype has an empty set of values and the union of all operations.

>>>> 3. Domain of a function. See function, math context.

*>*> On the other hand, mathematics does not require a domain to be non-empty.

*>*>>>> [Function] >>>> For now we have to live with different meanings >>>> of _function_ when talking about databases: >>>> "The function of this function is to get the tuples from B >>>> that are functionally dependant on A."

*>*> No, there is always just one meaning of function in database.

I got "and", "but", and "or". They'll get you pretty far. (Apologies to our European friends and the younger crowd in the audience for the inside joke.)

>>>> Three different contexts, but just about the same meaning: >>>> >>>> 1. General >>>> A purpose or use. >>>> >>>> 2. Math >>>> A binary mathematical relation over two sets D and C that associates >>>> with each element in D exactly one element in C. >>>> Set D is called the domain of the function, C its codomain.

*>*> Essentially correct, although to be rigorous you need to define how such

*> binary relation can define the meaning of "associating each element in D**> exactly one element in C."**>**> Not all binary relation has this property.**>*>>>> 3. Software >>>> A subroutine, procedure, or method.

*>*> Yea. It's really an abused use of the term in software design.

*> Subroutines in software has no clear domain since same input arguments**> can product different outputs.*If one considers internal state an input, I am not entirely sure what you said is true.

>>>> In both the math and software context, there is a sense of >>>> direction from domain (input) to codomain (output). >>>> For most purposes, this intuitive picture is good enough: >>>> >>>> |------------| >>>> --- x ---- >| f-machine |------ f(x) ----- > >>>> |------------| >>>> >>>> Where x is input in the "f-machine" and f(x) is output.

*>*> Fair.

*>*>>>> >>>> notes: >>>> every operator is a function >>>> every function is a relation

*>**> Yes.*Technically, in the standard vocabularies, every operator is a symbol not a function. Received on Tue Jan 15 2008 - 19:22:50 CET