# Re: foreign key constraint versus referential integrity constraint

From: paul c <toledobythesea_at_oohay.ac>
Date: Wed, 28 Oct 2009 22:57:15 GMT
Message-ID: <f%3Gm.50644\$PH1.37179_at_edtnps82>

```>> Tegiri Nenashi wrote:
>> ...
>>
>>> Is view definition a constraint? IMO it's purely terminological
>>> matter. Consider relations x and y defined by some algebraic
>>> identities. Is adding new view z (as a function of x and y) adding a
>>> constraint to the system?
>>>
>>> Let's analyze a simpler example. Consider two real values constrained
>>> by the equality:
>>>
>>> x + y = 5
>>>
>>> Is introducing a new variable z, say
>>>
>>> z = x - 2y
>>>
>>> a new constraint imposed onto the system? Not really, because,
>>> variable z is redundant and can be eliminated, and it doesn't affect
>>> the formal property of the system of being under constrained.
>>
>> That is a form of argument that I've seen quite often regarding
>> various RM questions, not just this one.  I'd have no problem with it
>> were it not called an "example".  Since it is about arithmetic, it's
>> at best a mere analogy to relations and we need to decide whether the
>> analogy should apply.
```

>
> Ahem.
>
> x + y = 5 is a relation. z = x - 2y is a relation. They are linear
> polynomial functions, and all functions are relations.
>
> x*x + y*y + z*z - r*r = 0 is also a relation. It is a relation
> describing a sphere of radius r centered at the origin. It is also a
> polynomial. While it is not a function, it is a relation.
>
>
```>> To try to answer that I would ask when do we ever record "extensions"
>> of arithmetic equations?
```

>
> Whenever anyone writes the word "let":
>
> Let u = x-3, v=y+2, w=z-1...
>
>
```>> In other words, just because we have abstract operations for both
>> numbers and relations doesn't mean one should mimic the other.  If
>> that's so, maybe somebody else can put it better.
```

>
> Whether involving numbers or no numbers, a relation is a relation. What
> we can do with relations doesn't change because some of them involve
> numbers and some of them do not.

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