On Jun 14, 2:48 pm, ····@zedat.fu-berlin.de (Stefan Ram) wrote:
> I was searching for a word referring to the »x« and »y« in the
> relation »R(x,y)«. Assume, for a moment, the word would be
> »alpha« and »beta«, respectively, then I would like to write
> this explanation of "is a":
>
> "is a"
> the relation, where the alpha "is a"(n) instance of the beta
> ¯¯¯¯¯ ¯¯¯¯
> I looked up these web pages to find common, simple words for
> the placeholders »alpha« and »beta«:
>
> ://en.wikipedia.org/wiki/Relation_algebra
>
>'the relation, where the alpha "is a"(n) instance of the beta'
"Is a" is recursively defined? Except you don't seem to have a
limiting condition.
Perhaps if you used a more concrete starting definition you wouldn't
have so much trouble.
(car (1 2 3)) => 1
(cdr (1 2 3)) => (2 3)
car is an instance of the cdr?
1 is an instance of 2 3
> .
>
> I found none.
>
(member 1 (set 1 2 3))
member is an instance of set
1 is an instance of 1 2 3
How about member and set?
> So actually, »CAR« and »CDR« are the nicest words for these
> concepts I am aware of. I can pronounce them, I do not think
> of IBM 704 registers when I use them. And they are well
> established. Or are there any other terms, I could use instead
> of »alpha« and »beta« above?
>
> I could use »first component« and »second component«, but this
> is a two-word term (compound term). I do not deem compound
> terms to be appropriate for such fundamental concepts. For the
> same reason, I prefer »pair« to »2-tuple«. A 2-tuple might
> have a »first component« and a »second component«, but a pair
> should have a CAR and a CDR (or some other single-word term).
A pair should have car and cdr? a pair or a cons? a cons maybe.