Christoph Zwerschke wrote:
> Bryan Olson schrieb:
>
>>> Still think there is no such thing?
>>
>>
>> Uh, yes.
>>
>> The Cartesian product of two sets A and B (also called the
>> product set, set direct product, or cross product) is defined to
>> be the set of [...]
>>
>> All sets, no strings. What were you looking at?
>
>
> Not only sets. This goes on (anyway "everything is a set"). You can also
> have the Cartesian product of functions. And you can think of a string
> as a function from a countable index set I to the set of all characters
> C. So the Cartesian product of two strings will become a function from
> IxI to CxC. Since IxX is countable again, this is equivalent to a tuple
> of 2-tuples of characters which you can also interpret as a tuple of
> strings with 2 chars:
>
> "ab" x "cd" = ("ac", "ad", "bc", "bd")
>
> Do I have eliminated all remaining clarities now? :-)
>
> -- Christoph
Christoph,
i think you raised a great issue: a lack of efficient support for
"combining" objects. Any language, if has smth to do with reality,
needs that kind of functionality. The combination dynamics, or growth
(multiplication) dynamics is a critically important functionality in
chemistry, physics, biology. It probably may be emulated by standard
means such as lists and dictionaries. If such support is available
though, this is a sign of mature language designed to cover the
realistic processes with rich growth/combination dynamics.
For instance, the dynamics of aperiodic growth that generates a 3D
aperiodic arrays/structures with the controllable "bits" in each unit to
be configured by dynamic masks to match the environmental ("boundary")
conditions would be a significant step in building next-generation
languages/silicon to support synthesis of realistic 3D structures (and
functions). Accordingly, the command "line" may need to be 2D and the
interpreter be designed to handle/understand not only a (command) text.
Just reflecting aloud..
val
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