[Jprogramming] CS Jokes (was Re: Functors in mathematics, Haskell and an example in J)

[Viktor Cerovski]

Raul Miller-4 wrote:
> 
> On Tue, Apr 3, 2012 at 2:49 PM, Viktor Cerovski
> <viktor.cerovski at gmail.com> wrote:
>> I've counted 4 contradictions:
>>  1) 1d empty array,
> 
> That's not a contradiction.  '' is an example of a 1d empty array.
> i.0 is another example
> 
>>  2) empty array of numbers,
> 
> That would be an array which contains no numbers, yes?
> 
Given all the examples I've given in another post some time ago
about empties in J/Haskell/LISP, the answer is: no.  So the following:


> Actually it probably means "An array with a numeric
> type for atoms which has a zero in at least one of
> its dimensions."
> 
is not true because...


> Since type and dimension are different, and since in
> a homogeneous array the type is stored independent of
> the array elements, I do not think that there are any
> contradictions here.
> 
type information is not stored anywhere, at least not in J/Haskell/LISP.


>>  3) 1d array with rank > 1
> 
> That is a contradiction.
> 
which accidentally is my claim from the functor example, without
"contradiction" part.


>>  4) empty array with rank > 1
> 
> That is not a contradiction.  i.0 0 is an example of
> an empty array with rank greater than 1.  In fact there
> are arbitrarily many such arrays.  rank > 1 means that
> there are more than one non-negative integers to describe
> its shape.  Empty means that at least one of those
> integers is 0.
> 
> So this would be: an array which has multiple dimensions
> at least one of which is 0.
> 
which is exactly arrays I consider in the example. The example plays on
the fact that whenever we say "rank", and we say it a lot, we also say 
"one dimensional array of non-negative numbers" and 1d arrays has, 
just like any other array, also rank.
That's the main magic of the example that I tried to captured with
functor, which then fuels these paradoxes/contradictions.

-- 
Raul
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