If I understand properly, the Haskell concept of "such that" is
roughly analogous to the J concept of verb rank (which is a built in
property of all J verbs).
If this is the case, maybe what you want is already there?
Thanks,
--
Raul
On Sat, Dec 27, 2014 at 10:01 AM, Jon Hough <jgho...@outlook.com> wrote:
> Hi Aai,
>
> I'm sorry, we may be talking past each other. You are correct abut list
> comprehensions, but I am interested in being able to get a "such that" idea
> in J, to make translating math definitions {A | B} (A such that B) into
> computable J.
>
> This isn't to make anything computationally faster or anytihng like that,
> it's for the ease of the human to understand what the conditions for creating
> a set (or list or array ) is.
>
> As a simple example, the group C4 (cyclic group on 4 letters) is
> 0 1 2 3
> 1 2 3 0
> 2 3 0 1
> 3 0 1 2
> (where each row is a permutation)
> This group can be defined (in standard math notation, not J) as
>
> < x | order(x) == 4>
> where angle brackets replace curly brackets to denote "generated by". That
> is, we get the set of permutations generated by a permutation of order 4.
>
> I'm sure there are several ways to get this set in J, but the one I am
> interested in needs some sort of "such that" clause to keep it as close as
> possible to the mathematical notation.
>
> So I can do:
>
>
>
> x =: (sym 4) where (4&=@:order)This gives a set of permutations from Sym 4
> that have order 4. I just want one.
> generatorList =: 2 4 $ ((i. 4) , {. x)
> I take the head of the list and append the identity permutation to it and
> then use
> generate generatorList
> which should give me the Cyclic group on 4 letters.(where "generate" is the
> verb m35 found here http://www.jsoftware.com/phrases/permutations.htm )
> This actually works well I think, because it gives a flexible way to change
> the conditional clause and create different sets, groups.
>
>
>
>
>> Date: Sat, 27 Dec 2014 15:44:10 +0100
>> From: agroeneveld...@gmail.com
>> To: programm...@jsoftware.com
>> Subject: Re: [Jprogramming] "Such that" syntax in J
>>
>> Hello John,
>>
>> just interpreting what you mean (but I may misunderstand it completely).
>> With a list comprehension you can formulate:
>> (just a simple example)
>>
>> Prelude> take 6 $ [ (^2) x | x <- [0..], 0 == x `mod` 2]
>> [0,4,16,36,64,100]
>>
>> In J:
>>
>> (*:#~0=2&|) i.12
>> 0 4 16 36 64 100
>>
>> Perhaps something like this?
>>
>>
>> Jon Hough schreef op 27-12-14 om 15:26:
>> > Hi Aai,
>> >
>> > I see what you are saying, but I would say that implicitly inside f there
>> > is some sort of "such that" syntax.
>> > My motivation for asking for a "such that / where" construct is to create
>> > computable math definitions, as in Haskell.
>> >
>> > for example, if I want the set (or group):
>> >
>> > { x e. Sym(4) | order(x) = 4} (where Sym(4) is the symmetric group on 4
>> > letters)
>> >
>> > then, assuming I have a verb "sym" and a verb "order" I can do
>> >
>> >
>> > (sym 4) where (4&=@:order)
>> > Then it may just be possible to generate groups from group presentations (
>> > http://en.wikipedia.org/wiki/Presentation_of_a_group)(I haven't figured
>> > out how to do this, I am just thinking about it over the holidays)
>> >
>> >> Date: Sat, 27 Dec 2014 08:46:12 +0100
>> >> From: agroeneveld...@gmail.com
>> >> To: programm...@jsoftware.com
>> >> Subject: Re: [Jprogramming] "Such that" syntax in J
>> >>
>> >> Sorry for jumping in late.
>> >>
>> >> The Haskell expression you showed here is called a list comprehansion
>> >> which can be easily formulated as
>> >>
>> >> map f xs
>> >>
>> >> and this is in J simply:
>> >>
>> >> f xs
>> >>
>> >>
>> >>
>> >>
>> >>
>> >>
>> >>
>> >> Jon Hough schreef op 26-12-14 om 17:04:
>> >>> In Haskell (and other languages I'm sure) one can express the idea of
>> >>> "such that" to denote one expression depending on another. In Haskell we
>> >>> can use the syntax:
>> >>>
>> >>> [ f x | x <- xs ]
>> >>>
>> >>> which means
>> >>> "the list of all f x
>> >>> such that x is drawn from xs."
>> >>>
>> >>> So | is syntactically similar to the English "such that". (and very much
>> >>> like | in mathematical sets)
>> >>>
>> >>> I would like to know if J has a construct to express the above Haskell
>> >>> code.
>> >>>
>> >>> Thanks,
>> >>> Jon.
>> >>>
>> >>> ----------------------------------------------------------------------
>> >>> For information about J forums see http://www.jsoftware.com/forums.htm
>> >> --
>> >> Met vriendelijke groet,
>> >> @@i = Arie Groeneveld
>> >>
>> >> ----------------------------------------------------------------------
>> >> For information about J forums see http://www.jsoftware.com/forums.htm
>> >
>> > ----------------------------------------------------------------------
>> > For information about J forums see http://www.jsoftware.com/forums.htm
>>
>> --
>> Met vriendelijke groet,
>> @@i = Arie Groeneveld
>>
>> ----------------------------------------------------------------------
>> For information about J forums see http://www.jsoftware.com/forums.htm
>
> ----------------------------------------------------------------------
> For information about J forums see http://www.jsoftware.com/forums.htm
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