https://www.haskell.org/haskellwiki/List_comprehension
On 27 December 2014 at 18:31, Aai <agroeneveld...@gmail.com> wrote:
> Ok, I misinterpreted this enormously (I was just focused on the Haslell
> expression you started with). It would be nice if you could illustrate your
> last mail with an example in Haskell (but that's specifically for me).
>
> You started with the Haskell expression
>
> [ f x | x <- xs ]
>
> and described that as follows
>
> which means
> "the list of all f x
> such that x is drawn from xs."
>
> But in my opion it is more like:
>
> Apply function f on all x element of the list xs and of course f can be a
> very complex expression. As I said before this is often expressed with the
> higher order function map.
>
>
>
>
>
> Jon Hough schreef op 27-12-14 om 16:01:
>
> 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
>>
>
> --
> Met vriendelijke groet,
> @@i = Arie Groeneveld
>
> ----------------------------------------------------------------------
> For information about J forums see http://www.jsoftware.com/forums.htm
>
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