[Jprogramming] @: and capped fork

[km]

(1) You could also have done

   isint =: [: (= >.) ]  NB. ignores left argument if given
   isint 2 0.5
1 0
   13 isint 2 0.5
1 0

(2) Check out the monad/dyad "core" lab.  The following is from the iPad version of J.

   Hlab  NB. Help for labs
labs are interactive tutorials
manage labs with the following sentences:
   jx ''     NB. category list
   jx 'core' NB. labs in category core
   jx 0      NB. open lab 0
   jx -1     NB. close lab

↵ with empty textfield advances lab

   jx 'core'
  0 A J Introduction                  
  1 A Taste of J (1)                  
  2 A Taste of J (2)                  
  3 An Idiosyncratic Introduction to J
  4 An Introductory Course in J       
  5 Function Display                  
  6 Locales                           
  7 Monad/Dyad                        
  8 Object Oriented Programming       
  9 Sparse Arrays                     
   jx 7
-------------------------------------------------------------
Lab: Monad/Dyad
To advance the lab, press ↵

-- (1 of 4) INTRODUCTION ------------------------------------

If u and v are functions, then f=: u : v defines f to be a
function whose monadic case is u and whose dyadic case is v

For example, if v=: +, then 3 v 4 is 7 and v 4 is 4, i.e.
since the monadic case of + is the conjugate, which produces
an effect only on a complex argument such as 6j10.

We may, however, define a function add that performs addition
on two arguments, and increments a single argument. Thus:
)
   add=: >: : +
   
   3 add 4
7
   
   add 4
5
   
   add 4 5 6 7 8
5 6 7 8 9
   
   v=: +
   
   3 v 4
7
   
   v 4
4

(3) The use of Cap [: is explained in this four-step lab.


Kip Murray

Sent from my iPad


On Nov 30, 2012, at 10:41 PM, Alex Giannakopoulos <aegean at blueyonder.co.uk> wrote:

> Hm, yes, I hadn't realised both cases could be specified implicitly, that's
> really useful.
> Another one for the FAQ!
> 
> On 1 December 2012 04:37, Alex Giannakopoulos <aegean at blueyonder.co.uk>wrote:
> 
>> Great, thanks, hadn't seen that technique before!
>> 
>> 
>> On 1 December 2012 04:35, km <km at math.uh.edu> wrote:
>> 
>>> About your closing question, you can do
>>> 
>>>   isint =: (= <.) : [:
>>>   isint 2 0.5
>>> 1 0
>>>   2 isint 3
>>> |domain error: isint
>>> |   2     isint 3
>>> 
>>> 
>>> The definition of isint specifies [: as the dyadic case, and [; rejects
>>> every argument with a domain error.
>>> 
>>> Kip Murray
>>> 
>>> Sent from my iPad
>>> 
>>> 
>>> On Nov 30, 2012, at 10:14 PM, Alex Giannakopoulos <
>>> aegean at blueyonder.co.uk> wrote:
>>> 
>>>> On 30 November 2012 16:17, Bo Jacoby <bojacoby at yahoo.dk> wrote:
>>>> 
>>>>> J is a rich language, and it might be a good idea to define an
>>> elementary
>>>>> subset for beginners.
>>>> 
>>>> 
>>>> Couldn't agree more.
>>>> A simple startup configuration file.  Define verbs for trig functions so
>>>> they don't look stupidly arbitrary.
>>>> Some other elementary functions too, like polar2rect and rect2polar
>>>> conversions that act on vectors (none of this xfy binary stuff here
>>>> please), you know, stuff like you can find on *calculators*.
>>>> Define dot-product, matrix-multiplication, cross-product, determinant,
>>> etc,
>>>> as user-friendly built-in verbs.  When I am a beginner, I DO NOT, repeat
>>>> NOT want to know about the . operator at the level of the jdict, it is a
>>>> highly advanced subject, intriguing - yes, but not for newbies.  Yet I
>>> do
>>>> want to do matrix ops.  I was told this was a language for linear
>>> algebra.
>>>> It would probably be a good idea, then, if we could do some linalg -
>>>> straight out of the box - without serious brain damage.  I have had
>>> abuse
>>>> hurled at me by math teachers who have seen J's linalg primitives (LOL).
>>>> Add some nice libs for equation solving while we're at it.  Simultaneous
>>>> and also some numeric solvers.  This is what people want.  A language,
>>> not
>>>> an assembler for a language.
>>>> 
>>>> 
>>>>> J is a nice calculator for elementary computations. You can do a lot of
>>>>> computing without knowing anything about binomial coefficients and
>>> taylor
>>>>> expansions and capped forks.
>>>> 
>>>> 
>>>> Agree with the first two, NO way on the third.  Even the 13 verb gives
>>> you
>>>> capped verbs, there is no way to begin learning J without it.  Also they
>>>> solve the problem of having to figure if you should use At or Atop,
>>>> invaluable for a beginner who hasn;t quite mastered rank yet.
>>>> 
>>>> This problem, which once again gives rise to a long thread, could
>>> easily be
>>>> solved by a highly visible Programming FAQ page, with lots of links to.
>>>> Deal with capped forks, @ and @:  and why you can't have things like
>>> +/ a
>>>> b c   You know, the questions people *keep asking*.   Remove ancient
>>>> irrelevant stuff like the use of x. and y.   We are not at J401 any
>>> more.
>>>> 
>>>> 
>>>>> If you need to understand everything in order to be happy, then you
>>> may be
>>>>> unhappy. I taught my son elementary APL when he was 10 years old, and
>>> he
>>>>> loved it!
>>>> 
>>>> Would he have been just as happy at 14 when he had to use the cosine
>>> rule
>>>> to solve a triangle?  Would he really prefer
>>>> cosrule_getang =: 13 : '_2&o.(((+/*:}.y)-*:{.y) % */ 2, }.y)'
>>>> or
>>>> cosrule_getang =: [: _2&o. (([: +/ [: *: }.) - [: *: {.) % [: */ 2 , }.
>>>> to
>>>> cosrule_getang := (Aa,B,C) -> acos((B^2+C^2-Aa^2)/(2.0*B*C));
>>>> Just wondering...
>>>> 
>>>> These are simple enough things to do, and I speak as a J newcomer.
>>> There's
>>>> not many languages you can say that about after two and a half years!
>>> The
>>>> Zen of J, grasshopper.
>>>> 
>>>> Incidentally, is there a way to cap a monadic hook on the left?
>>>> For example (=<.) was mentioned, but obviously it allows dyadic
>>> arguments,
>>>> and fails if they are offered.
>>>> Short of wrting monad : 'y=<.y'  is there a way I can keep it monadic
>>> (and
>>>> implicit)?
>>>> ----------------------------------------------------------------------
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>>> ----------------------------------------------------------------------
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> ----------------------------------------------------------------------
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