m&v y ↔ m v y This is the definition of bond (monadic)
u&v y ↔ u v y . This is the definition of compose (dyadic)
=&{: is the definition which I used earlier as =&{: B
I was told that I was using & dyadically so it was compose.
Here is a slight simplification:
'A B'=:3|L:0(([:<i.)"1)3 5,:5 4
m=: 13 :';x([:<(=&{:)"1#(, }.)"1)"1 _ y'
A m B
0 1 2 0 1 2 0 1
0 1 2 0 1 2 0 1
2 0 1 2 0 1 2 0
2 0 1 2 0 1 2 0
1 2 0 1 2 0 1 2
m
[: ; ([: < =&{:"1 # (, }.)"1)"1 _
Linda
Linda
-----Original Message-----
From: [email protected]
[mailto:[email protected]] On Behalf Of Henry Rich
Sent: Tuesday, October 23, 2012 4:28 PM
To: [email protected]
Subject: Re: [Jprogramming] stitching matrices
Just remember that u&v y IS NOT u v y .
u&:v y IS u v y .
u&v y is the same as u&:v"v y .
Henry Rich
On 10/23/2012 9:57 AM, Linda Alvord wrote:
> I know that your explanation works because the dictionary defines & as u&v
> y ↔ u v y .
>
> What I am trying to do is sort out a sequence for developing concepts in
> mathematics education. A starting point is Easy J. Also. I favor explicit
> definitions using 13 : as they clearly indicate the placement of arguments.
>
> However, students who become interested in J can look at the tacit verbs and
> begin to see a more terse version of the language.
>
> So, if I begin to embrace & to form a hook like =&{: and it is equivalent
> to [:={: and I enter it as ([:={:) in an explicit definition, I'd like it
> to work and also both versions should display in a similar fashion in a tree.
>
> As I typed that last paragraph I wondered if I really need y somewhere in my
> explicit definition.
>
> Thanks for your thoughts as they have forced me to continue to ponder this
> issue.
>
> Linda
>
>
> -----Original Message-----
> From: [email protected]
> [mailto:programming-boune [email protected]] On Behalf Of Aai
> Sent: Monday, October 22, 2012 4:01 AM
> taTo: [email protected]
> Subject: Re: [Jprogramming] stitching matrices
>
> If you insist in a version of
>
> (=&{: |.)
>
> with caps then you'll have to use something like this (written out
> version)
>
> LAT=: 13 :'( {: x ) = {: |. y'
>
> LAT
> ([: {: [) = [: {: [: |. ]
>
> Then insert this into my cleaned code (thanks to Raul):
>
> zlav=:[: ;([: < LAT"1 # (, }.)"1)"1 _
>
> A zlav B
> 0 1 2 0 1 2 0 1
> 0 1 2 0 1 2 0 1
> 2 0 1 2 0 1 2 0
> 2 0 1 2 0 1 2 0
> 1 2 0 1 2 0 1 2
>
> zlav f.
> [: ; ([: < (([: {: [) = [: {: [: |. ])"1 # (, }.)"1)"1 _
>
>
>
> On 22-10-12 03:46, Linda Alvord wrote:
>> Check your message below, Raul, which indicate that both m and n should work
>> on your new version:
>>
>> i=:[: ;([: < (=&{: |.)"1 # (, }.)"1)"1 _
>> i
>> [: ; ([: < (=&{: |.)"1 # (, }.)"1)"1 _
>> A i B
>> 0 1 2 0 1 2 0 1
>> 0 1 2 0 1 2 0 1
>> 2 0 1 2 0 1 2 0
>> 2 0 1 2 0 1 2 0
>> 1 2 0 1 2 0 1 2
>>
>>
>> m=: 13 :';x ([:< (([:={: :[:) |.)"1 # (, }.)"1)"1 _ y'
>> m
>> [: ; ([: < (([: = {: :[:) |.)"1 # (, }.)"1)"1 _
>> A m B
>> |domain error: m
>> | A m B
>> n=: 13 :';x ([:< (([:={: :[:) |.)"1 # (, }.)"1)"1 _ y'
>> n
>> [: ; ([: < (([: = {: :[:) |.)"1 # (, }.)"1)"1 _
>> A n B
>> |domain error: n
>> | A n B
>>
>> Spacing of [:={: similar to =&{: would be geat.
>> So I could write an explicit definition of o that will have the
>> following result and produce the correct result that i does.
>>
>>
>> o=:
>> [: ; ([: < ([:={: |.)"1 # (, }.)"1)"1 _
>>
>>
>> -----Original Message-----
>> From: [email protected]
>> [mailto:[email protected]] On Behalf Of Raul
>> Miller
>> Sent: Saturday, October 20, 2012 12:19 PM
>> To: [email protected]
>> Subject: Re: [Jprogramming] stitching matrices
>>
>> If you actually wanted to only be using monadic definitions for f and g,
>> these would be equivalent definitions:
>>
>> f=: =&{: :[:
>>
>> g=: ([:={:) :[:
>>
>> Here, you would be declaring that these verbs have empty dyadic domains.
>>
>> You could even get away with
>>
>> g=: [:={: :[:
>>
>> (Do you see why?)
>>
>> --
>> Raul
>>
>> On Sat, Oct 20, 2012 at 2:57 AM, Linda Alvord <[email protected]>
>> wrote:
>>> I am using them monadically.
>>>
>>> Linda
>>>
>>> -----Original Message-----
>>> From: [email protected]
>>> [mailto:[email protected]] On Behalf Of km
>>> Sent: Saturday, October 20, 2012 2:54 AM
>>> To: [email protected]
>>> Subject: Re: [Jprogramming] stitching matrices
>>>
>>> Identical?
>>>
>>> f =: =&{:
>>> g =: [:={:
>>> 1 4 f 2 3 4
>>> 1
>>> 1 4 g 2 3 4
>>> |domain error: g
>>> | 1 4 g 2 3 4
>>>
>>> Kip Murray
>>>
>>> Sent from my iPad
>>>
>>>
>>> On Oct 20, 2012, at 1:11 AM, "Linda Alvord" <[email protected]> wrote:
>>>
>>>> Here's a problem that bothers me about this example before I leave it.
>>>>
>>>>
>>>>
>>>> First establish that =&{: and [:={: are identical and compare
>>>> tree and boxed versions:
>>>>
>>>>
>>>>
>>>>
>>>>
>>>> ]'A B'=:3|L:0(([:<i.)"1)3 5,:5 4
>>>>
>>>> ----------T-------┐
>>>> │0 1 2 0 1│0 1 2 0│
>>>> │2 0 1 2 0│1 2 0 1│
>>>> │1 2 0 1 2│2 0 1 2│
>>>> │ │0 1 2 0│
>>>> │ │1 2 0 1│
>>>> L---------+--------
>>>>
>>>> f=:=&{:
>>>>
>>>> g=:[:={:
>>>>
>>>> 5!:4 <'f'
>>>>
>>>> -- =
>>>> -- & -+- {:
>>>>
>>>> 5!:4 <'g'
>>>>
>>>> -- [:
>>>> --+- =
>>>> L- {:
>>>>
>>>> B
>>>>
>>>> 0 1 2 0
>>>> 1 2 0 1
>>>> 2 0 1 2
>>>> 0 1 2 0
>>>> 1 2 0 1
>>>>
>>>> f B
>>>>
>>>> 1 0 0 1
>>>> 0 1 0 0
>>>> 0 0 1 0
>>>>
>>>> g B
>>>>
>>>> 1 0 0 1
>>>> 0 1 0 0
>>>> 0 0 1 0
>>>>
>>>>
>>>>
>>>> Now look at two "trees":
>>>>
>>>>
>>>>
>>>> elm=: 13 :'((=&{:)|.)"1 y'
>>>>
>>>> oak=: 13 :'(([:={:)|.)"1 y'
>>>>
>>>> 5!:4 <'elm'
>>>>
>>>> -- =
>>>> -- & -+- {:
>>>> ----+- |.
>>>> -- " -+- 1
>>>>
>>>> 5!:4 <'oak'
>>>>
>>>> -- [:
>>>> -----+- =
>>>> ----+ L- {:
>>>> -- " -+ L- |.
>>>> L- 1
>>>>
>>>> 5!:2 <'elm'
>>>>
>>>> --------------T-T-┐
>>>> │---------T--┐│"│1│
>>>> ││--T-T--┐│|.││ │ │
>>>> │││=│&│{:││ ││ │ │
>>>> ││L-+-+---│ ││ │ │
>>>> │L--------+---│ │ │
>>>> L-------------+-+--
>>>>
>>>> 5!:2 <'oak'
>>>>
>>>> ---------------T-T-┐
>>>> │----------T--┐│"│1│
>>>> ││---T-T--┐│|.││ │ │
>>>> │││[:│=│{:││ ││ │ │
>>>> ││L--+-+---│ ││ │ │
>>>> │L---------+---│ │ │
>>>> L--------------+-+--
>>>>
>>>> B
>>>>
>>>> 0 1 2 0
>>>> 1 2 0 1
>>>> 2 0 1 2
>>>> 0 1 2 0
>>>> 1 2 0 1
>>>>
>>>> elm B
>>>>
>>>> 1 1 1 1 1
>>>>
>>>> oak B
>>>>
>>>> ran with error:
>>>> |domain error: oak
>>>> | oak B
>>>> |[-16] c:\users\owner\j701-user\temp\42.ijs
>>>>
>>>>
>>>>
>>>> I'm not troubled by the fact that these results are different. I am
>>>> bothered that their differences do not appear in the tree and boxed
>>>> version, because I expect them both to be elm trees!
>>>>
>>>>
>>>>
>>>> If these versions don't show any differences shouldn't the results
>>>> agree. I think the tree versions must be missing some way to tell them
>>>> apart.
>>>>
>>>>
>>>>
>>>> Any thoughts?
>>>>
>>>>
>>>>
>>>> Linda
>>>>
>>>>
>>>>
>>>> Linda
>>>>
>>>>
>>>>
>>>>
>>>>
>>>>
>>>>
>>>> -----Original Message-----
>>>>
>>>> From: <mailto:[email protected]>
>>>> [email protected]
>>>>
>>>> [ <mailto:[email protected]>
>>>> mailto:[email protected]] On Behalf Of Raul
>>>> Miller
>>>>
>>>> Sent: Friday, October 19, 2012 9:30 AM
>>>>
>>>> To: <mailto:[email protected]> [email protected]
>>>>
>>>> Subject: Re: [Jprogramming] stitching matrices
>>>>
>>>>
>>>>
>>>> On Fri, Oct 19, 2012 at 4:00 AM, Linda Alvord <
>>>> <mailto:[email protected]> [email protected]>
>>>>
>>>> wrote:
>>>>
>>>>> G B
>>>>> 1 1 1 1 1
>>>>> H B
>>>>> ran with error:
>>>>> |domain error: H
>>>>> | H B
>>>>> |[-30] c:\users\owner\j701-user\temp\37.ijs
>>>>
>>>>> G WORKS! H DOESN'T!
>>>>
>>>>> How can I write the function H without & and get 1 1 1 1 ?
>>>>
>>>>
>>>> Here's G B
>>>>
>>>> ((=&{:)|.)"1 $~&5 4 i.3
>>>>
>>>> 1 1 1 1 1
>>>>
>>>>
>>>>
>>>> Here, I rephrase G by eliminating the &
>>>>
>>>> (({:@[ = {:@])|.)"1 $~&5 4 i.3
>>>>
>>>> 1 1 1 1 1
>>>>
>>>>
>>>>
>>>> Note that I am testing the result at each step, here, to make sure
>>>> I've not made any bad assumptions (for example, hypothetically
>>>> speaking some intermediate results in these kinds of
>>>> transformations might need some explicit treatment of rank).
>>>>
>>>>
>>>>
>>>> Here, I further rephrase G by also eliminating both of the @
>>>> conjunctions
>>>>
>>>> ((([: {: [) = ([: {: ]))|.)"1 $~&5 4 i.3
>>>>
>>>> 1 1 1 1 1
>>>>
>>>>
>>>>
>>>> Here, I simplify slightly by using a hook
>>>>
>>>> (((([: {: [) = ]) {:)|.)"1 $~&5 4 i.3
>>>>
>>>> 1 1 1 1 1
>>>>
>>>>
>>>>
>>>> Here, I simplify again by using a cross hook
>>>>
>>>> (((= {:)~ {:) |.)"1 $~&5 4 i.3
>>>>
>>>> 1 1 1 1 1
>>>>
>>>>
>>>>
>>>> Good enough?
>>>>
>>>>
>>>>
>>>> Thanks,
>>>>
>>>>
>>>>
>>>> --
>>>>
>>>> Raul
>>>>
>>>> -------------------------------------------------------------------
>>>> -
>>>> -
>>>> -
>>>>
>>>> For information about J forums see
>>>> <http://www.jsoftware.com/forums.htm>
>>>> http://www.jsoftware.com/forums.htm
>>>>
>>>>
>>>>
>>>> -------------------------------------------------------------------
>>>> -
>>>> -
>>>> -
>>>>
>>>> For information about J forums see
>>>> <http://www.jsoftware.com/forums.htm>
>>>> http://www.jsoftware.com/forums.htm
>>>>
>>>> -------------------------------------------------------------------
>>>> -
>>>> -
>>>> - For information about J forums see
>>>> http://www.jsoftware.com/forums.htm
>>> --------------------------------------------------------------------
>>> -
>>> - For information about J forums see
>>> http://www.jsoftware.com/forums.htm
>>>
>>> --------------------------------------------------------------------
>>> -
>>> - 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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>> 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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>
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