⍶ is the left argument to a monadic or dyadic operator that takes
a function as an argument AND one or two actual arguments.
⍹ is the right (optional) second argument. Keep in mind that these
can also be data, not just a function.
A couple of other examples:
-foldleft 1 2 3 4 5 <—> 1-(2-(3-(4-5))) <—> ¯2
-foldright 1 2 3 4 5 <—> (((1-2)-3)-4)-5 <—> ¯8
If
foldleft←{⍶/⍵}
then
foldright←{⍶⍨/⌽⍵}
Since
⍶/⍵[1 2 3] <—> ⍵[1] ⍶ ⍵[2] ⍶ ⍵[3] <—> ⍵[1] ⍶ (⍵[2] ⍶ ⍵[3]),
then
⍶⍨/⌽⍵[1 2 3] <—> ⍶⍨/⍵[3 2 1] <—> ⍵[3] ⍶⍨ ⍵[2] ⍶⍨ ⍵[1]
<—> ⍵[3] ⍶⍨ ⍵[1] ⍶ ⍵[2] <—> (⍵[1] ⍶ ⍵[2]) ⍶ ⍵[3]
Derivative:
d←{((⍶⍵+⍺)-⍶⍵)÷⍺}
1E¯7 {⍵*2}d 3 <—> 6.000…
In conventional mathematical notation,
f'(x) = (f(x+h) - f(x)) / h
⍶d ⍵ ⍶ ⍵ ⍺ ⍶ ⍵ ⍺
Basically, the arguments are organised as
⍺ {} ⍵ for functions and ⍺ (⍶ {} ⍹) ⍵ for operators,
where your function/operator is in the {}.
⍺ and ⍵ cannot be functions, but ⍶ and ⍹ can.
⍺ and ⍹ are optional.
Best regards,
Louis
> On 18 May 2016, at 05:39, Christian Robert <[email protected]>
> wrote:
>
> Now pretty clear.
>
> > It’s a definition for an operator receiving two function arguments ⍶ and ⍹,
> > for which you can not do ⎕←⍹ or ⎕←⍶. ...
>
> many thanks.
>
> Xtian.
>
> On 2016-05-17 23:12, Xiao-Yong Jin wrote:
>>
>>> On May 17, 2016, at 9:48 PM, Christian Robert <[email protected]>
>>> wrote:
>>>
>>> Sorry, no explanations given.
>>>
>>> hook←{⍵⍶⍹⍵}
>>> +hook÷2
>>> 2.5
>> You can look at the definition
>> ∇hook[⎕]∇
>> ∇
>> [0] λ←(⍶ hook ⍹ ) ⍵
>> [1] λ←⍵⍶⍹⍵
>> ∇
>> It’s a definition for an operator receiving two function arguments ⍶ and ⍹,
>> for which you can not do ⎕←⍹ or ⎕←⍶. The result is a monadic function with
>> right argument ⍵. Explicitly for the example,
>> +hook÷2
>> is equivalent to
>> 2+÷2
>>
>>> hook←{⍵⍶⍹⍵⊣⎕←⍵⊣⎕←⍶⊣⎕←⍹⊣⎕←⍵}
>>> +hook÷2
>>> 2
>>> DOMAIN ERROR
>>> hook[1] λ←⍵ ⍶ ⍹ ⍵⊣⎕←⍵⊣⎕←⍶⊣⎕←⍹⊣⎕←⍵
>>> ^^
>>> please explain the principle to a newbie.
>>>
>>> I really want a working examples.
>>>
>>>
>>> Xtian.
>>>
>>>
>>> On 2016-05-17 22:30, Xiao-Yong Jin wrote:
>>>> They are for direct function (operator?) definitions. Try:
>>>>
>>>> hook←{⍵⍶⍹⍵}
>>>> +hook÷2
>>>> 2.5
>>>>
>>>>> On May 17, 2016, at 8:24 PM, Christian Robert
>>>>> <[email protected]> wrote:
>>>>>
>>>>> hi,
>>>>>
>>>>> in the result of "]help" I can see:
>>>>>
>>>>>
>>>>> λ { ... } result
>>>>> ⍺ { ... } left value argument
>>>>> ⍵ { ... } right value argument
>>>>> χ { ... } axis argument
>>>>> ⍶ { ... } left function argument
>>>>> ⍹ { ... } right function argument
>>>>>
>>>>>
>>>>> can someone explain to me the usage of ⍶ and ⍹
>>>>> with some examples ?
>>>>>
>>>>> I understant the first four, but not the last two.
>>>>>
>>>>> many thanks,
>>>>>
>>>>> Xtian.
>>>>>
>>>>
>>>>
>>
>>
