Re: [Bug-apl] A couple of bugs, and a question on the power operator

[Louis de Forcrand]

Of course. If G could be either monadic or dyadic / ambivalent, F⍣G where G is 
a primitive
function and not a lambda would be ambiguous as to the valence of G. I should 
have thought
of that.

Thanks,
Louis

> On 15 Aug 2016, at 22:10, Christian Robert <address@hidden> wrote:
> 
> Look at this
> 
>      {1+÷⍵}⍣= 256
> 1.618033989
>      {1+÷⍵}⍣{⍺=⍵} 256
> 1.618033989
>      {1+÷⍵}⍣{⍺=⍵⊣⎕←⍺ ⍵ (⍵-⍺)} 256
> 1.00390625 256 254.9960938
> 1.996108949 1.00390625 ¯0.9922026994
> 1.500974659 1.996108949 0.4951342905
> 1.666233766 1.500974659 ¯0.1652591074
> 1.600155885 1.666233766 0.06607788159
> 1.624939113 1.600155885 ¯0.02478322885
> 1.615407674 1.624939113 0.009531439632
> 1.619038783 1.615407674 ¯0.003631108845
> 1.61765043 1.619038783 0.001388352906
> 1.61818053 1.61765043 ¯0.0005301001708
> 1.61797802 1.61818053 0.0002025099168
> 1.618055368 1.61797802 ¯0.00007734757573
> 1.618025823 1.618055368 0.00002954477659
> 1.618037108 1.618025823 ¯0.00001128500832
> 1.618032797 1.618037108 0.000004310503058
> 1.618034444 1.618032797 ¯0.000001646463698
> 1.618033815 1.618034444 6.288934578E¯7
> 1.618034055 1.618033815 ¯2.402158839E¯7
> 1.618033963 1.618034055 9.175430926E¯8
> 1.618033998 1.618033963 ¯3.504702684E¯8
> 1.618033985 1.618033998 1.338677325E¯8
> 1.61803399 1.618033985 ¯5.113292456E¯9
> 1.618033988 1.61803399 1.953103901E¯9
> 1.618033989 1.618033988 ¯7.460192464E¯10
> 1.618033989 1.618033989 2.849540603E¯10
> 1.618033989 1.618033989 ¯1.088429347E¯10
> 1.618033989 1.618033989 4.157429956E¯11
> 1.618033989 1.618033989 ¯1.587974197E¯11
> 1.618033989 1.618033989 6.065370428E¯12
> 1.618033989 1.618033989 ¯2.316813408E¯12
> 1.618033989 1.618033989 8.850697952E¯13
> 1.618033989 1.618033989 ¯3.379518887E¯13
> 1.618033989 1.618033989 1.290079155E¯13
> 1.618033989
> 
> power is always diadic on the function it call.
> 
> > Its right argument then is _always_ the result of the previous iteration. 
> > Is that correct?
> 
> I really hope so. That was my understanding since several months. I may still 
> be wrong.
> 
> Xtian.
> 
> On 2016-08-15 21:54, Louis de Forcrand wrote:
>> I'm sorry, _I_ misunderstood the manual. I did not know that Dyalog dfns 
>> were always dyadic / ambivalent.
>> 
>> If I understand correctly then, in F {pow} G, G's left argument is _always_ 
>> the result of the power operator if G is true. Its right argument then is 
>> _always_ the result of the previous iteration. Is that correct?
>> 
>> If it is, I believe always ambivalent lambdas would be convenient (aside 
>> from possible implementation problems), but not at all essential; it's 
>> probably rare to check something about the previous iteration without 
>> comparing it to the current one. But wouldn't have been simpler to model 
>> them as ambivalent from the ground up?
>> 
>> Louis
>> 
>> On 15 Aug 2016, at 08:22, Jay Foad <address@hidden <mailto:address@hidden>> 
>> wrote:
>> 
>>> The manual is here, see page 145: 
>>> http://docs.dyalog.com/15.0/Dyalog%20APL%20Language%20Reference%20Guide.pdf
>>> 
>>> I'm not sure where Louis got the information about monadic G. I assure you 
>>> that Dyalog APL does not examine G to see if it's monadic or dyadic. It 
>>> always tries to apply G dyadically.
>>> 
>>> Jay.
>>> 
>>> On 15 August 2016 at 12:30, Juergen Sauermann <address@hidden 
>>> <mailto:address@hidden>> wrote:
>>> 
>>>    Hi Jay,
>>> 
>>>    I see. Maybe I misunderstood Louis,s email from last Saturday completely?
>>>    The way I read this email was that in Dyalog APL version 15 you can have
>>>    a monadic condition function G in F⍣G . Quote from the email:
>>> 
>>> 
>>>    ///The Dyalog 15.0 manual states that the power operator can take a/
>>>    ///function right argument. In this case, that function can be/
>>>    ///either monadic or dyadic, and can be a lambda./
>>>    ///If it’s monadic:/
>>>    /
>>>    /
>>>    ///  (F⍣G) ⍵  ←→  ⍵ ←   F ⍵  until          G ⍵/
>>>    ///⍺ (F⍣G) ⍵  ←→  ⍵ ← ⍺ F ⍵  until          G ⍵/
>>>    /
>>>    /
>>>    ///If it’s dyadic:/
>>>    /
>>>    /
>>>    ///  (F⍣G) ⍵  ←→  ⍵ ←   F ⍵  until  (  F ⍵) G ⍵/
>>>    ///⍺ (F⍣G) ⍵  ←→  ⍵ ← ⍺ F ⍵  until  (⍺ F ⍵) G ⍵/
>>>    /
>>>    /
>>>    ///(Note that G is checked before the first time F is executed.)/
>>> 
>>>    I don't know if that statement is correct or not, but if it is then I 
>>> would prefer to not
>>>    introduce this "monadic case" in GNU APL for the reasons explained 
>>> earlier.
>>> 
>>>    Thanks,
>>>    Jürgen
>>> 
>>> 
>>>    On 08/15/2016 10:16 AM, Jay Foad wrote:
>>>>    On 13 August 2016 at 13:05, Juergen Sauermann <address@hidden 
>>>> <mailto:address@hidden>> wrote:
>>>> 
>>>>        In "Mastering Dyalog APL" I haven't found the monadic case for the 
>>>> right function argument
>>>>        G of the power operator. In that book G seems to be always dyadic. 
>>>> So the monadic case looks
>>>>        like a new Dyalog invention. And, if it is defined like you say, 
>>>> IMHO not the ultimate wisdom.
>>>> 
>>>> 
>>>>    There is no "monadic case". G is always applied dyadically, and if it 
>>>> happens to be a strictly monadic function then you'll get a SYNTAX ERROR:
>>>> 
>>>>          ⎕FX'r←g y' 'r←g>10' ⍝ g is strictly monadic
>>>>          2 g 4 ⍝ applying it dyadically gives an error
>>>>    SYNTAX ERROR
>>>>          (+⍨⍣g)1 ⍝ power operator tries to apply g dyadically
>>>>    SYNTAX ERROR
>>>> 
>>>>    In general, Dyalog APL /never/ examines a function operand to see 
>>>> whether it is monadic or dyadic, in order to treat them differently.
>>>> 
>>>>    Jay.
>>> 
>>> 
>