The APL2 manual (p35) says "The right operand of a dyadic operator is the
function or array to its immediate right." This is their way of saying that
operator expressions are left-associative. For example, in ∘.∘.+ the right
operand of the leftmost dot is ∘ (not ∘.+); so ∘.∘.+ is parsed as (∘.∘).+
The fact that operator-operand expressions are left-associative while
function-array expressions are right-associative is one of the beautiful
symmetries of APL!
Some more examples demonstrating the left-associativity of operator
expressions:
≡⊂⍣4⍣6⊢'hello'
25
≡(⊂⍣4)⍣6⊢'hello'
25
≡⊂⍣(4⍣6)⊢'hello'
DOMAIN ERROR
⎕FX'R←(F L G)Y' 'R←F Y'
L
⎕FX'R←(F R G)Y' 'R←G Y'
R
+ L × R - 33
¯33
(+ L ×) R - 33
¯33
+ L (× R -) 33
33
Jay.
On 27 June 2016 at 12:37, Juergen Sauermann <[email protected]>
wrote:
> Hi,
>
> not sure. First of all, both IBM APL2 and GNU APL return the same result
> in Alex's example:
>
> * 5 ∘.∘.+ 9*
> *14*
> * 5 (∘.∘).+ 9*
> *14*
> * 5 ∘.(∘.+) 9*
> *14*
>
> Then the IBM language reference says this (p. 35):
>
> *"For example, the function expression +.×/ is a reduction by a **+.×**
> inner product*
> *because the **×** binds as right operand to the array product operator
> (. ), and not as*
> *left operand to the slash operator (/). The + binds as left operand to
> the dot; then*
> *the resulting product binds to the slash as its left operand.*
>
> *+.×/ ←→ (+.× )/ not + .(**×** /)*
>
>
> *" *However, the binding strength resolves the ambiguity in the IBM
> example only
> because / is not a dyadic operator. In Alex's example the operator is
> dyadic, and one
> could either bind the middle ∘ to the left ∘ or the + to the middle ∘
> without violating
> the binding strengths. In this case I would argue that the "basic APL2
> evaluation rule"
> should be applied because ∘.+ can be evaluated (yielding a derived
> function) because all arguments
> of . are available before the . and ∘ on the left show up.
>
> What is missing in both the ISO standard and in the APL2 language
> reference is a
> statement about left-to-right or right-to-left associativity of APL
> operators. I personally
> would find it counter-intuitive if functions are evaluated left-to-right
> while operators are
> evaluated right-to-left.
>
> /// Jürgen
>
>
> On 06/27/2016 11:48 AM, Jay Foad wrote:
>
> So it looks like GNU APL parses ∘.∘.+ as ∘.(∘.+).
>
> IBM APL2 and Dyalog appear to parse it as (∘.∘).+.
>
> Jay.
>
> On 15 June 2016 at 04:05, Xiao-Yong Jin <[email protected]> wrote:
>
>> Hi Alex,
>>
>> It is correct. You need nested vectors to see the effect.
>>
>> Try the following.
>>
>> (⊂[2]2 3⍴⍳6)∘.{⍺∘.{⍺+⍵⊣⎕←⍺,'I',⍵}⍵⊣⎕←⍺,'O',⍵}(⊂[2]10×2 3⍴⍳6)
>>
>> Best,
>> Xiao-Yong
>>
>> > On Jun 14, 2016, at 6:39 PM, Alex Weiner <[email protected]>
>> wrote:
>> >
>> > Hi Bug-APL,
>> >
>> > Surely this is not correct:
>> >
>> > 5∘.∘.+9
>> > 14
>> >
>> >
>> > I would expect a syntax error.
>> > If this is valid, then I stand corrected
>> >
>> > -Alex
>> >
>>
>>
>>
>
>
