Operator binding

[Dr . Jürgen Sauermann]

    Hi,
      
      in following up the recent email discussions with Jay Foad and
      Hans-Peter Sorge,
      I have changed the operator-to-operator binding in GNU APL. SVN
        1367.
      
      Before the change an _expression_ with 2 adjacent operators,
      for example 2 /
      / 3 4⍴5, would have given this:
      
         B←3 4⍴5
             2 / / B
       5 5 5 5 5  5 5 5 5 5  5 5 5 5 5·
       5 5 5 5 5  5 5 5 5 5  5 5 5 5 5·
       5 5 5 5 5  5 5 5 5 5  5 5 5 5 5·
      
    GNU APL would have bound the left / to the right / and evaluation
    the _expression_ with:
    
    * the left / being function compress, and
    * the right / being operator reduce with function compress as left
    operand.
    
    After the change the same _expression_ now evaluates to:
    
               B←3 4⍴5
                 2 / / B
       5 5 5 5 5 5 5 5  5 5 5 5 5 5 5 5  5 5 5 5 5 5 5 5
      
    
    GNU APL now binds 2 to / as discussed earlier. This creates a
    derived function,
    say TWICE, like:
    
    ∇ Z←A TWICE B
        ⍝ A not used
        Z←2 / B
      ∇
      
    and then reduces TWICE with B:
    
          TWICE / B
       5 5 5 5 5 5 5 5  5 5 5 5 5 5 5 5  5 5 5 5 5 5 5 5
      
      
    Interestingly:
    
    * as seen above, TWICE / B  and  2 / / B now give
    the same result in GNU APL,
    
    * TWICE / B gives the same result in GNU APL and in
    IBM APL2,
      but:  2 / / B gives a DOMAIN ERROR
    in IBM APL2, and
    
    * TWICE / B also give the same results in GNU APL
    and in Dyalog APL,
    but  Dyalog APL gives a different result (apparently the same as 
    the old
    GNU APL implementation) for 2 / / B (from tryapl.org):
    
    
          B←3 4 ⍴ 5  
            TWICE←{⍺ ⊢ 2/⍵}
            TWICE / B
      ┌───────────────┬───────────────┬───────────────┐
      │5 5 5 5 5 5 5 5│5 5 5 5 5 5 5 5│5 5 5 5 5 5 5 5│
      └───────────────┴───────────────┴───────────────┘
            
            2 / / B
      ┌─────────┬─────────┬─────────┐
      │5 5 5 5 5│5 5 5 5 5│5 5 5 5 5│
      ├─────────┼─────────┼─────────┤
      │5 5 5 5 5│5 5 5 5 5│5 5 5 5 5│
      ├─────────┼─────────┼─────────┤
      │5 5 5 5 5│5 5 5 5 5│5 5 5 5 5│
      └─────────┴─────────┴─────────┘
    
    That suggest that the binding of operators is not very portable
    between interpreters and one should not rely on them in the first
    place. It seems to be more reliable bind explicitly as shown above
    as to avoid unexpected surprises later on.
    
    Best Regards,
    Jürgen