Dops

The operator equivalent of a dfn is distinguished by the presence of either of the compound symbols ⍺⍺ or ⍵⍵ anywhere in its definition.

The syntax of a dop is:

• monadic – ⍺ (⍺⍺ op) ⍵
• dyadic – ⍺ (⍺⍺ op ⍵⍵) ⍵

where ⍺⍺ and ⍵⍵ are the left and right operands (functions or arrays) respectively, and ⍺ and ⍵ are the arguments of the derived function.

Example

The following monadic each operator applies its function operand only to unique elements of its argument. It then distributes the result to match the original argument. This can deliver a performance improvement over the primitive each (¨) operator if the operand function is costly and the argument contains a significant number of duplicate elements. Note however, that if the operand function causes side effects, the operation of dop and primitive versions will be different.

      each←{              ⍝ Fast each:                           
          shp←⍴⍵          ⍝ Shape and ...                        
          vec←,⍵          ⍝ ... ravel of arg.                    
          nub←∪vec        ⍝ Vector of unique elements.           
          res←⍺⍺¨nub      ⍝ Result for unique elts.              
          idx←nub⍳vec     ⍝ Indices of arg in nub ...
          shp⍴idx⊃¨⊂res   ⍝ ... distribute result.
      }

The dyadic else operator applies its left (else right) operand to its right argument depending on its left argument.

      else←{
          ⍺: ⍺⍺ ⍵     ⍝ True: apply Left operand
             ⍵⍵ ⍵     ⍝ Else,  ..   Right   ..
      }
      0 1 ⌈else⌊¨ 2.5     ⍝ Try both false and true.
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