Left and right operand

[jmosk]

I am confused over the use of ⍺⍺ and ⍵⍵. Can someone please explain this as the manual is confusing and the examples do not clear it up. Maybe a couple of simple examples would make it easier to understand when one would use this.

[RichardP|Dyalog]

⍺⍺ and ⍵⍵ are the operands of a Dop. Where a Dfn is a function denoted by curly braces and the use of ⍺ and ⍵ to refer to the left and right arguments, a Dop is an operator denoted by curly braces, the use of ⍺⍺ and ⍵⍵ to refer to the left and right operands.

An operator binds to its operands to create a derived function. This derived function is then applied to arguments in an expression.

A simple example is to recreate the dyadic use of the over operator as a Dop.

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      _Over_ ← {(⍵⍵ ⍺) ⍺⍺ ⍵⍵ ⍵}

      2 4 6 +⍥÷ 1 2 3
1.5 0.75 0.5

      2 4 6 +_Over_÷ 1 2 3
1.5 0.75 0.5

So here ⍺⍺ refers to the left operand function, which is + in this case. The right operand function ÷ is referred to using ⍵⍵. First we take the inverse of the arguments by applying ⍵⍵ monadically, then we apply ⍺⍺ between those inverted arguments.

Note that we still need to refer to the arguments ⍺ and ⍵ of the derived function in order to specify how our operator behaves.

Operands can be arrays as well, as seen in the case of the rank operator and the power operator.

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(+⌿⍤2)   ⍝ Sum down the columns of sub-matrices
(+⌿⍣3)   ⍝ Sum 3 times - equivalent to +⌿+⌿+⌿