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Constant () is a monadic operator which takes an array as its operand and becomes a function which returns the operand array regardless of its arguments. It was first introduced in Extended Dyalog APL, sharing its glyph with Commute, and was adopted in Dyalog APL 18.0 as an alternative to the constant dfn such as {0}.


The need for Constant arises in various contexts, such as at the rightmost branch in a train and mapping over an array to create a constant-filled one. The major advantage of Constant A⍨ over a constant dfn {A} is that the array A is evaluated only once at definition time, rather than every time the function is called.


If the rightmost branch of a train is an array, it is not recognised as a train at all. This problem can be worked around in many ways, but none is visually appealing. The Constant operator gives a natural solution to this problem.

f0←{(⍺+⍵)*3}  ⍝ Converting this function to a train was a mess:
fx←+*3        ⍝ This does not work; it evaluates to a number (conjugate of exponential of 3)
f1←3*⍨+       ⍝ A workaround using Commute; it changes the order of visual tokens
f2←*∘3+       ⍝ A workaround using Bind; ditto
f3←+*{3}      ⍝ A workaround using a constant dfn
f4←+*3⊣⊢      ⍝ A workaround using Identity

f5←+*3⍨       ⍝ A solution using Constant

Other uses

Sometimes, one needs a constant function that returns one of the arguments of the outer dfn. Simply writing {⍺} does not work; ⍺⍨ does.

      1 0 0 1{'⎕'@{⍺}⍵}'AbcD'
VALUE ERROR             
 1 0 0 1{'⎕'@{⍺}⍵}'AbcD'
      1 0 0 1{'⎕'@(⍺⍨)⍵}'AbcD'

Using Constant is also cleaner when doing a constant fill.

      {1}¨2 3⍴⎕A  ⍝ Without Constant
1 1 1
1 1 1
      1⍨¨2 3⍴⎕A   ⍝ With Constant
1 1 1
1 1 1

External links




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