Derived function

A derived function is the result of applying an operator to its operands. Since it is a function, it can then be applied to argument arrays, resulting in other arrays.

Consider for example applying a Windowed Reduction to an array:

      3 ⌈/ 2 9 0 ¯1 0 2 5
9 9 0 2 5

In this statement the Reduce operator (/) is applied to the Minimum function (⌈) resulting in the derived function ⌈/. In most modern APLs this function can be manipulated like any other function, for example to assign it to a name:

      f ← ⌈/
      3 f 2 9 0 ¯1 0 2 5
9 9 0 2 5

Here the value of f is a derived function. Many APLs display a derived function by placing its operands next to the operator, as it is written:

      f
⌈/

Works in: Dyalog APL

In APL a user-defined operator such as a tradop or dop creates a derived function from its arguments without executing any of the user's code. In J, the user's code is evaluated and must return a value, which could but doesn't have to be a derived function.

APL syntax [edit]
General	Comparison with traditional mathematics ∙ Precedence ∙ Tacit programming (Train, Hook, Split composition)
Array	Numeric literal ∙ String ∙ Strand notation ∙ Object literal ∙ Array notation (design considerations)
Function	Argument ∙ Function valence ∙ Derived function ∙ Derived operator ∙ Niladic function ∙ Monadic function ∙ Dyadic function ∙ Ambivalent function ∙ Defined function (traditional) ∙ Dfn ∙ Function train
Operator	Operand ∙ Operator valence ∙ Tradop ∙ Dop ∙ Derived operator
Assignment	Multiple ∙ Indexed ∙ Selective ∙ Modified
Other	Function axis ∙ Bracket indexing ∙ Branch ∙ Statement separator ∙ Quad name ∙ System command ∙ User command ∙ Keyword ∙ Dot notation ∙ Function-operator overloading ∙ Control structure ∙ Comment

Derived function

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