Dfns & Dops

A dfn (dop)¹ is an alternative function definition style suitable for defining small to medium sized functions. It bridges the gap between operator expressions: rank←⍴∘⍴ and full "header style" definitions such as:

    ∇ rslt←larg func rarg;local...

In its simplest form, a dfn is an APL expression enclosed in curly braces {}, possibly including the special characters ⍺ and ⍵ to represent the left and right arguments of the function respectively. For example:

      {(+/⍵)÷⍴⍵} 1 2 3 4    ⍝ Arithmetic Mean (Average)
2.5
      3 {⍵*÷⍺} 64           ⍝ ⍺th root
4

dfns can be named in the normal fashion:

      mean←{(+/⍵)÷⍴⍵}
      mean¨(2 3)(4 5)
 2.5  4.5

dfns can be defined and used in any context where an APL function may be found, in particular:

• In immediate execution mode as in the examples above.
• Within a defined function or operator.
• As the operand of an operator such as each (¨).
• Within another dfn.
• The last point means that it is easy to define nested local functions.

Supplied Workspaces

There are many samples of dfns and dops in [DYALOG]/ws/, for example, in the workspaces min.dws, max.dws, tube.dws, and eval.dws.