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"dfns" redirects here. For the workspace by Scholes, see dfns workspace.

A dfn (contraction of direct function or dynamic function, pronounced "dee fun") is an alternative way to define a function and operator, invented by John Scholes. A dfn operator can also be called a dop (pronounced "dee op").

John Scholes was responsible for numerous presentations and publications on and about dfns, and until his passing he maintained the dfns workspace, a collection of dfns examples.

As of 2020, dfns are fully implemented in Dyalog APL, NARS2000, ngn/apl, dzaima/APL, and partially in GNU APL, although not all dialects implement lexical scoping, in contrast to the dynamic scoping of tradfns. In other words, a dfn cannot "see" locals of its caller, but can see locals of its definer.

Wikipedia includes a thorough treatment of dfns.


      {⍵*0.5} 16        ⍝ square root
      3 {⍵*÷⍺} 27       ⍝ ⍺th root

Default left arguments

Assignment to is unusual in that the entire statement is only executed if the dfn is called monadically:[1]

          ⍺←2           ⍝ square root by default
          ⍵*÷⍺          ⍝ result


Guards provide dfns with support for basic flow control.[2] This is a multiline dfn with a conditional result:

          ⍺=0:0         ⍝ return zero if zeroth root
          ⍵*÷⍺          ⍝ result


Dyalog APL dfns support error-guards for processing errors by error codes.[3]

In the following example, there are two error-guards for the error code 11 (DOMAIN ERROR):[4]

    G←6.6743E¯11       ⍝ gravitational constant
    11::'N/A'          ⍝ second DOMAIN ERROR: return 'N/A'
    11::∇⍎¨⍵           ⍝ first DOMAIN ERROR: maybe the argument is a vector of strings?
    G×⍵[1]×⍵[2]÷⍵[3]*2 ⍝ the argument is a vector of numbers

      ⍝ Calculate gravity force between the Earth and the Sun
      Gravity '1.99e30' '5.97e24' '1.50e11'
      Gravity 1.99e30 5.97e24 1.50e11
      Gravity 1.99e30 5.97e24 0   ⍝ trigger division by zero

Shy results

Roger Hui's assert is a dfn that has become the de facto standard when it comes to test suites.[5]. In it, Hui uses both a default left argument and a final assignment to make the dfn shy:

assert ← {⍺←'assertion failure' ⋄ 0∊⍵:⍺ ⎕signal 8 ⋄ shy←0}

External links




  1. Default Left Argument – Dyalog APL.
  2. Guards – Dyalog APL.
  3. Error Guards – Dyalog APL.
  4. APL Error Messages and Codes – Dyalog APL.
  5. Stefan Kruger. 2020 Problem Solving Competition – Phase II highlights. Dyalog blog. April 30, 2021.

APL syntax [edit]
General Comparison with traditional mathematicsPrecedenceTacit programming (Train, Hook, Split composition)
Array Numeric literalStringStrand notationObject literalArray notation (design considerations)
Function ArgumentFunction valenceDerived functionDerived operatorNiladic functionMonadic functionDyadic functionAmbivalent functionDefined function (traditional)DfnFunction train
Operator OperandOperator valenceTradopDopDerived operator
Assignment MultipleIndexedSelectiveModified
Other Function axisBracket indexingBranchStatement separatorQuad nameSystem commandUser commandKeywordDot notationFunction-operator overloadingControl structureComment