Palindromic Expression for Phi

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Some find that APL expressions can have a poetic beauty. Phil Last submitted the following variable-free recursive dfn to compute the limit of a converging function, equivalent to the derived monadic operator :[1]

limit{             ⍝ Function power limit (fixpoint).
     ⍺⍺{           ⍝ 'old' value:
        ⍵:⍵       ⍝       old matches new: finished.
          ⍺⍺     ⍝       otherwise: try new value.
    }⍺⍺            ⍝ 'new' value.

John Scholes noted that it was close to being a palindrome, so he inlined it and he amended it with dummy code to make its invocation for finding the golden ratio even closer to palindromic:

      1{1}{ ⍺⍺{⍵:⍵   ⍺⍺ ∇∇ ⍺⍺   ⍵:⍵}⍺⍺ }{÷+1}1

Scholes then published a minute-long video with musical accompaniment where he types the expression in a symmetric fashion, culminating with the execution.[2]


  1. Dyalog. Function power limit (fixpoint). Dfns workspace. 2019-02-07.
  2. DFunctionista. Palindromic Expression for Phi in APL. YouTube. 2009-02-13.