Letter: Ajay Askoolum’s APL Idioms

from Steve Mansour (steve@carlislegroup.com)

All solutions are written using dynamic functions in Dyalog APL, ⎕ml←3. All are origin independent.

Some notes:¶

I have two solutions to idiom #1, CE and CE1. CE1 doesn't use the rho symbol or the comma symbol.

  CE←{×/⍴⍵}
  CE1←{+/∊⍵≡¨⍵}

I have two solutions to idiom #2, RA and RA1. Both require a 2-item vector on the left as the range. RA requires a scalar right argument. RA1 permits any array as the right argument and doesn’t use each. For more details on this solution, please see my article “Arithmetic Boundary Checking”in Vector Vol 21 No. 2. Solution to this particular problem is at the top of page 122.

  RA←{+/×⍵-⍺}
  RA1←{+/×⍵∘.-⍺}

Idiom #3:

  SN←{⍵[⍋⌊10⍟|⍵;]}

Idiom #4:

  LD←{{⍵}⌿⍵}

Idiom #5: Curried left argument can be any suitable value > 0. Domain error may result if the base of the exponential function is not chosen correctly.

  LS←0.9∘{⍺⍟×⌿⍺*⍵}

Idiom #6: Note – ⎕D is equivalent to '0123456789' :

  CN←{10⊥-⎕IO-⎕D⍳⍵}

Idiom #7:

  ZM←{0+/⍵}

Idiom #8:

  FO←{2</0,⍵}

Idiom #9:

  LO←{2>/⍵,0}

Idiom #10:

  RE←{↑¨↓∘⍺¨↓⍵-1}