Useful APL snippets

Jul 13 2026

Editors🔗

In RIDE, to display function trains in tree format:

    ]box ON -trains=tree
Was OFF -trains=box
    +/÷≢
  ┌─┼─┐
  / ÷ ≢
┌─┘
+

Basic array operations🔗

Turn a scalar into an array.

First element of an array.

⊃

Last element of an array. Note the lack of symmetry with ⊃.

⊢/

Flatten an array.

{,⍵}

Check that an array is a palindrome.

⌽≡⊢

Pad a number with a desired number of 0s.

    11↑1 ⍝ 1 followed by ten 0's.
1 0 0 0 0 0 0 0 0 0 0

Find the number of leading 1s in a boolean array.

    +/∧\

Numbers🔗

Sign of a number.

×

Get the integral and fractional part of a non-negative real number.

0 1∘⊤

Profiling🔗

Compare the performance of 3 functions F, G and H on the same input s.

'cmpx' ⎕CY 'dfns'
cmpx 'F s' 'G s' 'H s'

Sorting🔗

Sort an array in ascending order.

{⍵[⍋⍵]}

Order the rows of a matrix according to the sorted order of the second row.

    ⊢ mat ← 2 3 ⍴ 1 4 2 5 9 7
1 4 2
5 9 7
    mat[; ⍋mat[2;]]
1 2 4
5 7 9

Find the index of the maximum element of an array. Recall that in APL indices start at 1.

⊃⍒

Strings🔗

All uppercase English letters.

    ⎕A
ABCDEFGHIJKLMNOPQRSTUVWXYZ

All lowercase English letters.

    ⎕UCS 96+⍳26
abcdefghijklmnopqrstuvwxyz

Discard all characters except English letters.

    a ← 'The quick brown fox! Jumps over the lazy... dog?'
    a∩⎕A,⎕UCS 96+⍳26
ThequickbrownfoxJumpsoverthelazydog

Convert a string to lowercase.

    ⎕C 'dYALog`
dyalog
    ¯1 ⎕C 'dYALog`
dyalog

Convert a string to uppercase.

    1 ⎕C 'dYALog`
dyalog

Case-insensitive string comparison. Note the use of ⍥ (over), which monadically applies its right function to both arguments, and then dyadically applies its left function to the results.

    'Dyalog' ≡⍥⎕C 'DYALOG'
1

Check that a string is a palindrome after discarding non-alphabet characters. We convert to uppercase, discard everything that is not an uppercase letter, and then check that the result is a palindrome.

{(⌽≡⊢) ⎕A∩⍨1⎕C ⍵}

Mathematics🔗

Generate an identity matrix.

∘.=⍨ ⍳

This is basically a tacit rephrasing of

{(⍳⍵)∘.=⍳⍵}

The following method is about as fast as it gets for generating an identity matrix. Right-pad 1 with ⍵ zeroes and then repeat that array until the shape is ⍵ ⍵.

{⍵ ⍵⍴(⍵+1)↑1}

This can be rephrased in tacit form as a 5-train. Note that we use × (sign) to replace the positive input with 1. We could also use 1⍨ or ≢ instead of ×.

,⍨⍴+∘1↑×

Generate a random float between 0 and 1.

?0

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