=≤<>≥≡≢

Comparisons =≤<>≥≡≢

= is comparison (not assignment!) and penetrates all structures, giving a single Boolean (0 or 1) per leaf element. ≠ is the negation of that.

≤<>≥ work as you’d expect, again penetrating all structure.

A≡B is match. It compares the entire arrays A and B in all respects, even the invisible prototype:

''≡⍬   ⍝ does the empty char vector match the empty numeric vector?

0

A≢B is not match, the negation of A≡B.

Depth, tally ≡≢

Monadic ≡B gives the depth of B, which is the amount of nesting. A simple scalar is 0, a vector is 1, a vector of vectors is 2, etc. If the amount of nesting is uneven throughout the array, the result will be negative, and indicate the maximum depth.

≢B is the tally of B, i.e. how many major cells B has. For a scalar, that’s 1. For a vector, it is the number of elements, for a matrix it is the number of rows, for a 3D array it is the number of layers, and so on.

≡(1 2 (3 4 5 (6 7 8)))  ⍝ unevenly nested vector
≢1                      ⍝ scalars tally to 1
≢3 2⍴⍳6                 ⍝ matrix tally is the number of rows

¯3

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