author: Bharathi Ramana Joshi
title: Notes on APL
- Depth (
≡): layers of nesting, or length of largest layer (prepended with - if uneven array). - Shape (
⍴): exact lengths of each dimension. - Rank: number of dimensions, i.e. shape of shape!
- Important identity:
X ≡ ⍴ (X ⍴ A), i.e. the shape of an array is always the same after reshaping. - Empty shape:
⍬(numbers)/''(character). - Light bulb
⍝for comments (since the illuminate us). - Scalar functions: functions that penetrate the arrays, all the way down to simple scalars before application.
- Scalar functions applied dyadically throw errors if argument shapes don't match up.
- Scalar extension
- Mixed function: works with larger structures of its arguments.
- Dynamic functions (
dfns): expressions enclosed in{}, left argument⍺and right argument⍵. - Use "self"
∇for recursive definitions, can rename functions without having to change the body. - Tacit function: APL statement that does not have data on the right
- Two-train/atop:
(f g) X ←→ f (g X) - Dyadic trains:
and,
X (f g) Y ←→ f (X g Y)X (f g h) Y ←→ (X f Y) g (X h Y) - Tree-trains/forks:
and,
(f g h) X ←→ (f X) g (h X)(A g h) X ←→ A g (h X)