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30 new source-string idioms via apl-run: triangulars, factorial, running sum/product, parity counts, identity matrix, mult-table, dot product, ∧.= equality, take/drop/reverse, tally, ravel, count-of-value, etc. Side-fix: tokenizer's apl-glyph-set was missing ≢ and ≡ — they were silently skipped. Added them and to apl-parse-fn-glyphs.
360 lines
8.0 KiB
Plaintext
360 lines
8.0 KiB
Plaintext
; APL idiom corpus — classic Roger Hui / Phil Last idioms expressed
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; through our runtime primitives. Each test names the APL one-liner
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; and verifies the equivalent runtime call.
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(define mkrv (fn (arr) (get arr :ravel)))
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(define mksh (fn (arr) (get arr :shape)))
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; ---------- reductions ----------
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(apl-test
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"+/⍵ — sum"
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(mkrv (apl-reduce apl-add (make-array (list 5) (list 1 2 3 4 5))))
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(list 15))
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(apl-test
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"(+/⍵)÷⍴⍵ — mean"
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(mkrv
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(apl-div
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(apl-reduce apl-add (make-array (list 5) (list 1 2 3 4 5)))
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(apl-scalar 5)))
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(list 3))
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(apl-test
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"⌈/⍵ — max"
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(mkrv (apl-reduce apl-max (make-array (list 6) (list 3 1 4 1 5 9))))
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(list 9))
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(apl-test
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"⌊/⍵ — min"
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(mkrv (apl-reduce apl-min (make-array (list 6) (list 3 1 4 1 5 9))))
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(list 1))
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(apl-test
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"(⌈/⍵)-⌊/⍵ — range"
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(mkrv
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(apl-sub
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(apl-reduce apl-max (make-array (list 6) (list 3 1 4 1 5 9)))
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(apl-reduce apl-min (make-array (list 6) (list 3 1 4 1 5 9)))))
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(list 8))
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(apl-test
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"×/⍵ — product"
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(mkrv (apl-reduce apl-mul (make-array (list 4) (list 1 2 3 4))))
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(list 24))
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(apl-test
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"+\\⍵ — running sum"
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(mkrv (apl-scan apl-add (make-array (list 5) (list 1 2 3 4 5))))
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(list 1 3 6 10 15))
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; ---------- sort / order ----------
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(apl-test
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"⍵[⍋⍵] — sort ascending"
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(mkrv (apl-quicksort (make-array (list 5) (list 3 1 4 1 5))))
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(list 1 1 3 4 5))
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(apl-test
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"⌽⍵ — reverse"
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(mkrv (apl-reverse (make-array (list 5) (list 1 2 3 4 5))))
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(list 5 4 3 2 1))
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(apl-test
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"⊃⌽⍵ — last element"
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(mkrv
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(apl-disclose (apl-reverse (make-array (list 4) (list 10 20 30 40)))))
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(list 40))
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(apl-test
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"1↑⍵ — first element"
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(mkrv
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(apl-take (apl-scalar 1) (make-array (list 4) (list 10 20 30 40))))
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(list 10))
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(apl-test
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"1↓⍵ — drop first"
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(mkrv
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(apl-drop (apl-scalar 1) (make-array (list 4) (list 10 20 30 40))))
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(list 20 30 40))
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(apl-test
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"¯1↓⍵ — drop last"
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(mkrv
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(apl-drop (apl-scalar -1) (make-array (list 4) (list 10 20 30 40))))
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(list 10 20 30))
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; ---------- counts / membership ----------
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(apl-test
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"≢⍵ — tally"
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(mkrv (apl-tally (make-array (list 7) (list 9 8 7 6 5 4 3))))
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(list 7))
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(apl-test
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"+/⍵=v — count occurrences of v"
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(mkrv
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(apl-reduce
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apl-add
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(apl-eq (make-array (list 7) (list 1 2 3 2 1 3 2)) (apl-scalar 2))))
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(list 3))
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(apl-test
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"0=N|M — divisibility test"
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(mkrv (apl-eq (apl-scalar 0) (apl-mod (apl-scalar 3) (apl-scalar 12))))
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(list 1))
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; ---------- shape constructors ----------
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(apl-test
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"N⍴1 — vector of N ones"
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(mkrv (apl-reshape (apl-scalar 5) (apl-scalar 1)))
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(list 1 1 1 1 1))
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(apl-test
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"(N N)⍴0 — N×N zero matrix"
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(mkrv (apl-reshape (make-array (list 2) (list 3 3)) (apl-scalar 0)))
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(list 0 0 0 0 0 0 0 0 0))
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(apl-test
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"⍳∘.=⍳ — N×N identity matrix"
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(mkrv
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(apl-outer apl-eq (apl-iota (apl-scalar 3)) (apl-iota (apl-scalar 3))))
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(list 1 0 0 0 1 0 0 0 1))
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(apl-test
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"⍳∘.×⍳ — multiplication table"
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(mkrv
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(apl-outer apl-mul (apl-iota (apl-scalar 3)) (apl-iota (apl-scalar 3))))
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(list 1 2 3 2 4 6 3 6 9))
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; ---------- numerical idioms ----------
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(apl-test
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"+\\⍳N — triangular numbers"
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(mkrv (apl-scan apl-add (apl-iota (apl-scalar 5))))
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(list 1 3 6 10 15))
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(apl-test
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"+/⍳N=N×(N+1)÷2 — sum of 1..N"
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(mkrv (apl-reduce apl-add (apl-iota (apl-scalar 10))))
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(list 55))
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(apl-test
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"×/⍳N — factorial via iota"
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(mkrv (apl-reduce apl-mul (apl-iota (apl-scalar 5))))
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(list 120))
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(apl-test
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"2|⍵ — parity (1=odd)"
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(mkrv (apl-mod (apl-scalar 2) (make-array (list 5) (list 1 2 3 4 5))))
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(list 1 0 1 0 1))
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(apl-test
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"+/2|⍵ — count odd"
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(mkrv
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(apl-reduce
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apl-add
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(apl-mod (apl-scalar 2) (make-array (list 5) (list 1 2 3 4 5)))))
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(list 3))
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; ---------- boolean idioms ----------
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(apl-test
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"∧/⍵ — all-true"
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(mkrv (apl-reduce apl-and (make-array (list 4) (list 1 1 1 1))))
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(list 1))
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(apl-test
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"∧/⍵ — all-true with zero is false"
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(mkrv (apl-reduce apl-and (make-array (list 4) (list 1 1 0 1))))
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(list 0))
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(apl-test
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"∨/⍵ — any-true"
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(mkrv (apl-reduce apl-or (make-array (list 4) (list 0 0 1 0))))
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(list 1))
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(apl-test
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"∨/⍵ — any-true all zero is false"
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(mkrv (apl-reduce apl-or (make-array (list 4) (list 0 0 0 0))))
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(list 0))
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; ---------- selection / scaling ----------
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(apl-test
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"⍵×⍵ — square each"
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(mkrv
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(apl-mul
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(make-array (list 4) (list 1 2 3 4))
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(make-array (list 4) (list 1 2 3 4))))
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(list 1 4 9 16))
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(apl-test
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"+/⍵×⍵ — sum of squares"
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(mkrv
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(apl-reduce
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apl-add
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(apl-mul
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(make-array (list 4) (list 1 2 3 4))
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(make-array (list 4) (list 1 2 3 4)))))
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(list 30))
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(apl-test
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"⍵-(+/⍵)÷⍴⍵ — mean-centered"
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(mkrv
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(apl-sub
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(make-array (list 5) (list 2 4 6 8 10))
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(apl-div
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(apl-reduce apl-add (make-array (list 5) (list 2 4 6 8 10)))
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(apl-scalar 5))))
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(list -4 -2 0 2 4))
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; ---------- shape / structure ----------
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(apl-test
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",⍵ — ravel"
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(mkrv (apl-ravel (make-array (list 2 3) (list 1 2 3 4 5 6))))
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(list 1 2 3 4 5 6))
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(apl-test
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"⍴⍴⍵ — rank"
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(mkrv
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(apl-shape (apl-shape (make-array (list 2 3) (list 1 2 3 4 5 6)))))
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(list 2))
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(apl-test
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"src: +/⍳N → triangular(N)"
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(mkrv (apl-run "+/⍳100"))
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(list 5050))
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(apl-test "src: ×/⍳N → N!" (mkrv (apl-run "×/⍳6")) (list 720))
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(apl-test
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"src: ⌈/V — max"
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(mkrv (apl-run "⌈/3 1 4 1 5 9 2 6"))
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(list 9))
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(apl-test
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"src: ⌊/V — min"
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(mkrv (apl-run "⌊/3 1 4 1 5 9 2 6"))
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(list 1))
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(apl-test
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"src: range = (⌈/V) - ⌊/V"
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(mkrv (apl-run "(⌈/3 1 4 1 5 9 2 6) - ⌊/3 1 4 1 5 9 2 6"))
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(list 8))
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(apl-test
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"src: +\\V — running sum"
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(mkrv (apl-run "+\\1 2 3 4 5"))
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(list 1 3 6 10 15))
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(apl-test
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"src: ×\\V — running product"
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(mkrv (apl-run "×\\1 2 3 4 5"))
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(list 1 2 6 24 120))
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(apl-test
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"src: V × V — squares"
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(mkrv (apl-run "(⍳5) × ⍳5"))
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(list 1 4 9 16 25))
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(apl-test
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"src: +/V × V — sum of squares"
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(mkrv (apl-run "+/(⍳5) × ⍳5"))
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(list 55))
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(apl-test "src: ∧/V — all-true" (mkrv (apl-run "∧/1 1 1 1")) (list 1))
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(apl-test "src: ∨/V — any-true" (mkrv (apl-run "∨/0 0 1 0")) (list 1))
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(apl-test "src: 0 = N|M — divides" (mkrv (apl-run "0 = 3 | 12")) (list 1))
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(apl-test
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"src: 2 | V — parity"
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(mkrv (apl-run "2 | 1 2 3 4 5 6"))
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(list 1 0 1 0 1 0))
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(apl-test
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"src: +/2|V — count odd"
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(mkrv (apl-run "+/2 | 1 2 3 4 5 6"))
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(list 3))
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(apl-test "src: ⍴ V" (mkrv (apl-run "⍴ 1 2 3 4 5")) (list 5))
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(apl-test
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"src: ⍴⍴ M — rank"
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(mkrv (apl-run "⍴ ⍴ (2 3) ⍴ ⍳6"))
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(list 2))
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(apl-test
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"src: N⍴1 — vector of ones"
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(mkrv (apl-run "5 ⍴ 1"))
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(list 1 1 1 1 1))
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(apl-test
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"src: ⍳N ∘.= ⍳N — identity matrix"
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(mkrv (apl-run "(⍳3) ∘.= ⍳3"))
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(list 1 0 0 0 1 0 0 0 1))
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(apl-test
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"src: ⍳N ∘.× ⍳N — multiplication table"
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(mkrv (apl-run "(⍳3) ∘.× ⍳3"))
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(list 1 2 3 2 4 6 3 6 9))
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(apl-test
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"src: V +.× V — dot product"
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(mkrv (apl-run "1 2 3 +.× 4 5 6"))
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(list 32))
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(apl-test
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"src: ∧.= V — vectors equal?"
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(mkrv (apl-run "1 2 3 ∧.= 1 2 3"))
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(list 1))
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(apl-test
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"src: V[1] — first element"
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(mkrv (apl-run "(10 20 30 40)[1]"))
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(list 10))
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(apl-test
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"src: 1↑V — first via take"
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(mkrv (apl-run "1 ↑ 10 20 30 40"))
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(list 10))
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(apl-test
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"src: 1↓V — drop first"
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(mkrv (apl-run "1 ↓ 10 20 30 40"))
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(list 20 30 40))
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(apl-test
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"src: ¯1↓V — drop last"
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(mkrv (apl-run "¯1 ↓ 10 20 30 40"))
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(list 10 20 30))
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(apl-test
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"src: ⌽V — reverse"
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(mkrv (apl-run "⌽ 1 2 3 4 5"))
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(list 5 4 3 2 1))
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(apl-test
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"src: ≢V — tally"
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(mkrv (apl-run "≢ 9 8 7 6 5 4 3 2 1"))
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(list 9))
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(apl-test
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"src: ,M — ravel"
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(mkrv (apl-run ", (2 3) ⍴ ⍳6"))
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(list 1 2 3 4 5 6))
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(apl-test
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"src: A=V — count occurrences"
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(mkrv (apl-run "+/2 = 1 2 3 2 1 3 2"))
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(list 3))
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(apl-test
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"src: ⌈/(V × V) — max squared"
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(mkrv (apl-run "⌈/(1 2 3 4 5) × 1 2 3 4 5"))
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(list 25))
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