apl: idiom corpus — 34 classic idioms; entire plan complete (362/362)

lib/apl/tests/idioms.sx

@@ -0,0 +1,224 @@
+; APL idiom corpus — classic Roger Hui / Phil Last idioms expressed
+; through our runtime primitives.  Each test names the APL one-liner
+; and verifies the equivalent runtime call.
+
+(define mkrv (fn (arr) (get arr :ravel)))
+(define mksh (fn (arr) (get arr :shape)))
+
+; ---------- reductions ----------
+
+(apl-test
+  "+/⍵ — sum"
+  (mkrv (apl-reduce apl-add (make-array (list 5) (list 1 2 3 4 5))))
+  (list 15))
+
+(apl-test
+  "(+/⍵)÷⍴⍵ — mean"
+  (mkrv
+    (apl-div
+      (apl-reduce apl-add (make-array (list 5) (list 1 2 3 4 5)))
+      (apl-scalar 5)))
+  (list 3))
+
+(apl-test
+  "⌈/⍵ — max"
+  (mkrv (apl-reduce apl-max (make-array (list 6) (list 3 1 4 1 5 9))))
+  (list 9))
+
+(apl-test
+  "⌊/⍵ — min"
+  (mkrv (apl-reduce apl-min (make-array (list 6) (list 3 1 4 1 5 9))))
+  (list 1))
+
+(apl-test
+  "(⌈/⍵)-⌊/⍵ — range"
+  (mkrv
+    (apl-sub
+      (apl-reduce apl-max (make-array (list 6) (list 3 1 4 1 5 9)))
+      (apl-reduce apl-min (make-array (list 6) (list 3 1 4 1 5 9)))))
+  (list 8))
+
+(apl-test
+  "×/⍵ — product"
+  (mkrv (apl-reduce apl-mul (make-array (list 4) (list 1 2 3 4))))
+  (list 24))
+
+(apl-test
+  "+\\⍵ — running sum"
+  (mkrv (apl-scan apl-add (make-array (list 5) (list 1 2 3 4 5))))
+  (list 1 3 6 10 15))
+
+; ---------- sort / order ----------
+
+(apl-test
+  "⍵[⍋⍵] — sort ascending"
+  (mkrv (apl-quicksort (make-array (list 5) (list 3 1 4 1 5))))
+  (list 1 1 3 4 5))
+
+(apl-test
+  "⌽⍵ — reverse"
+  (mkrv (apl-reverse (make-array (list 5) (list 1 2 3 4 5))))
+  (list 5 4 3 2 1))
+
+(apl-test
+  "⊃⌽⍵ — last element"
+  (mkrv
+    (apl-disclose (apl-reverse (make-array (list 4) (list 10 20 30 40)))))
+  (list 40))
+
+(apl-test
+  "1↑⍵ — first element"
+  (mkrv
+    (apl-take (apl-scalar 1) (make-array (list 4) (list 10 20 30 40))))
+  (list 10))
+
+(apl-test
+  "1↓⍵ — drop first"
+  (mkrv
+    (apl-drop (apl-scalar 1) (make-array (list 4) (list 10 20 30 40))))
+  (list 20 30 40))
+
+(apl-test
+  "¯1↓⍵ — drop last"
+  (mkrv
+    (apl-drop (apl-scalar -1) (make-array (list 4) (list 10 20 30 40))))
+  (list 10 20 30))
+
+; ---------- counts / membership ----------
+
+(apl-test
+  "≢⍵ — tally"
+  (mkrv (apl-tally (make-array (list 7) (list 9 8 7 6 5 4 3))))
+  (list 7))
+
+(apl-test
+  "+/⍵=v — count occurrences of v"
+  (mkrv
+    (apl-reduce
+      apl-add
+      (apl-eq (make-array (list 7) (list 1 2 3 2 1 3 2)) (apl-scalar 2))))
+  (list 3))
+
+(apl-test
+  "0=N|M — divisibility test"
+  (mkrv (apl-eq (apl-scalar 0) (apl-mod (apl-scalar 3) (apl-scalar 12))))
+  (list 1))
+
+; ---------- shape constructors ----------
+
+(apl-test
+  "N⍴1 — vector of N ones"
+  (mkrv (apl-reshape (apl-scalar 5) (apl-scalar 1)))
+  (list 1 1 1 1 1))
+
+(apl-test
+  "(N N)⍴0 — N×N zero matrix"
+  (mkrv (apl-reshape (make-array (list 2) (list 3 3)) (apl-scalar 0)))
+  (list 0 0 0 0 0 0 0 0 0))
+
+(apl-test
+  "⍳∘.=⍳ — N×N identity matrix"
+  (mkrv
+    (apl-outer apl-eq (apl-iota (apl-scalar 3)) (apl-iota (apl-scalar 3))))
+  (list 1 0 0 0 1 0 0 0 1))
+
+(apl-test
+  "⍳∘.×⍳ — multiplication table"
+  (mkrv
+    (apl-outer apl-mul (apl-iota (apl-scalar 3)) (apl-iota (apl-scalar 3))))
+  (list 1 2 3 2 4 6 3 6 9))
+
+; ---------- numerical idioms ----------
+
+(apl-test
+  "+\\⍳N — triangular numbers"
+  (mkrv (apl-scan apl-add (apl-iota (apl-scalar 5))))
+  (list 1 3 6 10 15))
+
+(apl-test
+  "+/⍳N=N×(N+1)÷2 — sum of 1..N"
+  (mkrv (apl-reduce apl-add (apl-iota (apl-scalar 10))))
+  (list 55))
+
+(apl-test
+  "×/⍳N — factorial via iota"
+  (mkrv (apl-reduce apl-mul (apl-iota (apl-scalar 5))))
+  (list 120))
+
+(apl-test
+  "2|⍵ — parity (1=odd)"
+  (mkrv (apl-mod (apl-scalar 2) (make-array (list 5) (list 1 2 3 4 5))))
+  (list 1 0 1 0 1))
+
+(apl-test
+  "+/2|⍵ — count odd"
+  (mkrv
+    (apl-reduce
+      apl-add
+      (apl-mod (apl-scalar 2) (make-array (list 5) (list 1 2 3 4 5)))))
+  (list 3))
+
+; ---------- boolean idioms ----------
+
+(apl-test
+  "∧/⍵ — all-true"
+  (mkrv (apl-reduce apl-and (make-array (list 4) (list 1 1 1 1))))
+  (list 1))
+
+(apl-test
+  "∧/⍵ — all-true with zero is false"
+  (mkrv (apl-reduce apl-and (make-array (list 4) (list 1 1 0 1))))
+  (list 0))
+
+(apl-test
+  "∨/⍵ — any-true"
+  (mkrv (apl-reduce apl-or (make-array (list 4) (list 0 0 1 0))))
+  (list 1))
+
+(apl-test
+  "∨/⍵ — any-true all zero is false"
+  (mkrv (apl-reduce apl-or (make-array (list 4) (list 0 0 0 0))))
+  (list 0))
+
+; ---------- selection / scaling ----------
+
+(apl-test
+  "⍵×⍵ — square each"
+  (mkrv
+    (apl-mul
+      (make-array (list 4) (list 1 2 3 4))
+      (make-array (list 4) (list 1 2 3 4))))
+  (list 1 4 9 16))
+
+(apl-test
+  "+/⍵×⍵ — sum of squares"
+  (mkrv
+    (apl-reduce
+      apl-add
+      (apl-mul
+        (make-array (list 4) (list 1 2 3 4))
+        (make-array (list 4) (list 1 2 3 4)))))
+  (list 30))
+
+(apl-test
+  "⍵-(+/⍵)÷⍴⍵ — mean-centered"
+  (mkrv
+    (apl-sub
+      (make-array (list 5) (list 2 4 6 8 10))
+      (apl-div
+        (apl-reduce apl-add (make-array (list 5) (list 2 4 6 8 10)))
+        (apl-scalar 5))))
+  (list -4 -2 0 2 4))
+
+; ---------- shape / structure ----------
+
+(apl-test
+  ",⍵ — ravel"
+  (mkrv (apl-ravel (make-array (list 2 3) (list 1 2 3 4 5 6))))
+  (list 1 2 3 4 5 6))
+
+(apl-test
+  "⍴⍴⍵ — rank"
+  (mkrv
+    (apl-shape (apl-shape (make-array (list 2 3) (list 1 2 3 4 5 6)))))
+  (list 2))