apl: compose f∘g (+9 tests, 182/182)

lib/apl/runtime.sx

@@ -1062,3 +1062,7 @@
 (define apl-commute (fn (f x) (f x x)))
 
 (define apl-commute-dyadic (fn (f x y) (f y x)))
+
+(define apl-compose (fn (f g x) (f (g x))))
+
+(define apl-compose-dyadic (fn (f g x y) (f x (g y))))

lib/apl/tests/operators.sx

@@ -517,4 +517,66 @@
       apl-mul
       (make-array (list 3) (list 2 3 4))
       (make-array (list 3) (list 5 6 7))))
-  (list 10 18 28))
+  (list 10 18 28))
+
+(apl-test
+  "compose -∘| scalar (negative abs)"
+  (rv (apl-compose apl-neg-m apl-abs (apl-scalar -7)))
+  (list -7))
+
+(apl-test
+  "compose -∘| vector"
+  (rv
+    (apl-compose apl-neg-m apl-abs (make-array (list 4) (list -1 2 -3 4))))
+  (list -1 -2 -3 -4))
+
+(apl-test
+  "compose ⌊∘- (floor of negate)"
+  (rv (apl-compose apl-floor apl-neg-m (make-array (list 3) (list 1 2 3))))
+  (list -1 -2 -3))
+
+(apl-test
+  "compose -∘| matrix shape preserved"
+  (sh
+    (apl-compose apl-neg-m apl-abs (make-array (list 2 2) (list -1 2 -3 4))))
+  (list 2 2))
+
+(apl-test
+  "compose-dyadic +∘- equals subtract scalar"
+  (rv (apl-compose-dyadic apl-add apl-neg-m (apl-scalar 10) (apl-scalar 3)))
+  (list 7))
+
+(apl-test
+  "compose-dyadic +∘- equals subtract vector"
+  (rv
+    (apl-compose-dyadic
+      apl-add
+      apl-neg-m
+      (make-array (list 3) (list 10 20 30))
+      (make-array (list 3) (list 1 2 3))))
+  (list 9 18 27))
+
+(apl-test
+  "compose-dyadic -∘| (subtract abs)"
+  (rv (apl-compose-dyadic apl-sub apl-abs (apl-scalar 10) (apl-scalar -3)))
+  (list 7))
+
+(apl-test
+  "compose-dyadic ×∘- (multiply by negative)"
+  (rv
+    (apl-compose-dyadic
+      apl-mul
+      apl-neg-m
+      (make-array (list 3) (list 2 3 4))
+      (make-array (list 3) (list 1 2 3))))
+  (list -2 -6 -12))
+
+(apl-test
+  "compose-dyadic shape preserved"
+  (sh
+    (apl-compose-dyadic
+      apl-add
+      apl-neg-m
+      (make-array (list 2 3) (list 1 2 3 4 5 6))
+      (make-array (list 2 3) (list 1 1 1 1 1 1))))
+  (list 2 3))

plans/apl-on-sx.md

@@ -79,7 +79,7 @@ Core mapping:
 - [x] Outer product `∘.f` — `1 2 3 ∘.× 1 2 3` ↦ multiplication table
 - [x] Inner product `f.g` — `+.×` is matrix multiply
 - [x] Commute `f⍨` — `f⍨ x` ↔ `x f x`, `x f⍨ y` ↔ `y f x`
-- [ ] Compose `f∘g` — applies `g` first then `f`
+- [x] Compose `f∘g` — applies `g` first then `f`
 - [ ] Power `f⍣n` — apply f n times; `f⍣≡` until fixed point
 - [ ] Rank `f⍤k` — apply f at sub-rank k
 - [ ] At `@` — selective replace
@@ -118,6 +118,7 @@ data; format for string templating.
 
 _Newest first._
 
+- 2026-05-06: Phase 4 step 7 — compose f∘g (apl-compose monadic f∘g x, apl-compose-dyadic dyadic f x (g y)); 182/182 tests
 - 2026-05-06: Phase 4 step 6 — commute f⍨ (apl-commute monadic dup, apl-commute-dyadic swap); 173/173 tests
 - 2026-05-06: Phase 4 step 5 — inner product f.g (apl-inner); +.× matrix multiply, ∧.= equal-vectors; 163/163 tests
 - 2026-05-06: Phase 4 step 4 — outer product ∘.f (apl-outer); rank-doubling result shape = a-shape++b-shape; 151/151 tests