apl: life Conway via 9-shift toroidal sum (+7 tests, 287/287)

lib/apl/runtime.sx

@@ -824,6 +824,18 @@
               ((prime-mask (apl-eq (apl-scalar 2) divisor-counts)))
               (apl-compress prime-mask a))))))))
 
+(define
+  apl-life-step
+  (fn
+    (board)
+    (let
+      ((zero-board (apl-mul board (apl-scalar 0))))
+      (let
+        ((sum-board (reduce (fn (acc dr) (reduce (fn (acc2 dc) (apl-add acc2 (apl-rotate-first (apl-scalar dr) (apl-rotate (apl-scalar dc) board)))) acc (list -1 0 1))) zero-board (list -1 0 1))))
+        (apl-or
+          (apl-eq sum-board (apl-scalar 3))
+          (apl-and board (apl-eq sum-board (apl-scalar 4))))))))
+
 (define
   apl-reduce
   (fn

lib/apl/scoreboard.json

@@ -5,9 +5,9 @@
     "dfn": {"pass": 24, "fail": 0},
     "tradfn": {"pass": 20, "fail": 0},
     "valence": {"pass": 14, "fail": 0},
-    "programs": {"pass": 11, "fail": 0}
+    "programs": {"pass": 18, "fail": 0}
   },
-  "total_pass": 280,
+  "total_pass": 287,
   "total_fail": 0,
-  "total": 280
+  "total": 287
 }

lib/apl/scoreboard.md

@@ -9,8 +9,8 @@ _Generated by `lib/apl/conformance.sh`_
 | dfn | 24 | 0 | 24 |
 | tradfn | 20 | 0 | 20 |
 | valence | 14 | 0 | 14 |
-| programs | 11 | 0 | 11 |
+| programs | 18 | 0 | 18 |
-| **Total** | **280** | **0** | **280** |
+| **Total** | **287** | **0** | **287** |
 
 ## Notes
 

lib/apl/tests/programs.sx

@@ -56,3 +56,139 @@
       (make-array (list 3) (list 1 1 1))
       (make-array (list 3) (list 1 2 3))))
   (list 1 2 3))
+
+(apl-test
+  "life: empty 5x5 stays empty"
+  (mkrv
+    (apl-life-step
+      (make-array
+        (list 5 5)
+        (list 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0))))
+  (list 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0))
+
+(apl-test
+  "life: horizontal blinker → vertical blinker"
+  (mkrv
+    (apl-life-step
+      (make-array
+        (list 5 5)
+        (list 0 0 0 0 0 0 0 0 0 0 0 1 1 1 0 0 0 0 0 0 0 0 0 0 0))))
+  (list 0 0 0 0 0 0 0 1 0 0 0 0 1 0 0 0 0 1 0 0 0 0 0 0 0))
+
+(apl-test
+  "life: vertical blinker → horizontal blinker"
+  (mkrv
+    (apl-life-step
+      (make-array
+        (list 5 5)
+        (list 0 0 0 0 0 0 0 1 0 0 0 0 1 0 0 0 0 1 0 0 0 0 0 0 0))))
+  (list 0 0 0 0 0 0 0 0 0 0 0 1 1 1 0 0 0 0 0 0 0 0 0 0 0))
+
+(apl-test
+  "life: blinker has period 2"
+  (mkrv
+    (apl-life-step
+      (apl-life-step
+        (make-array
+          (list 5 5)
+          (list 0 0 0 0 0 0 0 0 0 0 0 1 1 1 0 0 0 0 0 0 0 0 0 0 0)))))
+  (list 0 0 0 0 0 0 0 0 0 0 0 1 1 1 0 0 0 0 0 0 0 0 0 0 0))
+
+(apl-test
+  "life: 2x2 block stable on 5x5"
+  (mkrv
+    (apl-life-step
+      (make-array
+        (list 5 5)
+        (list 0 0 0 0 0 0 1 1 0 0 0 1 1 0 0 0 0 0 0 0 0 0 0 0 0))))
+  (list 0 0 0 0 0 0 1 1 0 0 0 1 1 0 0 0 0 0 0 0 0 0 0 0 0))
+
+(apl-test
+  "life: shape preserved"
+  (mksh
+    (apl-life-step
+      (make-array
+        (list 5 5)
+        (list 0 0 0 0 0 0 0 0 0 0 0 1 1 1 0 0 0 0 0 0 0 0 0 0 0))))
+  (list 5 5))
+
+(apl-test
+  "life: glider on 6x6 advances"
+  (mkrv
+    (apl-life-step
+      (make-array
+        (list 6 6)
+        (list
+          0
+          0
+          0
+          0
+          0
+          0
+          0
+          0
+          1
+          0
+          0
+          0
+          0
+          0
+          0
+          1
+          0
+          0
+          0
+          1
+          1
+          1
+          0
+          0
+          0
+          0
+          0
+          0
+          0
+          0
+          0
+          0
+          0
+          0
+          0
+          0))))
+  (list
+    0
+    0
+    0
+    0
+    0
+    0
+    0
+    0
+    0
+    0
+    0
+    0
+    0
+    1
+    0
+    1
+    0
+    0
+    0
+    0
+    1
+    1
+    0
+    0
+    0
+    0
+    1
+    0
+    0
+    0
+    0
+    0
+    0
+    0
+    0
+    0))

lib/apl/tests/programs/life.apl

@@ -0,0 +1,22 @@
+⍝ Conway's Game of Life — toroidal one-liner
+⍝
+⍝ The classic Roger Hui formulation:
+⍝   life ← {⊃1 ⍵ ∨.∧ 3 4 = +/ +/ ¯1 0 1 ∘.⊖ ¯1 0 1 ⌽¨ ⊂⍵}
+⍝
+⍝ Read right-to-left:
+⍝   ⊂⍵                : enclose the board (so it's a single scalar item)
+⍝   ¯1 0 1 ⌽¨ ⊂⍵      : produce 3 horizontally-shifted copies
+⍝   ¯1 0 1 ∘.⊖ …      : outer-product with vertical shifts → 3×3 = 9 shifts
+⍝   +/ +/ …           : sum the 9 boards element-wise → neighbor-count + self
+⍝   3 4 = …           : boolean — count is exactly 3 or exactly 4
+⍝   1 ⍵ ∨.∧ …         : "alive next" iff (count=3) or (alive AND count=4)
+⍝   ⊃ …               : disclose back to a 2D board
+⍝
+⍝ Rules in plain language:
+⍝   - dead cell + 3 live neighbors → born
+⍝   - live cell + 2 or 3 live neighbors → survives
+⍝   - all else → dies
+⍝
+⍝ Toroidal: edges wrap (rotate is cyclic).
+
+life ← {⊃1 ⍵ ∨.∧ 3 4 = +/ +/ ¯1 0 1 ∘.⊖ ¯1 0 1 ⌽¨ ⊂⍵}

plans/apl-on-sx.md

@@ -95,7 +95,7 @@ Core mapping:
 
 ### Phase 6 — classic programs + drive corpus
 - [ ] Classic programs in `lib/apl/tests/programs/`:
-  - [ ] `life.apl` — Conway's Game of Life as a one-liner using `⊂` `⊖` `⌽` `+/`
+  - [x] `life.apl` — Conway's Game of Life as a one-liner using `⊂` `⊖` `⌽` `+/`
   - [ ] `mandelbrot.apl` — complex iteration with rank-polymorphic `+ × ⌊` (or real-axis subset)
   - [x] `primes.apl` — `(2=+⌿0=A∘.|A)/A←⍳N` sieve
   - [ ] `n-queens.apl` — backtracking via reduce
@@ -118,6 +118,7 @@ data; format for string templating.
 
 _Newest first._
 
+- 2026-05-07: Phase 6 life — Conway via 9-shift toroidal sum + alive-rule (cnt=3 OR alive∧cnt=4); apl-life-step + life.apl source; blinker oscillates, block stable, glider advances; +7 tests; 287/287
 - 2026-05-07: Phase 6 primes — sieve via outer-product residue + reduce-first + compress; apl-compress added; lib/apl/tests/programs/primes.apl source; +11 tests; 280/280
 - 2026-05-07: Phase 5 conformance.sh + scoreboard.{json,md} — per-suite runner; current snapshot 269/269; **Phase 5 complete**
 - 2026-05-07: Phase 5 valence dispatch — apl-dfn-valence (AST scan for ⍺/⍵), apl-tradfn-valence (slot check), apl-call unified entry; +14 tests; 269/269 tests