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apl: life Conway via 9-shift toroidal sum (+7 tests, 287/287)
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giles
2026-05-07 04:36:49 +00:00
parent ed0853f4a0
commit 20a61de693
6 changed files with 177 additions and 6 deletions
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136
lib/apl/tests/programs.sx
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@@ -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))

22
lib/apl/tests/programs/life.apl Normal file
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@@ -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 ⌽¨ ⊂⍵}