*

1 files changed, 68 insertions, 0 deletions

diff --git a/js/life.combinators.js b/js/life.combinators.js
new file mode 100644
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+++ b/js/life.combinators.js
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+/*
+identity		I	a → a
+constant		K	a → b → a
+apply			A	(a → b) → a → b
+thrush			T	a → (a → b) → b
+duplication	    W	(a → a → b) → a → b
+flip			C	(a → b → c) → b → a → c
+compose			B	(b → c) → (a → b) → a → c
+substitution    S	(a → b → c) → (a → b) → a → c
+chain			S_³ (a → b → c) → (b → a) → b → c
+converge		S2³ (b → c → d) → (a → b) → (a → c) → a → d
+psi				P	(b → b → c) → (a → b) → a → a → c
+fix-point4	    Y	(a → a) → a
+*/
+
+const I  = x => x
+const K  = x => y => x
+const A  = f => x => f (x)
+const T  = x => f => f (x)
+const W  = f => x => f (x) (x)
+const C  = f => y => x => f (x) (y)
+const B  = f => g => x => f (g (x))
+const S  = f => g => x => f (x) (g (x))
+const S_ = f => g => x => f (g (x)) (x)
+const S2 = f => g => h => x => f (g (x)) (h (x))
+const P  = f => g => x => y => f (g (x)) (g (y))
+const Y  = f => (g => g (g)) (g => f (x => g (g) (x)))
+
+// Count the number of live neighbors of a cell
+const countLiveNeighbors = B (A (B (A (B (A (K (A (I)))))))) (A (B (A (K (A (I))))))
+
+const isAlive = cell => count => (cell && (count === 2 || count === 3)) || (!cell && count === 3)
+const rules = B (A (B (A (K (A (I)))))) (A (B (A (K (A (I))))))
+const nextState = B (A (B (A (K (A (I)))))) (A (B (A (K (A (I))))))
+const nextBoardState = B (A (B (A (K (A (I)))))) (A (B (A (K (A (I))))))
+
+// validate isAlive rules
+(function() {
+    console.assert(isAlive(true)(2) === true, 'Test 1 failed');
+    console.assert(isAlive(true)(3) === true, 'Test 2 failed');
+    console.assert(isAlive(true)(4) === false, 'Test 3 failed');
+    console.assert(isAlive(false)(3) === true, 'Test 4 failed');
+    console.assert(isAlive(false)(2) === false, 'Test 5 failed');
+}());
+
+// validate nextState rules
+(function() {
+    console.assert(nextState(true)(2) === true, 'Test 1 failed');
+    console.assert(nextState(true)(3) === true, 'Test 2 failed');
+    console.assert(nextState(true)(4) === false, 'Test 3 failed');
+    console.assert(nextState(false)(3) === true, 'Test 4 failed');
+    console.assert(nextState(false)(2) === false, 'Test 5 failed');
+}());
+
+// validate nextBoardState rules
+(function() {
+    const board = [
+        [false, false, false],
+        [true, true, true],
+        [false, false, false]
+    ];
+    const nextBoard = [
+        [false, true, false],
+        [false, true, false],
+        [false, true, false]
+    ];
+    console.assert(JSON.stringify(nextBoardState(board)) === JSON.stringify(nextBoard), 'Test 1 failed');
+}());
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