Data commit

Task/Fibonacci-sequence/Lean/fibonacci-sequence-1.lean

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+-- Our first implementation is the usual recursive definition:
+def fib1 : ℕ → ℕ
+| 0       := 0
+| 1       := 1
+| (n + 2) := fib1 n + fib1 (n + 1)
+
+
+-- We can give a second more efficient implementation using an auxiliary function:
+def fib_aux : ℕ → ℕ → ℕ → ℕ
+| 0 a b       := b
+| (n + 1) a b := fib_aux n (a + b) a
+
+def fib2 : ℕ → ℕ
+| n := fib_aux n 1 0
+
+
+-- Use #eval to check computations:
+#eval fib1 20
+#eval fib2 20

Task/Fibonacci-sequence/Lean/fibonacci-sequence-2.lean

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+-- Naive version
+def fib1 (n : Nat) : Nat :=
+  match n with
+  | 0 => 0
+  | 1 => 1
+  | (k + 2) => fib1 k + fib1 (k + 1)
+
+-- More efficient version
+def fib_aux (n : Nat) (a : Nat) (b : Nat) : Nat :=
+  match n with
+  | 0 => b
+  | (k + 1) => fib_aux k (a + b) a
+
+def fib2 (n : Nat) : Nat :=
+  fib_aux n 1 0
+
+-- Examples
+#eval fib1 20
+#eval fib2 20