72 lines
1.5 KiB
Text
72 lines
1.5 KiB
Text
module
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import all Init.Data.Array.Basic
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public def fib : Nat → Nat
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| 0 => 0
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| 1 => 1
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| n+2 => fib n + fib (n+1)
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termination_by n => n
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/--
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error: Failed: `fail` tactic was invoked
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⊢ fib 8 + fib (8 + 1) = 55
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-/
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#guard_msgs in
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example : fib 10 = 55 := by
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unfold fib
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fail
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public def ack : Nat → Nat → Nat
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| 0, m => m + 1
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| n+1, 0 => ack n 1
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| n+1, m+1 => ack n (ack (n+1) m)
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termination_by n m => (n, m)
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/--
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error: Failed: `fail` tactic was invoked
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⊢ ack 1 (ack (1 + 1) 1) = 7
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-/
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#guard_msgs in
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example : ack 2 2 = 7 := by
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unfold ack
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fail
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-- This checks that we can unfold definitions in the prelude
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/--
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error: Failed: `fail` tactic was invoked
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α : Type u_1
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as : Array α
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i : Nat
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j : Fin as.size
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⊢ (if i < ↑j then
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let j' := ⟨↑j - 1, ⋯⟩;
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let as_1 := as.swap ↑j' ↑j ⋯ ⋯;
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Array.insertIdx.loop✝ i as_1 ⟨↑j', ⋯⟩
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else as).size =
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as.size
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-/
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#guard_msgs in
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@[simp] private theorem Array.size_insertIdx_loop (as : Array α) (i : Nat) (j : Fin as.size) :
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(insertIdx.loop i as j).size = as.size := by
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unfold insertIdx.loop
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fail
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public theorem fib_eq_fib (n : Nat) : n ≤ fib (n + 2) :=
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match h : n with
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| 0 => by simp [fib]
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| 1 => by simp [fib]
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| n+2 => by
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have := fib_eq_fib n
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have := fib_eq_fib (n+1)
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simp only [fib] at *
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omega
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termination_by n
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-- This should not exist!
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/-- error: Unknown constant `fib_eq_fib.eq_def` -/
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#guard_msgs in
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#check fib_eq_fib.eq_def
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