a5a525f6a1
This PR changes how the unfold theorems for well-founded recursion are created. They are created eagerly (anticipating that the behaivor may be affected by simp sets soon), and without the detour of going through equational theorems.
68 lines
1.3 KiB
Text
68 lines
1.3 KiB
Text
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: tactic 'fail' failed
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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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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: tactic 'fail' failed
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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: tactic 'fail' failed
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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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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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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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