119 lines
3.6 KiB
Text
119 lines
3.6 KiB
Text
opaque q : Nat → Nat
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def f (x : Nat) : Nat :=
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match x with
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| 0 => 1
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| x+1 => q (f x)
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theorem f_eq : f (x + 1) = q (f x) := rfl
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axiom q_eq (x : Nat) : q x = x
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/--
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info: [simp] used theorems (max: 50, num: 2):
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f_eq ↦ 50
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⏎
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q_eq ↦ 50[simp] tried theorems (max: 101, num: 2):
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f_eq ↦ 101, succeeded: 50
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q_eq ↦ 50, succeeded: 50use `set_option diagnostics.threshold <num>` to control threshold for reporting counters
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-/
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#guard_msgs in
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example : f (x + 50) = f x := by
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set_option diagnostics true in
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simp [f_eq, q_eq]
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example : f (x + 50) = f x := by
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set_option diagnostics true in
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simp [f_eq, q_eq]
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def ack : Nat → Nat → Nat
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| 0, y => y+1
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| x+1, 0 => ack x 1
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| x+1, y+1 => ack x (ack (x+1) y)
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/--
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info: [simp] used theorems (max: 1201, num: 3):
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ack.eq_3 ↦ 1201
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⏎
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Nat.reduceAdd (builtin simproc) ↦ 771
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⏎
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ack.eq_1 ↦ 768[simp] tried theorems (max: 1974, num: 2):
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ack.eq_3 ↦ 1974, succeeded: 1201
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⏎
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ack.eq_1 ↦ 768, succeeded: 768use `set_option diagnostics.threshold <num>` to control threshold for reporting counters
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---
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error: tactic 'simp' failed, nested error:
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maximum recursion depth has been reached
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use `set_option maxRecDepth <num>` to increase limit
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use `set_option diagnostics true` to get diagnostic information
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-/
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#guard_msgs in
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example : ack 4 4 = x := by
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set_option diagnostics true in
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simp [ack.eq_2, ack.eq_1, ack.eq_3]
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-- TODO: In the following test we just want to check whether we
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-- diagnostics for `simp` when there is a failure. However, the
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-- actual counters make the test very unstable since small
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-- changes to Lean affect heartbeat consumption, and consequently
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-- the number of rewrites tried.
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-- /--
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-- info: [simp] used theorems (max: 22, num: 5):
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-- ack.eq_3 ↦ 22
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-- ⏎
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-- Nat.reduceAdd (builtin simproc) ↦ 14
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-- ⏎
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-- ack.eq_1 ↦ 11
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-- ⏎
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-- ack.eq_2 ↦ 4
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-- ⏎
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-- Nat.zero_add ↦ 1[simp] tried theorems (max: 38, num: 4):
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-- ack.eq_3 ↦ 38, succeeded: 22
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-- ⏎
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-- ack.eq_1 ↦ 11, succeeded: 11
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-- ⏎
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-- ack.eq_2 ↦ 4, succeeded: 4
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-- ⏎
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-- Nat.zero_add ↦ 1, succeeded: 1[reduction] unfolded reducible declarations (max: 7, num: 1):
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-- outParam ↦ 7use `set_option diagnostics.threshold <num>` to control threshold for reporting counters
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-- ---
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-- error: tactic 'simp' failed, nested error:
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-- (deterministic) timeout at `whnf`, maximum number of heartbeats (500) has been reached
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-- use `set_option maxHeartbeats <num>` to set the limit
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-- use `set_option diagnostics true` to get diagnostic information
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-- -/
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-- #guard_msgs in
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-- set_option maxHeartbeats 500 in
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-- example : ack 4 4 = x := by
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-- set_option diagnostics true in
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-- set_option diagnostics.threshold 0 in
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-- simp [ack.eq_2, ack.eq_1, ack.eq_3]
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@[reducible] def h (x : Nat) :=
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match x with
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| 0 => 10
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| x + 1 => h x
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opaque q1 : Nat → Nat → Prop
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@[simp] axiom q1_ax (x : Nat) : q1 x 10
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/--
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info: [simp] used theorems (max: 1, num: 1):
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q1_ax ↦ 1[simp] tried theorems (max: 1, num: 1):
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q1_ax ↦ 1, succeeded: 1use `set_option diagnostics.threshold <num>` to control threshold for reporting counters
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---
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info: [reduction] unfolded declarations (max: 246, num: 2):
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Nat.rec ↦ 246
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⏎
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OfNat.ofNat ↦ 24[reduction] unfolded reducible declarations (max: 246, num: 2):
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h ↦ 246
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Nat.casesOn ↦ 246use `set_option diagnostics.threshold <num>` to control threshold for reporting counters
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-/
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#guard_msgs in
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example : q1 x (h 40) := by
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set_option diagnostics true in
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set_option diagnostics.threshold 0 in
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simp
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example : q1 x (h 40) := by
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set_option diagnostics true in
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set_option diagnostics.threshold 0 in
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simp
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