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.
126 lines
3.8 KiB
Text
126 lines
3.8 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] Diagnostics
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[simp] used theorems (max: 50, num: 2):
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[simp] f_eq ↦ 50
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[simp] q_eq ↦ 50
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[simp] tried theorems (max: 101, num: 2):
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[simp] f_eq ↦ 101, succeeded: 50
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[simp] q_eq ↦ 50, succeeded: 50
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use `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] Diagnostics
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[simp] used theorems (max: 1201, num: 3):
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[simp] ack.eq_3 ↦ 1201
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[simp] Nat.reduceAdd (builtin simproc) ↦ 771
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[simp] ack.eq_1 ↦ 768
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[simp] tried theorems (max: 1973, num: 2):
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[simp] ack.eq_3 ↦ 1973, succeeded: 1201
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[simp] ack.eq_1 ↦ 768, succeeded: 768
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use `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] Diagnostics
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[simp] used theorems (max: 1, num: 1):
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[simp] q1_ax ↦ 1
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[simp] tried theorems (max: 1, num: 1):
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[simp] q1_ax ↦ 1, succeeded: 1
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use `set_option diagnostics.threshold <num>` to control threshold for reporting counters
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---
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info: [diag] Diagnostics
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[reduction] unfolded declarations (max: 246, num: 2):
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[reduction] Nat.rec ↦ 246
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[reduction] OfNat.ofNat ↦ 24
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[reduction] unfolded reducible declarations (max: 246, num: 2):
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[reduction] h ↦ 246
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[reduction] Nat.casesOn ↦ 246
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use `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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