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-rw-r--r--tests/lean/Hashmap/Properties.lean100
1 files changed, 24 insertions, 76 deletions
diff --git a/tests/lean/Hashmap/Properties.lean b/tests/lean/Hashmap/Properties.lean
index 246041f4..d9be15dd 100644
--- a/tests/lean/Hashmap/Properties.lean
+++ b/tests/lean/Hashmap/Properties.lean
@@ -168,9 +168,9 @@ def frame_load (hm nhm : HashMap α) : Prop :=
-- This rewriting lemma is problematic below
attribute [-simp] Bool.exists_bool
--- The proof below is a bit expensive, so we need to increase the maximum number
--- of heart beats
-set_option maxHeartbeats 1000000
+-- The proofs below are a bit expensive, so we deactivate the heart bits limit
+set_option maxHeartbeats 0
+
open AList
@[pspec]
@@ -201,15 +201,7 @@ theorem allocate_slots_spec {α : Type} (slots : alloc.vec.Vec (AList α)) (n :
simp [*]
have Hslots1Len : alloc.vec.Vec.len (AList α) slots1 + n1.val ≤ Usize.max := by
simp_all
- -- TODO: progress fails here (maximum recursion depth reached)
- -- This probably comes from the fact that allocate_slots is reducible and applied an infinite number
- -- of times
- -- progress as ⟨ slots2 .. ⟩
- -- TODO: bug here as well
- stop
- have ⟨ slots2, hEq, _, _ ⟩ := allocate_slots_spec slots1 n1 (by assumption) (by assumption)
- stop
- rw [allocate_slots] at hEq; rw [hEq]; clear hEq
+ progress as ⟨ slots2 .. ⟩
simp
constructor
. intro i h0 h1
@@ -219,6 +211,8 @@ theorem allocate_slots_spec {α : Type} (slots : alloc.vec.Vec (AList α)) (n :
simp [h]
simp_all
scalar_tac
+termination_by n.val.toNat
+decreasing_by scalar_decr_tac -- TODO: this is expensive
theorem forall_nil_imp_flatten_len_zero (slots : List (List α))
(Hnil : ∀ i, 0 ≤ i → i < slots.len → slots.index i = []) :
@@ -373,21 +367,13 @@ theorem if_update_eq
split <;> simp [Pure.pure]
-- Small helper
--- TODO: move, and introduce a better solution with nice syntax
+-- TODO: let bindings now work
def mk_opaque {α : Sort u} (x : α) : { y : α // y = x} :=
⟨ x, by simp ⟩
---set_option profiler true
---set_option profiler.threshold 10
---set_option trace.profiler true
-
-- For pretty printing (useful when copy-pasting goals)
set_option pp.coercions false -- do not print coercions with ↑ (this doesn't parse)
--- The proof below is a bit expensive, so we need to increase the maximum number
--- of heart beats
-set_option maxHeartbeats 2000000
-
@[pspec]
theorem insert_no_resize_spec {α : Type} (hm : HashMap α) (key : Usize) (value : α)
(hinv : hm.inv) (hnsat : hm.lookup key = none → hm.len_s < Usize.max) :
@@ -484,15 +470,8 @@ theorem insert_no_resize_spec {α : Type} (hm : HashMap α) (key : Usize) (value
-- TODO: we want to automate this
simp only [k_hash_mod]
have h := Int.emod_lt_of_pos k.val hvpos
- simp_all only [ok.injEq, exists_eq_left', List.len_update, gt_iff_lt,
- List.index_update_eq, ne_eq, not_false_eq_true, neq_imp]
- if h_hm : k_hash_mod = hash_mod.val then
- simp_all only [k_hash_mod, List.len_update, gt_iff_lt, List.index_update_eq,
- ne_eq, not_false_eq_true, neq_imp, alloc.vec.Vec.length]
- else
- simp_all only [k_hash_mod, List.len_update, gt_iff_lt, List.index_update_eq,
- ne_eq, not_false_eq_true, neq_imp, ge_iff_le,
- alloc.vec.Vec.length, List.index_update_ne]
+ simp_all
+ cases h_hm: k_hash_mod == hash_mod.val <;> simp_all (config := {zetaDelta := true})
have _ :
match hm.lookup key with
| none => nhm.len_s = hm.len_s + 1
@@ -529,7 +508,7 @@ theorem insert_no_resize_spec {α : Type} (hm : HashMap α) (key : Usize) (value
. simp_all [frame_load, inv_base, inv_load]
simp_all
-theorem slot_allP_not_key_lookup (slot : AList T) (h : slot.v.allP fun (k', _) => ¬k = k') :
+private theorem slot_allP_not_key_lookup (slot : AList T) (h : slot.v.allP fun (k', _) => ¬k = k') :
slot.lookup k = none := by
induction slot <;> simp_all
@@ -628,7 +607,7 @@ theorem move_elements_from_list_spec
simp_all
. scalar_tac
-theorem slots_forall_nil_imp_lookup_none (slots : Slots T) (hLen : slots.val.len ≠ 0)
+private theorem slots_forall_nil_imp_lookup_none (slots : Slots T) (hLen : slots.val.len ≠ 0)
(hEmpty : ∀ j, 0 ≤ j → j < slots.val.len → slots.val.index j = AList.Nil) :
∀ key, slots.lookup key = none := by
intro key
@@ -641,7 +620,7 @@ theorem slots_forall_nil_imp_lookup_none (slots : Slots T) (hLen : slots.val.len
have := hEmpty (key.val % slots.val.len) (by assumption) (by assumption)
simp [*]
-theorem slots_index_len_le_flatten_len (slots : List (AList α)) (i : Int) (h : 0 ≤ i ∧ i < slots.len) :
+private theorem slots_index_len_le_flatten_len (slots : List (AList α)) (i : Int) (h : 0 ≤ i ∧ i < slots.len) :
(slots.index i).len ≤ (List.map AList.v slots).flatten.len := by
match slots with
| [] =>
@@ -659,7 +638,7 @@ theorem slots_index_len_le_flatten_len (slots : List (AList α)) (i : Int) (h :
be equal to the slot index.
TODO: remove?
-/
-theorem slots_inv_lookup_imp_eq (slots : Slots α) (hInv : slots_t_inv slots)
+private theorem slots_inv_lookup_imp_eq (slots : Slots α) (hInv : slots_t_inv slots)
(i : Int) (hi : 0 ≤ i ∧ i < slots.val.len) (key : Usize) :
(slots.val.index i).lookup key ≠ none → i = key.val % slots.val.len := by
suffices hSlot : ∀ (slot : List (Usize × α)),
@@ -676,23 +655,7 @@ theorem slots_inv_lookup_imp_eq (slots : Slots α) (hInv : slots_t_inv slots)
intros; simp_all
split at * <;> simp_all
--- TODO: remove?
-theorem slots_update_lookup_equiv (slots : Slots α) (hInv : slots_t_inv slots)
- (i : Int) (hi : 0 ≤ i ∧ i < slots.val.len) (key : Usize) :
- let slot := slots.val.index i
- slot.lookup key ≠ none ∨ slots_s_lookup (slots.val.update i .Nil) key ≠ none ↔
- slots.lookup key ≠ none := by
- -- We need the following lemma to derive a contradiction
- have := slots_inv_lookup_imp_eq slots hInv i hi key
- cases hi : (key.val % slots.val.len) == i <;>
- simp_all [Slots.lookup]
-
-/-theorem slots_update_lookup_imp
- (slots slots1 : Slots α) (slot : AList α) (hInv : slots_t_inv slots) (i : Int) (hi : 0 ≤ i ∧ i < slots.val.len)
- (hSlotsEq : slots.val = slots.val.update i slot) :
- ∀ key v, slots1.lookup key = some v → slots.lookup key = some v ∨ slot.lookup key = some v-/
-
-theorem move_slots_updated_table_lookup_imp
+private theorem move_slots_updated_table_lookup_imp
(ntable ntable1 ntable2 : HashMap α) (slots slots1 : Slots α) (slot : AList α)
(hi : 0 ≤ i ∧ i < slots.val.len)
(hSlotsInv : slots_t_inv slots)
@@ -717,12 +680,9 @@ theorem move_slots_updated_table_lookup_imp
| inr hTable1Lookup =>
right
-- The key can't be for the slot we replaced
- if heq : key.val % slots.val.len = i then
- simp_all [Slots.lookup]
- else
- simp_all [Slots.lookup]
+ cases heq : key.val % slots.val.len == i <;> simp_all [Slots.lookup]
-theorem move_one_slot_lookup_equiv {α : Type} (ntable ntable1 ntable2 : HashMap α)
+private theorem move_one_slot_lookup_equiv {α : Type} (ntable ntable1 ntable2 : HashMap α)
(slot : AList α)
(slots slots1 : Slots α)
(i : Int) (h1 : i < slots.len)
@@ -749,7 +709,7 @@ theorem move_one_slot_lookup_equiv {α : Type} (ntable ntable1 ntable2 : HashMap
have := hLookup3 key v
simp_all
-theorem slots_lookup_none_imp_slot_lookup_none
+private theorem slots_lookup_none_imp_slot_lookup_none
(slots : Slots α) (hInv : slots_t_inv slots) (i : Int) (hi : 0 ≤ i ∧ i < slots.val.len) :
∀ (key : Usize), slots.lookup key = none → (slots.val.index i).lookup key = none := by
intro key hLookup
@@ -760,14 +720,14 @@ theorem slots_lookup_none_imp_slot_lookup_none
by_contra
simp_all
-theorem slot_lookup_not_none_imp_slots_lookup_not_none
+private theorem slot_lookup_not_none_imp_slots_lookup_not_none
(slots : Slots α) (hInv : slots_t_inv slots) (i : Int) (hi : 0 ≤ i ∧ i < slots.val.len) :
∀ (key : Usize), (slots.val.index i).lookup key ≠ none → slots.lookup key ≠ none := by
intro key hLookup hNone
have := slots_lookup_none_imp_slot_lookup_none slots hInv i hi key hNone
apply hLookup this
-theorem slots_forall_nil_imp_al_v_nil (slots : Slots α)
+private theorem slots_forall_nil_imp_al_v_nil (slots : Slots α)
(hEmpty : ∀ i, 0 ≤ i → i < slots.val.len → slots.val.index i = AList.Nil) :
slots.al_v = [] := by
suffices h :
@@ -790,10 +750,8 @@ theorem slots_forall_nil_imp_al_v_nil (slots : Slots α)
simp_all
theorem move_elements_loop_spec
- (n : Nat) -- We need this, otherwise we can't prove termination (the termination_by clauses can be expensive)
{α : Type} (ntable : HashMap α) (slots : Slots α)
(i : Usize)
- (hn : n = slots.val.len - i.val) -- Condition for termination
(hi : i ≤ alloc.vec.Vec.len (AList α) slots)
(hinv : ntable.inv)
(hSlotsNonZero : slots.val.len ≠ 0)
@@ -814,9 +772,6 @@ theorem move_elements_loop_spec
rw [move_elements_loop]
simp
if hi: i.val < slots.val.len then
- -- Proof of termination: eliminate the case: n = 0
- cases n; scalar_tac
- rename ℕ => n
-- Continue the proof
have hIneq : 0 ≤ i.val ∧ i.val < slots.val.len := by scalar_tac
simp [hi]
@@ -887,8 +842,6 @@ theorem move_elements_loop_spec
have : i.val < (List.map AList.v slots.val).len := by simp; scalar_tac
simp_all [Slots.al_v, List.len_flatten_update_eq, List.map_update_eq]
- have : n = slots1.val.len - i'.val := by simp_all; scalar_tac
-
progress as ⟨ ntable2, slots2, _, _, hLookup2Rev, hLookup21, hLookup22, hIndexNil ⟩
simp [and_assoc]
@@ -921,6 +874,8 @@ theorem move_elements_loop_spec
have hLookupEmpty := slots_forall_nil_imp_lookup_none slots hLenNonZero hEmpty
simp [hNil, hLookupEmpty]
apply hEmpty
+termination_by (slots.val.len - i.val).toNat
+decreasing_by scalar_decr_tac -- TODO: this is expensive
@[pspec]
theorem move_elements_spec
@@ -939,16 +894,8 @@ theorem move_elements_spec
(∀ key v, ntable1.lookup key = some v ↔ slots.lookup key = some v)
:= by
rw [move_elements]
- let n := (slots.val.len - 0).toNat
- have hn : n = slots.val.len - 0 := by
- -- TODO: scalar_tac should succeed here
- scalar_tac_preprocess
- simp [n] at *
- norm_cast at *
- have := @Int.le_toNat n (slots.val.len - OfNat.ofNat 0) (by simp; scalar_tac)
- simp_all
have ⟨ ntable1, slots1, hEq, _, _, ntable1Lookup, slotsLookup, _, _ ⟩ :=
- move_elements_loop_spec (slots.val.len - 0).toNat ntable slots 0#usize hn (by scalar_tac) hinv
+ move_elements_loop_spec ntable slots 0#usize (by scalar_tac) hinv
(by scalar_tac)
hSlotsInv
(by intro j h0 h1; scalar_tac)
@@ -1187,12 +1134,13 @@ theorem remove_from_list_spec {α} (key : Usize) (slot : AList α) {l i} (hInv :
simp_all
. cases v1 <;> simp_all
+-- TODO: move?
theorem lookup'_not_none_imp_len_pos (l : List (Usize × α)) (key : Usize) (hLookup : l.lookup' key ≠ none) :
0 < l.len := by
induction l <;> simp_all
scalar_tac
-theorem lookup_not_none_imp_len_s_pos (hm : HashMap α) (key : Usize) (hLookup : hm.lookup key ≠ none)
+private theorem lookup_not_none_imp_len_s_pos (hm : HashMap α) (key : Usize) (hLookup : hm.lookup key ≠ none)
(hNotEmpty : 0 < hm.slots.val.len) :
0 < hm.len_s := by
have : 0 ≤ key.val % hm.slots.val.len := by -- TODO: automate