diff options
Diffstat (limited to 'tests')
| -rw-r--r-- | tests/lean/Hashmap/Properties.lean | 76 |
1 files changed, 65 insertions, 11 deletions
diff --git a/tests/lean/Hashmap/Properties.lean b/tests/lean/Hashmap/Properties.lean index baa8f5c8..e065bb36 100644 --- a/tests/lean/Hashmap/Properties.lean +++ b/tests/lean/Hashmap/Properties.lean @@ -21,8 +21,9 @@ end List namespace HashMap -@[pspec] -theorem insert_in_list_spec {α : Type} (key: Usize) (value: α) (ls: List α) : +abbrev Core.List := _root_.List + +theorem insert_in_list_spec0 {α : Type} (key: Usize) (value: α) (ls: List α) : ∃ b, insert_in_list α key value ls = ret b ∧ (b ↔ List.lookup ls.v key = none) @@ -35,7 +36,7 @@ theorem insert_in_list_spec {α : Type} (key: Usize) (value: α) (ls: List α) : rw [insert_in_list_loop] simp [h] else - have ⟨ b, hi ⟩ := insert_in_list_spec key value tl + have ⟨ b, hi ⟩ := insert_in_list_spec0 key value tl by exists b simp [insert_in_list, List.lookup] @@ -45,7 +46,6 @@ theorem insert_in_list_spec {α : Type} (key: Usize) (value: α) (ls: List α) : exact hi -- Variation: use progress -@[pspec] theorem insert_in_list_spec1 {α : Type} (key: Usize) (value: α) (ls: List α) : ∃ b, insert_in_list α key value ls = ret b ∧ @@ -70,7 +70,6 @@ theorem insert_in_list_spec1 {α : Type} (key: Usize) (value: α) (ls: List α) simp [*, List.lookup] -- Variation: use tactics from the beginning -@[pspec] theorem insert_in_list_spec2 {α : Type} (key: Usize) (value: α) (ls: List α) : ∃ b, insert_in_list α key value ls = ret b ∧ @@ -91,10 +90,10 @@ theorem insert_in_list_spec2 {α : Type} (key: Usize) (value: α) (ls: List α) progress as ⟨ b h ⟩ simp [*] -@[pspec] theorem insert_in_list_back_spec {α : Type} (key: Usize) (value: α) (l0: List α) : ∃ l1, insert_in_list_back α key value l0 = ret l1 ∧ + -- We update the binding List.lookup l1.v key = value ∧ (∀ k, k ≠ key → List.lookup l1.v k = List.lookup l0.v k) := match l0 with @@ -112,11 +111,66 @@ theorem insert_in_list_back_spec {α : Type} (key: Usize) (value: α) (l0: List simp [insert_in_list_back, List.lookup] rw [insert_in_list_loop_back] simp [h, List.lookup] - have ⟨tl0 , _, _ ⟩ := insert_in_list_back_spec key value tl -- TODO: Use progress - simp [insert_in_list_back] at * - simp [List.lookup, *] - simp (config := {contextual := true}) [*] - + progress keep as heq as ⟨ tl hp1 hp2 ⟩ + simp [insert_in_list_back] at heq + simp (config := {contextual := true}) [*, List.lookup] + +def distinct_keys (ls : Core.List (Usize × α)) := ls.pairwise_rel (λ x y => x.fst ≠ y.fst) + +def hash_mod_key (k : Usize) (l : Int) : Int := + match hash_key k with + | .ret k => k.val % l + | _ => 0 + +def slot_s_inv_hash (l i : Int) (ls : Core.List (Usize × α)) : Prop := + ls.allP (λ (k, _) => hash_mod_key k l = i) + +@[simp] +def slot_s_inv (l i : Int) (ls : Core.List (Usize × α)) : Prop := + distinct_keys ls ∧ + slot_s_inv_hash l i ls + +def slot_t_inv (l i : Int) (s : List α) : Prop := slot_s_inv l i s.v + +@[pspec] +theorem insert_in_list_back_spec1 {α : Type} (l : Int) (key: Usize) (value: α) (l0: List α) + (hinv : slot_s_inv_hash l (hash_mod_key key l) l0.v) : + ∃ l1, + insert_in_list_back α key value l0 = ret l1 ∧ + -- We update the binding + List.lookup l1.v key = value ∧ + (∀ k, k ≠ key → List.lookup l1.v k = List.lookup l0.v k) ∧ + -- We preserve part of the key invariant + slot_s_inv_hash l (hash_mod_key key l) l1.v + := match l0 with + | .Nil => by + simp [insert_in_list_back, insert_in_list_loop_back, List.lookup, List.v, slot_s_inv_hash] + tauto + | .Cons k v tl0 => + if h: k = key then + by + simp [insert_in_list_back, List.lookup] + rw [insert_in_list_loop_back] + simp [h, List.lookup] + constructor + . intros; simp [*] + . simp [List.v, slot_s_inv_hash] at * + simp [*] + else + by + simp [insert_in_list_back, List.lookup] + rw [insert_in_list_loop_back] + simp [h, List.lookup] + have : slot_s_inv_hash l (hash_mod_key key l) (List.v tl0) := by + simp_all [List.v, slot_s_inv_hash] + progress keep as heq as ⟨ tl1 hp1 hp2 hp3 ⟩ + simp only [insert_in_list_back] at heq + have : slot_s_inv_hash l (hash_mod_key key l) (List.v (List.Cons k v tl1)) := by + simp [List.v, slot_s_inv_hash] at * + simp [*] + simp (config := {contextual := true}) [*, List.lookup] + + end HashMap end hashmap |