diff options
Diffstat (limited to '')
| -rw-r--r-- | tests/lean/Hashmap/Properties.lean | 76 |
1 files changed, 20 insertions, 56 deletions
diff --git a/tests/lean/Hashmap/Properties.lean b/tests/lean/Hashmap/Properties.lean index d9be15dd..76bd2598 100644 --- a/tests/lean/Hashmap/Properties.lean +++ b/tests/lean/Hashmap/Properties.lean @@ -3,34 +3,19 @@ import Hashmap.Funs open Primitives open Result -namespace List - --- TODO: we don't want to use the original List.lookup because it uses BEq --- TODO: rewrite rule: match x == y with ... -> if x = y then ... else ... ? (actually doesn't work because of sugar) --- TODO: move? -@[simp] -def lookup' {α : Type} (ls: List (Usize × α)) (key: Usize) : Option α := - match ls with - | [] => none - | (k, x) :: tl => if k = key then some x else lookup' tl key - -end List - namespace hashmap namespace AList +@[simp] def v {α : Type} (ls: AList α) : List (Usize × α) := match ls with | Nil => [] | Cons k x tl => (k, x) :: v tl -@[simp] theorem v_nil (α : Type) : (Nil : AList α).v = [] := by rfl -@[simp] theorem v_cons {α : Type} k x (tl: AList α) : (Cons k x tl).v = (k, x) :: v tl := by rfl - @[simp] abbrev lookup {α : Type} (ls: AList α) (key: Usize) : Option α := - ls.v.lookup' key + ls.v.lookup key @[simp] abbrev len {α : Type} (ls : AList α) : Int := ls.v.len @@ -39,20 +24,6 @@ end AList namespace HashMap -namespace List - -end List - --- TODO: move -@[simp] theorem neq_imp_nbeq [BEq α] [LawfulBEq α] (x y : α) (heq : ¬ x = y) : ¬ x == y := by simp [*] -@[simp] theorem neq_imp_nbeq_rev [BEq α] [LawfulBEq α] (x y : α) (heq : ¬ x = y) : ¬ y == x := by simp [*] - --- TODO: move --- TODO: this doesn't work because of sugar -theorem match_lawful_beq [BEq α] [LawfulBEq α] [DecidableEq α] (x y : α) : - (x == y) = (if x = y then true else false) := by - split <;> simp_all - def distinct_keys (ls : List (Usize × α)) := ls.pairwise_rel (λ x y => x.fst ≠ y.fst) def hash_mod_key (k : Usize) (l : Int) : Int := @@ -168,6 +139,8 @@ def frame_load (hm nhm : HashMap α) : Prop := -- This rewriting lemma is problematic below attribute [-simp] Bool.exists_bool +attribute [local simp] List.lookup + -- The proofs below are a bit expensive, so we deactivate the heart bits limit set_option maxHeartbeats 0 @@ -276,6 +249,9 @@ theorem new_spec (α : Type) : progress as ⟨ hm ⟩ simp_all +--set_option pp.all true +example (key : Usize) : key == key := by simp [beq_iff_eq] + theorem insert_in_list_spec_aux {α : Type} (l : Int) (key: Usize) (value: α) (l0: AList α) (hinv : slot_s_inv_hash l (hash_mod_key key l) l0.v) (hdk : distinct_keys l0.v) : @@ -307,14 +283,8 @@ theorem insert_in_list_spec_aux {α : Type} (l : Int) (key: Usize) (value: α) ( if h: k = key then rw [insert_in_list] rw [insert_in_list_loop] - simp [h] - exists false; simp only [true_and, exists_eq_left', List.lookup', ↓reduceIte, AList.v_cons] -- TODO: why do we need to do this? - split_conjs - . intros; simp [*] - . simp_all [slot_s_inv_hash] - . simp at hinv; tauto - . simp_all [slot_s_inv_hash] - . simp_all + simp [h, and_assoc] + split_conjs <;> simp_all [slot_s_inv_hash] else rw [insert_in_list] rw [insert_in_list_loop] @@ -448,10 +418,10 @@ theorem insert_no_resize_spec {α : Type} (hm : HashMap α) (key : Usize) (value slots := v } exists nhm have hupdt : lookup nhm key = some value := by - simp [lookup, List.lookup] at * + simp [lookup] at * simp_all have hlkp : ∀ k, ¬ k = key → nhm.lookup k = hm.lookup k := by - simp [lookup, List.lookup] at * + simp [lookup] at * intro k hk -- We have to make a case disjunction: either the hashes are different, -- in which case we don't even lookup the same slots, or the hashes @@ -476,7 +446,7 @@ theorem insert_no_resize_spec {α : Type} (hm : HashMap α) (key : Usize) (value match hm.lookup key with | none => nhm.len_s = hm.len_s + 1 | some _ => nhm.len_s = hm.len_s := by - simp only [lookup, List.lookup, len_s, al_v, HashMap.v, slots_s_lookup] at * + simp only [lookup, len_s, al_v, HashMap.v, slots_s_lookup] at * -- We have to do a case disjunction simp_all [List.map_update_eq] -- TODO: dependent rewrites @@ -508,7 +478,7 @@ theorem insert_no_resize_spec {α : Type} (hm : HashMap α) (key : Usize) (value . simp_all [frame_load, inv_base, inv_load] simp_all -private 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 α) (h : slot.v.allP fun (k', _) => ¬k = k') : slot.lookup k = none := by induction slot <;> simp_all @@ -624,7 +594,7 @@ private theorem slots_index_len_le_flatten_len (slots : List (AList α)) (i : In (slots.index i).len ≤ (List.map AList.v slots).flatten.len := by match slots with | [] => - simp at *; scalar_tac + simp at * | slot :: slots' => simp at * if hi : i = 0 then @@ -643,7 +613,7 @@ private theorem slots_inv_lookup_imp_eq (slots : Slots α) (hInv : slots_t_inv s (slots.val.index i).lookup key ≠ none → i = key.val % slots.val.len := by suffices hSlot : ∀ (slot : List (Usize × α)), slot_s_inv slots.val.len i slot → - slot.lookup' key ≠ none → + slot.lookup key ≠ none → i = key.val % slots.val.len from by rw [slots_t_inv, slots_s_inv] at hInv @@ -965,8 +935,8 @@ theorem try_resize_spec {α : Type} (hm : HashMap α) (hInv : hm.inv): simp_all [lookup, al_v, v, alloc.vec.Vec.len] intro key replace hLookup := hLookup key - cases h1: (ntable2.slots.val.index (key.val % ntable2.slots.val.len)).v.lookup' key <;> - cases h2: (hm.slots.val.index (key.val % hm.slots.val.len)).v.lookup' key <;> + cases h1: (ntable2.slots.val.index (key.val % ntable2.slots.val.len)).v.lookup key <;> + cases h2: (hm.slots.val.index (key.val % hm.slots.val.len)).v.lookup key <;> simp_all [Slots.lookup] else simp [hSmaller] @@ -1002,7 +972,7 @@ theorem get_in_list_spec {α} (key : Usize) (slot : AList α) (hLookup : slot.lo ∃ v, get_in_list α key slot = ok v ∧ slot.lookup key = some v := by induction slot <;> rw [get_in_list, get_in_list_loop] <;> - simp_all [AList.lookup] + simp_all split <;> simp_all @[pspec] @@ -1038,7 +1008,7 @@ theorem get_mut_in_list_spec {α} (key : Usize) (slot : AList α) := by induction slot <;> rw [get_mut_in_list, get_mut_in_list_loop] <;> - simp_all [AList.lookup] + simp_all split . -- Non-recursive case simp_all [and_assoc, slot_t_inv] @@ -1134,12 +1104,6 @@ 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 - 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 @@ -1148,7 +1112,7 @@ private theorem lookup_not_none_imp_len_s_pos (hm : HashMap α) (key : Usize) (h have : key.val % hm.slots.val.len < hm.slots.val.len := by -- TODO: automate apply Int.emod_lt_of_pos; scalar_tac have := List.len_index_le_len_flatten hm.v (key.val % hm.slots.val.len) - have := lookup'_not_none_imp_len_pos (hm.slots.val.index (key.val % hm.slots.val.len)).v key + have := List.lookup_not_none_imp_len_pos (hm.slots.val.index (key.val % hm.slots.val.len)).v key simp_all [lookup, len_s, al_v, v] scalar_tac |