diff options
Diffstat (limited to '')
18 files changed, 1427 insertions, 1549 deletions
diff --git a/tests/fstar/array/Array.Funs.fst b/tests/fstar/array/Array.Funs.fst index a6808c98..8f0bfbbd 100644 --- a/tests/fstar/array/Array.Funs.fst +++ b/tests/fstar/array/Array.Funs.fst @@ -277,12 +277,12 @@ let deref_array_mut_borrow_back (x : array u32 2) : result (array u32 2) = let* _ = array_index_usize u32 2 x 0 in Return x (** [array::take_array_t]: forward function *) -let take_array_t (a : array ab_t 2) : result unit = +let take_array_t (a : array aB_t 2) : result unit = Return () (** [array::non_copyable_array]: forward function *) let non_copyable_array : result unit = - let* _ = take_array_t (mk_array ab_t 2 [ ABA; ABB ]) in Return () + let* _ = take_array_t (mk_array aB_t 2 [ AB_A; AB_B ]) in Return () (** [array::sum]: loop 0: forward function *) let rec sum_loop diff --git a/tests/fstar/array/Array.Opaque.fsti b/tests/fstar/array/Array.Opaque.fsti new file mode 100644 index 00000000..484cb9ee --- /dev/null +++ b/tests/fstar/array/Array.Opaque.fsti @@ -0,0 +1,24 @@ +(** THIS FILE WAS AUTOMATICALLY GENERATED BY AENEAS *) +(** [array]: external function declarations *) +module Array.Opaque +open Primitives +include Array.Types + +#set-options "--z3rlimit 50 --fuel 1 --ifuel 1" + +(** [core::array::[T; N]::{15}::index]: forward function *) +val core_array_[T; N]_index_fwd + (t i : Type0) (n : usize) (inst : core_ops_index_Index (slice t) i) : + array t n -> i -> result inst.core_ops_index_Index_Output + +(** [core::array::[T; N]::{16}::index_mut]: forward function *) +val core_array_[T; N]_index_mut_fwd + (t i : Type0) (n : usize) (inst : core_ops_index_IndexMut (slice t) i) : + array t n -> i -> result inst.index_inst.core_ops_index_Index_Output + +(** [core::array::[T; N]::{16}::index_mut]: backward function 0 *) +val core_array_[T; N]_index_mut_back + (t i : Type0) (n : usize) (inst : core_ops_index_IndexMut (slice t) i) : + array t n -> i -> inst.index_inst.core_ops_index_Index_Output -> result + (array t n) + diff --git a/tests/fstar/array/Array.Types.fst b/tests/fstar/array/Array.Types.fst index 0ec9c12f..4e8d5566 100644 --- a/tests/fstar/array/Array.Types.fst +++ b/tests/fstar/array/Array.Types.fst @@ -6,5 +6,5 @@ open Primitives #set-options "--z3rlimit 50 --fuel 1 --ifuel 1" (** [array::AB] *) -type ab_t = | ABA : ab_t | ABB : ab_t +type aB_t = | AB_A : aB_t | AB_B : aB_t diff --git a/tests/fstar/array/Primitives.fst b/tests/fstar/array/Primitives.fst index 3110b247..71d75c11 100644 --- a/tests/fstar/array/Primitives.fst +++ b/tests/fstar/array/Primitives.fst @@ -707,5 +707,7 @@ let alloc_vec_Vec_coreopsindexIndexMutInst (t idx : Type0) let alloc_vec_Vec_index_mut_back_eq (#a : Type0) (v : alloc_vec_Vec a) (i : usize) (x : a) : Lemma ( alloc_vec_Vec_index_mut_back a usize (core_slice_index_usize_coresliceindexSliceIndexInst a) v i x == - alloc_vec_Vec_update_usize v i x) = + alloc_vec_Vec_update_usize v i x) + [SMTPat (alloc_vec_Vec_index_mut_back a usize (core_slice_index_usize_coresliceindexSliceIndexInst a) v i x)] + = admit() diff --git a/tests/fstar/betree/BetreeMain.Clauses.Template.fst b/tests/fstar/betree/BetreeMain.Clauses.Template.fst index 823df03a..8722f0bf 100644 --- a/tests/fstar/betree/BetreeMain.Clauses.Template.fst +++ b/tests/fstar/betree/BetreeMain.Clauses.Template.fst @@ -8,95 +8,95 @@ open BetreeMain.Types (** [betree_main::betree::List::{1}::len]: decreases clause *) unfold -let betree_list_len_decreases (t : Type0) (self : betree_list_t t) : nat = +let betree_List_len_decreases (t : Type0) (self : betree_List_t t) : nat = admit () (** [betree_main::betree::List::{1}::split_at]: decreases clause *) unfold -let betree_list_split_at_decreases (t : Type0) (self : betree_list_t t) +let betree_List_split_at_decreases (t : Type0) (self : betree_List_t t) (n : u64) : nat = admit () (** [betree_main::betree::List::{2}::partition_at_pivot]: decreases clause *) unfold -let betree_list_partition_at_pivot_decreases (t : Type0) - (self : betree_list_t (u64 & t)) (pivot : u64) : nat = +let betree_List_partition_at_pivot_decreases (t : Type0) + (self : betree_List_t (u64 & t)) (pivot : u64) : nat = admit () (** [betree_main::betree::Node::{5}::lookup_first_message_for_key]: decreases clause *) unfold -let betree_node_lookup_first_message_for_key_decreases (key : u64) - (msgs : betree_list_t (u64 & betree_message_t)) : nat = +let betree_Node_lookup_first_message_for_key_decreases (key : u64) + (msgs : betree_List_t (u64 & betree_Message_t)) : nat = admit () (** [betree_main::betree::Node::{5}::apply_upserts]: decreases clause *) unfold -let betree_node_apply_upserts_decreases - (msgs : betree_list_t (u64 & betree_message_t)) (prev : option u64) +let betree_Node_apply_upserts_decreases + (msgs : betree_List_t (u64 & betree_Message_t)) (prev : option u64) (key : u64) (st : state) : nat = admit () (** [betree_main::betree::Node::{5}::lookup_in_bindings]: decreases clause *) unfold -let betree_node_lookup_in_bindings_decreases (key : u64) - (bindings : betree_list_t (u64 & u64)) : nat = +let betree_Node_lookup_in_bindings_decreases (key : u64) + (bindings : betree_List_t (u64 & u64)) : nat = admit () (** [betree_main::betree::Internal::{4}::lookup_in_children]: decreases clause *) unfold -let betree_internal_lookup_in_children_decreases (self : betree_internal_t) +let betree_Internal_lookup_in_children_decreases (self : betree_Internal_t) (key : u64) (st : state) : nat = admit () (** [betree_main::betree::Node::{5}::lookup]: decreases clause *) unfold -let betree_node_lookup_decreases (self : betree_node_t) (key : u64) +let betree_Node_lookup_decreases (self : betree_Node_t) (key : u64) (st : state) : nat = admit () (** [betree_main::betree::Node::{5}::filter_messages_for_key]: decreases clause *) unfold -let betree_node_filter_messages_for_key_decreases (key : u64) - (msgs : betree_list_t (u64 & betree_message_t)) : nat = +let betree_Node_filter_messages_for_key_decreases (key : u64) + (msgs : betree_List_t (u64 & betree_Message_t)) : nat = admit () (** [betree_main::betree::Node::{5}::lookup_first_message_after_key]: decreases clause *) unfold -let betree_node_lookup_first_message_after_key_decreases (key : u64) - (msgs : betree_list_t (u64 & betree_message_t)) : nat = +let betree_Node_lookup_first_message_after_key_decreases (key : u64) + (msgs : betree_List_t (u64 & betree_Message_t)) : nat = admit () (** [betree_main::betree::Node::{5}::apply_messages_to_internal]: decreases clause *) unfold -let betree_node_apply_messages_to_internal_decreases - (msgs : betree_list_t (u64 & betree_message_t)) - (new_msgs : betree_list_t (u64 & betree_message_t)) : nat = +let betree_Node_apply_messages_to_internal_decreases + (msgs : betree_List_t (u64 & betree_Message_t)) + (new_msgs : betree_List_t (u64 & betree_Message_t)) : nat = admit () (** [betree_main::betree::Node::{5}::lookup_mut_in_bindings]: decreases clause *) unfold -let betree_node_lookup_mut_in_bindings_decreases (key : u64) - (bindings : betree_list_t (u64 & u64)) : nat = +let betree_Node_lookup_mut_in_bindings_decreases (key : u64) + (bindings : betree_List_t (u64 & u64)) : nat = admit () (** [betree_main::betree::Node::{5}::apply_messages_to_leaf]: decreases clause *) unfold -let betree_node_apply_messages_to_leaf_decreases - (bindings : betree_list_t (u64 & u64)) - (new_msgs : betree_list_t (u64 & betree_message_t)) : nat = +let betree_Node_apply_messages_to_leaf_decreases + (bindings : betree_List_t (u64 & u64)) + (new_msgs : betree_List_t (u64 & betree_Message_t)) : nat = admit () (** [betree_main::betree::Internal::{4}::flush]: decreases clause *) unfold -let betree_internal_flush_decreases (self : betree_internal_t) - (params : betree_params_t) (node_id_cnt : betree_node_id_counter_t) - (content : betree_list_t (u64 & betree_message_t)) (st : state) : nat = +let betree_Internal_flush_decreases (self : betree_Internal_t) + (params : betree_Params_t) (node_id_cnt : betree_NodeIdCounter_t) + (content : betree_List_t (u64 & betree_Message_t)) (st : state) : nat = admit () (** [betree_main::betree::Node::{5}::apply_messages]: decreases clause *) unfold -let betree_node_apply_messages_decreases (self : betree_node_t) - (params : betree_params_t) (node_id_cnt : betree_node_id_counter_t) - (msgs : betree_list_t (u64 & betree_message_t)) (st : state) : nat = +let betree_Node_apply_messages_decreases (self : betree_Node_t) + (params : betree_Params_t) (node_id_cnt : betree_NodeIdCounter_t) + (msgs : betree_List_t (u64 & betree_Message_t)) (st : state) : nat = admit () diff --git a/tests/fstar/betree/BetreeMain.Clauses.fst b/tests/fstar/betree/BetreeMain.Clauses.fst index 07484711..cda7b920 100644 --- a/tests/fstar/betree/BetreeMain.Clauses.fst +++ b/tests/fstar/betree/BetreeMain.Clauses.fst @@ -8,8 +8,8 @@ open BetreeMain.Types (*** Well-founded relations *) (* We had a few issues when proving termination of the mutually recursive functions: - * - betree_internal_flush - * - betree_node_apply_messages + * - betree_Internal_flush + * - betree_Node_apply_messages * * The quantity which effectively decreases is: * (betree_size, messages_length) @@ -103,108 +103,108 @@ let wf_nat_pair_lem (p0 p1 : nat_pair) : (** [betree_main::betree::List::{1}::len]: decreases clause *) unfold -let betree_list_len_decreases (t : Type0) (self : betree_list_t t) : betree_list_t t = +let betree_List_len_decreases (t : Type0) (self : betree_List_t t) : betree_List_t t = self (** [betree_main::betree::List::{1}::split_at]: decreases clause *) unfold -let betree_list_split_at_decreases (t : Type0) (self : betree_list_t t) +let betree_List_split_at_decreases (t : Type0) (self : betree_List_t t) (n : u64) : nat = n (** [betree_main::betree::List::{2}::partition_at_pivot]: decreases clause *) unfold -let betree_list_partition_at_pivot_decreases (t : Type0) - (self : betree_list_t (u64 & t)) (pivot : u64) : betree_list_t (u64 & t) = +let betree_List_partition_at_pivot_decreases (t : Type0) + (self : betree_List_t (u64 & t)) (pivot : u64) : betree_List_t (u64 & t) = self (** [betree_main::betree::Node::{5}::lookup_in_bindings]: decreases clause *) unfold -let betree_node_lookup_in_bindings_decreases (key : u64) - (bindings : betree_list_t (u64 & u64)) : betree_list_t (u64 & u64) = +let betree_Node_lookup_in_bindings_decreases (key : u64) + (bindings : betree_List_t (u64 & u64)) : betree_List_t (u64 & u64) = bindings (** [betree_main::betree::Node::{5}::lookup_first_message_for_key]: decreases clause *) unfold -let betree_node_lookup_first_message_for_key_decreases (key : u64) - (msgs : betree_list_t (u64 & betree_message_t)) : betree_list_t (u64 & betree_message_t) = +let betree_Node_lookup_first_message_for_key_decreases (key : u64) + (msgs : betree_List_t (u64 & betree_Message_t)) : betree_List_t (u64 & betree_Message_t) = msgs (** [betree_main::betree::Node::{5}::apply_upserts]: decreases clause *) unfold -let betree_node_apply_upserts_decreases - (msgs : betree_list_t (u64 & betree_message_t)) (prev : option u64) - (key : u64) (st : state) : betree_list_t (u64 & betree_message_t) = +let betree_Node_apply_upserts_decreases + (msgs : betree_List_t (u64 & betree_Message_t)) (prev : option u64) + (key : u64) (st : state) : betree_List_t (u64 & betree_Message_t) = msgs (** [betree_main::betree::Internal::{4}::lookup_in_children]: decreases clause *) unfold -let betree_internal_lookup_in_children_decreases (self : betree_internal_t) - (key : u64) (st : state) : betree_internal_t = +let betree_Internal_lookup_in_children_decreases (self : betree_Internal_t) + (key : u64) (st : state) : betree_Internal_t = self (** [betree_main::betree::Node::{5}::lookup]: decreases clause *) unfold -let betree_node_lookup_decreases (self : betree_node_t) (key : u64) - (st : state) : betree_node_t = +let betree_Node_lookup_decreases (self : betree_Node_t) (key : u64) + (st : state) : betree_Node_t = self (** [betree_main::betree::Node::{5}::lookup_mut_in_bindings]: decreases clause *) unfold -let betree_node_lookup_mut_in_bindings_decreases (key : u64) - (bindings : betree_list_t (u64 & u64)) : betree_list_t (u64 & u64) = +let betree_Node_lookup_mut_in_bindings_decreases (key : u64) + (bindings : betree_List_t (u64 & u64)) : betree_List_t (u64 & u64) = bindings unfold -let betree_node_apply_messages_to_leaf_decreases - (bindings : betree_list_t (u64 & u64)) - (new_msgs : betree_list_t (u64 & betree_message_t)) : betree_list_t (u64 & betree_message_t) = +let betree_Node_apply_messages_to_leaf_decreases + (bindings : betree_List_t (u64 & u64)) + (new_msgs : betree_List_t (u64 & betree_Message_t)) : betree_List_t (u64 & betree_Message_t) = new_msgs (** [betree_main::betree::Node::{5}::filter_messages_for_key]: decreases clause *) unfold -let betree_node_filter_messages_for_key_decreases (key : u64) - (msgs : betree_list_t (u64 & betree_message_t)) : betree_list_t (u64 & betree_message_t) = +let betree_Node_filter_messages_for_key_decreases (key : u64) + (msgs : betree_List_t (u64 & betree_Message_t)) : betree_List_t (u64 & betree_Message_t) = msgs (** [betree_main::betree::Node::{5}::lookup_first_message_after_key]: decreases clause *) unfold -let betree_node_lookup_first_message_after_key_decreases (key : u64) - (msgs : betree_list_t (u64 & betree_message_t)) : betree_list_t (u64 & betree_message_t) = +let betree_Node_lookup_first_message_after_key_decreases (key : u64) + (msgs : betree_List_t (u64 & betree_Message_t)) : betree_List_t (u64 & betree_Message_t) = msgs -let betree_node_apply_messages_to_internal_decreases - (msgs : betree_list_t (u64 & betree_message_t)) - (new_msgs : betree_list_t (u64 & betree_message_t)) : betree_list_t (u64 & betree_message_t) = +let betree_Node_apply_messages_to_internal_decreases + (msgs : betree_List_t (u64 & betree_Message_t)) + (new_msgs : betree_List_t (u64 & betree_Message_t)) : betree_List_t (u64 & betree_Message_t) = new_msgs (*** Decrease clauses - nat_pair *) /// The following decrease clauses use the [nat_pair] definition and the well-founded /// relation proven above. -let rec betree_size (bt : betree_node_t) : nat = +let rec betree_size (bt : betree_Node_t) : nat = match bt with - | BetreeNodeInternal node -> 1 + betree_internal_size node - | BetreeNodeLeaf _ -> 1 + | Betree_Node_Internal node -> 1 + betree_Internal_size node + | Betree_Node_Leaf _ -> 1 -and betree_internal_size (node : betree_internal_t) : nat = - 1 + betree_size node.betree_internal_left + betree_size node.betree_internal_right +and betree_Internal_size (node : betree_Internal_t) : nat = + 1 + betree_size node.left + betree_size node.right -let rec betree_list_len (#a : Type0) (ls : betree_list_t a) : nat = +let rec betree_List_len (#a : Type0) (ls : betree_List_t a) : nat = match ls with - | BetreeListCons _ tl -> 1 + betree_list_len tl - | BetreeListNil -> 0 + | Betree_List_Cons _ tl -> 1 + betree_List_len tl + | Betree_List_Nil -> 0 (** [betree_main::betree::Internal::{4}::flush]: decreases clause *) unfold -let betree_internal_flush_decreases (self : betree_internal_t) - (params : betree_params_t) (node_id_cnt : betree_node_id_counter_t) - (content : betree_list_t (u64 & betree_message_t)) (st : state) : nat_pair = - (|betree_internal_size self, 0|) +let betree_Internal_flush_decreases (self : betree_Internal_t) + (params : betree_Params_t) (node_id_cnt : betree_NodeIdCounter_t) + (content : betree_List_t (u64 & betree_Message_t)) (st : state) : nat_pair = + (|betree_Internal_size self, 0|) (** [betree_main::betree::Node::{5}::apply_messages]: decreases clause *) unfold -let betree_node_apply_messages_decreases (self : betree_node_t) - (params : betree_params_t) (node_id_cnt : betree_node_id_counter_t) - (msgs : betree_list_t (u64 & betree_message_t)) (st : state) : nat_pair = - (|betree_size self, betree_list_len msgs|) +let betree_Node_apply_messages_decreases (self : betree_Node_t) + (params : betree_Params_t) (node_id_cnt : betree_NodeIdCounter_t) + (msgs : betree_List_t (u64 & betree_Message_t)) (st : state) : nat_pair = + (|betree_size self, betree_List_len msgs|) diff --git a/tests/fstar/betree/BetreeMain.Funs.fst b/tests/fstar/betree/BetreeMain.Funs.fst index 2bb2352b..d2bf5c7c 100644 --- a/tests/fstar/betree/BetreeMain.Funs.fst +++ b/tests/fstar/betree/BetreeMain.Funs.fst @@ -9,35 +9,35 @@ include BetreeMain.Clauses #set-options "--z3rlimit 50 --fuel 1 --ifuel 1" (** [betree_main::betree::load_internal_node]: forward function *) -let betree_load_internal_node_fwd +let betree_load_internal_node (id : u64) (st : state) : - result (state & (betree_list_t (u64 & betree_message_t))) + result (state & (betree_List_t (u64 & betree_Message_t))) = - betree_utils_load_internal_node_fwd id st + betree_utils_load_internal_node id st (** [betree_main::betree::store_internal_node]: forward function *) -let betree_store_internal_node_fwd - (id : u64) (content : betree_list_t (u64 & betree_message_t)) (st : state) : +let betree_store_internal_node + (id : u64) (content : betree_List_t (u64 & betree_Message_t)) (st : state) : result (state & unit) = - let* (st0, _) = betree_utils_store_internal_node_fwd id content st in + let* (st0, _) = betree_utils_store_internal_node id content st in Return (st0, ()) (** [betree_main::betree::load_leaf_node]: forward function *) -let betree_load_leaf_node_fwd - (id : u64) (st : state) : result (state & (betree_list_t (u64 & u64))) = - betree_utils_load_leaf_node_fwd id st +let betree_load_leaf_node + (id : u64) (st : state) : result (state & (betree_List_t (u64 & u64))) = + betree_utils_load_leaf_node id st (** [betree_main::betree::store_leaf_node]: forward function *) -let betree_store_leaf_node_fwd - (id : u64) (content : betree_list_t (u64 & u64)) (st : state) : +let betree_store_leaf_node + (id : u64) (content : betree_List_t (u64 & u64)) (st : state) : result (state & unit) = - let* (st0, _) = betree_utils_store_leaf_node_fwd id content st in + let* (st0, _) = betree_utils_store_leaf_node id content st in Return (st0, ()) (** [betree_main::betree::fresh_node_id]: forward function *) -let betree_fresh_node_id_fwd (counter : u64) : result u64 = +let betree_fresh_node_id (counter : u64) : result u64 = let* _ = u64_add counter 1 in Return counter (** [betree_main::betree::fresh_node_id]: backward function 0 *) @@ -45,972 +45,909 @@ let betree_fresh_node_id_back (counter : u64) : result u64 = u64_add counter 1 (** [betree_main::betree::NodeIdCounter::{0}::new]: forward function *) -let betree_node_id_counter_new_fwd : result betree_node_id_counter_t = - Return { betree_node_id_counter_next_node_id = 0 } +let betree_NodeIdCounter_new : result betree_NodeIdCounter_t = + Return { next_node_id = 0 } (** [betree_main::betree::NodeIdCounter::{0}::fresh_id]: forward function *) -let betree_node_id_counter_fresh_id_fwd - (self : betree_node_id_counter_t) : result u64 = - let* _ = u64_add self.betree_node_id_counter_next_node_id 1 in - Return self.betree_node_id_counter_next_node_id +let betree_NodeIdCounter_fresh_id + (self : betree_NodeIdCounter_t) : result u64 = + let* _ = u64_add self.next_node_id 1 in Return self.next_node_id (** [betree_main::betree::NodeIdCounter::{0}::fresh_id]: backward function 0 *) -let betree_node_id_counter_fresh_id_back - (self : betree_node_id_counter_t) : result betree_node_id_counter_t = - let* i = u64_add self.betree_node_id_counter_next_node_id 1 in - Return { betree_node_id_counter_next_node_id = i } +let betree_NodeIdCounter_fresh_id_back + (self : betree_NodeIdCounter_t) : result betree_NodeIdCounter_t = + let* i = u64_add self.next_node_id 1 in Return { next_node_id = i } (** [betree_main::betree::upsert_update]: forward function *) -let betree_upsert_update_fwd - (prev : option u64) (st : betree_upsert_fun_state_t) : result u64 = +let betree_upsert_update + (prev : option u64) (st : betree_UpsertFunState_t) : result u64 = begin match prev with | None -> begin match st with - | BetreeUpsertFunStateAdd v -> Return v - | BetreeUpsertFunStateSub i -> Return 0 + | Betree_UpsertFunState_Add v -> Return v + | Betree_UpsertFunState_Sub i -> Return 0 end | Some prev0 -> begin match st with - | BetreeUpsertFunStateAdd v -> + | Betree_UpsertFunState_Add v -> let* margin = u64_sub core_u64_max prev0 in if margin >= v then u64_add prev0 v else Return core_u64_max - | BetreeUpsertFunStateSub v -> + | Betree_UpsertFunState_Sub v -> if prev0 >= v then u64_sub prev0 v else Return 0 end end (** [betree_main::betree::List::{1}::len]: forward function *) -let rec betree_list_len_fwd - (t : Type0) (self : betree_list_t t) : - Tot (result u64) (decreases (betree_list_len_decreases t self)) +let rec betree_List_len + (t : Type0) (self : betree_List_t t) : + Tot (result u64) (decreases (betree_List_len_decreases t self)) = begin match self with - | BetreeListCons x tl -> let* i = betree_list_len_fwd t tl in u64_add 1 i - | BetreeListNil -> Return 0 + | Betree_List_Cons x tl -> let* i = betree_List_len t tl in u64_add 1 i + | Betree_List_Nil -> Return 0 end (** [betree_main::betree::List::{1}::split_at]: forward function *) -let rec betree_list_split_at_fwd - (t : Type0) (self : betree_list_t t) (n : u64) : - Tot (result ((betree_list_t t) & (betree_list_t t))) - (decreases (betree_list_split_at_decreases t self n)) +let rec betree_List_split_at + (t : Type0) (self : betree_List_t t) (n : u64) : + Tot (result ((betree_List_t t) & (betree_List_t t))) + (decreases (betree_List_split_at_decreases t self n)) = if n = 0 - then Return (BetreeListNil, self) + then Return (Betree_List_Nil, self) else begin match self with - | BetreeListCons hd tl -> + | Betree_List_Cons hd tl -> let* i = u64_sub n 1 in - let* p = betree_list_split_at_fwd t tl i in + let* p = betree_List_split_at t tl i in let (ls0, ls1) = p in let l = ls0 in - Return (BetreeListCons hd l, ls1) - | BetreeListNil -> Fail Failure + Return (Betree_List_Cons hd l, ls1) + | Betree_List_Nil -> Fail Failure end (** [betree_main::betree::List::{1}::push_front]: merged forward/backward function (there is a single backward function, and the forward function returns ()) *) -let betree_list_push_front_fwd_back - (t : Type0) (self : betree_list_t t) (x : t) : result (betree_list_t t) = - let tl = mem_replace_fwd (betree_list_t t) self BetreeListNil in +let betree_List_push_front + (t : Type0) (self : betree_List_t t) (x : t) : result (betree_List_t t) = + let tl = core_mem_replace (betree_List_t t) self Betree_List_Nil in let l = tl in - Return (BetreeListCons x l) + Return (Betree_List_Cons x l) (** [betree_main::betree::List::{1}::pop_front]: forward function *) -let betree_list_pop_front_fwd (t : Type0) (self : betree_list_t t) : result t = - let ls = mem_replace_fwd (betree_list_t t) self BetreeListNil in +let betree_List_pop_front (t : Type0) (self : betree_List_t t) : result t = + let ls = core_mem_replace (betree_List_t t) self Betree_List_Nil in begin match ls with - | BetreeListCons x tl -> Return x - | BetreeListNil -> Fail Failure + | Betree_List_Cons x tl -> Return x + | Betree_List_Nil -> Fail Failure end (** [betree_main::betree::List::{1}::pop_front]: backward function 0 *) -let betree_list_pop_front_back - (t : Type0) (self : betree_list_t t) : result (betree_list_t t) = - let ls = mem_replace_fwd (betree_list_t t) self BetreeListNil in +let betree_List_pop_front_back + (t : Type0) (self : betree_List_t t) : result (betree_List_t t) = + let ls = core_mem_replace (betree_List_t t) self Betree_List_Nil in begin match ls with - | BetreeListCons x tl -> Return tl - | BetreeListNil -> Fail Failure + | Betree_List_Cons x tl -> Return tl + | Betree_List_Nil -> Fail Failure end (** [betree_main::betree::List::{1}::hd]: forward function *) -let betree_list_hd_fwd (t : Type0) (self : betree_list_t t) : result t = +let betree_List_hd (t : Type0) (self : betree_List_t t) : result t = begin match self with - | BetreeListCons hd l -> Return hd - | BetreeListNil -> Fail Failure + | Betree_List_Cons hd l -> Return hd + | Betree_List_Nil -> Fail Failure end (** [betree_main::betree::List::{2}::head_has_key]: forward function *) -let betree_list_head_has_key_fwd - (t : Type0) (self : betree_list_t (u64 & t)) (key : u64) : result bool = +let betree_List_head_has_key + (t : Type0) (self : betree_List_t (u64 & t)) (key : u64) : result bool = begin match self with - | BetreeListCons hd l -> let (i, _) = hd in Return (i = key) - | BetreeListNil -> Return false + | Betree_List_Cons hd l -> let (i, _) = hd in Return (i = key) + | Betree_List_Nil -> Return false end (** [betree_main::betree::List::{2}::partition_at_pivot]: forward function *) -let rec betree_list_partition_at_pivot_fwd - (t : Type0) (self : betree_list_t (u64 & t)) (pivot : u64) : - Tot (result ((betree_list_t (u64 & t)) & (betree_list_t (u64 & t)))) - (decreases (betree_list_partition_at_pivot_decreases t self pivot)) +let rec betree_List_partition_at_pivot + (t : Type0) (self : betree_List_t (u64 & t)) (pivot : u64) : + Tot (result ((betree_List_t (u64 & t)) & (betree_List_t (u64 & t)))) + (decreases (betree_List_partition_at_pivot_decreases t self pivot)) = begin match self with - | BetreeListCons hd tl -> + | Betree_List_Cons hd tl -> let (i, x) = hd in if i >= pivot - then Return (BetreeListNil, BetreeListCons (i, x) tl) + then Return (Betree_List_Nil, Betree_List_Cons (i, x) tl) else - let* p = betree_list_partition_at_pivot_fwd t tl pivot in + let* p = betree_List_partition_at_pivot t tl pivot in let (ls0, ls1) = p in let l = ls0 in - Return (BetreeListCons (i, x) l, ls1) - | BetreeListNil -> Return (BetreeListNil, BetreeListNil) + Return (Betree_List_Cons (i, x) l, ls1) + | Betree_List_Nil -> Return (Betree_List_Nil, Betree_List_Nil) end (** [betree_main::betree::Leaf::{3}::split]: forward function *) -let betree_leaf_split_fwd - (self : betree_leaf_t) (content : betree_list_t (u64 & u64)) - (params : betree_params_t) (node_id_cnt : betree_node_id_counter_t) +let betree_Leaf_split + (self : betree_Leaf_t) (content : betree_List_t (u64 & u64)) + (params : betree_Params_t) (node_id_cnt : betree_NodeIdCounter_t) (st : state) : - result (state & betree_internal_t) + result (state & betree_Internal_t) = - let* p = - betree_list_split_at_fwd (u64 & u64) content - params.betree_params_split_size in + let* p = betree_List_split_at (u64 & u64) content params.split_size in let (content0, content1) = p in - let* p0 = betree_list_hd_fwd (u64 & u64) content1 in + let* p0 = betree_List_hd (u64 & u64) content1 in let (pivot, _) = p0 in - let* id0 = betree_node_id_counter_fresh_id_fwd node_id_cnt in - let* node_id_cnt0 = betree_node_id_counter_fresh_id_back node_id_cnt in - let* id1 = betree_node_id_counter_fresh_id_fwd node_id_cnt0 in - let* (st0, _) = betree_store_leaf_node_fwd id0 content0 st in - let* (st1, _) = betree_store_leaf_node_fwd id1 content1 st0 in - let n = BetreeNodeLeaf - { betree_leaf_id = id0; betree_leaf_size = params.betree_params_split_size - } in - let n0 = BetreeNodeLeaf - { betree_leaf_id = id1; betree_leaf_size = params.betree_params_split_size - } in - Return (st1, - { - betree_internal_id = self.betree_leaf_id; - betree_internal_pivot = pivot; - betree_internal_left = n; - betree_internal_right = n0 - }) + let* id0 = betree_NodeIdCounter_fresh_id node_id_cnt in + let* node_id_cnt0 = betree_NodeIdCounter_fresh_id_back node_id_cnt in + let* id1 = betree_NodeIdCounter_fresh_id node_id_cnt0 in + let* (st0, _) = betree_store_leaf_node id0 content0 st in + let* (st1, _) = betree_store_leaf_node id1 content1 st0 in + let n = Betree_Node_Leaf { id = id0; size = params.split_size } in + let n0 = Betree_Node_Leaf { id = id1; size = params.split_size } in + Return (st1, { id = self.id; pivot = pivot; left = n; right = n0 }) (** [betree_main::betree::Leaf::{3}::split]: backward function 2 *) -let betree_leaf_split_back - (self : betree_leaf_t) (content : betree_list_t (u64 & u64)) - (params : betree_params_t) (node_id_cnt : betree_node_id_counter_t) +let betree_Leaf_split_back + (self : betree_Leaf_t) (content : betree_List_t (u64 & u64)) + (params : betree_Params_t) (node_id_cnt : betree_NodeIdCounter_t) (st : state) : - result betree_node_id_counter_t + result betree_NodeIdCounter_t = - let* p = - betree_list_split_at_fwd (u64 & u64) content - params.betree_params_split_size in + let* p = betree_List_split_at (u64 & u64) content params.split_size in let (content0, content1) = p in - let* _ = betree_list_hd_fwd (u64 & u64) content1 in - let* id0 = betree_node_id_counter_fresh_id_fwd node_id_cnt in - let* node_id_cnt0 = betree_node_id_counter_fresh_id_back node_id_cnt in - let* id1 = betree_node_id_counter_fresh_id_fwd node_id_cnt0 in - let* (st0, _) = betree_store_leaf_node_fwd id0 content0 st in - let* _ = betree_store_leaf_node_fwd id1 content1 st0 in - betree_node_id_counter_fresh_id_back node_id_cnt0 + let* _ = betree_List_hd (u64 & u64) content1 in + let* id0 = betree_NodeIdCounter_fresh_id node_id_cnt in + let* node_id_cnt0 = betree_NodeIdCounter_fresh_id_back node_id_cnt in + let* id1 = betree_NodeIdCounter_fresh_id node_id_cnt0 in + let* (st0, _) = betree_store_leaf_node id0 content0 st in + let* _ = betree_store_leaf_node id1 content1 st0 in + betree_NodeIdCounter_fresh_id_back node_id_cnt0 (** [betree_main::betree::Node::{5}::lookup_first_message_for_key]: forward function *) -let rec betree_node_lookup_first_message_for_key_fwd - (key : u64) (msgs : betree_list_t (u64 & betree_message_t)) : - Tot (result (betree_list_t (u64 & betree_message_t))) - (decreases (betree_node_lookup_first_message_for_key_decreases key msgs)) +let rec betree_Node_lookup_first_message_for_key + (key : u64) (msgs : betree_List_t (u64 & betree_Message_t)) : + Tot (result (betree_List_t (u64 & betree_Message_t))) + (decreases (betree_Node_lookup_first_message_for_key_decreases key msgs)) = begin match msgs with - | BetreeListCons x next_msgs -> + | Betree_List_Cons x next_msgs -> let (i, m) = x in if i >= key - then Return (BetreeListCons (i, m) next_msgs) - else betree_node_lookup_first_message_for_key_fwd key next_msgs - | BetreeListNil -> Return BetreeListNil + then Return (Betree_List_Cons (i, m) next_msgs) + else betree_Node_lookup_first_message_for_key key next_msgs + | Betree_List_Nil -> Return Betree_List_Nil end (** [betree_main::betree::Node::{5}::lookup_first_message_for_key]: backward function 0 *) -let rec betree_node_lookup_first_message_for_key_back - (key : u64) (msgs : betree_list_t (u64 & betree_message_t)) - (ret : betree_list_t (u64 & betree_message_t)) : - Tot (result (betree_list_t (u64 & betree_message_t))) - (decreases (betree_node_lookup_first_message_for_key_decreases key msgs)) +let rec betree_Node_lookup_first_message_for_key_back + (key : u64) (msgs : betree_List_t (u64 & betree_Message_t)) + (ret : betree_List_t (u64 & betree_Message_t)) : + Tot (result (betree_List_t (u64 & betree_Message_t))) + (decreases (betree_Node_lookup_first_message_for_key_decreases key msgs)) = begin match msgs with - | BetreeListCons x next_msgs -> + | Betree_List_Cons x next_msgs -> let (i, m) = x in if i >= key then Return ret else let* next_msgs0 = - betree_node_lookup_first_message_for_key_back key next_msgs ret in - Return (BetreeListCons (i, m) next_msgs0) - | BetreeListNil -> Return ret + betree_Node_lookup_first_message_for_key_back key next_msgs ret in + Return (Betree_List_Cons (i, m) next_msgs0) + | Betree_List_Nil -> Return ret end (** [betree_main::betree::Node::{5}::apply_upserts]: forward function *) -let rec betree_node_apply_upserts_fwd - (msgs : betree_list_t (u64 & betree_message_t)) (prev : option u64) +let rec betree_Node_apply_upserts + (msgs : betree_List_t (u64 & betree_Message_t)) (prev : option u64) (key : u64) (st : state) : Tot (result (state & u64)) - (decreases (betree_node_apply_upserts_decreases msgs prev key st)) + (decreases (betree_Node_apply_upserts_decreases msgs prev key st)) = - let* b = betree_list_head_has_key_fwd betree_message_t msgs key in + let* b = betree_List_head_has_key betree_Message_t msgs key in if b then - let* msg = betree_list_pop_front_fwd (u64 & betree_message_t) msgs in + let* msg = betree_List_pop_front (u64 & betree_Message_t) msgs in let (_, m) = msg in begin match m with - | BetreeMessageInsert i -> Fail Failure - | BetreeMessageDelete -> Fail Failure - | BetreeMessageUpsert s -> - let* v = betree_upsert_update_fwd prev s in - let* msgs0 = betree_list_pop_front_back (u64 & betree_message_t) msgs in - betree_node_apply_upserts_fwd msgs0 (Some v) key st + | Betree_Message_Insert i -> Fail Failure + | Betree_Message_Delete -> Fail Failure + | Betree_Message_Upsert s -> + let* v = betree_upsert_update prev s in + let* msgs0 = betree_List_pop_front_back (u64 & betree_Message_t) msgs in + betree_Node_apply_upserts msgs0 (Some v) key st end else - let* (st0, v) = core_option_option_unwrap_fwd u64 prev st in + let* (st0, v) = core_option_Option_unwrap u64 prev st in let* _ = - betree_list_push_front_fwd_back (u64 & betree_message_t) msgs (key, - BetreeMessageInsert v) in + betree_List_push_front (u64 & betree_Message_t) msgs (key, + Betree_Message_Insert v) in Return (st0, v) (** [betree_main::betree::Node::{5}::apply_upserts]: backward function 0 *) -let rec betree_node_apply_upserts_back - (msgs : betree_list_t (u64 & betree_message_t)) (prev : option u64) +let rec betree_Node_apply_upserts_back + (msgs : betree_List_t (u64 & betree_Message_t)) (prev : option u64) (key : u64) (st : state) : - Tot (result (betree_list_t (u64 & betree_message_t))) - (decreases (betree_node_apply_upserts_decreases msgs prev key st)) + Tot (result (betree_List_t (u64 & betree_Message_t))) + (decreases (betree_Node_apply_upserts_decreases msgs prev key st)) = - let* b = betree_list_head_has_key_fwd betree_message_t msgs key in + let* b = betree_List_head_has_key betree_Message_t msgs key in if b then - let* msg = betree_list_pop_front_fwd (u64 & betree_message_t) msgs in + let* msg = betree_List_pop_front (u64 & betree_Message_t) msgs in let (_, m) = msg in begin match m with - | BetreeMessageInsert i -> Fail Failure - | BetreeMessageDelete -> Fail Failure - | BetreeMessageUpsert s -> - let* v = betree_upsert_update_fwd prev s in - let* msgs0 = betree_list_pop_front_back (u64 & betree_message_t) msgs in - betree_node_apply_upserts_back msgs0 (Some v) key st + | Betree_Message_Insert i -> Fail Failure + | Betree_Message_Delete -> Fail Failure + | Betree_Message_Upsert s -> + let* v = betree_upsert_update prev s in + let* msgs0 = betree_List_pop_front_back (u64 & betree_Message_t) msgs in + betree_Node_apply_upserts_back msgs0 (Some v) key st end else - let* (_, v) = core_option_option_unwrap_fwd u64 prev st in - betree_list_push_front_fwd_back (u64 & betree_message_t) msgs (key, - BetreeMessageInsert v) + let* (_, v) = core_option_Option_unwrap u64 prev st in + betree_List_push_front (u64 & betree_Message_t) msgs (key, + Betree_Message_Insert v) (** [betree_main::betree::Node::{5}::lookup_in_bindings]: forward function *) -let rec betree_node_lookup_in_bindings_fwd - (key : u64) (bindings : betree_list_t (u64 & u64)) : +let rec betree_Node_lookup_in_bindings + (key : u64) (bindings : betree_List_t (u64 & u64)) : Tot (result (option u64)) - (decreases (betree_node_lookup_in_bindings_decreases key bindings)) + (decreases (betree_Node_lookup_in_bindings_decreases key bindings)) = begin match bindings with - | BetreeListCons hd tl -> + | Betree_List_Cons hd tl -> let (i, i0) = hd in if i = key then Return (Some i0) - else - if i > key - then Return None - else betree_node_lookup_in_bindings_fwd key tl - | BetreeListNil -> Return None + else if i > key then Return None else betree_Node_lookup_in_bindings key tl + | Betree_List_Nil -> Return None end (** [betree_main::betree::Internal::{4}::lookup_in_children]: forward function *) -let rec betree_internal_lookup_in_children_fwd - (self : betree_internal_t) (key : u64) (st : state) : +let rec betree_Internal_lookup_in_children + (self : betree_Internal_t) (key : u64) (st : state) : Tot (result (state & (option u64))) - (decreases (betree_internal_lookup_in_children_decreases self key st)) + (decreases (betree_Internal_lookup_in_children_decreases self key st)) = - if key < self.betree_internal_pivot - then betree_node_lookup_fwd self.betree_internal_left key st - else betree_node_lookup_fwd self.betree_internal_right key st + if key < self.pivot + then betree_Node_lookup self.left key st + else betree_Node_lookup self.right key st (** [betree_main::betree::Internal::{4}::lookup_in_children]: backward function 0 *) -and betree_internal_lookup_in_children_back - (self : betree_internal_t) (key : u64) (st : state) : - Tot (result betree_internal_t) - (decreases (betree_internal_lookup_in_children_decreases self key st)) +and betree_Internal_lookup_in_children_back + (self : betree_Internal_t) (key : u64) (st : state) : + Tot (result betree_Internal_t) + (decreases (betree_Internal_lookup_in_children_decreases self key st)) = - if key < self.betree_internal_pivot + if key < self.pivot then - let* n = betree_node_lookup_back self.betree_internal_left key st in - Return { self with betree_internal_left = n } + let* n = betree_Node_lookup_back self.left key st in + Return { self with left = n } else - let* n = betree_node_lookup_back self.betree_internal_right key st in - Return { self with betree_internal_right = n } + let* n = betree_Node_lookup_back self.right key st in + Return { self with right = n } (** [betree_main::betree::Node::{5}::lookup]: forward function *) -and betree_node_lookup_fwd - (self : betree_node_t) (key : u64) (st : state) : +and betree_Node_lookup + (self : betree_Node_t) (key : u64) (st : state) : Tot (result (state & (option u64))) - (decreases (betree_node_lookup_decreases self key st)) + (decreases (betree_Node_lookup_decreases self key st)) = begin match self with - | BetreeNodeInternal node -> - let* (st0, msgs) = betree_load_internal_node_fwd node.betree_internal_id st - in - let* pending = betree_node_lookup_first_message_for_key_fwd key msgs in + | Betree_Node_Internal node -> + let* (st0, msgs) = betree_load_internal_node node.id st in + let* pending = betree_Node_lookup_first_message_for_key key msgs in begin match pending with - | BetreeListCons p l -> + | Betree_List_Cons p l -> let (k, msg) = p in if k <> key then - let* (st1, opt) = betree_internal_lookup_in_children_fwd node key st0 - in + let* (st1, o) = betree_Internal_lookup_in_children node key st0 in let* _ = - betree_node_lookup_first_message_for_key_back key msgs - (BetreeListCons (k, msg) l) in - Return (st1, opt) + betree_Node_lookup_first_message_for_key_back key msgs + (Betree_List_Cons (k, msg) l) in + Return (st1, o) else begin match msg with - | BetreeMessageInsert v -> + | Betree_Message_Insert v -> let* _ = - betree_node_lookup_first_message_for_key_back key msgs - (BetreeListCons (k, BetreeMessageInsert v) l) in + betree_Node_lookup_first_message_for_key_back key msgs + (Betree_List_Cons (k, Betree_Message_Insert v) l) in Return (st0, Some v) - | BetreeMessageDelete -> + | Betree_Message_Delete -> let* _ = - betree_node_lookup_first_message_for_key_back key msgs - (BetreeListCons (k, BetreeMessageDelete) l) in + betree_Node_lookup_first_message_for_key_back key msgs + (Betree_List_Cons (k, Betree_Message_Delete) l) in Return (st0, None) - | BetreeMessageUpsert ufs -> - let* (st1, v) = betree_internal_lookup_in_children_fwd node key st0 - in + | Betree_Message_Upsert ufs -> + let* (st1, v) = betree_Internal_lookup_in_children node key st0 in let* (st2, v0) = - betree_node_apply_upserts_fwd (BetreeListCons (k, - BetreeMessageUpsert ufs) l) v key st1 in - let* node0 = betree_internal_lookup_in_children_back node key st0 in + betree_Node_apply_upserts (Betree_List_Cons (k, + Betree_Message_Upsert ufs) l) v key st1 in + let* node0 = betree_Internal_lookup_in_children_back node key st0 in let* pending0 = - betree_node_apply_upserts_back (BetreeListCons (k, - BetreeMessageUpsert ufs) l) v key st1 in + betree_Node_apply_upserts_back (Betree_List_Cons (k, + Betree_Message_Upsert ufs) l) v key st1 in let* msgs0 = - betree_node_lookup_first_message_for_key_back key msgs pending0 in - let* (st3, _) = - betree_store_internal_node_fwd node0.betree_internal_id msgs0 st2 - in + betree_Node_lookup_first_message_for_key_back key msgs pending0 in + let* (st3, _) = betree_store_internal_node node0.id msgs0 st2 in Return (st3, Some v0) end - | BetreeListNil -> - let* (st1, opt) = betree_internal_lookup_in_children_fwd node key st0 in + | Betree_List_Nil -> + let* (st1, o) = betree_Internal_lookup_in_children node key st0 in let* _ = - betree_node_lookup_first_message_for_key_back key msgs BetreeListNil in - Return (st1, opt) + betree_Node_lookup_first_message_for_key_back key msgs Betree_List_Nil + in + Return (st1, o) end - | BetreeNodeLeaf node -> - let* (st0, bindings) = betree_load_leaf_node_fwd node.betree_leaf_id st in - let* opt = betree_node_lookup_in_bindings_fwd key bindings in - Return (st0, opt) + | Betree_Node_Leaf node -> + let* (st0, bindings) = betree_load_leaf_node node.id st in + let* o = betree_Node_lookup_in_bindings key bindings in + Return (st0, o) end (** [betree_main::betree::Node::{5}::lookup]: backward function 0 *) -and betree_node_lookup_back - (self : betree_node_t) (key : u64) (st : state) : - Tot (result betree_node_t) - (decreases (betree_node_lookup_decreases self key st)) +and betree_Node_lookup_back + (self : betree_Node_t) (key : u64) (st : state) : + Tot (result betree_Node_t) + (decreases (betree_Node_lookup_decreases self key st)) = begin match self with - | BetreeNodeInternal node -> - let* (st0, msgs) = betree_load_internal_node_fwd node.betree_internal_id st - in - let* pending = betree_node_lookup_first_message_for_key_fwd key msgs in + | Betree_Node_Internal node -> + let* (st0, msgs) = betree_load_internal_node node.id st in + let* pending = betree_Node_lookup_first_message_for_key key msgs in begin match pending with - | BetreeListCons p l -> + | Betree_List_Cons p l -> let (k, msg) = p in if k <> key then let* _ = - betree_node_lookup_first_message_for_key_back key msgs - (BetreeListCons (k, msg) l) in - let* node0 = betree_internal_lookup_in_children_back node key st0 in - Return (BetreeNodeInternal node0) + betree_Node_lookup_first_message_for_key_back key msgs + (Betree_List_Cons (k, msg) l) in + let* node0 = betree_Internal_lookup_in_children_back node key st0 in + Return (Betree_Node_Internal node0) else begin match msg with - | BetreeMessageInsert v -> + | Betree_Message_Insert v -> let* _ = - betree_node_lookup_first_message_for_key_back key msgs - (BetreeListCons (k, BetreeMessageInsert v) l) in - Return (BetreeNodeInternal node) - | BetreeMessageDelete -> + betree_Node_lookup_first_message_for_key_back key msgs + (Betree_List_Cons (k, Betree_Message_Insert v) l) in + Return (Betree_Node_Internal node) + | Betree_Message_Delete -> let* _ = - betree_node_lookup_first_message_for_key_back key msgs - (BetreeListCons (k, BetreeMessageDelete) l) in - Return (BetreeNodeInternal node) - | BetreeMessageUpsert ufs -> - let* (st1, v) = betree_internal_lookup_in_children_fwd node key st0 - in + betree_Node_lookup_first_message_for_key_back key msgs + (Betree_List_Cons (k, Betree_Message_Delete) l) in + Return (Betree_Node_Internal node) + | Betree_Message_Upsert ufs -> + let* (st1, v) = betree_Internal_lookup_in_children node key st0 in let* (st2, _) = - betree_node_apply_upserts_fwd (BetreeListCons (k, - BetreeMessageUpsert ufs) l) v key st1 in - let* node0 = betree_internal_lookup_in_children_back node key st0 in + betree_Node_apply_upserts (Betree_List_Cons (k, + Betree_Message_Upsert ufs) l) v key st1 in + let* node0 = betree_Internal_lookup_in_children_back node key st0 in let* pending0 = - betree_node_apply_upserts_back (BetreeListCons (k, - BetreeMessageUpsert ufs) l) v key st1 in + betree_Node_apply_upserts_back (Betree_List_Cons (k, + Betree_Message_Upsert ufs) l) v key st1 in let* msgs0 = - betree_node_lookup_first_message_for_key_back key msgs pending0 in - let* _ = - betree_store_internal_node_fwd node0.betree_internal_id msgs0 st2 - in - Return (BetreeNodeInternal node0) + betree_Node_lookup_first_message_for_key_back key msgs pending0 in + let* _ = betree_store_internal_node node0.id msgs0 st2 in + Return (Betree_Node_Internal node0) end - | BetreeListNil -> + | Betree_List_Nil -> let* _ = - betree_node_lookup_first_message_for_key_back key msgs BetreeListNil in - let* node0 = betree_internal_lookup_in_children_back node key st0 in - Return (BetreeNodeInternal node0) + betree_Node_lookup_first_message_for_key_back key msgs Betree_List_Nil + in + let* node0 = betree_Internal_lookup_in_children_back node key st0 in + Return (Betree_Node_Internal node0) end - | BetreeNodeLeaf node -> - let* (_, bindings) = betree_load_leaf_node_fwd node.betree_leaf_id st in - let* _ = betree_node_lookup_in_bindings_fwd key bindings in - Return (BetreeNodeLeaf node) + | Betree_Node_Leaf node -> + let* (_, bindings) = betree_load_leaf_node node.id st in + let* _ = betree_Node_lookup_in_bindings key bindings in + Return (Betree_Node_Leaf node) end (** [betree_main::betree::Node::{5}::filter_messages_for_key]: merged forward/backward function (there is a single backward function, and the forward function returns ()) *) -let rec betree_node_filter_messages_for_key_fwd_back - (key : u64) (msgs : betree_list_t (u64 & betree_message_t)) : - Tot (result (betree_list_t (u64 & betree_message_t))) - (decreases (betree_node_filter_messages_for_key_decreases key msgs)) +let rec betree_Node_filter_messages_for_key + (key : u64) (msgs : betree_List_t (u64 & betree_Message_t)) : + Tot (result (betree_List_t (u64 & betree_Message_t))) + (decreases (betree_Node_filter_messages_for_key_decreases key msgs)) = begin match msgs with - | BetreeListCons p l -> + | Betree_List_Cons p l -> let (k, m) = p in if k = key then let* msgs0 = - betree_list_pop_front_back (u64 & betree_message_t) (BetreeListCons (k, - m) l) in - betree_node_filter_messages_for_key_fwd_back key msgs0 - else Return (BetreeListCons (k, m) l) - | BetreeListNil -> Return BetreeListNil + betree_List_pop_front_back (u64 & betree_Message_t) (Betree_List_Cons + (k, m) l) in + betree_Node_filter_messages_for_key key msgs0 + else Return (Betree_List_Cons (k, m) l) + | Betree_List_Nil -> Return Betree_List_Nil end (** [betree_main::betree::Node::{5}::lookup_first_message_after_key]: forward function *) -let rec betree_node_lookup_first_message_after_key_fwd - (key : u64) (msgs : betree_list_t (u64 & betree_message_t)) : - Tot (result (betree_list_t (u64 & betree_message_t))) - (decreases (betree_node_lookup_first_message_after_key_decreases key msgs)) +let rec betree_Node_lookup_first_message_after_key + (key : u64) (msgs : betree_List_t (u64 & betree_Message_t)) : + Tot (result (betree_List_t (u64 & betree_Message_t))) + (decreases (betree_Node_lookup_first_message_after_key_decreases key msgs)) = begin match msgs with - | BetreeListCons p next_msgs -> + | Betree_List_Cons p next_msgs -> let (k, m) = p in if k = key - then betree_node_lookup_first_message_after_key_fwd key next_msgs - else Return (BetreeListCons (k, m) next_msgs) - | BetreeListNil -> Return BetreeListNil + then betree_Node_lookup_first_message_after_key key next_msgs + else Return (Betree_List_Cons (k, m) next_msgs) + | Betree_List_Nil -> Return Betree_List_Nil end (** [betree_main::betree::Node::{5}::lookup_first_message_after_key]: backward function 0 *) -let rec betree_node_lookup_first_message_after_key_back - (key : u64) (msgs : betree_list_t (u64 & betree_message_t)) - (ret : betree_list_t (u64 & betree_message_t)) : - Tot (result (betree_list_t (u64 & betree_message_t))) - (decreases (betree_node_lookup_first_message_after_key_decreases key msgs)) +let rec betree_Node_lookup_first_message_after_key_back + (key : u64) (msgs : betree_List_t (u64 & betree_Message_t)) + (ret : betree_List_t (u64 & betree_Message_t)) : + Tot (result (betree_List_t (u64 & betree_Message_t))) + (decreases (betree_Node_lookup_first_message_after_key_decreases key msgs)) = begin match msgs with - | BetreeListCons p next_msgs -> + | Betree_List_Cons p next_msgs -> let (k, m) = p in if k = key then let* next_msgs0 = - betree_node_lookup_first_message_after_key_back key next_msgs ret in - Return (BetreeListCons (k, m) next_msgs0) + betree_Node_lookup_first_message_after_key_back key next_msgs ret in + Return (Betree_List_Cons (k, m) next_msgs0) else Return ret - | BetreeListNil -> Return ret + | Betree_List_Nil -> Return ret end (** [betree_main::betree::Node::{5}::apply_to_internal]: merged forward/backward function (there is a single backward function, and the forward function returns ()) *) -let betree_node_apply_to_internal_fwd_back - (msgs : betree_list_t (u64 & betree_message_t)) (key : u64) - (new_msg : betree_message_t) : - result (betree_list_t (u64 & betree_message_t)) +let betree_Node_apply_to_internal + (msgs : betree_List_t (u64 & betree_Message_t)) (key : u64) + (new_msg : betree_Message_t) : + result (betree_List_t (u64 & betree_Message_t)) = - let* msgs0 = betree_node_lookup_first_message_for_key_fwd key msgs in - let* b = betree_list_head_has_key_fwd betree_message_t msgs0 key in + let* msgs0 = betree_Node_lookup_first_message_for_key key msgs in + let* b = betree_List_head_has_key betree_Message_t msgs0 key in if b then begin match new_msg with - | BetreeMessageInsert i -> - let* msgs1 = betree_node_filter_messages_for_key_fwd_back key msgs0 in + | Betree_Message_Insert i -> + let* msgs1 = betree_Node_filter_messages_for_key key msgs0 in let* msgs2 = - betree_list_push_front_fwd_back (u64 & betree_message_t) msgs1 (key, - BetreeMessageInsert i) in - betree_node_lookup_first_message_for_key_back key msgs msgs2 - | BetreeMessageDelete -> - let* msgs1 = betree_node_filter_messages_for_key_fwd_back key msgs0 in + betree_List_push_front (u64 & betree_Message_t) msgs1 (key, + Betree_Message_Insert i) in + betree_Node_lookup_first_message_for_key_back key msgs msgs2 + | Betree_Message_Delete -> + let* msgs1 = betree_Node_filter_messages_for_key key msgs0 in let* msgs2 = - betree_list_push_front_fwd_back (u64 & betree_message_t) msgs1 (key, - BetreeMessageDelete) in - betree_node_lookup_first_message_for_key_back key msgs msgs2 - | BetreeMessageUpsert s -> - let* p = betree_list_hd_fwd (u64 & betree_message_t) msgs0 in + betree_List_push_front (u64 & betree_Message_t) msgs1 (key, + Betree_Message_Delete) in + betree_Node_lookup_first_message_for_key_back key msgs msgs2 + | Betree_Message_Upsert s -> + let* p = betree_List_hd (u64 & betree_Message_t) msgs0 in let (_, m) = p in begin match m with - | BetreeMessageInsert prev -> - let* v = betree_upsert_update_fwd (Some prev) s in - let* msgs1 = betree_list_pop_front_back (u64 & betree_message_t) msgs0 + | Betree_Message_Insert prev -> + let* v = betree_upsert_update (Some prev) s in + let* msgs1 = betree_List_pop_front_back (u64 & betree_Message_t) msgs0 in let* msgs2 = - betree_list_push_front_fwd_back (u64 & betree_message_t) msgs1 (key, - BetreeMessageInsert v) in - betree_node_lookup_first_message_for_key_back key msgs msgs2 - | BetreeMessageDelete -> - let* v = betree_upsert_update_fwd None s in - let* msgs1 = betree_list_pop_front_back (u64 & betree_message_t) msgs0 + betree_List_push_front (u64 & betree_Message_t) msgs1 (key, + Betree_Message_Insert v) in + betree_Node_lookup_first_message_for_key_back key msgs msgs2 + | Betree_Message_Delete -> + let* v = betree_upsert_update None s in + let* msgs1 = betree_List_pop_front_back (u64 & betree_Message_t) msgs0 in let* msgs2 = - betree_list_push_front_fwd_back (u64 & betree_message_t) msgs1 (key, - BetreeMessageInsert v) in - betree_node_lookup_first_message_for_key_back key msgs msgs2 - | BetreeMessageUpsert ufs -> - let* msgs1 = betree_node_lookup_first_message_after_key_fwd key msgs0 - in + betree_List_push_front (u64 & betree_Message_t) msgs1 (key, + Betree_Message_Insert v) in + betree_Node_lookup_first_message_for_key_back key msgs msgs2 + | Betree_Message_Upsert ufs -> + let* msgs1 = betree_Node_lookup_first_message_after_key key msgs0 in let* msgs2 = - betree_list_push_front_fwd_back (u64 & betree_message_t) msgs1 (key, - BetreeMessageUpsert s) in + betree_List_push_front (u64 & betree_Message_t) msgs1 (key, + Betree_Message_Upsert s) in let* msgs3 = - betree_node_lookup_first_message_after_key_back key msgs0 msgs2 in - betree_node_lookup_first_message_for_key_back key msgs msgs3 + betree_Node_lookup_first_message_after_key_back key msgs0 msgs2 in + betree_Node_lookup_first_message_for_key_back key msgs msgs3 end end else let* msgs1 = - betree_list_push_front_fwd_back (u64 & betree_message_t) msgs0 (key, - new_msg) in - betree_node_lookup_first_message_for_key_back key msgs msgs1 + betree_List_push_front (u64 & betree_Message_t) msgs0 (key, new_msg) in + betree_Node_lookup_first_message_for_key_back key msgs msgs1 (** [betree_main::betree::Node::{5}::apply_messages_to_internal]: merged forward/backward function (there is a single backward function, and the forward function returns ()) *) -let rec betree_node_apply_messages_to_internal_fwd_back - (msgs : betree_list_t (u64 & betree_message_t)) - (new_msgs : betree_list_t (u64 & betree_message_t)) : - Tot (result (betree_list_t (u64 & betree_message_t))) - (decreases (betree_node_apply_messages_to_internal_decreases msgs new_msgs)) +let rec betree_Node_apply_messages_to_internal + (msgs : betree_List_t (u64 & betree_Message_t)) + (new_msgs : betree_List_t (u64 & betree_Message_t)) : + Tot (result (betree_List_t (u64 & betree_Message_t))) + (decreases (betree_Node_apply_messages_to_internal_decreases msgs new_msgs)) = begin match new_msgs with - | BetreeListCons new_msg new_msgs_tl -> + | Betree_List_Cons new_msg new_msgs_tl -> let (i, m) = new_msg in - let* msgs0 = betree_node_apply_to_internal_fwd_back msgs i m in - betree_node_apply_messages_to_internal_fwd_back msgs0 new_msgs_tl - | BetreeListNil -> Return msgs + let* msgs0 = betree_Node_apply_to_internal msgs i m in + betree_Node_apply_messages_to_internal msgs0 new_msgs_tl + | Betree_List_Nil -> Return msgs end (** [betree_main::betree::Node::{5}::lookup_mut_in_bindings]: forward function *) -let rec betree_node_lookup_mut_in_bindings_fwd - (key : u64) (bindings : betree_list_t (u64 & u64)) : - Tot (result (betree_list_t (u64 & u64))) - (decreases (betree_node_lookup_mut_in_bindings_decreases key bindings)) +let rec betree_Node_lookup_mut_in_bindings + (key : u64) (bindings : betree_List_t (u64 & u64)) : + Tot (result (betree_List_t (u64 & u64))) + (decreases (betree_Node_lookup_mut_in_bindings_decreases key bindings)) = begin match bindings with - | BetreeListCons hd tl -> + | Betree_List_Cons hd tl -> let (i, i0) = hd in if i >= key - then Return (BetreeListCons (i, i0) tl) - else betree_node_lookup_mut_in_bindings_fwd key tl - | BetreeListNil -> Return BetreeListNil + then Return (Betree_List_Cons (i, i0) tl) + else betree_Node_lookup_mut_in_bindings key tl + | Betree_List_Nil -> Return Betree_List_Nil end (** [betree_main::betree::Node::{5}::lookup_mut_in_bindings]: backward function 0 *) -let rec betree_node_lookup_mut_in_bindings_back - (key : u64) (bindings : betree_list_t (u64 & u64)) - (ret : betree_list_t (u64 & u64)) : - Tot (result (betree_list_t (u64 & u64))) - (decreases (betree_node_lookup_mut_in_bindings_decreases key bindings)) +let rec betree_Node_lookup_mut_in_bindings_back + (key : u64) (bindings : betree_List_t (u64 & u64)) + (ret : betree_List_t (u64 & u64)) : + Tot (result (betree_List_t (u64 & u64))) + (decreases (betree_Node_lookup_mut_in_bindings_decreases key bindings)) = begin match bindings with - | BetreeListCons hd tl -> + | Betree_List_Cons hd tl -> let (i, i0) = hd in if i >= key then Return ret else - let* tl0 = betree_node_lookup_mut_in_bindings_back key tl ret in - Return (BetreeListCons (i, i0) tl0) - | BetreeListNil -> Return ret + let* tl0 = betree_Node_lookup_mut_in_bindings_back key tl ret in + Return (Betree_List_Cons (i, i0) tl0) + | Betree_List_Nil -> Return ret end (** [betree_main::betree::Node::{5}::apply_to_leaf]: merged forward/backward function (there is a single backward function, and the forward function returns ()) *) -let betree_node_apply_to_leaf_fwd_back - (bindings : betree_list_t (u64 & u64)) (key : u64) - (new_msg : betree_message_t) : - result (betree_list_t (u64 & u64)) +let betree_Node_apply_to_leaf + (bindings : betree_List_t (u64 & u64)) (key : u64) + (new_msg : betree_Message_t) : + result (betree_List_t (u64 & u64)) = - let* bindings0 = betree_node_lookup_mut_in_bindings_fwd key bindings in - let* b = betree_list_head_has_key_fwd u64 bindings0 key in + let* bindings0 = betree_Node_lookup_mut_in_bindings key bindings in + let* b = betree_List_head_has_key u64 bindings0 key in if b then - let* hd = betree_list_pop_front_fwd (u64 & u64) bindings0 in + let* hd = betree_List_pop_front (u64 & u64) bindings0 in begin match new_msg with - | BetreeMessageInsert v -> - let* bindings1 = betree_list_pop_front_back (u64 & u64) bindings0 in - let* bindings2 = - betree_list_push_front_fwd_back (u64 & u64) bindings1 (key, v) in - betree_node_lookup_mut_in_bindings_back key bindings bindings2 - | BetreeMessageDelete -> - let* bindings1 = betree_list_pop_front_back (u64 & u64) bindings0 in - betree_node_lookup_mut_in_bindings_back key bindings bindings1 - | BetreeMessageUpsert s -> + | Betree_Message_Insert v -> + let* bindings1 = betree_List_pop_front_back (u64 & u64) bindings0 in + let* bindings2 = betree_List_push_front (u64 & u64) bindings1 (key, v) in + betree_Node_lookup_mut_in_bindings_back key bindings bindings2 + | Betree_Message_Delete -> + let* bindings1 = betree_List_pop_front_back (u64 & u64) bindings0 in + betree_Node_lookup_mut_in_bindings_back key bindings bindings1 + | Betree_Message_Upsert s -> let (_, i) = hd in - let* v = betree_upsert_update_fwd (Some i) s in - let* bindings1 = betree_list_pop_front_back (u64 & u64) bindings0 in - let* bindings2 = - betree_list_push_front_fwd_back (u64 & u64) bindings1 (key, v) in - betree_node_lookup_mut_in_bindings_back key bindings bindings2 + let* v = betree_upsert_update (Some i) s in + let* bindings1 = betree_List_pop_front_back (u64 & u64) bindings0 in + let* bindings2 = betree_List_push_front (u64 & u64) bindings1 (key, v) in + betree_Node_lookup_mut_in_bindings_back key bindings bindings2 end else begin match new_msg with - | BetreeMessageInsert v -> - let* bindings1 = - betree_list_push_front_fwd_back (u64 & u64) bindings0 (key, v) in - betree_node_lookup_mut_in_bindings_back key bindings bindings1 - | BetreeMessageDelete -> - betree_node_lookup_mut_in_bindings_back key bindings bindings0 - | BetreeMessageUpsert s -> - let* v = betree_upsert_update_fwd None s in - let* bindings1 = - betree_list_push_front_fwd_back (u64 & u64) bindings0 (key, v) in - betree_node_lookup_mut_in_bindings_back key bindings bindings1 + | Betree_Message_Insert v -> + let* bindings1 = betree_List_push_front (u64 & u64) bindings0 (key, v) in + betree_Node_lookup_mut_in_bindings_back key bindings bindings1 + | Betree_Message_Delete -> + betree_Node_lookup_mut_in_bindings_back key bindings bindings0 + | Betree_Message_Upsert s -> + let* v = betree_upsert_update None s in + let* bindings1 = betree_List_push_front (u64 & u64) bindings0 (key, v) in + betree_Node_lookup_mut_in_bindings_back key bindings bindings1 end (** [betree_main::betree::Node::{5}::apply_messages_to_leaf]: merged forward/backward function (there is a single backward function, and the forward function returns ()) *) -let rec betree_node_apply_messages_to_leaf_fwd_back - (bindings : betree_list_t (u64 & u64)) - (new_msgs : betree_list_t (u64 & betree_message_t)) : - Tot (result (betree_list_t (u64 & u64))) - (decreases (betree_node_apply_messages_to_leaf_decreases bindings new_msgs)) +let rec betree_Node_apply_messages_to_leaf + (bindings : betree_List_t (u64 & u64)) + (new_msgs : betree_List_t (u64 & betree_Message_t)) : + Tot (result (betree_List_t (u64 & u64))) + (decreases (betree_Node_apply_messages_to_leaf_decreases bindings new_msgs)) = begin match new_msgs with - | BetreeListCons new_msg new_msgs_tl -> + | Betree_List_Cons new_msg new_msgs_tl -> let (i, m) = new_msg in - let* bindings0 = betree_node_apply_to_leaf_fwd_back bindings i m in - betree_node_apply_messages_to_leaf_fwd_back bindings0 new_msgs_tl - | BetreeListNil -> Return bindings + let* bindings0 = betree_Node_apply_to_leaf bindings i m in + betree_Node_apply_messages_to_leaf bindings0 new_msgs_tl + | Betree_List_Nil -> Return bindings end (** [betree_main::betree::Internal::{4}::flush]: forward function *) -let rec betree_internal_flush_fwd - (self : betree_internal_t) (params : betree_params_t) - (node_id_cnt : betree_node_id_counter_t) - (content : betree_list_t (u64 & betree_message_t)) (st : state) : - Tot (result (state & (betree_list_t (u64 & betree_message_t)))) +let rec betree_Internal_flush + (self : betree_Internal_t) (params : betree_Params_t) + (node_id_cnt : betree_NodeIdCounter_t) + (content : betree_List_t (u64 & betree_Message_t)) (st : state) : + Tot (result (state & (betree_List_t (u64 & betree_Message_t)))) (decreases ( - betree_internal_flush_decreases self params node_id_cnt content st)) + betree_Internal_flush_decreases self params node_id_cnt content st)) = - let* p = - betree_list_partition_at_pivot_fwd betree_message_t content - self.betree_internal_pivot in + let* p = betree_List_partition_at_pivot betree_Message_t content self.pivot + in let (msgs_left, msgs_right) = p in - let* len_left = betree_list_len_fwd (u64 & betree_message_t) msgs_left in - if len_left >= params.betree_params_min_flush_size + let* len_left = betree_List_len (u64 & betree_Message_t) msgs_left in + if len_left >= params.min_flush_size then let* (st0, _) = - betree_node_apply_messages_fwd self.betree_internal_left params - node_id_cnt msgs_left st in + betree_Node_apply_messages self.left params node_id_cnt msgs_left st in let* (_, node_id_cnt0) = - betree_node_apply_messages_back self.betree_internal_left params - node_id_cnt msgs_left st in - let* len_right = betree_list_len_fwd (u64 & betree_message_t) msgs_right in - if len_right >= params.betree_params_min_flush_size + betree_Node_apply_messages_back self.left params node_id_cnt msgs_left st + in + let* len_right = betree_List_len (u64 & betree_Message_t) msgs_right in + if len_right >= params.min_flush_size then let* (st1, _) = - betree_node_apply_messages_fwd self.betree_internal_right params - node_id_cnt0 msgs_right st0 in + betree_Node_apply_messages self.right params node_id_cnt0 msgs_right + st0 in let* _ = - betree_node_apply_messages_back self.betree_internal_right params - node_id_cnt0 msgs_right st0 in - Return (st1, BetreeListNil) + betree_Node_apply_messages_back self.right params node_id_cnt0 + msgs_right st0 in + Return (st1, Betree_List_Nil) else Return (st0, msgs_right) else let* (st0, _) = - betree_node_apply_messages_fwd self.betree_internal_right params - node_id_cnt msgs_right st in + betree_Node_apply_messages self.right params node_id_cnt msgs_right st in let* _ = - betree_node_apply_messages_back self.betree_internal_right params - node_id_cnt msgs_right st in + betree_Node_apply_messages_back self.right params node_id_cnt msgs_right + st in Return (st0, msgs_left) (** [betree_main::betree::Internal::{4}::flush]: backward function 0 *) -and betree_internal_flush_back - (self : betree_internal_t) (params : betree_params_t) - (node_id_cnt : betree_node_id_counter_t) - (content : betree_list_t (u64 & betree_message_t)) (st : state) : - Tot (result (betree_internal_t & betree_node_id_counter_t)) +and betree_Internal_flush_back + (self : betree_Internal_t) (params : betree_Params_t) + (node_id_cnt : betree_NodeIdCounter_t) + (content : betree_List_t (u64 & betree_Message_t)) (st : state) : + Tot (result (betree_Internal_t & betree_NodeIdCounter_t)) (decreases ( - betree_internal_flush_decreases self params node_id_cnt content st)) + betree_Internal_flush_decreases self params node_id_cnt content st)) = - let* p = - betree_list_partition_at_pivot_fwd betree_message_t content - self.betree_internal_pivot in + let* p = betree_List_partition_at_pivot betree_Message_t content self.pivot + in let (msgs_left, msgs_right) = p in - let* len_left = betree_list_len_fwd (u64 & betree_message_t) msgs_left in - if len_left >= params.betree_params_min_flush_size + let* len_left = betree_List_len (u64 & betree_Message_t) msgs_left in + if len_left >= params.min_flush_size then let* (st0, _) = - betree_node_apply_messages_fwd self.betree_internal_left params - node_id_cnt msgs_left st in + betree_Node_apply_messages self.left params node_id_cnt msgs_left st in let* (n, node_id_cnt0) = - betree_node_apply_messages_back self.betree_internal_left params - node_id_cnt msgs_left st in - let* len_right = betree_list_len_fwd (u64 & betree_message_t) msgs_right in - if len_right >= params.betree_params_min_flush_size + betree_Node_apply_messages_back self.left params node_id_cnt msgs_left st + in + let* len_right = betree_List_len (u64 & betree_Message_t) msgs_right in + if len_right >= params.min_flush_size then let* (n0, node_id_cnt1) = - betree_node_apply_messages_back self.betree_internal_right params - node_id_cnt0 msgs_right st0 in - Return - ({ self with betree_internal_left = n; betree_internal_right = n0 }, - node_id_cnt1) - else Return ({ self with betree_internal_left = n }, node_id_cnt0) + betree_Node_apply_messages_back self.right params node_id_cnt0 + msgs_right st0 in + Return ({ self with left = n; right = n0 }, node_id_cnt1) + else Return ({ self with left = n }, node_id_cnt0) else let* (n, node_id_cnt0) = - betree_node_apply_messages_back self.betree_internal_right params - node_id_cnt msgs_right st in - Return ({ self with betree_internal_right = n }, node_id_cnt0) + betree_Node_apply_messages_back self.right params node_id_cnt msgs_right + st in + Return ({ self with right = n }, node_id_cnt0) (** [betree_main::betree::Node::{5}::apply_messages]: forward function *) -and betree_node_apply_messages_fwd - (self : betree_node_t) (params : betree_params_t) - (node_id_cnt : betree_node_id_counter_t) - (msgs : betree_list_t (u64 & betree_message_t)) (st : state) : +and betree_Node_apply_messages + (self : betree_Node_t) (params : betree_Params_t) + (node_id_cnt : betree_NodeIdCounter_t) + (msgs : betree_List_t (u64 & betree_Message_t)) (st : state) : Tot (result (state & unit)) (decreases ( - betree_node_apply_messages_decreases self params node_id_cnt msgs st)) + betree_Node_apply_messages_decreases self params node_id_cnt msgs st)) = begin match self with - | BetreeNodeInternal node -> - let* (st0, content) = - betree_load_internal_node_fwd node.betree_internal_id st in - let* content0 = - betree_node_apply_messages_to_internal_fwd_back content msgs in - let* num_msgs = betree_list_len_fwd (u64 & betree_message_t) content0 in - if num_msgs >= params.betree_params_min_flush_size + | Betree_Node_Internal node -> + let* (st0, content) = betree_load_internal_node node.id st in + let* content0 = betree_Node_apply_messages_to_internal content msgs in + let* num_msgs = betree_List_len (u64 & betree_Message_t) content0 in + if num_msgs >= params.min_flush_size then let* (st1, content1) = - betree_internal_flush_fwd node params node_id_cnt content0 st0 in + betree_Internal_flush node params node_id_cnt content0 st0 in let* (node0, _) = - betree_internal_flush_back node params node_id_cnt content0 st0 in - let* (st2, _) = - betree_store_internal_node_fwd node0.betree_internal_id content1 st1 in + betree_Internal_flush_back node params node_id_cnt content0 st0 in + let* (st2, _) = betree_store_internal_node node0.id content1 st1 in Return (st2, ()) else - let* (st1, _) = - betree_store_internal_node_fwd node.betree_internal_id content0 st0 in + let* (st1, _) = betree_store_internal_node node.id content0 st0 in Return (st1, ()) - | BetreeNodeLeaf node -> - let* (st0, content) = betree_load_leaf_node_fwd node.betree_leaf_id st in - let* content0 = betree_node_apply_messages_to_leaf_fwd_back content msgs in - let* len = betree_list_len_fwd (u64 & u64) content0 in - let* i = u64_mul 2 params.betree_params_split_size in + | Betree_Node_Leaf node -> + let* (st0, content) = betree_load_leaf_node node.id st in + let* content0 = betree_Node_apply_messages_to_leaf content msgs in + let* len = betree_List_len (u64 & u64) content0 in + let* i = u64_mul 2 params.split_size in if len >= i then - let* (st1, _) = - betree_leaf_split_fwd node content0 params node_id_cnt st0 in - let* (st2, _) = - betree_store_leaf_node_fwd node.betree_leaf_id BetreeListNil st1 in + let* (st1, _) = betree_Leaf_split node content0 params node_id_cnt st0 in + let* (st2, _) = betree_store_leaf_node node.id Betree_List_Nil st1 in Return (st2, ()) else - let* (st1, _) = - betree_store_leaf_node_fwd node.betree_leaf_id content0 st0 in + let* (st1, _) = betree_store_leaf_node node.id content0 st0 in Return (st1, ()) end (** [betree_main::betree::Node::{5}::apply_messages]: backward function 0 *) -and betree_node_apply_messages_back - (self : betree_node_t) (params : betree_params_t) - (node_id_cnt : betree_node_id_counter_t) - (msgs : betree_list_t (u64 & betree_message_t)) (st : state) : - Tot (result (betree_node_t & betree_node_id_counter_t)) +and betree_Node_apply_messages_back + (self : betree_Node_t) (params : betree_Params_t) + (node_id_cnt : betree_NodeIdCounter_t) + (msgs : betree_List_t (u64 & betree_Message_t)) (st : state) : + Tot (result (betree_Node_t & betree_NodeIdCounter_t)) (decreases ( - betree_node_apply_messages_decreases self params node_id_cnt msgs st)) + betree_Node_apply_messages_decreases self params node_id_cnt msgs st)) = begin match self with - | BetreeNodeInternal node -> - let* (st0, content) = - betree_load_internal_node_fwd node.betree_internal_id st in - let* content0 = - betree_node_apply_messages_to_internal_fwd_back content msgs in - let* num_msgs = betree_list_len_fwd (u64 & betree_message_t) content0 in - if num_msgs >= params.betree_params_min_flush_size + | Betree_Node_Internal node -> + let* (st0, content) = betree_load_internal_node node.id st in + let* content0 = betree_Node_apply_messages_to_internal content msgs in + let* num_msgs = betree_List_len (u64 & betree_Message_t) content0 in + if num_msgs >= params.min_flush_size then let* (st1, content1) = - betree_internal_flush_fwd node params node_id_cnt content0 st0 in + betree_Internal_flush node params node_id_cnt content0 st0 in let* (node0, node_id_cnt0) = - betree_internal_flush_back node params node_id_cnt content0 st0 in - let* _ = - betree_store_internal_node_fwd node0.betree_internal_id content1 st1 in - Return (BetreeNodeInternal node0, node_id_cnt0) + betree_Internal_flush_back node params node_id_cnt content0 st0 in + let* _ = betree_store_internal_node node0.id content1 st1 in + Return (Betree_Node_Internal node0, node_id_cnt0) else - let* _ = - betree_store_internal_node_fwd node.betree_internal_id content0 st0 in - Return (BetreeNodeInternal node, node_id_cnt) - | BetreeNodeLeaf node -> - let* (st0, content) = betree_load_leaf_node_fwd node.betree_leaf_id st in - let* content0 = betree_node_apply_messages_to_leaf_fwd_back content msgs in - let* len = betree_list_len_fwd (u64 & u64) content0 in - let* i = u64_mul 2 params.betree_params_split_size in + let* _ = betree_store_internal_node node.id content0 st0 in + Return (Betree_Node_Internal node, node_id_cnt) + | Betree_Node_Leaf node -> + let* (st0, content) = betree_load_leaf_node node.id st in + let* content0 = betree_Node_apply_messages_to_leaf content msgs in + let* len = betree_List_len (u64 & u64) content0 in + let* i = u64_mul 2 params.split_size in if len >= i then let* (st1, new_node) = - betree_leaf_split_fwd node content0 params node_id_cnt st0 in - let* _ = betree_store_leaf_node_fwd node.betree_leaf_id BetreeListNil st1 - in + betree_Leaf_split node content0 params node_id_cnt st0 in + let* _ = betree_store_leaf_node node.id Betree_List_Nil st1 in let* node_id_cnt0 = - betree_leaf_split_back node content0 params node_id_cnt st0 in - Return (BetreeNodeInternal new_node, node_id_cnt0) + betree_Leaf_split_back node content0 params node_id_cnt st0 in + Return (Betree_Node_Internal new_node, node_id_cnt0) else - let* _ = betree_store_leaf_node_fwd node.betree_leaf_id content0 st0 in - Return (BetreeNodeLeaf { node with betree_leaf_size = len }, node_id_cnt) + let* _ = betree_store_leaf_node node.id content0 st0 in + Return (Betree_Node_Leaf { node with size = len }, node_id_cnt) end (** [betree_main::betree::Node::{5}::apply]: forward function *) -let betree_node_apply_fwd - (self : betree_node_t) (params : betree_params_t) - (node_id_cnt : betree_node_id_counter_t) (key : u64) - (new_msg : betree_message_t) (st : state) : +let betree_Node_apply + (self : betree_Node_t) (params : betree_Params_t) + (node_id_cnt : betree_NodeIdCounter_t) (key : u64) + (new_msg : betree_Message_t) (st : state) : result (state & unit) = - let l = BetreeListNil in + let l = Betree_List_Nil in let* (st0, _) = - betree_node_apply_messages_fwd self params node_id_cnt (BetreeListCons - (key, new_msg) l) st in + betree_Node_apply_messages self params node_id_cnt (Betree_List_Cons (key, + new_msg) l) st in let* _ = - betree_node_apply_messages_back self params node_id_cnt (BetreeListCons + betree_Node_apply_messages_back self params node_id_cnt (Betree_List_Cons (key, new_msg) l) st in Return (st0, ()) (** [betree_main::betree::Node::{5}::apply]: backward function 0 *) -let betree_node_apply_back - (self : betree_node_t) (params : betree_params_t) - (node_id_cnt : betree_node_id_counter_t) (key : u64) - (new_msg : betree_message_t) (st : state) : - result (betree_node_t & betree_node_id_counter_t) +let betree_Node_apply_back + (self : betree_Node_t) (params : betree_Params_t) + (node_id_cnt : betree_NodeIdCounter_t) (key : u64) + (new_msg : betree_Message_t) (st : state) : + result (betree_Node_t & betree_NodeIdCounter_t) = - let l = BetreeListNil in - betree_node_apply_messages_back self params node_id_cnt (BetreeListCons (key, - new_msg) l) st + let l = Betree_List_Nil in + betree_Node_apply_messages_back self params node_id_cnt (Betree_List_Cons + (key, new_msg) l) st (** [betree_main::betree::BeTree::{6}::new]: forward function *) -let betree_be_tree_new_fwd +let betree_BeTree_new (min_flush_size : u64) (split_size : u64) (st : state) : - result (state & betree_be_tree_t) + result (state & betree_BeTree_t) = - let* node_id_cnt = betree_node_id_counter_new_fwd in - let* id = betree_node_id_counter_fresh_id_fwd node_id_cnt in - let* (st0, _) = betree_store_leaf_node_fwd id BetreeListNil st in - let* node_id_cnt0 = betree_node_id_counter_fresh_id_back node_id_cnt in + let* node_id_cnt = betree_NodeIdCounter_new in + let* id = betree_NodeIdCounter_fresh_id node_id_cnt in + let* (st0, _) = betree_store_leaf_node id Betree_List_Nil st in + let* node_id_cnt0 = betree_NodeIdCounter_fresh_id_back node_id_cnt in Return (st0, { - betree_be_tree_params = - { - betree_params_min_flush_size = min_flush_size; - betree_params_split_size = split_size - }; - betree_be_tree_node_id_cnt = node_id_cnt0; - betree_be_tree_root = - (BetreeNodeLeaf { betree_leaf_id = id; betree_leaf_size = 0 }) + params = { min_flush_size = min_flush_size; split_size = split_size }; + node_id_cnt = node_id_cnt0; + root = (Betree_Node_Leaf { id = id; size = 0 }) }) (** [betree_main::betree::BeTree::{6}::apply]: forward function *) -let betree_be_tree_apply_fwd - (self : betree_be_tree_t) (key : u64) (msg : betree_message_t) (st : state) : +let betree_BeTree_apply + (self : betree_BeTree_t) (key : u64) (msg : betree_Message_t) (st : state) : result (state & unit) = let* (st0, _) = - betree_node_apply_fwd self.betree_be_tree_root self.betree_be_tree_params - self.betree_be_tree_node_id_cnt key msg st in + betree_Node_apply self.root self.params self.node_id_cnt key msg st in let* _ = - betree_node_apply_back self.betree_be_tree_root self.betree_be_tree_params - self.betree_be_tree_node_id_cnt key msg st in + betree_Node_apply_back self.root self.params self.node_id_cnt key msg st in Return (st0, ()) (** [betree_main::betree::BeTree::{6}::apply]: backward function 0 *) -let betree_be_tree_apply_back - (self : betree_be_tree_t) (key : u64) (msg : betree_message_t) (st : state) : - result betree_be_tree_t +let betree_BeTree_apply_back + (self : betree_BeTree_t) (key : u64) (msg : betree_Message_t) (st : state) : + result betree_BeTree_t = let* (n, nic) = - betree_node_apply_back self.betree_be_tree_root self.betree_be_tree_params - self.betree_be_tree_node_id_cnt key msg st in - Return - { self with betree_be_tree_node_id_cnt = nic; betree_be_tree_root = n } + betree_Node_apply_back self.root self.params self.node_id_cnt key msg st in + Return { self with node_id_cnt = nic; root = n } (** [betree_main::betree::BeTree::{6}::insert]: forward function *) -let betree_be_tree_insert_fwd - (self : betree_be_tree_t) (key : u64) (value : u64) (st : state) : +let betree_BeTree_insert + (self : betree_BeTree_t) (key : u64) (value : u64) (st : state) : result (state & unit) = - let* (st0, _) = - betree_be_tree_apply_fwd self key (BetreeMessageInsert value) st in - let* _ = betree_be_tree_apply_back self key (BetreeMessageInsert value) st in + let* (st0, _) = betree_BeTree_apply self key (Betree_Message_Insert value) st + in + let* _ = betree_BeTree_apply_back self key (Betree_Message_Insert value) st + in Return (st0, ()) (** [betree_main::betree::BeTree::{6}::insert]: backward function 0 *) -let betree_be_tree_insert_back - (self : betree_be_tree_t) (key : u64) (value : u64) (st : state) : - result betree_be_tree_t +let betree_BeTree_insert_back + (self : betree_BeTree_t) (key : u64) (value : u64) (st : state) : + result betree_BeTree_t = - betree_be_tree_apply_back self key (BetreeMessageInsert value) st + betree_BeTree_apply_back self key (Betree_Message_Insert value) st (** [betree_main::betree::BeTree::{6}::delete]: forward function *) -let betree_be_tree_delete_fwd - (self : betree_be_tree_t) (key : u64) (st : state) : result (state & unit) = - let* (st0, _) = betree_be_tree_apply_fwd self key BetreeMessageDelete st in - let* _ = betree_be_tree_apply_back self key BetreeMessageDelete st in +let betree_BeTree_delete + (self : betree_BeTree_t) (key : u64) (st : state) : result (state & unit) = + let* (st0, _) = betree_BeTree_apply self key Betree_Message_Delete st in + let* _ = betree_BeTree_apply_back self key Betree_Message_Delete st in Return (st0, ()) (** [betree_main::betree::BeTree::{6}::delete]: backward function 0 *) -let betree_be_tree_delete_back - (self : betree_be_tree_t) (key : u64) (st : state) : - result betree_be_tree_t - = - betree_be_tree_apply_back self key BetreeMessageDelete st +let betree_BeTree_delete_back + (self : betree_BeTree_t) (key : u64) (st : state) : result betree_BeTree_t = + betree_BeTree_apply_back self key Betree_Message_Delete st (** [betree_main::betree::BeTree::{6}::upsert]: forward function *) -let betree_be_tree_upsert_fwd - (self : betree_be_tree_t) (key : u64) (upd : betree_upsert_fun_state_t) +let betree_BeTree_upsert + (self : betree_BeTree_t) (key : u64) (upd : betree_UpsertFunState_t) (st : state) : result (state & unit) = - let* (st0, _) = - betree_be_tree_apply_fwd self key (BetreeMessageUpsert upd) st in - let* _ = betree_be_tree_apply_back self key (BetreeMessageUpsert upd) st in + let* (st0, _) = betree_BeTree_apply self key (Betree_Message_Upsert upd) st + in + let* _ = betree_BeTree_apply_back self key (Betree_Message_Upsert upd) st in Return (st0, ()) (** [betree_main::betree::BeTree::{6}::upsert]: backward function 0 *) -let betree_be_tree_upsert_back - (self : betree_be_tree_t) (key : u64) (upd : betree_upsert_fun_state_t) +let betree_BeTree_upsert_back + (self : betree_BeTree_t) (key : u64) (upd : betree_UpsertFunState_t) (st : state) : - result betree_be_tree_t + result betree_BeTree_t = - betree_be_tree_apply_back self key (BetreeMessageUpsert upd) st + betree_BeTree_apply_back self key (Betree_Message_Upsert upd) st (** [betree_main::betree::BeTree::{6}::lookup]: forward function *) -let betree_be_tree_lookup_fwd - (self : betree_be_tree_t) (key : u64) (st : state) : +let betree_BeTree_lookup + (self : betree_BeTree_t) (key : u64) (st : state) : result (state & (option u64)) = - betree_node_lookup_fwd self.betree_be_tree_root key st + betree_Node_lookup self.root key st (** [betree_main::betree::BeTree::{6}::lookup]: backward function 0 *) -let betree_be_tree_lookup_back - (self : betree_be_tree_t) (key : u64) (st : state) : - result betree_be_tree_t - = - let* n = betree_node_lookup_back self.betree_be_tree_root key st in - Return { self with betree_be_tree_root = n } +let betree_BeTree_lookup_back + (self : betree_BeTree_t) (key : u64) (st : state) : result betree_BeTree_t = + let* n = betree_Node_lookup_back self.root key st in + Return { self with root = n } (** [betree_main::main]: forward function *) -let main_fwd : result unit = +let main : result unit = Return () (** Unit test for [betree_main::main] *) -let _ = assert_norm (main_fwd = Return ()) +let _ = assert_norm (main = Return ()) diff --git a/tests/fstar/betree/BetreeMain.Opaque.fsti b/tests/fstar/betree/BetreeMain.Opaque.fsti index c33cf225..c5d0a814 100644 --- a/tests/fstar/betree/BetreeMain.Opaque.fsti +++ b/tests/fstar/betree/BetreeMain.Opaque.fsti @@ -7,24 +7,24 @@ include BetreeMain.Types #set-options "--z3rlimit 50 --fuel 1 --ifuel 1" (** [betree_main::betree_utils::load_internal_node]: forward function *) -val betree_utils_load_internal_node_fwd - : u64 -> state -> result (state & (betree_list_t (u64 & betree_message_t))) +val betree_utils_load_internal_node + : u64 -> state -> result (state & (betree_List_t (u64 & betree_Message_t))) (** [betree_main::betree_utils::store_internal_node]: forward function *) -val betree_utils_store_internal_node_fwd +val betree_utils_store_internal_node : - u64 -> betree_list_t (u64 & betree_message_t) -> state -> result (state & + u64 -> betree_List_t (u64 & betree_Message_t) -> state -> result (state & unit) (** [betree_main::betree_utils::load_leaf_node]: forward function *) -val betree_utils_load_leaf_node_fwd - : u64 -> state -> result (state & (betree_list_t (u64 & u64))) +val betree_utils_load_leaf_node + : u64 -> state -> result (state & (betree_List_t (u64 & u64))) (** [betree_main::betree_utils::store_leaf_node]: forward function *) -val betree_utils_store_leaf_node_fwd - : u64 -> betree_list_t (u64 & u64) -> state -> result (state & unit) +val betree_utils_store_leaf_node + : u64 -> betree_List_t (u64 & u64) -> state -> result (state & unit) (** [core::option::Option::{0}::unwrap]: forward function *) -val core_option_option_unwrap_fwd +val core_option_Option_unwrap (t : Type0) : option t -> state -> result (state & t) diff --git a/tests/fstar/betree/BetreeMain.Types.fsti b/tests/fstar/betree/BetreeMain.Types.fsti index a937c726..9320f6b7 100644 --- a/tests/fstar/betree/BetreeMain.Types.fsti +++ b/tests/fstar/betree/BetreeMain.Types.fsti @@ -6,53 +6,47 @@ open Primitives #set-options "--z3rlimit 50 --fuel 1 --ifuel 1" (** [betree_main::betree::List] *) -type betree_list_t (t : Type0) = -| BetreeListCons : t -> betree_list_t t -> betree_list_t t -| BetreeListNil : betree_list_t t +type betree_List_t (t : Type0) = +| Betree_List_Cons : t -> betree_List_t t -> betree_List_t t +| Betree_List_Nil : betree_List_t t (** [betree_main::betree::UpsertFunState] *) -type betree_upsert_fun_state_t = -| BetreeUpsertFunStateAdd : u64 -> betree_upsert_fun_state_t -| BetreeUpsertFunStateSub : u64 -> betree_upsert_fun_state_t +type betree_UpsertFunState_t = +| Betree_UpsertFunState_Add : u64 -> betree_UpsertFunState_t +| Betree_UpsertFunState_Sub : u64 -> betree_UpsertFunState_t (** [betree_main::betree::Message] *) -type betree_message_t = -| BetreeMessageInsert : u64 -> betree_message_t -| BetreeMessageDelete : betree_message_t -| BetreeMessageUpsert : betree_upsert_fun_state_t -> betree_message_t +type betree_Message_t = +| Betree_Message_Insert : u64 -> betree_Message_t +| Betree_Message_Delete : betree_Message_t +| Betree_Message_Upsert : betree_UpsertFunState_t -> betree_Message_t (** [betree_main::betree::Leaf] *) -type betree_leaf_t = { betree_leaf_id : u64; betree_leaf_size : u64; } +type betree_Leaf_t = { id : u64; size : u64; } (** [betree_main::betree::Internal] *) -type betree_internal_t = +type betree_Internal_t = { - betree_internal_id : u64; - betree_internal_pivot : u64; - betree_internal_left : betree_node_t; - betree_internal_right : betree_node_t; + id : u64; pivot : u64; left : betree_Node_t; right : betree_Node_t; } (** [betree_main::betree::Node] *) -and betree_node_t = -| BetreeNodeInternal : betree_internal_t -> betree_node_t -| BetreeNodeLeaf : betree_leaf_t -> betree_node_t +and betree_Node_t = +| Betree_Node_Internal : betree_Internal_t -> betree_Node_t +| Betree_Node_Leaf : betree_Leaf_t -> betree_Node_t (** [betree_main::betree::Params] *) -type betree_params_t = -{ - betree_params_min_flush_size : u64; betree_params_split_size : u64; -} +type betree_Params_t = { min_flush_size : u64; split_size : u64; } (** [betree_main::betree::NodeIdCounter] *) -type betree_node_id_counter_t = { betree_node_id_counter_next_node_id : u64; } +type betree_NodeIdCounter_t = { next_node_id : u64; } (** [betree_main::betree::BeTree] *) -type betree_be_tree_t = +type betree_BeTree_t = { - betree_be_tree_params : betree_params_t; - betree_be_tree_node_id_cnt : betree_node_id_counter_t; - betree_be_tree_root : betree_node_t; + params : betree_Params_t; + node_id_cnt : betree_NodeIdCounter_t; + root : betree_Node_t; } (** The state type used in the state-error monad *) diff --git a/tests/fstar/betree/Primitives.fst b/tests/fstar/betree/Primitives.fst index 3110b247..71d75c11 100644 --- a/tests/fstar/betree/Primitives.fst +++ b/tests/fstar/betree/Primitives.fst @@ -707,5 +707,7 @@ let alloc_vec_Vec_coreopsindexIndexMutInst (t idx : Type0) let alloc_vec_Vec_index_mut_back_eq (#a : Type0) (v : alloc_vec_Vec a) (i : usize) (x : a) : Lemma ( alloc_vec_Vec_index_mut_back a usize (core_slice_index_usize_coresliceindexSliceIndexInst a) v i x == - alloc_vec_Vec_update_usize v i x) = + alloc_vec_Vec_update_usize v i x) + [SMTPat (alloc_vec_Vec_index_mut_back a usize (core_slice_index_usize_coresliceindexSliceIndexInst a) v i x)] + = admit() diff --git a/tests/fstar/betree_back_stateful/BetreeMain.Clauses.Template.fst b/tests/fstar/betree_back_stateful/BetreeMain.Clauses.Template.fst index 823df03a..8722f0bf 100644 --- a/tests/fstar/betree_back_stateful/BetreeMain.Clauses.Template.fst +++ b/tests/fstar/betree_back_stateful/BetreeMain.Clauses.Template.fst @@ -8,95 +8,95 @@ open BetreeMain.Types (** [betree_main::betree::List::{1}::len]: decreases clause *) unfold -let betree_list_len_decreases (t : Type0) (self : betree_list_t t) : nat = +let betree_List_len_decreases (t : Type0) (self : betree_List_t t) : nat = admit () (** [betree_main::betree::List::{1}::split_at]: decreases clause *) unfold -let betree_list_split_at_decreases (t : Type0) (self : betree_list_t t) +let betree_List_split_at_decreases (t : Type0) (self : betree_List_t t) (n : u64) : nat = admit () (** [betree_main::betree::List::{2}::partition_at_pivot]: decreases clause *) unfold -let betree_list_partition_at_pivot_decreases (t : Type0) - (self : betree_list_t (u64 & t)) (pivot : u64) : nat = +let betree_List_partition_at_pivot_decreases (t : Type0) + (self : betree_List_t (u64 & t)) (pivot : u64) : nat = admit () (** [betree_main::betree::Node::{5}::lookup_first_message_for_key]: decreases clause *) unfold -let betree_node_lookup_first_message_for_key_decreases (key : u64) - (msgs : betree_list_t (u64 & betree_message_t)) : nat = +let betree_Node_lookup_first_message_for_key_decreases (key : u64) + (msgs : betree_List_t (u64 & betree_Message_t)) : nat = admit () (** [betree_main::betree::Node::{5}::apply_upserts]: decreases clause *) unfold -let betree_node_apply_upserts_decreases - (msgs : betree_list_t (u64 & betree_message_t)) (prev : option u64) +let betree_Node_apply_upserts_decreases + (msgs : betree_List_t (u64 & betree_Message_t)) (prev : option u64) (key : u64) (st : state) : nat = admit () (** [betree_main::betree::Node::{5}::lookup_in_bindings]: decreases clause *) unfold -let betree_node_lookup_in_bindings_decreases (key : u64) - (bindings : betree_list_t (u64 & u64)) : nat = +let betree_Node_lookup_in_bindings_decreases (key : u64) + (bindings : betree_List_t (u64 & u64)) : nat = admit () (** [betree_main::betree::Internal::{4}::lookup_in_children]: decreases clause *) unfold -let betree_internal_lookup_in_children_decreases (self : betree_internal_t) +let betree_Internal_lookup_in_children_decreases (self : betree_Internal_t) (key : u64) (st : state) : nat = admit () (** [betree_main::betree::Node::{5}::lookup]: decreases clause *) unfold -let betree_node_lookup_decreases (self : betree_node_t) (key : u64) +let betree_Node_lookup_decreases (self : betree_Node_t) (key : u64) (st : state) : nat = admit () (** [betree_main::betree::Node::{5}::filter_messages_for_key]: decreases clause *) unfold -let betree_node_filter_messages_for_key_decreases (key : u64) - (msgs : betree_list_t (u64 & betree_message_t)) : nat = +let betree_Node_filter_messages_for_key_decreases (key : u64) + (msgs : betree_List_t (u64 & betree_Message_t)) : nat = admit () (** [betree_main::betree::Node::{5}::lookup_first_message_after_key]: decreases clause *) unfold -let betree_node_lookup_first_message_after_key_decreases (key : u64) - (msgs : betree_list_t (u64 & betree_message_t)) : nat = +let betree_Node_lookup_first_message_after_key_decreases (key : u64) + (msgs : betree_List_t (u64 & betree_Message_t)) : nat = admit () (** [betree_main::betree::Node::{5}::apply_messages_to_internal]: decreases clause *) unfold -let betree_node_apply_messages_to_internal_decreases - (msgs : betree_list_t (u64 & betree_message_t)) - (new_msgs : betree_list_t (u64 & betree_message_t)) : nat = +let betree_Node_apply_messages_to_internal_decreases + (msgs : betree_List_t (u64 & betree_Message_t)) + (new_msgs : betree_List_t (u64 & betree_Message_t)) : nat = admit () (** [betree_main::betree::Node::{5}::lookup_mut_in_bindings]: decreases clause *) unfold -let betree_node_lookup_mut_in_bindings_decreases (key : u64) - (bindings : betree_list_t (u64 & u64)) : nat = +let betree_Node_lookup_mut_in_bindings_decreases (key : u64) + (bindings : betree_List_t (u64 & u64)) : nat = admit () (** [betree_main::betree::Node::{5}::apply_messages_to_leaf]: decreases clause *) unfold -let betree_node_apply_messages_to_leaf_decreases - (bindings : betree_list_t (u64 & u64)) - (new_msgs : betree_list_t (u64 & betree_message_t)) : nat = +let betree_Node_apply_messages_to_leaf_decreases + (bindings : betree_List_t (u64 & u64)) + (new_msgs : betree_List_t (u64 & betree_Message_t)) : nat = admit () (** [betree_main::betree::Internal::{4}::flush]: decreases clause *) unfold -let betree_internal_flush_decreases (self : betree_internal_t) - (params : betree_params_t) (node_id_cnt : betree_node_id_counter_t) - (content : betree_list_t (u64 & betree_message_t)) (st : state) : nat = +let betree_Internal_flush_decreases (self : betree_Internal_t) + (params : betree_Params_t) (node_id_cnt : betree_NodeIdCounter_t) + (content : betree_List_t (u64 & betree_Message_t)) (st : state) : nat = admit () (** [betree_main::betree::Node::{5}::apply_messages]: decreases clause *) unfold -let betree_node_apply_messages_decreases (self : betree_node_t) - (params : betree_params_t) (node_id_cnt : betree_node_id_counter_t) - (msgs : betree_list_t (u64 & betree_message_t)) (st : state) : nat = +let betree_Node_apply_messages_decreases (self : betree_Node_t) + (params : betree_Params_t) (node_id_cnt : betree_NodeIdCounter_t) + (msgs : betree_List_t (u64 & betree_Message_t)) (st : state) : nat = admit () diff --git a/tests/fstar/betree_back_stateful/BetreeMain.Clauses.fst b/tests/fstar/betree_back_stateful/BetreeMain.Clauses.fst index 07484711..cda7b920 100644 --- a/tests/fstar/betree_back_stateful/BetreeMain.Clauses.fst +++ b/tests/fstar/betree_back_stateful/BetreeMain.Clauses.fst @@ -8,8 +8,8 @@ open BetreeMain.Types (*** Well-founded relations *) (* We had a few issues when proving termination of the mutually recursive functions: - * - betree_internal_flush - * - betree_node_apply_messages + * - betree_Internal_flush + * - betree_Node_apply_messages * * The quantity which effectively decreases is: * (betree_size, messages_length) @@ -103,108 +103,108 @@ let wf_nat_pair_lem (p0 p1 : nat_pair) : (** [betree_main::betree::List::{1}::len]: decreases clause *) unfold -let betree_list_len_decreases (t : Type0) (self : betree_list_t t) : betree_list_t t = +let betree_List_len_decreases (t : Type0) (self : betree_List_t t) : betree_List_t t = self (** [betree_main::betree::List::{1}::split_at]: decreases clause *) unfold -let betree_list_split_at_decreases (t : Type0) (self : betree_list_t t) +let betree_List_split_at_decreases (t : Type0) (self : betree_List_t t) (n : u64) : nat = n (** [betree_main::betree::List::{2}::partition_at_pivot]: decreases clause *) unfold -let betree_list_partition_at_pivot_decreases (t : Type0) - (self : betree_list_t (u64 & t)) (pivot : u64) : betree_list_t (u64 & t) = +let betree_List_partition_at_pivot_decreases (t : Type0) + (self : betree_List_t (u64 & t)) (pivot : u64) : betree_List_t (u64 & t) = self (** [betree_main::betree::Node::{5}::lookup_in_bindings]: decreases clause *) unfold -let betree_node_lookup_in_bindings_decreases (key : u64) - (bindings : betree_list_t (u64 & u64)) : betree_list_t (u64 & u64) = +let betree_Node_lookup_in_bindings_decreases (key : u64) + (bindings : betree_List_t (u64 & u64)) : betree_List_t (u64 & u64) = bindings (** [betree_main::betree::Node::{5}::lookup_first_message_for_key]: decreases clause *) unfold -let betree_node_lookup_first_message_for_key_decreases (key : u64) - (msgs : betree_list_t (u64 & betree_message_t)) : betree_list_t (u64 & betree_message_t) = +let betree_Node_lookup_first_message_for_key_decreases (key : u64) + (msgs : betree_List_t (u64 & betree_Message_t)) : betree_List_t (u64 & betree_Message_t) = msgs (** [betree_main::betree::Node::{5}::apply_upserts]: decreases clause *) unfold -let betree_node_apply_upserts_decreases - (msgs : betree_list_t (u64 & betree_message_t)) (prev : option u64) - (key : u64) (st : state) : betree_list_t (u64 & betree_message_t) = +let betree_Node_apply_upserts_decreases + (msgs : betree_List_t (u64 & betree_Message_t)) (prev : option u64) + (key : u64) (st : state) : betree_List_t (u64 & betree_Message_t) = msgs (** [betree_main::betree::Internal::{4}::lookup_in_children]: decreases clause *) unfold -let betree_internal_lookup_in_children_decreases (self : betree_internal_t) - (key : u64) (st : state) : betree_internal_t = +let betree_Internal_lookup_in_children_decreases (self : betree_Internal_t) + (key : u64) (st : state) : betree_Internal_t = self (** [betree_main::betree::Node::{5}::lookup]: decreases clause *) unfold -let betree_node_lookup_decreases (self : betree_node_t) (key : u64) - (st : state) : betree_node_t = +let betree_Node_lookup_decreases (self : betree_Node_t) (key : u64) + (st : state) : betree_Node_t = self (** [betree_main::betree::Node::{5}::lookup_mut_in_bindings]: decreases clause *) unfold -let betree_node_lookup_mut_in_bindings_decreases (key : u64) - (bindings : betree_list_t (u64 & u64)) : betree_list_t (u64 & u64) = +let betree_Node_lookup_mut_in_bindings_decreases (key : u64) + (bindings : betree_List_t (u64 & u64)) : betree_List_t (u64 & u64) = bindings unfold -let betree_node_apply_messages_to_leaf_decreases - (bindings : betree_list_t (u64 & u64)) - (new_msgs : betree_list_t (u64 & betree_message_t)) : betree_list_t (u64 & betree_message_t) = +let betree_Node_apply_messages_to_leaf_decreases + (bindings : betree_List_t (u64 & u64)) + (new_msgs : betree_List_t (u64 & betree_Message_t)) : betree_List_t (u64 & betree_Message_t) = new_msgs (** [betree_main::betree::Node::{5}::filter_messages_for_key]: decreases clause *) unfold -let betree_node_filter_messages_for_key_decreases (key : u64) - (msgs : betree_list_t (u64 & betree_message_t)) : betree_list_t (u64 & betree_message_t) = +let betree_Node_filter_messages_for_key_decreases (key : u64) + (msgs : betree_List_t (u64 & betree_Message_t)) : betree_List_t (u64 & betree_Message_t) = msgs (** [betree_main::betree::Node::{5}::lookup_first_message_after_key]: decreases clause *) unfold -let betree_node_lookup_first_message_after_key_decreases (key : u64) - (msgs : betree_list_t (u64 & betree_message_t)) : betree_list_t (u64 & betree_message_t) = +let betree_Node_lookup_first_message_after_key_decreases (key : u64) + (msgs : betree_List_t (u64 & betree_Message_t)) : betree_List_t (u64 & betree_Message_t) = msgs -let betree_node_apply_messages_to_internal_decreases - (msgs : betree_list_t (u64 & betree_message_t)) - (new_msgs : betree_list_t (u64 & betree_message_t)) : betree_list_t (u64 & betree_message_t) = +let betree_Node_apply_messages_to_internal_decreases + (msgs : betree_List_t (u64 & betree_Message_t)) + (new_msgs : betree_List_t (u64 & betree_Message_t)) : betree_List_t (u64 & betree_Message_t) = new_msgs (*** Decrease clauses - nat_pair *) /// The following decrease clauses use the [nat_pair] definition and the well-founded /// relation proven above. -let rec betree_size (bt : betree_node_t) : nat = +let rec betree_size (bt : betree_Node_t) : nat = match bt with - | BetreeNodeInternal node -> 1 + betree_internal_size node - | BetreeNodeLeaf _ -> 1 + | Betree_Node_Internal node -> 1 + betree_Internal_size node + | Betree_Node_Leaf _ -> 1 -and betree_internal_size (node : betree_internal_t) : nat = - 1 + betree_size node.betree_internal_left + betree_size node.betree_internal_right +and betree_Internal_size (node : betree_Internal_t) : nat = + 1 + betree_size node.left + betree_size node.right -let rec betree_list_len (#a : Type0) (ls : betree_list_t a) : nat = +let rec betree_List_len (#a : Type0) (ls : betree_List_t a) : nat = match ls with - | BetreeListCons _ tl -> 1 + betree_list_len tl - | BetreeListNil -> 0 + | Betree_List_Cons _ tl -> 1 + betree_List_len tl + | Betree_List_Nil -> 0 (** [betree_main::betree::Internal::{4}::flush]: decreases clause *) unfold -let betree_internal_flush_decreases (self : betree_internal_t) - (params : betree_params_t) (node_id_cnt : betree_node_id_counter_t) - (content : betree_list_t (u64 & betree_message_t)) (st : state) : nat_pair = - (|betree_internal_size self, 0|) +let betree_Internal_flush_decreases (self : betree_Internal_t) + (params : betree_Params_t) (node_id_cnt : betree_NodeIdCounter_t) + (content : betree_List_t (u64 & betree_Message_t)) (st : state) : nat_pair = + (|betree_Internal_size self, 0|) (** [betree_main::betree::Node::{5}::apply_messages]: decreases clause *) unfold -let betree_node_apply_messages_decreases (self : betree_node_t) - (params : betree_params_t) (node_id_cnt : betree_node_id_counter_t) - (msgs : betree_list_t (u64 & betree_message_t)) (st : state) : nat_pair = - (|betree_size self, betree_list_len msgs|) +let betree_Node_apply_messages_decreases (self : betree_Node_t) + (params : betree_Params_t) (node_id_cnt : betree_NodeIdCounter_t) + (msgs : betree_List_t (u64 & betree_Message_t)) (st : state) : nat_pair = + (|betree_size self, betree_List_len msgs|) diff --git a/tests/fstar/betree_back_stateful/BetreeMain.Funs.fst b/tests/fstar/betree_back_stateful/BetreeMain.Funs.fst index 8083ee8f..08c4f615 100644 --- a/tests/fstar/betree_back_stateful/BetreeMain.Funs.fst +++ b/tests/fstar/betree_back_stateful/BetreeMain.Funs.fst @@ -9,35 +9,35 @@ include BetreeMain.Clauses #set-options "--z3rlimit 50 --fuel 1 --ifuel 1" (** [betree_main::betree::load_internal_node]: forward function *) -let betree_load_internal_node_fwd +let betree_load_internal_node (id : u64) (st : state) : - result (state & (betree_list_t (u64 & betree_message_t))) + result (state & (betree_List_t (u64 & betree_Message_t))) = - betree_utils_load_internal_node_fwd id st + betree_utils_load_internal_node id st (** [betree_main::betree::store_internal_node]: forward function *) -let betree_store_internal_node_fwd - (id : u64) (content : betree_list_t (u64 & betree_message_t)) (st : state) : +let betree_store_internal_node + (id : u64) (content : betree_List_t (u64 & betree_Message_t)) (st : state) : result (state & unit) = - let* (st0, _) = betree_utils_store_internal_node_fwd id content st in + let* (st0, _) = betree_utils_store_internal_node id content st in Return (st0, ()) (** [betree_main::betree::load_leaf_node]: forward function *) -let betree_load_leaf_node_fwd - (id : u64) (st : state) : result (state & (betree_list_t (u64 & u64))) = - betree_utils_load_leaf_node_fwd id st +let betree_load_leaf_node + (id : u64) (st : state) : result (state & (betree_List_t (u64 & u64))) = + betree_utils_load_leaf_node id st (** [betree_main::betree::store_leaf_node]: forward function *) -let betree_store_leaf_node_fwd - (id : u64) (content : betree_list_t (u64 & u64)) (st : state) : +let betree_store_leaf_node + (id : u64) (content : betree_List_t (u64 & u64)) (st : state) : result (state & unit) = - let* (st0, _) = betree_utils_store_leaf_node_fwd id content st in + let* (st0, _) = betree_utils_store_leaf_node id content st in Return (st0, ()) (** [betree_main::betree::fresh_node_id]: forward function *) -let betree_fresh_node_id_fwd (counter : u64) : result u64 = +let betree_fresh_node_id (counter : u64) : result u64 = let* _ = u64_add counter 1 in Return counter (** [betree_main::betree::fresh_node_id]: backward function 0 *) @@ -45,1204 +45,1123 @@ let betree_fresh_node_id_back (counter : u64) : result u64 = u64_add counter 1 (** [betree_main::betree::NodeIdCounter::{0}::new]: forward function *) -let betree_node_id_counter_new_fwd : result betree_node_id_counter_t = - Return { betree_node_id_counter_next_node_id = 0 } +let betree_NodeIdCounter_new : result betree_NodeIdCounter_t = + Return { next_node_id = 0 } (** [betree_main::betree::NodeIdCounter::{0}::fresh_id]: forward function *) -let betree_node_id_counter_fresh_id_fwd - (self : betree_node_id_counter_t) : result u64 = - let* _ = u64_add self.betree_node_id_counter_next_node_id 1 in - Return self.betree_node_id_counter_next_node_id +let betree_NodeIdCounter_fresh_id + (self : betree_NodeIdCounter_t) : result u64 = + let* _ = u64_add self.next_node_id 1 in Return self.next_node_id (** [betree_main::betree::NodeIdCounter::{0}::fresh_id]: backward function 0 *) -let betree_node_id_counter_fresh_id_back - (self : betree_node_id_counter_t) : result betree_node_id_counter_t = - let* i = u64_add self.betree_node_id_counter_next_node_id 1 in - Return { betree_node_id_counter_next_node_id = i } +let betree_NodeIdCounter_fresh_id_back + (self : betree_NodeIdCounter_t) : result betree_NodeIdCounter_t = + let* i = u64_add self.next_node_id 1 in Return { next_node_id = i } (** [betree_main::betree::upsert_update]: forward function *) -let betree_upsert_update_fwd - (prev : option u64) (st : betree_upsert_fun_state_t) : result u64 = +let betree_upsert_update + (prev : option u64) (st : betree_UpsertFunState_t) : result u64 = begin match prev with | None -> begin match st with - | BetreeUpsertFunStateAdd v -> Return v - | BetreeUpsertFunStateSub i -> Return 0 + | Betree_UpsertFunState_Add v -> Return v + | Betree_UpsertFunState_Sub i -> Return 0 end | Some prev0 -> begin match st with - | BetreeUpsertFunStateAdd v -> + | Betree_UpsertFunState_Add v -> let* margin = u64_sub core_u64_max prev0 in if margin >= v then u64_add prev0 v else Return core_u64_max - | BetreeUpsertFunStateSub v -> + | Betree_UpsertFunState_Sub v -> if prev0 >= v then u64_sub prev0 v else Return 0 end end (** [betree_main::betree::List::{1}::len]: forward function *) -let rec betree_list_len_fwd - (t : Type0) (self : betree_list_t t) : - Tot (result u64) (decreases (betree_list_len_decreases t self)) +let rec betree_List_len + (t : Type0) (self : betree_List_t t) : + Tot (result u64) (decreases (betree_List_len_decreases t self)) = begin match self with - | BetreeListCons x tl -> let* i = betree_list_len_fwd t tl in u64_add 1 i - | BetreeListNil -> Return 0 + | Betree_List_Cons x tl -> let* i = betree_List_len t tl in u64_add 1 i + | Betree_List_Nil -> Return 0 end (** [betree_main::betree::List::{1}::split_at]: forward function *) -let rec betree_list_split_at_fwd - (t : Type0) (self : betree_list_t t) (n : u64) : - Tot (result ((betree_list_t t) & (betree_list_t t))) - (decreases (betree_list_split_at_decreases t self n)) +let rec betree_List_split_at + (t : Type0) (self : betree_List_t t) (n : u64) : + Tot (result ((betree_List_t t) & (betree_List_t t))) + (decreases (betree_List_split_at_decreases t self n)) = if n = 0 - then Return (BetreeListNil, self) + then Return (Betree_List_Nil, self) else begin match self with - | BetreeListCons hd tl -> + | Betree_List_Cons hd tl -> let* i = u64_sub n 1 in - let* p = betree_list_split_at_fwd t tl i in + let* p = betree_List_split_at t tl i in let (ls0, ls1) = p in let l = ls0 in - Return (BetreeListCons hd l, ls1) - | BetreeListNil -> Fail Failure + Return (Betree_List_Cons hd l, ls1) + | Betree_List_Nil -> Fail Failure end (** [betree_main::betree::List::{1}::push_front]: merged forward/backward function (there is a single backward function, and the forward function returns ()) *) -let betree_list_push_front_fwd_back - (t : Type0) (self : betree_list_t t) (x : t) : result (betree_list_t t) = - let tl = mem_replace_fwd (betree_list_t t) self BetreeListNil in +let betree_List_push_front + (t : Type0) (self : betree_List_t t) (x : t) : result (betree_List_t t) = + let tl = core_mem_replace (betree_List_t t) self Betree_List_Nil in let l = tl in - Return (BetreeListCons x l) + Return (Betree_List_Cons x l) (** [betree_main::betree::List::{1}::pop_front]: forward function *) -let betree_list_pop_front_fwd (t : Type0) (self : betree_list_t t) : result t = - let ls = mem_replace_fwd (betree_list_t t) self BetreeListNil in +let betree_List_pop_front (t : Type0) (self : betree_List_t t) : result t = + let ls = core_mem_replace (betree_List_t t) self Betree_List_Nil in begin match ls with - | BetreeListCons x tl -> Return x - | BetreeListNil -> Fail Failure + | Betree_List_Cons x tl -> Return x + | Betree_List_Nil -> Fail Failure end (** [betree_main::betree::List::{1}::pop_front]: backward function 0 *) -let betree_list_pop_front_back - (t : Type0) (self : betree_list_t t) : result (betree_list_t t) = - let ls = mem_replace_fwd (betree_list_t t) self BetreeListNil in +let betree_List_pop_front_back + (t : Type0) (self : betree_List_t t) : result (betree_List_t t) = + let ls = core_mem_replace (betree_List_t t) self Betree_List_Nil in begin match ls with - | BetreeListCons x tl -> Return tl - | BetreeListNil -> Fail Failure + | Betree_List_Cons x tl -> Return tl + | Betree_List_Nil -> Fail Failure end (** [betree_main::betree::List::{1}::hd]: forward function *) -let betree_list_hd_fwd (t : Type0) (self : betree_list_t t) : result t = +let betree_List_hd (t : Type0) (self : betree_List_t t) : result t = begin match self with - | BetreeListCons hd l -> Return hd - | BetreeListNil -> Fail Failure + | Betree_List_Cons hd l -> Return hd + | Betree_List_Nil -> Fail Failure end (** [betree_main::betree::List::{2}::head_has_key]: forward function *) -let betree_list_head_has_key_fwd - (t : Type0) (self : betree_list_t (u64 & t)) (key : u64) : result bool = +let betree_List_head_has_key + (t : Type0) (self : betree_List_t (u64 & t)) (key : u64) : result bool = begin match self with - | BetreeListCons hd l -> let (i, _) = hd in Return (i = key) - | BetreeListNil -> Return false + | Betree_List_Cons hd l -> let (i, _) = hd in Return (i = key) + | Betree_List_Nil -> Return false end (** [betree_main::betree::List::{2}::partition_at_pivot]: forward function *) -let rec betree_list_partition_at_pivot_fwd - (t : Type0) (self : betree_list_t (u64 & t)) (pivot : u64) : - Tot (result ((betree_list_t (u64 & t)) & (betree_list_t (u64 & t)))) - (decreases (betree_list_partition_at_pivot_decreases t self pivot)) +let rec betree_List_partition_at_pivot + (t : Type0) (self : betree_List_t (u64 & t)) (pivot : u64) : + Tot (result ((betree_List_t (u64 & t)) & (betree_List_t (u64 & t)))) + (decreases (betree_List_partition_at_pivot_decreases t self pivot)) = begin match self with - | BetreeListCons hd tl -> + | Betree_List_Cons hd tl -> let (i, x) = hd in if i >= pivot - then Return (BetreeListNil, BetreeListCons (i, x) tl) + then Return (Betree_List_Nil, Betree_List_Cons (i, x) tl) else - let* p = betree_list_partition_at_pivot_fwd t tl pivot in + let* p = betree_List_partition_at_pivot t tl pivot in let (ls0, ls1) = p in let l = ls0 in - Return (BetreeListCons (i, x) l, ls1) - | BetreeListNil -> Return (BetreeListNil, BetreeListNil) + Return (Betree_List_Cons (i, x) l, ls1) + | Betree_List_Nil -> Return (Betree_List_Nil, Betree_List_Nil) end (** [betree_main::betree::Leaf::{3}::split]: forward function *) -let betree_leaf_split_fwd - (self : betree_leaf_t) (content : betree_list_t (u64 & u64)) - (params : betree_params_t) (node_id_cnt : betree_node_id_counter_t) +let betree_Leaf_split + (self : betree_Leaf_t) (content : betree_List_t (u64 & u64)) + (params : betree_Params_t) (node_id_cnt : betree_NodeIdCounter_t) (st : state) : - result (state & betree_internal_t) + result (state & betree_Internal_t) = - let* p = - betree_list_split_at_fwd (u64 & u64) content - params.betree_params_split_size in + let* p = betree_List_split_at (u64 & u64) content params.split_size in let (content0, content1) = p in - let* p0 = betree_list_hd_fwd (u64 & u64) content1 in + let* p0 = betree_List_hd (u64 & u64) content1 in let (pivot, _) = p0 in - let* id0 = betree_node_id_counter_fresh_id_fwd node_id_cnt in - let* node_id_cnt0 = betree_node_id_counter_fresh_id_back node_id_cnt in - let* id1 = betree_node_id_counter_fresh_id_fwd node_id_cnt0 in - let* (st0, _) = betree_store_leaf_node_fwd id0 content0 st in - let* (st1, _) = betree_store_leaf_node_fwd id1 content1 st0 in - let n = BetreeNodeLeaf - { betree_leaf_id = id0; betree_leaf_size = params.betree_params_split_size - } in - let n0 = BetreeNodeLeaf - { betree_leaf_id = id1; betree_leaf_size = params.betree_params_split_size - } in - Return (st1, - { - betree_internal_id = self.betree_leaf_id; - betree_internal_pivot = pivot; - betree_internal_left = n; - betree_internal_right = n0 - }) + let* id0 = betree_NodeIdCounter_fresh_id node_id_cnt in + let* node_id_cnt0 = betree_NodeIdCounter_fresh_id_back node_id_cnt in + let* id1 = betree_NodeIdCounter_fresh_id node_id_cnt0 in + let* (st0, _) = betree_store_leaf_node id0 content0 st in + let* (st1, _) = betree_store_leaf_node id1 content1 st0 in + let n = Betree_Node_Leaf { id = id0; size = params.split_size } in + let n0 = Betree_Node_Leaf { id = id1; size = params.split_size } in + Return (st1, { id = self.id; pivot = pivot; left = n; right = n0 }) (** [betree_main::betree::Leaf::{3}::split]: backward function 0 *) -let betree_leaf_split_back0 - (self : betree_leaf_t) (content : betree_list_t (u64 & u64)) - (params : betree_params_t) (node_id_cnt : betree_node_id_counter_t) +let betree_Leaf_split_back0 + (self : betree_Leaf_t) (content : betree_List_t (u64 & u64)) + (params : betree_Params_t) (node_id_cnt : betree_NodeIdCounter_t) (st : state) (st0 : state) : result (state & unit) = - let* p = - betree_list_split_at_fwd (u64 & u64) content - params.betree_params_split_size in + let* p = betree_List_split_at (u64 & u64) content params.split_size in let (content0, content1) = p in - let* _ = betree_list_hd_fwd (u64 & u64) content1 in - let* id0 = betree_node_id_counter_fresh_id_fwd node_id_cnt in - let* node_id_cnt0 = betree_node_id_counter_fresh_id_back node_id_cnt in - let* id1 = betree_node_id_counter_fresh_id_fwd node_id_cnt0 in - let* (st1, _) = betree_store_leaf_node_fwd id0 content0 st in - let* _ = betree_store_leaf_node_fwd id1 content1 st1 in + let* _ = betree_List_hd (u64 & u64) content1 in + let* id0 = betree_NodeIdCounter_fresh_id node_id_cnt in + let* node_id_cnt0 = betree_NodeIdCounter_fresh_id_back node_id_cnt in + let* id1 = betree_NodeIdCounter_fresh_id node_id_cnt0 in + let* (st1, _) = betree_store_leaf_node id0 content0 st in + let* _ = betree_store_leaf_node id1 content1 st1 in Return (st0, ()) (** [betree_main::betree::Leaf::{3}::split]: backward function 1 *) -let betree_leaf_split_back1 - (self : betree_leaf_t) (content : betree_list_t (u64 & u64)) - (params : betree_params_t) (node_id_cnt : betree_node_id_counter_t) +let betree_Leaf_split_back1 + (self : betree_Leaf_t) (content : betree_List_t (u64 & u64)) + (params : betree_Params_t) (node_id_cnt : betree_NodeIdCounter_t) (st : state) (st0 : state) : result (state & unit) = - let* p = - betree_list_split_at_fwd (u64 & u64) content - params.betree_params_split_size in + let* p = betree_List_split_at (u64 & u64) content params.split_size in let (content0, content1) = p in - let* _ = betree_list_hd_fwd (u64 & u64) content1 in - let* id0 = betree_node_id_counter_fresh_id_fwd node_id_cnt in - let* node_id_cnt0 = betree_node_id_counter_fresh_id_back node_id_cnt in - let* id1 = betree_node_id_counter_fresh_id_fwd node_id_cnt0 in - let* (st1, _) = betree_store_leaf_node_fwd id0 content0 st in - let* _ = betree_store_leaf_node_fwd id1 content1 st1 in + let* _ = betree_List_hd (u64 & u64) content1 in + let* id0 = betree_NodeIdCounter_fresh_id node_id_cnt in + let* node_id_cnt0 = betree_NodeIdCounter_fresh_id_back node_id_cnt in + let* id1 = betree_NodeIdCounter_fresh_id node_id_cnt0 in + let* (st1, _) = betree_store_leaf_node id0 content0 st in + let* _ = betree_store_leaf_node id1 content1 st1 in Return (st0, ()) (** [betree_main::betree::Leaf::{3}::split]: backward function 2 *) -let betree_leaf_split_back2 - (self : betree_leaf_t) (content : betree_list_t (u64 & u64)) - (params : betree_params_t) (node_id_cnt : betree_node_id_counter_t) +let betree_Leaf_split_back2 + (self : betree_Leaf_t) (content : betree_List_t (u64 & u64)) + (params : betree_Params_t) (node_id_cnt : betree_NodeIdCounter_t) (st : state) (st0 : state) : - result (state & betree_node_id_counter_t) + result (state & betree_NodeIdCounter_t) = - let* p = - betree_list_split_at_fwd (u64 & u64) content - params.betree_params_split_size in + let* p = betree_List_split_at (u64 & u64) content params.split_size in let (content0, content1) = p in - let* _ = betree_list_hd_fwd (u64 & u64) content1 in - let* id0 = betree_node_id_counter_fresh_id_fwd node_id_cnt in - let* node_id_cnt0 = betree_node_id_counter_fresh_id_back node_id_cnt in - let* id1 = betree_node_id_counter_fresh_id_fwd node_id_cnt0 in - let* (st1, _) = betree_store_leaf_node_fwd id0 content0 st in - let* _ = betree_store_leaf_node_fwd id1 content1 st1 in - let* node_id_cnt1 = betree_node_id_counter_fresh_id_back node_id_cnt0 in + let* _ = betree_List_hd (u64 & u64) content1 in + let* id0 = betree_NodeIdCounter_fresh_id node_id_cnt in + let* node_id_cnt0 = betree_NodeIdCounter_fresh_id_back node_id_cnt in + let* id1 = betree_NodeIdCounter_fresh_id node_id_cnt0 in + let* (st1, _) = betree_store_leaf_node id0 content0 st in + let* _ = betree_store_leaf_node id1 content1 st1 in + let* node_id_cnt1 = betree_NodeIdCounter_fresh_id_back node_id_cnt0 in Return (st0, node_id_cnt1) (** [betree_main::betree::Node::{5}::lookup_first_message_for_key]: forward function *) -let rec betree_node_lookup_first_message_for_key_fwd - (key : u64) (msgs : betree_list_t (u64 & betree_message_t)) : - Tot (result (betree_list_t (u64 & betree_message_t))) - (decreases (betree_node_lookup_first_message_for_key_decreases key msgs)) +let rec betree_Node_lookup_first_message_for_key + (key : u64) (msgs : betree_List_t (u64 & betree_Message_t)) : + Tot (result (betree_List_t (u64 & betree_Message_t))) + (decreases (betree_Node_lookup_first_message_for_key_decreases key msgs)) = begin match msgs with - | BetreeListCons x next_msgs -> + | Betree_List_Cons x next_msgs -> let (i, m) = x in if i >= key - then Return (BetreeListCons (i, m) next_msgs) - else betree_node_lookup_first_message_for_key_fwd key next_msgs - | BetreeListNil -> Return BetreeListNil + then Return (Betree_List_Cons (i, m) next_msgs) + else betree_Node_lookup_first_message_for_key key next_msgs + | Betree_List_Nil -> Return Betree_List_Nil end (** [betree_main::betree::Node::{5}::lookup_first_message_for_key]: backward function 0 *) -let rec betree_node_lookup_first_message_for_key_back - (key : u64) (msgs : betree_list_t (u64 & betree_message_t)) - (ret : betree_list_t (u64 & betree_message_t)) : - Tot (result (betree_list_t (u64 & betree_message_t))) - (decreases (betree_node_lookup_first_message_for_key_decreases key msgs)) +let rec betree_Node_lookup_first_message_for_key_back + (key : u64) (msgs : betree_List_t (u64 & betree_Message_t)) + (ret : betree_List_t (u64 & betree_Message_t)) : + Tot (result (betree_List_t (u64 & betree_Message_t))) + (decreases (betree_Node_lookup_first_message_for_key_decreases key msgs)) = begin match msgs with - | BetreeListCons x next_msgs -> + | Betree_List_Cons x next_msgs -> let (i, m) = x in if i >= key then Return ret else let* next_msgs0 = - betree_node_lookup_first_message_for_key_back key next_msgs ret in - Return (BetreeListCons (i, m) next_msgs0) - | BetreeListNil -> Return ret + betree_Node_lookup_first_message_for_key_back key next_msgs ret in + Return (Betree_List_Cons (i, m) next_msgs0) + | Betree_List_Nil -> Return ret end (** [betree_main::betree::Node::{5}::apply_upserts]: forward function *) -let rec betree_node_apply_upserts_fwd - (msgs : betree_list_t (u64 & betree_message_t)) (prev : option u64) +let rec betree_Node_apply_upserts + (msgs : betree_List_t (u64 & betree_Message_t)) (prev : option u64) (key : u64) (st : state) : Tot (result (state & u64)) - (decreases (betree_node_apply_upserts_decreases msgs prev key st)) + (decreases (betree_Node_apply_upserts_decreases msgs prev key st)) = - let* b = betree_list_head_has_key_fwd betree_message_t msgs key in + let* b = betree_List_head_has_key betree_Message_t msgs key in if b then - let* msg = betree_list_pop_front_fwd (u64 & betree_message_t) msgs in + let* msg = betree_List_pop_front (u64 & betree_Message_t) msgs in let (_, m) = msg in begin match m with - | BetreeMessageInsert i -> Fail Failure - | BetreeMessageDelete -> Fail Failure - | BetreeMessageUpsert s -> - let* v = betree_upsert_update_fwd prev s in - let* msgs0 = betree_list_pop_front_back (u64 & betree_message_t) msgs in - betree_node_apply_upserts_fwd msgs0 (Some v) key st + | Betree_Message_Insert i -> Fail Failure + | Betree_Message_Delete -> Fail Failure + | Betree_Message_Upsert s -> + let* v = betree_upsert_update prev s in + let* msgs0 = betree_List_pop_front_back (u64 & betree_Message_t) msgs in + betree_Node_apply_upserts msgs0 (Some v) key st end else - let* (st0, v) = core_option_option_unwrap_fwd u64 prev st in + let* (st0, v) = core_option_Option_unwrap u64 prev st in let* _ = - betree_list_push_front_fwd_back (u64 & betree_message_t) msgs (key, - BetreeMessageInsert v) in + betree_List_push_front (u64 & betree_Message_t) msgs (key, + Betree_Message_Insert v) in Return (st0, v) (** [betree_main::betree::Node::{5}::apply_upserts]: backward function 0 *) -let rec betree_node_apply_upserts_back - (msgs : betree_list_t (u64 & betree_message_t)) (prev : option u64) +let rec betree_Node_apply_upserts_back + (msgs : betree_List_t (u64 & betree_Message_t)) (prev : option u64) (key : u64) (st : state) (st0 : state) : - Tot (result (state & (betree_list_t (u64 & betree_message_t)))) - (decreases (betree_node_apply_upserts_decreases msgs prev key st)) + Tot (result (state & (betree_List_t (u64 & betree_Message_t)))) + (decreases (betree_Node_apply_upserts_decreases msgs prev key st)) = - let* b = betree_list_head_has_key_fwd betree_message_t msgs key in + let* b = betree_List_head_has_key betree_Message_t msgs key in if b then - let* msg = betree_list_pop_front_fwd (u64 & betree_message_t) msgs in + let* msg = betree_List_pop_front (u64 & betree_Message_t) msgs in let (_, m) = msg in begin match m with - | BetreeMessageInsert i -> Fail Failure - | BetreeMessageDelete -> Fail Failure - | BetreeMessageUpsert s -> - let* v = betree_upsert_update_fwd prev s in - let* msgs0 = betree_list_pop_front_back (u64 & betree_message_t) msgs in - betree_node_apply_upserts_back msgs0 (Some v) key st st0 + | Betree_Message_Insert i -> Fail Failure + | Betree_Message_Delete -> Fail Failure + | Betree_Message_Upsert s -> + let* v = betree_upsert_update prev s in + let* msgs0 = betree_List_pop_front_back (u64 & betree_Message_t) msgs in + betree_Node_apply_upserts_back msgs0 (Some v) key st st0 end else - let* (_, v) = core_option_option_unwrap_fwd u64 prev st in + let* (_, v) = core_option_Option_unwrap u64 prev st in let* msgs0 = - betree_list_push_front_fwd_back (u64 & betree_message_t) msgs (key, - BetreeMessageInsert v) in + betree_List_push_front (u64 & betree_Message_t) msgs (key, + Betree_Message_Insert v) in Return (st0, msgs0) (** [betree_main::betree::Node::{5}::lookup_in_bindings]: forward function *) -let rec betree_node_lookup_in_bindings_fwd - (key : u64) (bindings : betree_list_t (u64 & u64)) : +let rec betree_Node_lookup_in_bindings + (key : u64) (bindings : betree_List_t (u64 & u64)) : Tot (result (option u64)) - (decreases (betree_node_lookup_in_bindings_decreases key bindings)) + (decreases (betree_Node_lookup_in_bindings_decreases key bindings)) = begin match bindings with - | BetreeListCons hd tl -> + | Betree_List_Cons hd tl -> let (i, i0) = hd in if i = key then Return (Some i0) - else - if i > key - then Return None - else betree_node_lookup_in_bindings_fwd key tl - | BetreeListNil -> Return None + else if i > key then Return None else betree_Node_lookup_in_bindings key tl + | Betree_List_Nil -> Return None end (** [betree_main::betree::Internal::{4}::lookup_in_children]: forward function *) -let rec betree_internal_lookup_in_children_fwd - (self : betree_internal_t) (key : u64) (st : state) : +let rec betree_Internal_lookup_in_children + (self : betree_Internal_t) (key : u64) (st : state) : Tot (result (state & (option u64))) - (decreases (betree_internal_lookup_in_children_decreases self key st)) + (decreases (betree_Internal_lookup_in_children_decreases self key st)) = - if key < self.betree_internal_pivot - then betree_node_lookup_fwd self.betree_internal_left key st - else betree_node_lookup_fwd self.betree_internal_right key st + if key < self.pivot + then betree_Node_lookup self.left key st + else betree_Node_lookup self.right key st (** [betree_main::betree::Internal::{4}::lookup_in_children]: backward function 0 *) -and betree_internal_lookup_in_children_back - (self : betree_internal_t) (key : u64) (st : state) (st0 : state) : - Tot (result (state & betree_internal_t)) - (decreases (betree_internal_lookup_in_children_decreases self key st)) +and betree_Internal_lookup_in_children_back + (self : betree_Internal_t) (key : u64) (st : state) (st0 : state) : + Tot (result (state & betree_Internal_t)) + (decreases (betree_Internal_lookup_in_children_decreases self key st)) = - if key < self.betree_internal_pivot + if key < self.pivot then - let* (st1, n) = - betree_node_lookup_back self.betree_internal_left key st st0 in - Return (st1, { self with betree_internal_left = n }) + let* (st1, n) = betree_Node_lookup_back self.left key st st0 in + Return (st1, { self with left = n }) else - let* (st1, n) = - betree_node_lookup_back self.betree_internal_right key st st0 in - Return (st1, { self with betree_internal_right = n }) + let* (st1, n) = betree_Node_lookup_back self.right key st st0 in + Return (st1, { self with right = n }) (** [betree_main::betree::Node::{5}::lookup]: forward function *) -and betree_node_lookup_fwd - (self : betree_node_t) (key : u64) (st : state) : +and betree_Node_lookup + (self : betree_Node_t) (key : u64) (st : state) : Tot (result (state & (option u64))) - (decreases (betree_node_lookup_decreases self key st)) + (decreases (betree_Node_lookup_decreases self key st)) = begin match self with - | BetreeNodeInternal node -> - let* (st0, msgs) = betree_load_internal_node_fwd node.betree_internal_id st - in - let* pending = betree_node_lookup_first_message_for_key_fwd key msgs in + | Betree_Node_Internal node -> + let* (st0, msgs) = betree_load_internal_node node.id st in + let* pending = betree_Node_lookup_first_message_for_key key msgs in begin match pending with - | BetreeListCons p l -> + | Betree_List_Cons p l -> let (k, msg) = p in if k <> key then - let* (st1, opt) = betree_internal_lookup_in_children_fwd node key st0 - in + let* (st1, o) = betree_Internal_lookup_in_children node key st0 in let* _ = - betree_node_lookup_first_message_for_key_back key msgs - (BetreeListCons (k, msg) l) in - Return (st1, opt) + betree_Node_lookup_first_message_for_key_back key msgs + (Betree_List_Cons (k, msg) l) in + Return (st1, o) else begin match msg with - | BetreeMessageInsert v -> + | Betree_Message_Insert v -> let* _ = - betree_node_lookup_first_message_for_key_back key msgs - (BetreeListCons (k, BetreeMessageInsert v) l) in + betree_Node_lookup_first_message_for_key_back key msgs + (Betree_List_Cons (k, Betree_Message_Insert v) l) in Return (st0, Some v) - | BetreeMessageDelete -> + | Betree_Message_Delete -> let* _ = - betree_node_lookup_first_message_for_key_back key msgs - (BetreeListCons (k, BetreeMessageDelete) l) in + betree_Node_lookup_first_message_for_key_back key msgs + (Betree_List_Cons (k, Betree_Message_Delete) l) in Return (st0, None) - | BetreeMessageUpsert ufs -> - let* (st1, v) = betree_internal_lookup_in_children_fwd node key st0 - in + | Betree_Message_Upsert ufs -> + let* (st1, v) = betree_Internal_lookup_in_children node key st0 in let* (st2, v0) = - betree_node_apply_upserts_fwd (BetreeListCons (k, - BetreeMessageUpsert ufs) l) v key st1 in + betree_Node_apply_upserts (Betree_List_Cons (k, + Betree_Message_Upsert ufs) l) v key st1 in let* (st3, node0) = - betree_internal_lookup_in_children_back node key st0 st2 in + betree_Internal_lookup_in_children_back node key st0 st2 in let* (st4, pending0) = - betree_node_apply_upserts_back (BetreeListCons (k, - BetreeMessageUpsert ufs) l) v key st1 st3 in + betree_Node_apply_upserts_back (Betree_List_Cons (k, + Betree_Message_Upsert ufs) l) v key st1 st3 in let* msgs0 = - betree_node_lookup_first_message_for_key_back key msgs pending0 in - let* (st5, _) = - betree_store_internal_node_fwd node0.betree_internal_id msgs0 st4 - in + betree_Node_lookup_first_message_for_key_back key msgs pending0 in + let* (st5, _) = betree_store_internal_node node0.id msgs0 st4 in Return (st5, Some v0) end - | BetreeListNil -> - let* (st1, opt) = betree_internal_lookup_in_children_fwd node key st0 in + | Betree_List_Nil -> + let* (st1, o) = betree_Internal_lookup_in_children node key st0 in let* _ = - betree_node_lookup_first_message_for_key_back key msgs BetreeListNil in - Return (st1, opt) + betree_Node_lookup_first_message_for_key_back key msgs Betree_List_Nil + in + Return (st1, o) end - | BetreeNodeLeaf node -> - let* (st0, bindings) = betree_load_leaf_node_fwd node.betree_leaf_id st in - let* opt = betree_node_lookup_in_bindings_fwd key bindings in - Return (st0, opt) + | Betree_Node_Leaf node -> + let* (st0, bindings) = betree_load_leaf_node node.id st in + let* o = betree_Node_lookup_in_bindings key bindings in + Return (st0, o) end (** [betree_main::betree::Node::{5}::lookup]: backward function 0 *) -and betree_node_lookup_back - (self : betree_node_t) (key : u64) (st : state) (st0 : state) : - Tot (result (state & betree_node_t)) - (decreases (betree_node_lookup_decreases self key st)) +and betree_Node_lookup_back + (self : betree_Node_t) (key : u64) (st : state) (st0 : state) : + Tot (result (state & betree_Node_t)) + (decreases (betree_Node_lookup_decreases self key st)) = begin match self with - | BetreeNodeInternal node -> - let* (st1, msgs) = betree_load_internal_node_fwd node.betree_internal_id st - in - let* pending = betree_node_lookup_first_message_for_key_fwd key msgs in + | Betree_Node_Internal node -> + let* (st1, msgs) = betree_load_internal_node node.id st in + let* pending = betree_Node_lookup_first_message_for_key key msgs in begin match pending with - | BetreeListCons p l -> + | Betree_List_Cons p l -> let (k, msg) = p in if k <> key then let* _ = - betree_node_lookup_first_message_for_key_back key msgs - (BetreeListCons (k, msg) l) in + betree_Node_lookup_first_message_for_key_back key msgs + (Betree_List_Cons (k, msg) l) in let* (st2, node0) = - betree_internal_lookup_in_children_back node key st1 st0 in - Return (st2, BetreeNodeInternal node0) + betree_Internal_lookup_in_children_back node key st1 st0 in + Return (st2, Betree_Node_Internal node0) else begin match msg with - | BetreeMessageInsert v -> + | Betree_Message_Insert v -> let* _ = - betree_node_lookup_first_message_for_key_back key msgs - (BetreeListCons (k, BetreeMessageInsert v) l) in - Return (st0, BetreeNodeInternal node) - | BetreeMessageDelete -> + betree_Node_lookup_first_message_for_key_back key msgs + (Betree_List_Cons (k, Betree_Message_Insert v) l) in + Return (st0, Betree_Node_Internal node) + | Betree_Message_Delete -> let* _ = - betree_node_lookup_first_message_for_key_back key msgs - (BetreeListCons (k, BetreeMessageDelete) l) in - Return (st0, BetreeNodeInternal node) - | BetreeMessageUpsert ufs -> - let* (st2, v) = betree_internal_lookup_in_children_fwd node key st1 - in + betree_Node_lookup_first_message_for_key_back key msgs + (Betree_List_Cons (k, Betree_Message_Delete) l) in + Return (st0, Betree_Node_Internal node) + | Betree_Message_Upsert ufs -> + let* (st2, v) = betree_Internal_lookup_in_children node key st1 in let* (st3, _) = - betree_node_apply_upserts_fwd (BetreeListCons (k, - BetreeMessageUpsert ufs) l) v key st2 in + betree_Node_apply_upserts (Betree_List_Cons (k, + Betree_Message_Upsert ufs) l) v key st2 in let* (st4, node0) = - betree_internal_lookup_in_children_back node key st1 st3 in + betree_Internal_lookup_in_children_back node key st1 st3 in let* (st5, pending0) = - betree_node_apply_upserts_back (BetreeListCons (k, - BetreeMessageUpsert ufs) l) v key st2 st4 in + betree_Node_apply_upserts_back (Betree_List_Cons (k, + Betree_Message_Upsert ufs) l) v key st2 st4 in let* msgs0 = - betree_node_lookup_first_message_for_key_back key msgs pending0 in - let* _ = - betree_store_internal_node_fwd node0.betree_internal_id msgs0 st5 - in - Return (st0, BetreeNodeInternal node0) + betree_Node_lookup_first_message_for_key_back key msgs pending0 in + let* _ = betree_store_internal_node node0.id msgs0 st5 in + Return (st0, Betree_Node_Internal node0) end - | BetreeListNil -> + | Betree_List_Nil -> let* _ = - betree_node_lookup_first_message_for_key_back key msgs BetreeListNil in + betree_Node_lookup_first_message_for_key_back key msgs Betree_List_Nil + in let* (st2, node0) = - betree_internal_lookup_in_children_back node key st1 st0 in - Return (st2, BetreeNodeInternal node0) + betree_Internal_lookup_in_children_back node key st1 st0 in + Return (st2, Betree_Node_Internal node0) end - | BetreeNodeLeaf node -> - let* (_, bindings) = betree_load_leaf_node_fwd node.betree_leaf_id st in - let* _ = betree_node_lookup_in_bindings_fwd key bindings in - Return (st0, BetreeNodeLeaf node) + | Betree_Node_Leaf node -> + let* (_, bindings) = betree_load_leaf_node node.id st in + let* _ = betree_Node_lookup_in_bindings key bindings in + Return (st0, Betree_Node_Leaf node) end (** [betree_main::betree::Node::{5}::filter_messages_for_key]: merged forward/backward function (there is a single backward function, and the forward function returns ()) *) -let rec betree_node_filter_messages_for_key_fwd_back - (key : u64) (msgs : betree_list_t (u64 & betree_message_t)) : - Tot (result (betree_list_t (u64 & betree_message_t))) - (decreases (betree_node_filter_messages_for_key_decreases key msgs)) +let rec betree_Node_filter_messages_for_key + (key : u64) (msgs : betree_List_t (u64 & betree_Message_t)) : + Tot (result (betree_List_t (u64 & betree_Message_t))) + (decreases (betree_Node_filter_messages_for_key_decreases key msgs)) = begin match msgs with - | BetreeListCons p l -> + | Betree_List_Cons p l -> let (k, m) = p in if k = key then let* msgs0 = - betree_list_pop_front_back (u64 & betree_message_t) (BetreeListCons (k, - m) l) in - betree_node_filter_messages_for_key_fwd_back key msgs0 - else Return (BetreeListCons (k, m) l) - | BetreeListNil -> Return BetreeListNil + betree_List_pop_front_back (u64 & betree_Message_t) (Betree_List_Cons + (k, m) l) in + betree_Node_filter_messages_for_key key msgs0 + else Return (Betree_List_Cons (k, m) l) + | Betree_List_Nil -> Return Betree_List_Nil end (** [betree_main::betree::Node::{5}::lookup_first_message_after_key]: forward function *) -let rec betree_node_lookup_first_message_after_key_fwd - (key : u64) (msgs : betree_list_t (u64 & betree_message_t)) : - Tot (result (betree_list_t (u64 & betree_message_t))) - (decreases (betree_node_lookup_first_message_after_key_decreases key msgs)) +let rec betree_Node_lookup_first_message_after_key + (key : u64) (msgs : betree_List_t (u64 & betree_Message_t)) : + Tot (result (betree_List_t (u64 & betree_Message_t))) + (decreases (betree_Node_lookup_first_message_after_key_decreases key msgs)) = begin match msgs with - | BetreeListCons p next_msgs -> + | Betree_List_Cons p next_msgs -> let (k, m) = p in if k = key - then betree_node_lookup_first_message_after_key_fwd key next_msgs - else Return (BetreeListCons (k, m) next_msgs) - | BetreeListNil -> Return BetreeListNil + then betree_Node_lookup_first_message_after_key key next_msgs + else Return (Betree_List_Cons (k, m) next_msgs) + | Betree_List_Nil -> Return Betree_List_Nil end (** [betree_main::betree::Node::{5}::lookup_first_message_after_key]: backward function 0 *) -let rec betree_node_lookup_first_message_after_key_back - (key : u64) (msgs : betree_list_t (u64 & betree_message_t)) - (ret : betree_list_t (u64 & betree_message_t)) : - Tot (result (betree_list_t (u64 & betree_message_t))) - (decreases (betree_node_lookup_first_message_after_key_decreases key msgs)) +let rec betree_Node_lookup_first_message_after_key_back + (key : u64) (msgs : betree_List_t (u64 & betree_Message_t)) + (ret : betree_List_t (u64 & betree_Message_t)) : + Tot (result (betree_List_t (u64 & betree_Message_t))) + (decreases (betree_Node_lookup_first_message_after_key_decreases key msgs)) = begin match msgs with - | BetreeListCons p next_msgs -> + | Betree_List_Cons p next_msgs -> let (k, m) = p in if k = key then let* next_msgs0 = - betree_node_lookup_first_message_after_key_back key next_msgs ret in - Return (BetreeListCons (k, m) next_msgs0) + betree_Node_lookup_first_message_after_key_back key next_msgs ret in + Return (Betree_List_Cons (k, m) next_msgs0) else Return ret - | BetreeListNil -> Return ret + | Betree_List_Nil -> Return ret end (** [betree_main::betree::Node::{5}::apply_to_internal]: merged forward/backward function (there is a single backward function, and the forward function returns ()) *) -let betree_node_apply_to_internal_fwd_back - (msgs : betree_list_t (u64 & betree_message_t)) (key : u64) - (new_msg : betree_message_t) : - result (betree_list_t (u64 & betree_message_t)) +let betree_Node_apply_to_internal + (msgs : betree_List_t (u64 & betree_Message_t)) (key : u64) + (new_msg : betree_Message_t) : + result (betree_List_t (u64 & betree_Message_t)) = - let* msgs0 = betree_node_lookup_first_message_for_key_fwd key msgs in - let* b = betree_list_head_has_key_fwd betree_message_t msgs0 key in + let* msgs0 = betree_Node_lookup_first_message_for_key key msgs in + let* b = betree_List_head_has_key betree_Message_t msgs0 key in if b then begin match new_msg with - | BetreeMessageInsert i -> - let* msgs1 = betree_node_filter_messages_for_key_fwd_back key msgs0 in + | Betree_Message_Insert i -> + let* msgs1 = betree_Node_filter_messages_for_key key msgs0 in let* msgs2 = - betree_list_push_front_fwd_back (u64 & betree_message_t) msgs1 (key, - BetreeMessageInsert i) in - betree_node_lookup_first_message_for_key_back key msgs msgs2 - | BetreeMessageDelete -> - let* msgs1 = betree_node_filter_messages_for_key_fwd_back key msgs0 in + betree_List_push_front (u64 & betree_Message_t) msgs1 (key, + Betree_Message_Insert i) in + betree_Node_lookup_first_message_for_key_back key msgs msgs2 + | Betree_Message_Delete -> + let* msgs1 = betree_Node_filter_messages_for_key key msgs0 in let* msgs2 = - betree_list_push_front_fwd_back (u64 & betree_message_t) msgs1 (key, - BetreeMessageDelete) in - betree_node_lookup_first_message_for_key_back key msgs msgs2 - | BetreeMessageUpsert s -> - let* p = betree_list_hd_fwd (u64 & betree_message_t) msgs0 in + betree_List_push_front (u64 & betree_Message_t) msgs1 (key, + Betree_Message_Delete) in + betree_Node_lookup_first_message_for_key_back key msgs msgs2 + | Betree_Message_Upsert s -> + let* p = betree_List_hd (u64 & betree_Message_t) msgs0 in let (_, m) = p in begin match m with - | BetreeMessageInsert prev -> - let* v = betree_upsert_update_fwd (Some prev) s in - let* msgs1 = betree_list_pop_front_back (u64 & betree_message_t) msgs0 + | Betree_Message_Insert prev -> + let* v = betree_upsert_update (Some prev) s in + let* msgs1 = betree_List_pop_front_back (u64 & betree_Message_t) msgs0 in let* msgs2 = - betree_list_push_front_fwd_back (u64 & betree_message_t) msgs1 (key, - BetreeMessageInsert v) in - betree_node_lookup_first_message_for_key_back key msgs msgs2 - | BetreeMessageDelete -> - let* v = betree_upsert_update_fwd None s in - let* msgs1 = betree_list_pop_front_back (u64 & betree_message_t) msgs0 + betree_List_push_front (u64 & betree_Message_t) msgs1 (key, + Betree_Message_Insert v) in + betree_Node_lookup_first_message_for_key_back key msgs msgs2 + | Betree_Message_Delete -> + let* v = betree_upsert_update None s in + let* msgs1 = betree_List_pop_front_back (u64 & betree_Message_t) msgs0 in let* msgs2 = - betree_list_push_front_fwd_back (u64 & betree_message_t) msgs1 (key, - BetreeMessageInsert v) in - betree_node_lookup_first_message_for_key_back key msgs msgs2 - | BetreeMessageUpsert ufs -> - let* msgs1 = betree_node_lookup_first_message_after_key_fwd key msgs0 - in + betree_List_push_front (u64 & betree_Message_t) msgs1 (key, + Betree_Message_Insert v) in + betree_Node_lookup_first_message_for_key_back key msgs msgs2 + | Betree_Message_Upsert ufs -> + let* msgs1 = betree_Node_lookup_first_message_after_key key msgs0 in let* msgs2 = - betree_list_push_front_fwd_back (u64 & betree_message_t) msgs1 (key, - BetreeMessageUpsert s) in + betree_List_push_front (u64 & betree_Message_t) msgs1 (key, + Betree_Message_Upsert s) in let* msgs3 = - betree_node_lookup_first_message_after_key_back key msgs0 msgs2 in - betree_node_lookup_first_message_for_key_back key msgs msgs3 + betree_Node_lookup_first_message_after_key_back key msgs0 msgs2 in + betree_Node_lookup_first_message_for_key_back key msgs msgs3 end end else let* msgs1 = - betree_list_push_front_fwd_back (u64 & betree_message_t) msgs0 (key, - new_msg) in - betree_node_lookup_first_message_for_key_back key msgs msgs1 + betree_List_push_front (u64 & betree_Message_t) msgs0 (key, new_msg) in + betree_Node_lookup_first_message_for_key_back key msgs msgs1 (** [betree_main::betree::Node::{5}::apply_messages_to_internal]: merged forward/backward function (there is a single backward function, and the forward function returns ()) *) -let rec betree_node_apply_messages_to_internal_fwd_back - (msgs : betree_list_t (u64 & betree_message_t)) - (new_msgs : betree_list_t (u64 & betree_message_t)) : - Tot (result (betree_list_t (u64 & betree_message_t))) - (decreases (betree_node_apply_messages_to_internal_decreases msgs new_msgs)) +let rec betree_Node_apply_messages_to_internal + (msgs : betree_List_t (u64 & betree_Message_t)) + (new_msgs : betree_List_t (u64 & betree_Message_t)) : + Tot (result (betree_List_t (u64 & betree_Message_t))) + (decreases (betree_Node_apply_messages_to_internal_decreases msgs new_msgs)) = begin match new_msgs with - | BetreeListCons new_msg new_msgs_tl -> + | Betree_List_Cons new_msg new_msgs_tl -> let (i, m) = new_msg in - let* msgs0 = betree_node_apply_to_internal_fwd_back msgs i m in - betree_node_apply_messages_to_internal_fwd_back msgs0 new_msgs_tl - | BetreeListNil -> Return msgs + let* msgs0 = betree_Node_apply_to_internal msgs i m in + betree_Node_apply_messages_to_internal msgs0 new_msgs_tl + | Betree_List_Nil -> Return msgs end (** [betree_main::betree::Node::{5}::lookup_mut_in_bindings]: forward function *) -let rec betree_node_lookup_mut_in_bindings_fwd - (key : u64) (bindings : betree_list_t (u64 & u64)) : - Tot (result (betree_list_t (u64 & u64))) - (decreases (betree_node_lookup_mut_in_bindings_decreases key bindings)) +let rec betree_Node_lookup_mut_in_bindings + (key : u64) (bindings : betree_List_t (u64 & u64)) : + Tot (result (betree_List_t (u64 & u64))) + (decreases (betree_Node_lookup_mut_in_bindings_decreases key bindings)) = begin match bindings with - | BetreeListCons hd tl -> + | Betree_List_Cons hd tl -> let (i, i0) = hd in if i >= key - then Return (BetreeListCons (i, i0) tl) - else betree_node_lookup_mut_in_bindings_fwd key tl - | BetreeListNil -> Return BetreeListNil + then Return (Betree_List_Cons (i, i0) tl) + else betree_Node_lookup_mut_in_bindings key tl + | Betree_List_Nil -> Return Betree_List_Nil end (** [betree_main::betree::Node::{5}::lookup_mut_in_bindings]: backward function 0 *) -let rec betree_node_lookup_mut_in_bindings_back - (key : u64) (bindings : betree_list_t (u64 & u64)) - (ret : betree_list_t (u64 & u64)) : - Tot (result (betree_list_t (u64 & u64))) - (decreases (betree_node_lookup_mut_in_bindings_decreases key bindings)) +let rec betree_Node_lookup_mut_in_bindings_back + (key : u64) (bindings : betree_List_t (u64 & u64)) + (ret : betree_List_t (u64 & u64)) : + Tot (result (betree_List_t (u64 & u64))) + (decreases (betree_Node_lookup_mut_in_bindings_decreases key bindings)) = begin match bindings with - | BetreeListCons hd tl -> + | Betree_List_Cons hd tl -> let (i, i0) = hd in if i >= key then Return ret else - let* tl0 = betree_node_lookup_mut_in_bindings_back key tl ret in - Return (BetreeListCons (i, i0) tl0) - | BetreeListNil -> Return ret + let* tl0 = betree_Node_lookup_mut_in_bindings_back key tl ret in + Return (Betree_List_Cons (i, i0) tl0) + | Betree_List_Nil -> Return ret end (** [betree_main::betree::Node::{5}::apply_to_leaf]: merged forward/backward function (there is a single backward function, and the forward function returns ()) *) -let betree_node_apply_to_leaf_fwd_back - (bindings : betree_list_t (u64 & u64)) (key : u64) - (new_msg : betree_message_t) : - result (betree_list_t (u64 & u64)) +let betree_Node_apply_to_leaf + (bindings : betree_List_t (u64 & u64)) (key : u64) + (new_msg : betree_Message_t) : + result (betree_List_t (u64 & u64)) = - let* bindings0 = betree_node_lookup_mut_in_bindings_fwd key bindings in - let* b = betree_list_head_has_key_fwd u64 bindings0 key in + let* bindings0 = betree_Node_lookup_mut_in_bindings key bindings in + let* b = betree_List_head_has_key u64 bindings0 key in if b then - let* hd = betree_list_pop_front_fwd (u64 & u64) bindings0 in + let* hd = betree_List_pop_front (u64 & u64) bindings0 in begin match new_msg with - | BetreeMessageInsert v -> - let* bindings1 = betree_list_pop_front_back (u64 & u64) bindings0 in - let* bindings2 = - betree_list_push_front_fwd_back (u64 & u64) bindings1 (key, v) in - betree_node_lookup_mut_in_bindings_back key bindings bindings2 - | BetreeMessageDelete -> - let* bindings1 = betree_list_pop_front_back (u64 & u64) bindings0 in - betree_node_lookup_mut_in_bindings_back key bindings bindings1 - | BetreeMessageUpsert s -> + | Betree_Message_Insert v -> + let* bindings1 = betree_List_pop_front_back (u64 & u64) bindings0 in + let* bindings2 = betree_List_push_front (u64 & u64) bindings1 (key, v) in + betree_Node_lookup_mut_in_bindings_back key bindings bindings2 + | Betree_Message_Delete -> + let* bindings1 = betree_List_pop_front_back (u64 & u64) bindings0 in + betree_Node_lookup_mut_in_bindings_back key bindings bindings1 + | Betree_Message_Upsert s -> let (_, i) = hd in - let* v = betree_upsert_update_fwd (Some i) s in - let* bindings1 = betree_list_pop_front_back (u64 & u64) bindings0 in - let* bindings2 = - betree_list_push_front_fwd_back (u64 & u64) bindings1 (key, v) in - betree_node_lookup_mut_in_bindings_back key bindings bindings2 + let* v = betree_upsert_update (Some i) s in + let* bindings1 = betree_List_pop_front_back (u64 & u64) bindings0 in + let* bindings2 = betree_List_push_front (u64 & u64) bindings1 (key, v) in + betree_Node_lookup_mut_in_bindings_back key bindings bindings2 end else begin match new_msg with - | BetreeMessageInsert v -> - let* bindings1 = - betree_list_push_front_fwd_back (u64 & u64) bindings0 (key, v) in - betree_node_lookup_mut_in_bindings_back key bindings bindings1 - | BetreeMessageDelete -> - betree_node_lookup_mut_in_bindings_back key bindings bindings0 - | BetreeMessageUpsert s -> - let* v = betree_upsert_update_fwd None s in - let* bindings1 = - betree_list_push_front_fwd_back (u64 & u64) bindings0 (key, v) in - betree_node_lookup_mut_in_bindings_back key bindings bindings1 + | Betree_Message_Insert v -> + let* bindings1 = betree_List_push_front (u64 & u64) bindings0 (key, v) in + betree_Node_lookup_mut_in_bindings_back key bindings bindings1 + | Betree_Message_Delete -> + betree_Node_lookup_mut_in_bindings_back key bindings bindings0 + | Betree_Message_Upsert s -> + let* v = betree_upsert_update None s in + let* bindings1 = betree_List_push_front (u64 & u64) bindings0 (key, v) in + betree_Node_lookup_mut_in_bindings_back key bindings bindings1 end (** [betree_main::betree::Node::{5}::apply_messages_to_leaf]: merged forward/backward function (there is a single backward function, and the forward function returns ()) *) -let rec betree_node_apply_messages_to_leaf_fwd_back - (bindings : betree_list_t (u64 & u64)) - (new_msgs : betree_list_t (u64 & betree_message_t)) : - Tot (result (betree_list_t (u64 & u64))) - (decreases (betree_node_apply_messages_to_leaf_decreases bindings new_msgs)) +let rec betree_Node_apply_messages_to_leaf + (bindings : betree_List_t (u64 & u64)) + (new_msgs : betree_List_t (u64 & betree_Message_t)) : + Tot (result (betree_List_t (u64 & u64))) + (decreases (betree_Node_apply_messages_to_leaf_decreases bindings new_msgs)) = begin match new_msgs with - | BetreeListCons new_msg new_msgs_tl -> + | Betree_List_Cons new_msg new_msgs_tl -> let (i, m) = new_msg in - let* bindings0 = betree_node_apply_to_leaf_fwd_back bindings i m in - betree_node_apply_messages_to_leaf_fwd_back bindings0 new_msgs_tl - | BetreeListNil -> Return bindings + let* bindings0 = betree_Node_apply_to_leaf bindings i m in + betree_Node_apply_messages_to_leaf bindings0 new_msgs_tl + | Betree_List_Nil -> Return bindings end (** [betree_main::betree::Internal::{4}::flush]: forward function *) -let rec betree_internal_flush_fwd - (self : betree_internal_t) (params : betree_params_t) - (node_id_cnt : betree_node_id_counter_t) - (content : betree_list_t (u64 & betree_message_t)) (st : state) : - Tot (result (state & (betree_list_t (u64 & betree_message_t)))) +let rec betree_Internal_flush + (self : betree_Internal_t) (params : betree_Params_t) + (node_id_cnt : betree_NodeIdCounter_t) + (content : betree_List_t (u64 & betree_Message_t)) (st : state) : + Tot (result (state & (betree_List_t (u64 & betree_Message_t)))) (decreases ( - betree_internal_flush_decreases self params node_id_cnt content st)) + betree_Internal_flush_decreases self params node_id_cnt content st)) = - let* p = - betree_list_partition_at_pivot_fwd betree_message_t content - self.betree_internal_pivot in + let* p = betree_List_partition_at_pivot betree_Message_t content self.pivot + in let (msgs_left, msgs_right) = p in - let* len_left = betree_list_len_fwd (u64 & betree_message_t) msgs_left in - if len_left >= params.betree_params_min_flush_size + let* len_left = betree_List_len (u64 & betree_Message_t) msgs_left in + if len_left >= params.min_flush_size then let* (st0, _) = - betree_node_apply_messages_fwd self.betree_internal_left params - node_id_cnt msgs_left st in + betree_Node_apply_messages self.left params node_id_cnt msgs_left st in let* (st1, (_, node_id_cnt0)) = - betree_node_apply_messages_back'a self.betree_internal_left params - node_id_cnt msgs_left st st0 in + betree_Node_apply_messages_back'a self.left params node_id_cnt msgs_left + st st0 in let* (st2, ()) = - betree_node_apply_messages_back1 self.betree_internal_left params - node_id_cnt msgs_left st st1 in - let* len_right = betree_list_len_fwd (u64 & betree_message_t) msgs_right in - if len_right >= params.betree_params_min_flush_size + betree_Node_apply_messages_back1 self.left params node_id_cnt msgs_left + st st1 in + let* len_right = betree_List_len (u64 & betree_Message_t) msgs_right in + if len_right >= params.min_flush_size then let* (st3, _) = - betree_node_apply_messages_fwd self.betree_internal_right params - node_id_cnt0 msgs_right st2 in + betree_Node_apply_messages self.right params node_id_cnt0 msgs_right + st2 in let* (st4, (_, _)) = - betree_node_apply_messages_back'a self.betree_internal_right params - node_id_cnt0 msgs_right st2 st3 in + betree_Node_apply_messages_back'a self.right params node_id_cnt0 + msgs_right st2 st3 in let* (st5, ()) = - betree_node_apply_messages_back1 self.betree_internal_right params - node_id_cnt0 msgs_right st2 st4 in - Return (st5, BetreeListNil) + betree_Node_apply_messages_back1 self.right params node_id_cnt0 + msgs_right st2 st4 in + Return (st5, Betree_List_Nil) else Return (st2, msgs_right) else let* (st0, _) = - betree_node_apply_messages_fwd self.betree_internal_right params - node_id_cnt msgs_right st in + betree_Node_apply_messages self.right params node_id_cnt msgs_right st in let* (st1, (_, _)) = - betree_node_apply_messages_back'a self.betree_internal_right params - node_id_cnt msgs_right st st0 in + betree_Node_apply_messages_back'a self.right params node_id_cnt + msgs_right st st0 in let* (st2, ()) = - betree_node_apply_messages_back1 self.betree_internal_right params - node_id_cnt msgs_right st st1 in + betree_Node_apply_messages_back1 self.right params node_id_cnt msgs_right + st st1 in Return (st2, msgs_left) (** [betree_main::betree::Internal::{4}::flush]: backward function 0 *) -and betree_internal_flush_back'a - (self : betree_internal_t) (params : betree_params_t) - (node_id_cnt : betree_node_id_counter_t) - (content : betree_list_t (u64 & betree_message_t)) (st : state) (st0 : state) +and betree_Internal_flush_back'a + (self : betree_Internal_t) (params : betree_Params_t) + (node_id_cnt : betree_NodeIdCounter_t) + (content : betree_List_t (u64 & betree_Message_t)) (st : state) (st0 : state) : - Tot (result (state & (betree_internal_t & betree_node_id_counter_t))) + Tot (result (state & (betree_Internal_t & betree_NodeIdCounter_t))) (decreases ( - betree_internal_flush_decreases self params node_id_cnt content st)) + betree_Internal_flush_decreases self params node_id_cnt content st)) = - let* p = - betree_list_partition_at_pivot_fwd betree_message_t content - self.betree_internal_pivot in + let* p = betree_List_partition_at_pivot betree_Message_t content self.pivot + in let (msgs_left, msgs_right) = p in - let* len_left = betree_list_len_fwd (u64 & betree_message_t) msgs_left in - if len_left >= params.betree_params_min_flush_size + let* len_left = betree_List_len (u64 & betree_Message_t) msgs_left in + if len_left >= params.min_flush_size then let* (st1, _) = - betree_node_apply_messages_fwd self.betree_internal_left params - node_id_cnt msgs_left st in + betree_Node_apply_messages self.left params node_id_cnt msgs_left st in let* (st2, (n, node_id_cnt0)) = - betree_node_apply_messages_back'a self.betree_internal_left params - node_id_cnt msgs_left st st1 in + betree_Node_apply_messages_back'a self.left params node_id_cnt msgs_left + st st1 in let* (st3, ()) = - betree_node_apply_messages_back1 self.betree_internal_left params - node_id_cnt msgs_left st st2 in - let* len_right = betree_list_len_fwd (u64 & betree_message_t) msgs_right in - if len_right >= params.betree_params_min_flush_size + betree_Node_apply_messages_back1 self.left params node_id_cnt msgs_left + st st2 in + let* len_right = betree_List_len (u64 & betree_Message_t) msgs_right in + if len_right >= params.min_flush_size then let* (st4, _) = - betree_node_apply_messages_fwd self.betree_internal_right params - node_id_cnt0 msgs_right st3 in + betree_Node_apply_messages self.right params node_id_cnt0 msgs_right + st3 in let* (st5, (n0, node_id_cnt1)) = - betree_node_apply_messages_back'a self.betree_internal_right params - node_id_cnt0 msgs_right st3 st4 in + betree_Node_apply_messages_back'a self.right params node_id_cnt0 + msgs_right st3 st4 in let* _ = - betree_node_apply_messages_back1 self.betree_internal_right params - node_id_cnt0 msgs_right st3 st5 in - Return (st0, - ({ self with betree_internal_left = n; betree_internal_right = n0 }, - node_id_cnt1)) - else Return (st0, ({ self with betree_internal_left = n }, node_id_cnt0)) + betree_Node_apply_messages_back1 self.right params node_id_cnt0 + msgs_right st3 st5 in + Return (st0, ({ self with left = n; right = n0 }, node_id_cnt1)) + else Return (st0, ({ self with left = n }, node_id_cnt0)) else let* (st1, _) = - betree_node_apply_messages_fwd self.betree_internal_right params - node_id_cnt msgs_right st in + betree_Node_apply_messages self.right params node_id_cnt msgs_right st in let* (st2, (n, node_id_cnt0)) = - betree_node_apply_messages_back'a self.betree_internal_right params - node_id_cnt msgs_right st st1 in + betree_Node_apply_messages_back'a self.right params node_id_cnt + msgs_right st st1 in let* _ = - betree_node_apply_messages_back1 self.betree_internal_right params - node_id_cnt msgs_right st st2 in - Return (st0, ({ self with betree_internal_right = n }, node_id_cnt0)) + betree_Node_apply_messages_back1 self.right params node_id_cnt msgs_right + st st2 in + Return (st0, ({ self with right = n }, node_id_cnt0)) (** [betree_main::betree::Internal::{4}::flush]: backward function 1 *) -and betree_internal_flush_back1 - (self : betree_internal_t) (params : betree_params_t) - (node_id_cnt : betree_node_id_counter_t) - (content : betree_list_t (u64 & betree_message_t)) (st : state) (st0 : state) +and betree_Internal_flush_back1 + (self : betree_Internal_t) (params : betree_Params_t) + (node_id_cnt : betree_NodeIdCounter_t) + (content : betree_List_t (u64 & betree_Message_t)) (st : state) (st0 : state) : Tot (result (state & unit)) (decreases ( - betree_internal_flush_decreases self params node_id_cnt content st)) + betree_Internal_flush_decreases self params node_id_cnt content st)) = - let* p = - betree_list_partition_at_pivot_fwd betree_message_t content - self.betree_internal_pivot in + let* p = betree_List_partition_at_pivot betree_Message_t content self.pivot + in let (msgs_left, msgs_right) = p in - let* len_left = betree_list_len_fwd (u64 & betree_message_t) msgs_left in - if len_left >= params.betree_params_min_flush_size + let* len_left = betree_List_len (u64 & betree_Message_t) msgs_left in + if len_left >= params.min_flush_size then let* (st1, _) = - betree_node_apply_messages_fwd self.betree_internal_left params - node_id_cnt msgs_left st in + betree_Node_apply_messages self.left params node_id_cnt msgs_left st in let* (st2, (_, node_id_cnt0)) = - betree_node_apply_messages_back'a self.betree_internal_left params - node_id_cnt msgs_left st st1 in + betree_Node_apply_messages_back'a self.left params node_id_cnt msgs_left + st st1 in let* (st3, ()) = - betree_node_apply_messages_back1 self.betree_internal_left params - node_id_cnt msgs_left st st2 in - let* len_right = betree_list_len_fwd (u64 & betree_message_t) msgs_right in - if len_right >= params.betree_params_min_flush_size + betree_Node_apply_messages_back1 self.left params node_id_cnt msgs_left + st st2 in + let* len_right = betree_List_len (u64 & betree_Message_t) msgs_right in + if len_right >= params.min_flush_size then let* (st4, _) = - betree_node_apply_messages_fwd self.betree_internal_right params - node_id_cnt0 msgs_right st3 in + betree_Node_apply_messages self.right params node_id_cnt0 msgs_right + st3 in let* (st5, (_, _)) = - betree_node_apply_messages_back'a self.betree_internal_right params - node_id_cnt0 msgs_right st3 st4 in + betree_Node_apply_messages_back'a self.right params node_id_cnt0 + msgs_right st3 st4 in let* _ = - betree_node_apply_messages_back1 self.betree_internal_right params - node_id_cnt0 msgs_right st3 st5 in + betree_Node_apply_messages_back1 self.right params node_id_cnt0 + msgs_right st3 st5 in Return (st0, ()) else Return (st0, ()) else let* (st1, _) = - betree_node_apply_messages_fwd self.betree_internal_right params - node_id_cnt msgs_right st in + betree_Node_apply_messages self.right params node_id_cnt msgs_right st in let* (st2, (_, _)) = - betree_node_apply_messages_back'a self.betree_internal_right params - node_id_cnt msgs_right st st1 in + betree_Node_apply_messages_back'a self.right params node_id_cnt + msgs_right st st1 in let* _ = - betree_node_apply_messages_back1 self.betree_internal_right params - node_id_cnt msgs_right st st2 in + betree_Node_apply_messages_back1 self.right params node_id_cnt msgs_right + st st2 in Return (st0, ()) (** [betree_main::betree::Node::{5}::apply_messages]: forward function *) -and betree_node_apply_messages_fwd - (self : betree_node_t) (params : betree_params_t) - (node_id_cnt : betree_node_id_counter_t) - (msgs : betree_list_t (u64 & betree_message_t)) (st : state) : +and betree_Node_apply_messages + (self : betree_Node_t) (params : betree_Params_t) + (node_id_cnt : betree_NodeIdCounter_t) + (msgs : betree_List_t (u64 & betree_Message_t)) (st : state) : Tot (result (state & unit)) (decreases ( - betree_node_apply_messages_decreases self params node_id_cnt msgs st)) + betree_Node_apply_messages_decreases self params node_id_cnt msgs st)) = begin match self with - | BetreeNodeInternal node -> - let* (st0, content) = - betree_load_internal_node_fwd node.betree_internal_id st in - let* content0 = - betree_node_apply_messages_to_internal_fwd_back content msgs in - let* num_msgs = betree_list_len_fwd (u64 & betree_message_t) content0 in - if num_msgs >= params.betree_params_min_flush_size + | Betree_Node_Internal node -> + let* (st0, content) = betree_load_internal_node node.id st in + let* content0 = betree_Node_apply_messages_to_internal content msgs in + let* num_msgs = betree_List_len (u64 & betree_Message_t) content0 in + if num_msgs >= params.min_flush_size then let* (st1, content1) = - betree_internal_flush_fwd node params node_id_cnt content0 st0 in + betree_Internal_flush node params node_id_cnt content0 st0 in let* (st2, (node0, _)) = - betree_internal_flush_back'a node params node_id_cnt content0 st0 st1 + betree_Internal_flush_back'a node params node_id_cnt content0 st0 st1 in - let* (st3, _) = - betree_store_internal_node_fwd node0.betree_internal_id content1 st2 in + let* (st3, _) = betree_store_internal_node node0.id content1 st2 in Return (st3, ()) else - let* (st1, _) = - betree_store_internal_node_fwd node.betree_internal_id content0 st0 in + let* (st1, _) = betree_store_internal_node node.id content0 st0 in Return (st1, ()) - | BetreeNodeLeaf node -> - let* (st0, content) = betree_load_leaf_node_fwd node.betree_leaf_id st in - let* content0 = betree_node_apply_messages_to_leaf_fwd_back content msgs in - let* len = betree_list_len_fwd (u64 & u64) content0 in - let* i = u64_mul 2 params.betree_params_split_size in + | Betree_Node_Leaf node -> + let* (st0, content) = betree_load_leaf_node node.id st in + let* content0 = betree_Node_apply_messages_to_leaf content msgs in + let* len = betree_List_len (u64 & u64) content0 in + let* i = u64_mul 2 params.split_size in if len >= i then - let* (st1, _) = - betree_leaf_split_fwd node content0 params node_id_cnt st0 in - let* (st2, _) = - betree_store_leaf_node_fwd node.betree_leaf_id BetreeListNil st1 in - betree_leaf_split_back0 node content0 params node_id_cnt st0 st2 + let* (st1, _) = betree_Leaf_split node content0 params node_id_cnt st0 in + let* (st2, _) = betree_store_leaf_node node.id Betree_List_Nil st1 in + betree_Leaf_split_back0 node content0 params node_id_cnt st0 st2 else - let* (st1, _) = - betree_store_leaf_node_fwd node.betree_leaf_id content0 st0 in + let* (st1, _) = betree_store_leaf_node node.id content0 st0 in Return (st1, ()) end (** [betree_main::betree::Node::{5}::apply_messages]: backward function 0 *) -and betree_node_apply_messages_back'a - (self : betree_node_t) (params : betree_params_t) - (node_id_cnt : betree_node_id_counter_t) - (msgs : betree_list_t (u64 & betree_message_t)) (st : state) (st0 : state) : - Tot (result (state & (betree_node_t & betree_node_id_counter_t))) +and betree_Node_apply_messages_back'a + (self : betree_Node_t) (params : betree_Params_t) + (node_id_cnt : betree_NodeIdCounter_t) + (msgs : betree_List_t (u64 & betree_Message_t)) (st : state) (st0 : state) : + Tot (result (state & (betree_Node_t & betree_NodeIdCounter_t))) (decreases ( - betree_node_apply_messages_decreases self params node_id_cnt msgs st)) + betree_Node_apply_messages_decreases self params node_id_cnt msgs st)) = begin match self with - | BetreeNodeInternal node -> - let* (st1, content) = - betree_load_internal_node_fwd node.betree_internal_id st in - let* content0 = - betree_node_apply_messages_to_internal_fwd_back content msgs in - let* num_msgs = betree_list_len_fwd (u64 & betree_message_t) content0 in - if num_msgs >= params.betree_params_min_flush_size + | Betree_Node_Internal node -> + let* (st1, content) = betree_load_internal_node node.id st in + let* content0 = betree_Node_apply_messages_to_internal content msgs in + let* num_msgs = betree_List_len (u64 & betree_Message_t) content0 in + if num_msgs >= params.min_flush_size then let* (st2, content1) = - betree_internal_flush_fwd node params node_id_cnt content0 st1 in + betree_Internal_flush node params node_id_cnt content0 st1 in let* (st3, (node0, node_id_cnt0)) = - betree_internal_flush_back'a node params node_id_cnt content0 st1 st2 + betree_Internal_flush_back'a node params node_id_cnt content0 st1 st2 in - let* _ = - betree_store_internal_node_fwd node0.betree_internal_id content1 st3 in - Return (st0, (BetreeNodeInternal node0, node_id_cnt0)) + let* _ = betree_store_internal_node node0.id content1 st3 in + Return (st0, (Betree_Node_Internal node0, node_id_cnt0)) else - let* _ = - betree_store_internal_node_fwd node.betree_internal_id content0 st1 in - Return (st0, (BetreeNodeInternal node, node_id_cnt)) - | BetreeNodeLeaf node -> - let* (st1, content) = betree_load_leaf_node_fwd node.betree_leaf_id st in - let* content0 = betree_node_apply_messages_to_leaf_fwd_back content msgs in - let* len = betree_list_len_fwd (u64 & u64) content0 in - let* i = u64_mul 2 params.betree_params_split_size in + let* _ = betree_store_internal_node node.id content0 st1 in + Return (st0, (Betree_Node_Internal node, node_id_cnt)) + | Betree_Node_Leaf node -> + let* (st1, content) = betree_load_leaf_node node.id st in + let* content0 = betree_Node_apply_messages_to_leaf content msgs in + let* len = betree_List_len (u64 & u64) content0 in + let* i = u64_mul 2 params.split_size in if len >= i then let* (st2, new_node) = - betree_leaf_split_fwd node content0 params node_id_cnt st1 in - let* (st3, _) = - betree_store_leaf_node_fwd node.betree_leaf_id BetreeListNil st2 in - let* _ = betree_leaf_split_back0 node content0 params node_id_cnt st1 st3 + betree_Leaf_split node content0 params node_id_cnt st1 in + let* (st3, _) = betree_store_leaf_node node.id Betree_List_Nil st2 in + let* _ = betree_Leaf_split_back0 node content0 params node_id_cnt st1 st3 in let* (st4, node_id_cnt0) = - betree_leaf_split_back2 node content0 params node_id_cnt st1 st0 in - Return (st4, (BetreeNodeInternal new_node, node_id_cnt0)) + betree_Leaf_split_back2 node content0 params node_id_cnt st1 st0 in + Return (st4, (Betree_Node_Internal new_node, node_id_cnt0)) else - let* _ = betree_store_leaf_node_fwd node.betree_leaf_id content0 st1 in - Return (st0, (BetreeNodeLeaf { node with betree_leaf_size = len }, - node_id_cnt)) + let* _ = betree_store_leaf_node node.id content0 st1 in + Return (st0, (Betree_Node_Leaf { node with size = len }, node_id_cnt)) end (** [betree_main::betree::Node::{5}::apply_messages]: backward function 1 *) -and betree_node_apply_messages_back1 - (self : betree_node_t) (params : betree_params_t) - (node_id_cnt : betree_node_id_counter_t) - (msgs : betree_list_t (u64 & betree_message_t)) (st : state) (st0 : state) : +and betree_Node_apply_messages_back1 + (self : betree_Node_t) (params : betree_Params_t) + (node_id_cnt : betree_NodeIdCounter_t) + (msgs : betree_List_t (u64 & betree_Message_t)) (st : state) (st0 : state) : Tot (result (state & unit)) (decreases ( - betree_node_apply_messages_decreases self params node_id_cnt msgs st)) + betree_Node_apply_messages_decreases self params node_id_cnt msgs st)) = begin match self with - | BetreeNodeInternal node -> - let* (st1, content) = - betree_load_internal_node_fwd node.betree_internal_id st in - let* content0 = - betree_node_apply_messages_to_internal_fwd_back content msgs in - let* num_msgs = betree_list_len_fwd (u64 & betree_message_t) content0 in - if num_msgs >= params.betree_params_min_flush_size + | Betree_Node_Internal node -> + let* (st1, content) = betree_load_internal_node node.id st in + let* content0 = betree_Node_apply_messages_to_internal content msgs in + let* num_msgs = betree_List_len (u64 & betree_Message_t) content0 in + if num_msgs >= params.min_flush_size then let* (st2, content1) = - betree_internal_flush_fwd node params node_id_cnt content0 st1 in + betree_Internal_flush node params node_id_cnt content0 st1 in let* (st3, (node0, _)) = - betree_internal_flush_back'a node params node_id_cnt content0 st1 st2 + betree_Internal_flush_back'a node params node_id_cnt content0 st1 st2 in - let* _ = - betree_store_internal_node_fwd node0.betree_internal_id content1 st3 in - betree_internal_flush_back1 node params node_id_cnt content0 st1 st0 + let* _ = betree_store_internal_node node0.id content1 st3 in + betree_Internal_flush_back1 node params node_id_cnt content0 st1 st0 else - let* _ = - betree_store_internal_node_fwd node.betree_internal_id content0 st1 in + let* _ = betree_store_internal_node node.id content0 st1 in Return (st0, ()) - | BetreeNodeLeaf node -> - let* (st1, content) = betree_load_leaf_node_fwd node.betree_leaf_id st in - let* content0 = betree_node_apply_messages_to_leaf_fwd_back content msgs in - let* len = betree_list_len_fwd (u64 & u64) content0 in - let* i = u64_mul 2 params.betree_params_split_size in + | Betree_Node_Leaf node -> + let* (st1, content) = betree_load_leaf_node node.id st in + let* content0 = betree_Node_apply_messages_to_leaf content msgs in + let* len = betree_List_len (u64 & u64) content0 in + let* i = u64_mul 2 params.split_size in if len >= i then - let* (st2, _) = - betree_leaf_split_fwd node content0 params node_id_cnt st1 in - let* (st3, _) = - betree_store_leaf_node_fwd node.betree_leaf_id BetreeListNil st2 in - let* _ = betree_leaf_split_back0 node content0 params node_id_cnt st1 st3 + let* (st2, _) = betree_Leaf_split node content0 params node_id_cnt st1 in + let* (st3, _) = betree_store_leaf_node node.id Betree_List_Nil st2 in + let* _ = betree_Leaf_split_back0 node content0 params node_id_cnt st1 st3 in - betree_leaf_split_back1 node content0 params node_id_cnt st1 st0 + betree_Leaf_split_back1 node content0 params node_id_cnt st1 st0 else - let* _ = betree_store_leaf_node_fwd node.betree_leaf_id content0 st1 in - Return (st0, ()) + let* _ = betree_store_leaf_node node.id content0 st1 in Return (st0, ()) end (** [betree_main::betree::Node::{5}::apply]: forward function *) -let betree_node_apply_fwd - (self : betree_node_t) (params : betree_params_t) - (node_id_cnt : betree_node_id_counter_t) (key : u64) - (new_msg : betree_message_t) (st : state) : +let betree_Node_apply + (self : betree_Node_t) (params : betree_Params_t) + (node_id_cnt : betree_NodeIdCounter_t) (key : u64) + (new_msg : betree_Message_t) (st : state) : result (state & unit) = - let l = BetreeListNil in + let l = Betree_List_Nil in let* (st0, _) = - betree_node_apply_messages_fwd self params node_id_cnt (BetreeListCons - (key, new_msg) l) st in + betree_Node_apply_messages self params node_id_cnt (Betree_List_Cons (key, + new_msg) l) st in let* (st1, (_, _)) = - betree_node_apply_messages_back'a self params node_id_cnt (BetreeListCons + betree_Node_apply_messages_back'a self params node_id_cnt (Betree_List_Cons (key, new_msg) l) st st0 in - betree_node_apply_messages_back1 self params node_id_cnt (BetreeListCons + betree_Node_apply_messages_back1 self params node_id_cnt (Betree_List_Cons (key, new_msg) l) st st1 (** [betree_main::betree::Node::{5}::apply]: backward function 0 *) -let betree_node_apply_back'a - (self : betree_node_t) (params : betree_params_t) - (node_id_cnt : betree_node_id_counter_t) (key : u64) - (new_msg : betree_message_t) (st : state) (st0 : state) : - result (state & (betree_node_t & betree_node_id_counter_t)) +let betree_Node_apply_back'a + (self : betree_Node_t) (params : betree_Params_t) + (node_id_cnt : betree_NodeIdCounter_t) (key : u64) + (new_msg : betree_Message_t) (st : state) (st0 : state) : + result (state & (betree_Node_t & betree_NodeIdCounter_t)) = - let l = BetreeListNil in + let l = Betree_List_Nil in let* (st1, _) = - betree_node_apply_messages_fwd self params node_id_cnt (BetreeListCons - (key, new_msg) l) st in + betree_Node_apply_messages self params node_id_cnt (Betree_List_Cons (key, + new_msg) l) st in let* (st2, (self0, node_id_cnt0)) = - betree_node_apply_messages_back'a self params node_id_cnt (BetreeListCons + betree_Node_apply_messages_back'a self params node_id_cnt (Betree_List_Cons (key, new_msg) l) st st1 in let* _ = - betree_node_apply_messages_back1 self params node_id_cnt (BetreeListCons + betree_Node_apply_messages_back1 self params node_id_cnt (Betree_List_Cons (key, new_msg) l) st st2 in Return (st0, (self0, node_id_cnt0)) (** [betree_main::betree::Node::{5}::apply]: backward function 1 *) -let betree_node_apply_back1 - (self : betree_node_t) (params : betree_params_t) - (node_id_cnt : betree_node_id_counter_t) (key : u64) - (new_msg : betree_message_t) (st : state) (st0 : state) : +let betree_Node_apply_back1 + (self : betree_Node_t) (params : betree_Params_t) + (node_id_cnt : betree_NodeIdCounter_t) (key : u64) + (new_msg : betree_Message_t) (st : state) (st0 : state) : result (state & unit) = - let l = BetreeListNil in + let l = Betree_List_Nil in let* (st1, _) = - betree_node_apply_messages_fwd self params node_id_cnt (BetreeListCons - (key, new_msg) l) st in + betree_Node_apply_messages self params node_id_cnt (Betree_List_Cons (key, + new_msg) l) st in let* (st2, (_, _)) = - betree_node_apply_messages_back'a self params node_id_cnt (BetreeListCons + betree_Node_apply_messages_back'a self params node_id_cnt (Betree_List_Cons (key, new_msg) l) st st1 in let* _ = - betree_node_apply_messages_back1 self params node_id_cnt (BetreeListCons + betree_Node_apply_messages_back1 self params node_id_cnt (Betree_List_Cons (key, new_msg) l) st st2 in Return (st0, ()) (** [betree_main::betree::BeTree::{6}::new]: forward function *) -let betree_be_tree_new_fwd +let betree_BeTree_new (min_flush_size : u64) (split_size : u64) (st : state) : - result (state & betree_be_tree_t) + result (state & betree_BeTree_t) = - let* node_id_cnt = betree_node_id_counter_new_fwd in - let* id = betree_node_id_counter_fresh_id_fwd node_id_cnt in - let* (st0, _) = betree_store_leaf_node_fwd id BetreeListNil st in - let* node_id_cnt0 = betree_node_id_counter_fresh_id_back node_id_cnt in + let* node_id_cnt = betree_NodeIdCounter_new in + let* id = betree_NodeIdCounter_fresh_id node_id_cnt in + let* (st0, _) = betree_store_leaf_node id Betree_List_Nil st in + let* node_id_cnt0 = betree_NodeIdCounter_fresh_id_back node_id_cnt in Return (st0, { - betree_be_tree_params = - { - betree_params_min_flush_size = min_flush_size; - betree_params_split_size = split_size - }; - betree_be_tree_node_id_cnt = node_id_cnt0; - betree_be_tree_root = - (BetreeNodeLeaf { betree_leaf_id = id; betree_leaf_size = 0 }) + params = { min_flush_size = min_flush_size; split_size = split_size }; + node_id_cnt = node_id_cnt0; + root = (Betree_Node_Leaf { id = id; size = 0 }) }) (** [betree_main::betree::BeTree::{6}::apply]: forward function *) -let betree_be_tree_apply_fwd - (self : betree_be_tree_t) (key : u64) (msg : betree_message_t) (st : state) : +let betree_BeTree_apply + (self : betree_BeTree_t) (key : u64) (msg : betree_Message_t) (st : state) : result (state & unit) = let* (st0, _) = - betree_node_apply_fwd self.betree_be_tree_root self.betree_be_tree_params - self.betree_be_tree_node_id_cnt key msg st in + betree_Node_apply self.root self.params self.node_id_cnt key msg st in let* (st1, (_, _)) = - betree_node_apply_back'a self.betree_be_tree_root - self.betree_be_tree_params self.betree_be_tree_node_id_cnt key msg st st0 - in - betree_node_apply_back1 self.betree_be_tree_root self.betree_be_tree_params - self.betree_be_tree_node_id_cnt key msg st st1 + betree_Node_apply_back'a self.root self.params self.node_id_cnt key msg st + st0 in + betree_Node_apply_back1 self.root self.params self.node_id_cnt key msg st st1 (** [betree_main::betree::BeTree::{6}::apply]: backward function 0 *) -let betree_be_tree_apply_back - (self : betree_be_tree_t) (key : u64) (msg : betree_message_t) (st : state) +let betree_BeTree_apply_back + (self : betree_BeTree_t) (key : u64) (msg : betree_Message_t) (st : state) (st0 : state) : - result (state & betree_be_tree_t) + result (state & betree_BeTree_t) = let* (st1, _) = - betree_node_apply_fwd self.betree_be_tree_root self.betree_be_tree_params - self.betree_be_tree_node_id_cnt key msg st in + betree_Node_apply self.root self.params self.node_id_cnt key msg st in let* (st2, (n, nic)) = - betree_node_apply_back'a self.betree_be_tree_root - self.betree_be_tree_params self.betree_be_tree_node_id_cnt key msg st st1 - in + betree_Node_apply_back'a self.root self.params self.node_id_cnt key msg st + st1 in let* _ = - betree_node_apply_back1 self.betree_be_tree_root self.betree_be_tree_params - self.betree_be_tree_node_id_cnt key msg st st2 in - Return (st0, - { self with betree_be_tree_node_id_cnt = nic; betree_be_tree_root = n }) + betree_Node_apply_back1 self.root self.params self.node_id_cnt key msg st + st2 in + Return (st0, { self with node_id_cnt = nic; root = n }) (** [betree_main::betree::BeTree::{6}::insert]: forward function *) -let betree_be_tree_insert_fwd - (self : betree_be_tree_t) (key : u64) (value : u64) (st : state) : +let betree_BeTree_insert + (self : betree_BeTree_t) (key : u64) (value : u64) (st : state) : result (state & unit) = - let* (st0, _) = - betree_be_tree_apply_fwd self key (BetreeMessageInsert value) st in + let* (st0, _) = betree_BeTree_apply self key (Betree_Message_Insert value) st + in let* (st1, _) = - betree_be_tree_apply_back self key (BetreeMessageInsert value) st st0 in + betree_BeTree_apply_back self key (Betree_Message_Insert value) st st0 in Return (st1, ()) (** [betree_main::betree::BeTree::{6}::insert]: backward function 0 *) -let betree_be_tree_insert_back - (self : betree_be_tree_t) (key : u64) (value : u64) (st : state) - (st0 : state) : - result (state & betree_be_tree_t) +let betree_BeTree_insert_back + (self : betree_BeTree_t) (key : u64) (value : u64) (st : state) (st0 : state) + : + result (state & betree_BeTree_t) = - let* (st1, _) = - betree_be_tree_apply_fwd self key (BetreeMessageInsert value) st in + let* (st1, _) = betree_BeTree_apply self key (Betree_Message_Insert value) st + in let* (_, self0) = - betree_be_tree_apply_back self key (BetreeMessageInsert value) st st1 in + betree_BeTree_apply_back self key (Betree_Message_Insert value) st st1 in Return (st0, self0) (** [betree_main::betree::BeTree::{6}::delete]: forward function *) -let betree_be_tree_delete_fwd - (self : betree_be_tree_t) (key : u64) (st : state) : result (state & unit) = - let* (st0, _) = betree_be_tree_apply_fwd self key BetreeMessageDelete st in - let* (st1, _) = betree_be_tree_apply_back self key BetreeMessageDelete st st0 - in +let betree_BeTree_delete + (self : betree_BeTree_t) (key : u64) (st : state) : result (state & unit) = + let* (st0, _) = betree_BeTree_apply self key Betree_Message_Delete st in + let* (st1, _) = + betree_BeTree_apply_back self key Betree_Message_Delete st st0 in Return (st1, ()) (** [betree_main::betree::BeTree::{6}::delete]: backward function 0 *) -let betree_be_tree_delete_back - (self : betree_be_tree_t) (key : u64) (st : state) (st0 : state) : - result (state & betree_be_tree_t) +let betree_BeTree_delete_back + (self : betree_BeTree_t) (key : u64) (st : state) (st0 : state) : + result (state & betree_BeTree_t) = - let* (st1, _) = betree_be_tree_apply_fwd self key BetreeMessageDelete st in + let* (st1, _) = betree_BeTree_apply self key Betree_Message_Delete st in let* (_, self0) = - betree_be_tree_apply_back self key BetreeMessageDelete st st1 in + betree_BeTree_apply_back self key Betree_Message_Delete st st1 in Return (st0, self0) (** [betree_main::betree::BeTree::{6}::upsert]: forward function *) -let betree_be_tree_upsert_fwd - (self : betree_be_tree_t) (key : u64) (upd : betree_upsert_fun_state_t) +let betree_BeTree_upsert + (self : betree_BeTree_t) (key : u64) (upd : betree_UpsertFunState_t) (st : state) : result (state & unit) = - let* (st0, _) = - betree_be_tree_apply_fwd self key (BetreeMessageUpsert upd) st in + let* (st0, _) = betree_BeTree_apply self key (Betree_Message_Upsert upd) st + in let* (st1, _) = - betree_be_tree_apply_back self key (BetreeMessageUpsert upd) st st0 in + betree_BeTree_apply_back self key (Betree_Message_Upsert upd) st st0 in Return (st1, ()) (** [betree_main::betree::BeTree::{6}::upsert]: backward function 0 *) -let betree_be_tree_upsert_back - (self : betree_be_tree_t) (key : u64) (upd : betree_upsert_fun_state_t) +let betree_BeTree_upsert_back + (self : betree_BeTree_t) (key : u64) (upd : betree_UpsertFunState_t) (st : state) (st0 : state) : - result (state & betree_be_tree_t) + result (state & betree_BeTree_t) = - let* (st1, _) = - betree_be_tree_apply_fwd self key (BetreeMessageUpsert upd) st in + let* (st1, _) = betree_BeTree_apply self key (Betree_Message_Upsert upd) st + in let* (_, self0) = - betree_be_tree_apply_back self key (BetreeMessageUpsert upd) st st1 in + betree_BeTree_apply_back self key (Betree_Message_Upsert upd) st st1 in Return (st0, self0) (** [betree_main::betree::BeTree::{6}::lookup]: forward function *) -let betree_be_tree_lookup_fwd - (self : betree_be_tree_t) (key : u64) (st : state) : +let betree_BeTree_lookup + (self : betree_BeTree_t) (key : u64) (st : state) : result (state & (option u64)) = - betree_node_lookup_fwd self.betree_be_tree_root key st + betree_Node_lookup self.root key st (** [betree_main::betree::BeTree::{6}::lookup]: backward function 0 *) -let betree_be_tree_lookup_back - (self : betree_be_tree_t) (key : u64) (st : state) (st0 : state) : - result (state & betree_be_tree_t) +let betree_BeTree_lookup_back + (self : betree_BeTree_t) (key : u64) (st : state) (st0 : state) : + result (state & betree_BeTree_t) = - let* (st1, n) = betree_node_lookup_back self.betree_be_tree_root key st st0 - in - Return (st1, { self with betree_be_tree_root = n }) + let* (st1, n) = betree_Node_lookup_back self.root key st st0 in + Return (st1, { self with root = n }) (** [betree_main::main]: forward function *) -let main_fwd : result unit = +let main : result unit = Return () (** Unit test for [betree_main::main] *) -let _ = assert_norm (main_fwd = Return ()) +let _ = assert_norm (main = Return ()) diff --git a/tests/fstar/betree_back_stateful/BetreeMain.Opaque.fsti b/tests/fstar/betree_back_stateful/BetreeMain.Opaque.fsti index c33cf225..c5d0a814 100644 --- a/tests/fstar/betree_back_stateful/BetreeMain.Opaque.fsti +++ b/tests/fstar/betree_back_stateful/BetreeMain.Opaque.fsti @@ -7,24 +7,24 @@ include BetreeMain.Types #set-options "--z3rlimit 50 --fuel 1 --ifuel 1" (** [betree_main::betree_utils::load_internal_node]: forward function *) -val betree_utils_load_internal_node_fwd - : u64 -> state -> result (state & (betree_list_t (u64 & betree_message_t))) +val betree_utils_load_internal_node + : u64 -> state -> result (state & (betree_List_t (u64 & betree_Message_t))) (** [betree_main::betree_utils::store_internal_node]: forward function *) -val betree_utils_store_internal_node_fwd +val betree_utils_store_internal_node : - u64 -> betree_list_t (u64 & betree_message_t) -> state -> result (state & + u64 -> betree_List_t (u64 & betree_Message_t) -> state -> result (state & unit) (** [betree_main::betree_utils::load_leaf_node]: forward function *) -val betree_utils_load_leaf_node_fwd - : u64 -> state -> result (state & (betree_list_t (u64 & u64))) +val betree_utils_load_leaf_node + : u64 -> state -> result (state & (betree_List_t (u64 & u64))) (** [betree_main::betree_utils::store_leaf_node]: forward function *) -val betree_utils_store_leaf_node_fwd - : u64 -> betree_list_t (u64 & u64) -> state -> result (state & unit) +val betree_utils_store_leaf_node + : u64 -> betree_List_t (u64 & u64) -> state -> result (state & unit) (** [core::option::Option::{0}::unwrap]: forward function *) -val core_option_option_unwrap_fwd +val core_option_Option_unwrap (t : Type0) : option t -> state -> result (state & t) diff --git a/tests/fstar/betree_back_stateful/BetreeMain.Types.fsti b/tests/fstar/betree_back_stateful/BetreeMain.Types.fsti index a937c726..9320f6b7 100644 --- a/tests/fstar/betree_back_stateful/BetreeMain.Types.fsti +++ b/tests/fstar/betree_back_stateful/BetreeMain.Types.fsti @@ -6,53 +6,47 @@ open Primitives #set-options "--z3rlimit 50 --fuel 1 --ifuel 1" (** [betree_main::betree::List] *) -type betree_list_t (t : Type0) = -| BetreeListCons : t -> betree_list_t t -> betree_list_t t -| BetreeListNil : betree_list_t t +type betree_List_t (t : Type0) = +| Betree_List_Cons : t -> betree_List_t t -> betree_List_t t +| Betree_List_Nil : betree_List_t t (** [betree_main::betree::UpsertFunState] *) -type betree_upsert_fun_state_t = -| BetreeUpsertFunStateAdd : u64 -> betree_upsert_fun_state_t -| BetreeUpsertFunStateSub : u64 -> betree_upsert_fun_state_t +type betree_UpsertFunState_t = +| Betree_UpsertFunState_Add : u64 -> betree_UpsertFunState_t +| Betree_UpsertFunState_Sub : u64 -> betree_UpsertFunState_t (** [betree_main::betree::Message] *) -type betree_message_t = -| BetreeMessageInsert : u64 -> betree_message_t -| BetreeMessageDelete : betree_message_t -| BetreeMessageUpsert : betree_upsert_fun_state_t -> betree_message_t +type betree_Message_t = +| Betree_Message_Insert : u64 -> betree_Message_t +| Betree_Message_Delete : betree_Message_t +| Betree_Message_Upsert : betree_UpsertFunState_t -> betree_Message_t (** [betree_main::betree::Leaf] *) -type betree_leaf_t = { betree_leaf_id : u64; betree_leaf_size : u64; } +type betree_Leaf_t = { id : u64; size : u64; } (** [betree_main::betree::Internal] *) -type betree_internal_t = +type betree_Internal_t = { - betree_internal_id : u64; - betree_internal_pivot : u64; - betree_internal_left : betree_node_t; - betree_internal_right : betree_node_t; + id : u64; pivot : u64; left : betree_Node_t; right : betree_Node_t; } (** [betree_main::betree::Node] *) -and betree_node_t = -| BetreeNodeInternal : betree_internal_t -> betree_node_t -| BetreeNodeLeaf : betree_leaf_t -> betree_node_t +and betree_Node_t = +| Betree_Node_Internal : betree_Internal_t -> betree_Node_t +| Betree_Node_Leaf : betree_Leaf_t -> betree_Node_t (** [betree_main::betree::Params] *) -type betree_params_t = -{ - betree_params_min_flush_size : u64; betree_params_split_size : u64; -} +type betree_Params_t = { min_flush_size : u64; split_size : u64; } (** [betree_main::betree::NodeIdCounter] *) -type betree_node_id_counter_t = { betree_node_id_counter_next_node_id : u64; } +type betree_NodeIdCounter_t = { next_node_id : u64; } (** [betree_main::betree::BeTree] *) -type betree_be_tree_t = +type betree_BeTree_t = { - betree_be_tree_params : betree_params_t; - betree_be_tree_node_id_cnt : betree_node_id_counter_t; - betree_be_tree_root : betree_node_t; + params : betree_Params_t; + node_id_cnt : betree_NodeIdCounter_t; + root : betree_Node_t; } (** The state type used in the state-error monad *) diff --git a/tests/fstar/betree_back_stateful/Primitives.fst b/tests/fstar/betree_back_stateful/Primitives.fst index 3110b247..71d75c11 100644 --- a/tests/fstar/betree_back_stateful/Primitives.fst +++ b/tests/fstar/betree_back_stateful/Primitives.fst @@ -707,5 +707,7 @@ let alloc_vec_Vec_coreopsindexIndexMutInst (t idx : Type0) let alloc_vec_Vec_index_mut_back_eq (#a : Type0) (v : alloc_vec_Vec a) (i : usize) (x : a) : Lemma ( alloc_vec_Vec_index_mut_back a usize (core_slice_index_usize_coresliceindexSliceIndexInst a) v i x == - alloc_vec_Vec_update_usize v i x) = + alloc_vec_Vec_update_usize v i x) + [SMTPat (alloc_vec_Vec_index_mut_back a usize (core_slice_index_usize_coresliceindexSliceIndexInst a) v i x)] + = admit() diff --git a/tests/fstar/hashmap/Primitives.fst b/tests/fstar/hashmap/Primitives.fst index 3110b247..71d75c11 100644 --- a/tests/fstar/hashmap/Primitives.fst +++ b/tests/fstar/hashmap/Primitives.fst @@ -707,5 +707,7 @@ let alloc_vec_Vec_coreopsindexIndexMutInst (t idx : Type0) let alloc_vec_Vec_index_mut_back_eq (#a : Type0) (v : alloc_vec_Vec a) (i : usize) (x : a) : Lemma ( alloc_vec_Vec_index_mut_back a usize (core_slice_index_usize_coresliceindexSliceIndexInst a) v i x == - alloc_vec_Vec_update_usize v i x) = + alloc_vec_Vec_update_usize v i x) + [SMTPat (alloc_vec_Vec_index_mut_back a usize (core_slice_index_usize_coresliceindexSliceIndexInst a) v i x)] + = admit() diff --git a/tests/fstar/hashmap_on_disk/Primitives.fst b/tests/fstar/hashmap_on_disk/Primitives.fst index 3110b247..71d75c11 100644 --- a/tests/fstar/hashmap_on_disk/Primitives.fst +++ b/tests/fstar/hashmap_on_disk/Primitives.fst @@ -707,5 +707,7 @@ let alloc_vec_Vec_coreopsindexIndexMutInst (t idx : Type0) let alloc_vec_Vec_index_mut_back_eq (#a : Type0) (v : alloc_vec_Vec a) (i : usize) (x : a) : Lemma ( alloc_vec_Vec_index_mut_back a usize (core_slice_index_usize_coresliceindexSliceIndexInst a) v i x == - alloc_vec_Vec_update_usize v i x) = + alloc_vec_Vec_update_usize v i x) + [SMTPat (alloc_vec_Vec_index_mut_back a usize (core_slice_index_usize_coresliceindexSliceIndexInst a) v i x)] + = admit() |