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+(** THIS FILE WAS AUTOMATICALLY GENERATED BY AENEAS *)
+(** [betree_main]: function definitions *)
+module BetreeMain.Funs
+open Primitives
+include BetreeMain.Types
+include BetreeMain.Opaque
+include BetreeMain.Clauses
+
+#set-options "--z3rlimit 50 --fuel 1 --ifuel 1"
+
+(** [betree_main::betree::load_internal_node] *)
+let betree_load_internal_node_fwd
+ (id : u64) (st : state) :
+ result (state & (betree_list_t (u64 & betree_message_t)))
+ =
+ begin match betree_utils_load_internal_node_fwd id st with
+ | Fail -> Fail
+ | Return (st0, l) -> Return (st0, l)
+ end
+
+(** [betree_main::betree::store_internal_node] *)
+let betree_store_internal_node_fwd
+ (id : u64) (content : betree_list_t (u64 & betree_message_t)) (st : state) :
+ result (state & unit)
+ =
+ begin match betree_utils_store_internal_node_fwd id content st with
+ | Fail -> Fail
+ | Return (st0, _) -> Return (st0, ())
+ end
+
+(** [betree_main::betree::load_leaf_node] *)
+let betree_load_leaf_node_fwd
+ (id : u64) (st : state) : result (state & (betree_list_t (u64 & u64))) =
+ begin match betree_utils_load_leaf_node_fwd id st with
+ | Fail -> Fail
+ | Return (st0, l) -> Return (st0, l)
+ end
+
+(** [betree_main::betree::store_leaf_node] *)
+let betree_store_leaf_node_fwd
+ (id : u64) (content : betree_list_t (u64 & u64)) (st : state) :
+ result (state & unit)
+ =
+ begin match betree_utils_store_leaf_node_fwd id content st with
+ | Fail -> Fail
+ | Return (st0, _) -> Return (st0, ())
+ end
+
+(** [betree_main::betree::fresh_node_id] *)
+let betree_fresh_node_id_fwd (counter : u64) : result u64 =
+ begin match u64_add counter 1 with
+ | Fail -> Fail
+ | Return _ -> Return counter
+ end
+
+(** [betree_main::betree::fresh_node_id] *)
+let betree_fresh_node_id_back (counter : u64) : result u64 =
+ begin match u64_add counter 1 with
+ | Fail -> Fail
+ | Return counter0 -> Return counter0
+ end
+
+(** [betree_main::betree::NodeIdCounter::{0}::new] *)
+let betree_node_id_counter_new_fwd : result betree_node_id_counter_t =
+ Return (Mkbetree_node_id_counter_t 0)
+
+(** [betree_main::betree::NodeIdCounter::{0}::fresh_id] *)
+let betree_node_id_counter_fresh_id_fwd
+ (self : betree_node_id_counter_t) : result u64 =
+ begin match u64_add self.betree_node_id_counter_next_node_id 1 with
+ | Fail -> Fail
+ | Return _ -> Return self.betree_node_id_counter_next_node_id
+ end
+
+(** [betree_main::betree::NodeIdCounter::{0}::fresh_id] *)
+let betree_node_id_counter_fresh_id_back
+ (self : betree_node_id_counter_t) : result betree_node_id_counter_t =
+ begin match u64_add self.betree_node_id_counter_next_node_id 1 with
+ | Fail -> Fail
+ | Return i -> Return (Mkbetree_node_id_counter_t i)
+ end
+
+(** [core::num::u64::{10}::MAX] *)
+let core_num_u64_max_body : result u64 = Return 18446744073709551615
+let core_num_u64_max_c : u64 = eval_global core_num_u64_max_body
+
+(** [betree_main::betree::upsert_update] *)
+let betree_upsert_update_fwd
+ (prev : option u64) (st : betree_upsert_fun_state_t) : result u64 =
+ begin match prev with
+ | None ->
+ begin match st with
+ | BetreeUpsertFunStateAdd v -> Return v
+ | BetreeUpsertFunStateSub i -> Return 0
+ end
+ | Some prev0 ->
+ begin match st with
+ | BetreeUpsertFunStateAdd v ->
+ begin match u64_sub core_num_u64_max_c prev0 with
+ | Fail -> Fail
+ | Return margin ->
+ if margin >= v
+ then
+ begin match u64_add prev0 v with
+ | Fail -> Fail
+ | Return i -> Return i
+ end
+ else Return core_num_u64_max_c
+ end
+ | BetreeUpsertFunStateSub v ->
+ if prev0 >= v
+ then
+ begin match u64_sub prev0 v with
+ | Fail -> Fail
+ | Return i -> Return i
+ end
+ else Return 0
+ end
+ end
+
+(** [betree_main::betree::List::{1}::len] *)
+let rec betree_list_len_fwd
+ (t : Type0) (self : betree_list_t t) :
+ Tot (result u64) (decreases (betree_list_len_decreases t self))
+ =
+ begin match self with
+ | BetreeListCons x tl ->
+ begin match betree_list_len_fwd t tl with
+ | Fail -> Fail
+ | Return i ->
+ begin match u64_add 1 i with | Fail -> Fail | Return i0 -> Return i0 end
+ end
+ | BetreeListNil -> Return 0
+ end
+
+(** [betree_main::betree::List::{1}::split_at] *)
+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))
+ =
+ if n = 0
+ then Return (BetreeListNil, self)
+ else
+ begin match self with
+ | BetreeListCons hd tl ->
+ begin match u64_sub n 1 with
+ | Fail -> Fail
+ | Return i ->
+ begin match betree_list_split_at_fwd t tl i with
+ | Fail -> Fail
+ | Return p ->
+ let (ls0, ls1) = p in
+ let l = ls0 in Return (BetreeListCons hd l, ls1)
+ end
+ end
+ | BetreeListNil -> Fail
+ end
+
+(** [betree_main::betree::List::{1}::push_front] *)
+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 l = tl in Return (BetreeListCons x l)
+
+(** [betree_main::betree::List::{1}::pop_front] *)
+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
+ begin match ls with
+ | BetreeListCons x tl -> Return x
+ | BetreeListNil -> Fail
+ end
+
+(** [betree_main::betree::List::{1}::pop_front] *)
+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
+ begin match ls with
+ | BetreeListCons x tl -> Return tl
+ | BetreeListNil -> Fail
+ end
+
+(** [betree_main::betree::List::{1}::hd] *)
+let betree_list_hd_fwd (t : Type0) (self : betree_list_t t) : result t =
+ begin match self with
+ | BetreeListCons hd l -> Return hd
+ | BetreeListNil -> Fail
+ end
+
+(** [betree_main::betree::List::{2}::head_has_key] *)
+let betree_list_head_has_key_fwd
+ (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
+ end
+
+(** [betree_main::betree::List::{2}::partition_at_pivot] *)
+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))
+ =
+ begin match self with
+ | BetreeListCons hd tl ->
+ let (i, x) = hd in
+ if i >= pivot
+ then Return (BetreeListNil, BetreeListCons (i, x) tl)
+ else
+ begin match betree_list_partition_at_pivot_fwd t tl pivot with
+ | Fail -> Fail
+ | Return p ->
+ let (ls0, ls1) = p in
+ let l = ls0 in Return (BetreeListCons (i, x) l, ls1)
+ end
+ | BetreeListNil -> Return (BetreeListNil, BetreeListNil)
+ end
+
+(** [betree_main::betree::Leaf::{3}::split] *)
+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)
+ (st : state) :
+ result (state & betree_internal_t)
+ =
+ begin match
+ betree_list_split_at_fwd (u64 & u64) content
+ params.betree_params_split_size with
+ | Fail -> Fail
+ | Return p ->
+ let (content0, content1) = p in
+ begin match betree_list_hd_fwd (u64 & u64) content1 with
+ | Fail -> Fail
+ | Return p0 ->
+ let (pivot, _) = p0 in
+ begin match betree_node_id_counter_fresh_id_fwd node_id_cnt with
+ | Fail -> Fail
+ | Return id0 ->
+ begin match betree_node_id_counter_fresh_id_back node_id_cnt with
+ | Fail -> Fail
+ | Return node_id_cnt0 ->
+ begin match betree_node_id_counter_fresh_id_fwd node_id_cnt0 with
+ | Fail -> Fail
+ | Return id1 ->
+ begin match betree_store_leaf_node_fwd id0 content0 st with
+ | Fail -> Fail
+ | Return (st0, _) ->
+ begin match betree_store_leaf_node_fwd id1 content1 st0 with
+ | Fail -> Fail
+ | Return (st1, _) ->
+ let n = BetreeNodeLeaf (Mkbetree_leaf_t id0
+ params.betree_params_split_size) in
+ let n0 = BetreeNodeLeaf (Mkbetree_leaf_t id1
+ params.betree_params_split_size) in
+ Return
+ (st1,
+ Mkbetree_internal_t
+ self.betree_leaf_id
+ pivot
+ n
+ n0)
+ end
+ end
+ end
+ end
+ end
+ end
+ end
+
+(** [betree_main::betree::Leaf::{3}::split] *)
+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)
+ (st : state) (st0 : state) :
+ result (state & unit)
+ =
+ begin match
+ betree_list_split_at_fwd (u64 & u64) content
+ params.betree_params_split_size with
+ | Fail -> Fail
+ | Return p ->
+ let (content0, content1) = p in
+ begin match betree_list_hd_fwd (u64 & u64) content1 with
+ | Fail -> Fail
+ | Return _ ->
+ begin match betree_node_id_counter_fresh_id_fwd node_id_cnt with
+ | Fail -> Fail
+ | Return id0 ->
+ begin match betree_node_id_counter_fresh_id_back node_id_cnt with
+ | Fail -> Fail
+ | Return node_id_cnt0 ->
+ begin match betree_node_id_counter_fresh_id_fwd node_id_cnt0 with
+ | Fail -> Fail
+ | Return id1 ->
+ begin match betree_store_leaf_node_fwd id0 content0 st with
+ | Fail -> Fail
+ | Return (st1, _) ->
+ begin match betree_store_leaf_node_fwd id1 content1 st1 with
+ | Fail -> Fail
+ | Return (_, _) -> Return (st0, ())
+ end
+ end
+ end
+ end
+ end
+ end
+ end
+
+(** [betree_main::betree::Leaf::{3}::split] *)
+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)
+ (st : state) (st0 : state) :
+ result (state & unit)
+ =
+ begin match
+ betree_list_split_at_fwd (u64 & u64) content
+ params.betree_params_split_size with
+ | Fail -> Fail
+ | Return p ->
+ let (content0, content1) = p in
+ begin match betree_list_hd_fwd (u64 & u64) content1 with
+ | Fail -> Fail
+ | Return _ ->
+ begin match betree_node_id_counter_fresh_id_fwd node_id_cnt with
+ | Fail -> Fail
+ | Return id0 ->
+ begin match betree_node_id_counter_fresh_id_back node_id_cnt with
+ | Fail -> Fail
+ | Return node_id_cnt0 ->
+ begin match betree_node_id_counter_fresh_id_fwd node_id_cnt0 with
+ | Fail -> Fail
+ | Return id1 ->
+ begin match betree_store_leaf_node_fwd id0 content0 st with
+ | Fail -> Fail
+ | Return (st1, _) ->
+ begin match betree_store_leaf_node_fwd id1 content1 st1 with
+ | Fail -> Fail
+ | Return (_, _) -> Return (st0, ())
+ end
+ end
+ end
+ end
+ end
+ end
+ end
+
+(** [betree_main::betree::Leaf::{3}::split] *)
+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)
+ (st : state) (st0 : state) :
+ result (state & betree_node_id_counter_t)
+ =
+ begin match
+ betree_list_split_at_fwd (u64 & u64) content
+ params.betree_params_split_size with
+ | Fail -> Fail
+ | Return p ->
+ let (content0, content1) = p in
+ begin match betree_list_hd_fwd (u64 & u64) content1 with
+ | Fail -> Fail
+ | Return _ ->
+ begin match betree_node_id_counter_fresh_id_fwd node_id_cnt with
+ | Fail -> Fail
+ | Return id0 ->
+ begin match betree_node_id_counter_fresh_id_back node_id_cnt with
+ | Fail -> Fail
+ | Return node_id_cnt0 ->
+ begin match betree_node_id_counter_fresh_id_fwd node_id_cnt0 with
+ | Fail -> Fail
+ | Return id1 ->
+ begin match betree_store_leaf_node_fwd id0 content0 st with
+ | Fail -> Fail
+ | Return (st1, _) ->
+ begin match betree_store_leaf_node_fwd id1 content1 st1 with
+ | Fail -> Fail
+ | Return (_, _) ->
+ begin match betree_node_id_counter_fresh_id_back node_id_cnt0
+ with
+ | Fail -> Fail
+ | Return node_id_cnt1 -> Return (st0, node_id_cnt1)
+ end
+ end
+ end
+ end
+ end
+ end
+ end
+ end
+
+(** [betree_main::betree::Node::{5}::lookup_in_bindings] *)
+let rec betree_node_lookup_in_bindings_fwd
+ (key : u64) (bindings : betree_list_t (u64 & u64)) :
+ Tot (result (option u64))
+ (decreases (betree_node_lookup_in_bindings_decreases key bindings))
+ =
+ begin match bindings with
+ | BetreeListCons hd tl ->
+ let (i, i0) = hd in
+ if i = key
+ then Return (Some i0)
+ else
+ if i > key
+ then Return None
+ else
+ begin match betree_node_lookup_in_bindings_fwd key tl with
+ | Fail -> Fail
+ | Return opt -> Return opt
+ end
+ | BetreeListNil -> Return None
+ end
+
+(** [betree_main::betree::Node::{5}::lookup_first_message_for_key] *)
+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))
+ =
+ begin match msgs with
+ | BetreeListCons x next_msgs ->
+ let (i, m) = x in
+ if i >= key
+ then Return (BetreeListCons (i, m) next_msgs)
+ else
+ begin match betree_node_lookup_first_message_for_key_fwd key next_msgs
+ with
+ | Fail -> Fail
+ | Return l -> Return l
+ end
+ | BetreeListNil -> Return BetreeListNil
+ end
+
+(** [betree_main::betree::Node::{5}::lookup_first_message_for_key] *)
+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 ->
+ let (i, m) = x in
+ if i >= key
+ then Return ret
+ else
+ begin match
+ betree_node_lookup_first_message_for_key_back key next_msgs ret with
+ | Fail -> Fail
+ | Return next_msgs0 -> Return (BetreeListCons (i, m) next_msgs0)
+ end
+ | BetreeListNil -> Return ret
+ end
+
+(** [betree_main::betree::Node::{5}::apply_upserts] *)
+let rec betree_node_apply_upserts_fwd
+ (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))
+ =
+ begin match betree_list_head_has_key_fwd betree_message_t msgs key with
+ | Fail -> Fail
+ | Return b ->
+ if b
+ then
+ begin match betree_list_pop_front_fwd (u64 & betree_message_t) msgs with
+ | Fail -> Fail
+ | Return msg ->
+ let (_, m) = msg in
+ begin match m with
+ | BetreeMessageInsert i -> Fail
+ | BetreeMessageDelete -> Fail
+ | BetreeMessageUpsert s ->
+ begin match betree_upsert_update_fwd prev s with
+ | Fail -> Fail
+ | Return v ->
+ begin match
+ betree_list_pop_front_back (u64 & betree_message_t) msgs with
+ | Fail -> Fail
+ | Return msgs0 ->
+ begin match betree_node_apply_upserts_fwd msgs0 (Some v) key st
+ with
+ | Fail -> Fail
+ | Return (st0, i) -> Return (st0, i)
+ end
+ end
+ end
+ end
+ end
+ else
+ begin match core_option_option_unwrap_fwd u64 prev st with
+ | Fail -> Fail
+ | Return (st0, v) ->
+ begin match
+ betree_list_push_front_fwd_back (u64 & betree_message_t) msgs (key,
+ BetreeMessageInsert v) with
+ | Fail -> Fail
+ | Return _ -> Return (st0, v)
+ end
+ end
+ end
+
+(** [betree_main::betree::Node::{5}::apply_upserts] *)
+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))
+ =
+ begin match betree_list_head_has_key_fwd betree_message_t msgs key with
+ | Fail -> Fail
+ | Return b ->
+ if b
+ then
+ begin match betree_list_pop_front_fwd (u64 & betree_message_t) msgs with
+ | Fail -> Fail
+ | Return msg ->
+ let (_, m) = msg in
+ begin match m with
+ | BetreeMessageInsert i -> Fail
+ | BetreeMessageDelete -> Fail
+ | BetreeMessageUpsert s ->
+ begin match betree_upsert_update_fwd prev s with
+ | Fail -> Fail
+ | Return v ->
+ begin match
+ betree_list_pop_front_back (u64 & betree_message_t) msgs with
+ | Fail -> Fail
+ | Return msgs0 ->
+ begin match
+ betree_node_apply_upserts_back msgs0 (Some v) key st st0 with
+ | Fail -> Fail
+ | Return (st1, msgs1) -> Return (st1, msgs1)
+ end
+ end
+ end
+ end
+ end
+ else
+ begin match core_option_option_unwrap_fwd u64 prev st with
+ | Fail -> Fail
+ | Return (_, v) ->
+ begin match
+ betree_list_push_front_fwd_back (u64 & betree_message_t) msgs (key,
+ BetreeMessageInsert v) with
+ | Fail -> Fail
+ | Return msgs0 -> Return (st0, msgs0)
+ end
+ end
+ end
+
+(** [betree_main::betree::Node::{5}::lookup] *)
+let rec betree_node_lookup_fwd
+ (self : betree_node_t) (key : u64) (st : state) :
+ Tot (result (state & (option u64)))
+ (decreases (betree_node_lookup_decreases self key st))
+ =
+ begin match self with
+ | BetreeNodeInternal node ->
+ begin match betree_load_internal_node_fwd node.betree_internal_id st with
+ | Fail -> Fail
+ | Return (st0, msgs) ->
+ begin match betree_node_lookup_first_message_for_key_fwd key msgs with
+ | Fail -> Fail
+ | Return pending ->
+ begin match pending with
+ | BetreeListCons p l ->
+ let (k, msg) = p in
+ if k <> key
+ then
+ begin match betree_internal_lookup_in_children_fwd node key st0
+ with
+ | Fail -> Fail
+ | Return (st1, opt) ->
+ begin match
+ betree_node_lookup_first_message_for_key_back key msgs
+ (BetreeListCons (k, msg) l) with
+ | Fail -> Fail
+ | Return _ -> Return (st1, opt)
+ end
+ end
+ else
+ begin match msg with
+ | BetreeMessageInsert v ->
+ begin match
+ betree_node_lookup_first_message_for_key_back key msgs
+ (BetreeListCons (k, BetreeMessageInsert v) l) with
+ | Fail -> Fail
+ | Return _ -> Return (st0, Some v)
+ end
+ | BetreeMessageDelete ->
+ begin match
+ betree_node_lookup_first_message_for_key_back key msgs
+ (BetreeListCons (k, BetreeMessageDelete) l) with
+ | Fail -> Fail
+ | Return _ -> Return (st0, None)
+ end
+ | BetreeMessageUpsert ufs ->
+ begin match betree_internal_lookup_in_children_fwd node key st0
+ with
+ | Fail -> Fail
+ | Return (st1, v) ->
+ begin match
+ betree_node_apply_upserts_fwd (BetreeListCons (k,
+ BetreeMessageUpsert ufs) l) v key st1 with
+ | Fail -> Fail
+ | Return (st2, v0) ->
+ begin match
+ betree_internal_lookup_in_children_back node key st0 st2
+ with
+ | Fail -> Fail
+ | Return (st3, node0) ->
+ begin match
+ betree_node_apply_upserts_back (BetreeListCons (k,
+ BetreeMessageUpsert ufs) l) v key st1 st3 with
+ | Fail -> Fail
+ | Return (st4, pending0) ->
+ begin match
+ betree_node_lookup_first_message_for_key_back key msgs
+ pending0 with
+ | Fail -> Fail
+ | Return msgs0 ->
+ begin match
+ betree_store_internal_node_fwd
+ node0.betree_internal_id msgs0 st4 with
+ | Fail -> Fail
+ | Return (st5, _) -> Return (st5, Some v0)
+ end
+ end
+ end
+ end
+ end
+ end
+ end
+ | BetreeListNil ->
+ begin match betree_internal_lookup_in_children_fwd node key st0 with
+ | Fail -> Fail
+ | Return (st1, opt) ->
+ begin match
+ betree_node_lookup_first_message_for_key_back key msgs
+ BetreeListNil with
+ | Fail -> Fail
+ | Return _ -> Return (st1, opt)
+ end
+ end
+ end
+ end
+ end
+ | BetreeNodeLeaf node ->
+ begin match betree_load_leaf_node_fwd node.betree_leaf_id st with
+ | Fail -> Fail
+ | Return (st0, bindings) ->
+ begin match betree_node_lookup_in_bindings_fwd key bindings with
+ | Fail -> Fail
+ | Return opt -> Return (st0, opt)
+ end
+ end
+ end
+
+(** [betree_main::betree::Node::{5}::lookup] *)
+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 ->
+ begin match betree_load_internal_node_fwd node.betree_internal_id st with
+ | Fail -> Fail
+ | Return (st1, msgs) ->
+ begin match betree_node_lookup_first_message_for_key_fwd key msgs with
+ | Fail -> Fail
+ | Return pending ->
+ begin match pending with
+ | BetreeListCons p l ->
+ let (k, msg) = p in
+ if k <> key
+ then
+ begin match
+ betree_node_lookup_first_message_for_key_back key msgs
+ (BetreeListCons (k, msg) l) with
+ | Fail -> Fail
+ | Return _ ->
+ begin match
+ betree_internal_lookup_in_children_back node key st1 st0 with
+ | Fail -> Fail
+ | Return (st2, node0) -> Return (st2, BetreeNodeInternal node0)
+ end
+ end
+ else
+ begin match msg with
+ | BetreeMessageInsert v ->
+ begin match
+ betree_node_lookup_first_message_for_key_back key msgs
+ (BetreeListCons (k, BetreeMessageInsert v) l) with
+ | Fail -> Fail
+ | Return _ -> Return (st0, BetreeNodeInternal node)
+ end
+ | BetreeMessageDelete ->
+ begin match
+ betree_node_lookup_first_message_for_key_back key msgs
+ (BetreeListCons (k, BetreeMessageDelete) l) with
+ | Fail -> Fail
+ | Return _ -> Return (st0, BetreeNodeInternal node)
+ end
+ | BetreeMessageUpsert ufs ->
+ begin match betree_internal_lookup_in_children_fwd node key st1
+ with
+ | Fail -> Fail
+ | Return (st2, v) ->
+ begin match
+ betree_node_apply_upserts_fwd (BetreeListCons (k,
+ BetreeMessageUpsert ufs) l) v key st2 with
+ | Fail -> Fail
+ | Return (st3, _) ->
+ begin match
+ betree_internal_lookup_in_children_back node key st1 st3
+ with
+ | Fail -> Fail
+ | Return (st4, node0) ->
+ begin match
+ betree_node_apply_upserts_back (BetreeListCons (k,
+ BetreeMessageUpsert ufs) l) v key st2 st4 with
+ | Fail -> Fail
+ | Return (st5, pending0) ->
+ begin match
+ betree_node_lookup_first_message_for_key_back key msgs
+ pending0 with
+ | Fail -> Fail
+ | Return msgs0 ->
+ begin match
+ betree_store_internal_node_fwd
+ node0.betree_internal_id msgs0 st5 with
+ | Fail -> Fail
+ | Return (_, _) ->
+ Return (st0, BetreeNodeInternal node0)
+ end
+ end
+ end
+ end
+ end
+ end
+ end
+ | BetreeListNil ->
+ begin match
+ betree_node_lookup_first_message_for_key_back key msgs
+ BetreeListNil with
+ | Fail -> Fail
+ | Return _ ->
+ begin match
+ betree_internal_lookup_in_children_back node key st1 st0 with
+ | Fail -> Fail
+ | Return (st2, node0) -> Return (st2, BetreeNodeInternal node0)
+ end
+ end
+ end
+ end
+ end
+ | BetreeNodeLeaf node ->
+ begin match betree_load_leaf_node_fwd node.betree_leaf_id st with
+ | Fail -> Fail
+ | Return (_, bindings) ->
+ begin match betree_node_lookup_in_bindings_fwd key bindings with
+ | Fail -> Fail
+ | Return _ -> Return (st0, BetreeNodeLeaf node)
+ end
+ end
+ end
+
+(** [betree_main::betree::Internal::{4}::lookup_in_children] *)
+and betree_internal_lookup_in_children_fwd
+ (self : betree_internal_t) (key : u64) (st : state) :
+ Tot (result (state & (option u64)))
+ (decreases (betree_internal_lookup_in_children_decreases self key st))
+ =
+ if key < self.betree_internal_pivot
+ then
+ begin match betree_node_lookup_fwd self.betree_internal_left key st with
+ | Fail -> Fail
+ | Return (st0, opt) -> Return (st0, opt)
+ end
+ else
+ begin match betree_node_lookup_fwd self.betree_internal_right key st with
+ | Fail -> Fail
+ | Return (st0, opt) -> Return (st0, opt)
+ end
+
+(** [betree_main::betree::Internal::{4}::lookup_in_children] *)
+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
+ then
+ begin match betree_node_lookup_back self.betree_internal_left key st st0
+ with
+ | Fail -> Fail
+ | Return (st1, n) ->
+ Return (st1, Mkbetree_internal_t self.betree_internal_id
+ self.betree_internal_pivot n self.betree_internal_right)
+ end
+ else
+ begin match betree_node_lookup_back self.betree_internal_right key st st0
+ with
+ | Fail -> Fail
+ | Return (st1, n) ->
+ Return (st1, Mkbetree_internal_t self.betree_internal_id
+ self.betree_internal_pivot self.betree_internal_left n)
+ end
+
+(** [betree_main::betree::Node::{5}::lookup_mut_in_bindings] *)
+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))
+ =
+ begin match bindings with
+ | BetreeListCons hd tl ->
+ let (i, i0) = hd in
+ if i >= key
+ then Return (BetreeListCons (i, i0) tl)
+ else
+ begin match betree_node_lookup_mut_in_bindings_fwd key tl with
+ | Fail -> Fail
+ | Return l -> Return l
+ end
+ | BetreeListNil -> Return BetreeListNil
+ end
+
+(** [betree_main::betree::Node::{5}::lookup_mut_in_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 ->
+ let (i, i0) = hd in
+ if i >= key
+ then Return ret
+ else
+ begin match betree_node_lookup_mut_in_bindings_back key tl ret with
+ | Fail -> Fail
+ | Return tl0 -> Return (BetreeListCons (i, i0) tl0)
+ end
+ | BetreeListNil -> Return ret
+ end
+
+(** [betree_main::betree::Node::{5}::apply_to_leaf] *)
+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))
+ =
+ begin match betree_node_lookup_mut_in_bindings_fwd key bindings with
+ | Fail -> Fail
+ | Return bindings0 ->
+ begin match betree_list_head_has_key_fwd u64 bindings0 key with
+ | Fail -> Fail
+ | Return b ->
+ if b
+ then
+ begin match betree_list_pop_front_fwd (u64 & u64) bindings0 with
+ | Fail -> Fail
+ | Return hd ->
+ begin match new_msg with
+ | BetreeMessageInsert v ->
+ begin match betree_list_pop_front_back (u64 & u64) bindings0 with
+ | Fail -> Fail
+ | Return bindings1 ->
+ begin match
+ betree_list_push_front_fwd_back (u64 & u64) bindings1 (key, v)
+ with
+ | Fail -> Fail
+ | Return bindings2 ->
+ begin match
+ betree_node_lookup_mut_in_bindings_back key bindings
+ bindings2 with
+ | Fail -> Fail
+ | Return bindings3 -> Return bindings3
+ end
+ end
+ end
+ | BetreeMessageDelete ->
+ begin match betree_list_pop_front_back (u64 & u64) bindings0 with
+ | Fail -> Fail
+ | Return bindings1 ->
+ begin match
+ betree_node_lookup_mut_in_bindings_back key bindings bindings1
+ with
+ | Fail -> Fail
+ | Return bindings2 -> Return bindings2
+ end
+ end
+ | BetreeMessageUpsert s ->
+ let (_, i) = hd in
+ begin match betree_upsert_update_fwd (Some i) s with
+ | Fail -> Fail
+ | Return v ->
+ begin match betree_list_pop_front_back (u64 & u64) bindings0 with
+ | Fail -> Fail
+ | Return bindings1 ->
+ begin match
+ betree_list_push_front_fwd_back (u64 & u64) bindings1 (key,
+ v) with
+ | Fail -> Fail
+ | Return bindings2 ->
+ begin match
+ betree_node_lookup_mut_in_bindings_back key bindings
+ bindings2 with
+ | Fail -> Fail
+ | Return bindings3 -> Return bindings3
+ end
+ end
+ end
+ end
+ end
+ end
+ else
+ begin match new_msg with
+ | BetreeMessageInsert v ->
+ begin match
+ betree_list_push_front_fwd_back (u64 & u64) bindings0 (key, v) with
+ | Fail -> Fail
+ | Return bindings1 ->
+ begin match
+ betree_node_lookup_mut_in_bindings_back key bindings bindings1
+ with
+ | Fail -> Fail
+ | Return bindings2 -> Return bindings2
+ end
+ end
+ | BetreeMessageDelete ->
+ begin match
+ betree_node_lookup_mut_in_bindings_back key bindings bindings0 with
+ | Fail -> Fail
+ | Return bindings1 -> Return bindings1
+ end
+ | BetreeMessageUpsert s ->
+ begin match betree_upsert_update_fwd None s with
+ | Fail -> Fail
+ | Return v ->
+ begin match
+ betree_list_push_front_fwd_back (u64 & u64) bindings0 (key, v)
+ with
+ | Fail -> Fail
+ | Return bindings1 ->
+ begin match
+ betree_node_lookup_mut_in_bindings_back key bindings bindings1
+ with
+ | Fail -> Fail
+ | Return bindings2 -> Return bindings2
+ end
+ end
+ end
+ end
+ end
+ end
+
+(** [betree_main::betree::Node::{5}::apply_messages_to_leaf] *)
+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))
+ =
+ begin match new_msgs with
+ | BetreeListCons new_msg new_msgs_tl ->
+ let (i, m) = new_msg in
+ begin match betree_node_apply_to_leaf_fwd_back bindings i m with
+ | Fail -> Fail
+ | Return bindings0 ->
+ begin match
+ betree_node_apply_messages_to_leaf_fwd_back bindings0 new_msgs_tl with
+ | Fail -> Fail
+ | Return bindings1 -> Return bindings1
+ end
+ end
+ | BetreeListNil -> Return bindings
+ end
+
+(** [betree_main::betree::Node::{5}::filter_messages_for_key] *)
+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))
+ =
+ begin match msgs with
+ | BetreeListCons p l ->
+ let (k, m) = p in
+ if k = key
+ then
+ begin match
+ betree_list_pop_front_back (u64 & betree_message_t) (BetreeListCons (k,
+ m) l) with
+ | Fail -> Fail
+ | Return msgs0 ->
+ begin match betree_node_filter_messages_for_key_fwd_back key msgs0 with
+ | Fail -> Fail
+ | Return msgs1 -> Return msgs1
+ end
+ end
+ else Return (BetreeListCons (k, m) l)
+ | BetreeListNil -> Return BetreeListNil
+ end
+
+(** [betree_main::betree::Node::{5}::lookup_first_message_after_key] *)
+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))
+ =
+ begin match msgs with
+ | BetreeListCons p next_msgs ->
+ let (k, m) = p in
+ if k = key
+ then
+ begin match betree_node_lookup_first_message_after_key_fwd key next_msgs
+ with
+ | Fail -> Fail
+ | Return l -> Return l
+ end
+ else Return (BetreeListCons (k, m) next_msgs)
+ | BetreeListNil -> Return BetreeListNil
+ end
+
+(** [betree_main::betree::Node::{5}::lookup_first_message_after_key] *)
+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 ->
+ let (k, m) = p in
+ if k = key
+ then
+ begin match
+ betree_node_lookup_first_message_after_key_back key next_msgs ret with
+ | Fail -> Fail
+ | Return next_msgs0 -> Return (BetreeListCons (k, m) next_msgs0)
+ end
+ else Return ret
+ | BetreeListNil -> Return ret
+ end
+
+(** [betree_main::betree::Node::{5}::apply_to_internal] *)
+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))
+ =
+ begin match betree_node_lookup_first_message_for_key_fwd key msgs with
+ | Fail -> Fail
+ | Return msgs0 ->
+ begin match betree_list_head_has_key_fwd betree_message_t msgs0 key with
+ | Fail -> Fail
+ | Return b ->
+ if b
+ then
+ begin match new_msg with
+ | BetreeMessageInsert i ->
+ begin match betree_node_filter_messages_for_key_fwd_back key msgs0
+ with
+ | Fail -> Fail
+ | Return msgs1 ->
+ begin match
+ betree_list_push_front_fwd_back (u64 & betree_message_t) msgs1
+ (key, BetreeMessageInsert i) with
+ | Fail -> Fail
+ | Return msgs2 ->
+ begin match
+ betree_node_lookup_first_message_for_key_back key msgs msgs2
+ with
+ | Fail -> Fail
+ | Return msgs3 -> Return msgs3
+ end
+ end
+ end
+ | BetreeMessageDelete ->
+ begin match betree_node_filter_messages_for_key_fwd_back key msgs0
+ with
+ | Fail -> Fail
+ | Return msgs1 ->
+ begin match
+ betree_list_push_front_fwd_back (u64 & betree_message_t) msgs1
+ (key, BetreeMessageDelete) with
+ | Fail -> Fail
+ | Return msgs2 ->
+ begin match
+ betree_node_lookup_first_message_for_key_back key msgs msgs2
+ with
+ | Fail -> Fail
+ | Return msgs3 -> Return msgs3
+ end
+ end
+ end
+ | BetreeMessageUpsert s ->
+ begin match betree_list_hd_fwd (u64 & betree_message_t) msgs0 with
+ | Fail -> Fail
+ | Return p ->
+ let (_, m) = p in
+ begin match m with
+ | BetreeMessageInsert prev ->
+ begin match betree_upsert_update_fwd (Some prev) s with
+ | Fail -> Fail
+ | Return v ->
+ begin match
+ betree_list_pop_front_back (u64 & betree_message_t) msgs0
+ with
+ | Fail -> Fail
+ | Return msgs1 ->
+ begin match
+ betree_list_push_front_fwd_back (u64 & betree_message_t)
+ msgs1 (key, BetreeMessageInsert v) with
+ | Fail -> Fail
+ | Return msgs2 ->
+ begin match
+ betree_node_lookup_first_message_for_key_back key msgs
+ msgs2 with
+ | Fail -> Fail
+ | Return msgs3 -> Return msgs3
+ end
+ end
+ end
+ end
+ | BetreeMessageDelete ->
+ begin match betree_upsert_update_fwd None s with
+ | Fail -> Fail
+ | Return v ->
+ begin match
+ betree_list_pop_front_back (u64 & betree_message_t) msgs0
+ with
+ | Fail -> Fail
+ | Return msgs1 ->
+ begin match
+ betree_list_push_front_fwd_back (u64 & betree_message_t)
+ msgs1 (key, BetreeMessageInsert v) with
+ | Fail -> Fail
+ | Return msgs2 ->
+ begin match
+ betree_node_lookup_first_message_for_key_back key msgs
+ msgs2 with
+ | Fail -> Fail
+ | Return msgs3 -> Return msgs3
+ end
+ end
+ end
+ end
+ | BetreeMessageUpsert ufs ->
+ begin match
+ betree_node_lookup_first_message_after_key_fwd key msgs0 with
+ | Fail -> Fail
+ | Return msgs1 ->
+ begin match
+ betree_list_push_front_fwd_back (u64 & betree_message_t)
+ msgs1 (key, BetreeMessageUpsert s) with
+ | Fail -> Fail
+ | Return msgs2 ->
+ begin match
+ betree_node_lookup_first_message_after_key_back key msgs0
+ msgs2 with
+ | Fail -> Fail
+ | Return msgs3 ->
+ begin match
+ betree_node_lookup_first_message_for_key_back key msgs
+ msgs3 with
+ | Fail -> Fail
+ | Return msgs4 -> Return msgs4
+ end
+ end
+ end
+ end
+ end
+ end
+ end
+ else
+ begin match
+ betree_list_push_front_fwd_back (u64 & betree_message_t) msgs0 (key,
+ new_msg) with
+ | Fail -> Fail
+ | Return msgs1 ->
+ begin match
+ betree_node_lookup_first_message_for_key_back key msgs msgs1 with
+ | Fail -> Fail
+ | Return msgs2 -> Return msgs2
+ end
+ end
+ end
+ end
+
+(** [betree_main::betree::Node::{5}::apply_messages_to_internal] *)
+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))
+ =
+ begin match new_msgs with
+ | BetreeListCons new_msg new_msgs_tl ->
+ let (i, m) = new_msg in
+ begin match betree_node_apply_to_internal_fwd_back msgs i m with
+ | Fail -> Fail
+ | Return msgs0 ->
+ begin match
+ betree_node_apply_messages_to_internal_fwd_back msgs0 new_msgs_tl with
+ | Fail -> Fail
+ | Return msgs1 -> Return msgs1
+ end
+ end
+ | BetreeListNil -> Return msgs
+ end
+
+(** [betree_main::betree::Node::{5}::apply_messages] *)
+let rec 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) :
+ Tot (result (state & unit))
+ (decreases (betree_node_apply_messages_decreases self params node_id_cnt msgs
+ st))
+ =
+ begin match self with
+ | BetreeNodeInternal node ->
+ begin match betree_load_internal_node_fwd node.betree_internal_id st with
+ | Fail -> Fail
+ | Return (st0, content) ->
+ begin match betree_node_apply_messages_to_internal_fwd_back content msgs
+ with
+ | Fail -> Fail
+ | Return content0 ->
+ begin match betree_list_len_fwd (u64 & betree_message_t) content0 with
+ | Fail -> Fail
+ | Return num_msgs ->
+ if num_msgs >= params.betree_params_min_flush_size
+ then
+ begin match
+ betree_internal_flush_fwd node params node_id_cnt content0 st0
+ with
+ | Fail -> Fail
+ | Return (st1, content1) ->
+ begin match
+ betree_internal_flush_back'a node params node_id_cnt content0
+ st0 st1 with
+ | Fail -> Fail
+ | Return (st2, (node0, _)) ->
+ begin match
+ betree_store_internal_node_fwd node0.betree_internal_id
+ content1 st2 with
+ | Fail -> Fail
+ | Return (st3, _) -> Return (st3, ())
+ end
+ end
+ end
+ else
+ begin match
+ betree_store_internal_node_fwd node.betree_internal_id content0
+ st0 with
+ | Fail -> Fail
+ | Return (st1, _) -> Return (st1, ())
+ end
+ end
+ end
+ end
+ | BetreeNodeLeaf node ->
+ begin match betree_load_leaf_node_fwd node.betree_leaf_id st with
+ | Fail -> Fail
+ | Return (st0, content) ->
+ begin match betree_node_apply_messages_to_leaf_fwd_back content msgs with
+ | Fail -> Fail
+ | Return content0 ->
+ begin match betree_list_len_fwd (u64 & u64) content0 with
+ | Fail -> Fail
+ | Return len ->
+ begin match u64_mul 2 params.betree_params_split_size with
+ | Fail -> Fail
+ | Return i ->
+ if len >= i
+ then
+ begin match
+ betree_leaf_split_fwd node content0 params node_id_cnt st0 with
+ | Fail -> Fail
+ | Return (st1, _) ->
+ begin match
+ betree_store_leaf_node_fwd node.betree_leaf_id BetreeListNil
+ st1 with
+ | Fail -> Fail
+ | Return (st2, _) ->
+ begin match
+ betree_leaf_split_back0 node content0 params node_id_cnt
+ st0 st2 with
+ | Fail -> Fail
+ | Return (st3, ()) -> Return (st3, ())
+ end
+ end
+ end
+ else
+ begin match
+ betree_store_leaf_node_fwd node.betree_leaf_id content0 st0
+ with
+ | Fail -> Fail
+ | Return (st1, _) -> Return (st1, ())
+ end
+ end
+ end
+ end
+ end
+ end
+
+(** [betree_main::betree::Node::{5}::apply_messages] *)
+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)))
+ (decreases (betree_node_apply_messages_decreases self params node_id_cnt msgs
+ st))
+ =
+ begin match self with
+ | BetreeNodeInternal node ->
+ begin match betree_load_internal_node_fwd node.betree_internal_id st with
+ | Fail -> Fail
+ | Return (st1, content) ->
+ begin match betree_node_apply_messages_to_internal_fwd_back content msgs
+ with
+ | Fail -> Fail
+ | Return content0 ->
+ begin match betree_list_len_fwd (u64 & betree_message_t) content0 with
+ | Fail -> Fail
+ | Return num_msgs ->
+ if num_msgs >= params.betree_params_min_flush_size
+ then
+ begin match
+ betree_internal_flush_fwd node params node_id_cnt content0 st1
+ with
+ | Fail -> Fail
+ | Return (st2, content1) ->
+ begin match
+ betree_internal_flush_back'a node params node_id_cnt content0
+ st1 st2 with
+ | Fail -> Fail
+ | Return (st3, (node0, node_id_cnt0)) ->
+ begin match
+ betree_store_internal_node_fwd node0.betree_internal_id
+ content1 st3 with
+ | Fail -> Fail
+ | Return (_, _) ->
+ Return (st0, (BetreeNodeInternal node0, node_id_cnt0))
+ end
+ end
+ end
+ else
+ begin match
+ betree_store_internal_node_fwd node.betree_internal_id content0
+ st1 with
+ | Fail -> Fail
+ | Return (_, _) ->
+ Return (st0, (BetreeNodeInternal node, node_id_cnt))
+ end
+ end
+ end
+ end
+ | BetreeNodeLeaf node ->
+ begin match betree_load_leaf_node_fwd node.betree_leaf_id st with
+ | Fail -> Fail
+ | Return (st1, content) ->
+ begin match betree_node_apply_messages_to_leaf_fwd_back content msgs with
+ | Fail -> Fail
+ | Return content0 ->
+ begin match betree_list_len_fwd (u64 & u64) content0 with
+ | Fail -> Fail
+ | Return len ->
+ begin match u64_mul 2 params.betree_params_split_size with
+ | Fail -> Fail
+ | Return i ->
+ if len >= i
+ then
+ begin match
+ betree_leaf_split_fwd node content0 params node_id_cnt st1 with
+ | Fail -> Fail
+ | Return (st2, new_node) ->
+ begin match
+ betree_store_leaf_node_fwd node.betree_leaf_id BetreeListNil
+ st2 with
+ | Fail -> Fail
+ | Return (st3, _) ->
+ begin match
+ betree_leaf_split_back0 node content0 params node_id_cnt
+ st1 st3 with
+ | Fail -> Fail
+ | Return (_, ()) ->
+ begin match
+ betree_leaf_split_back2 node content0 params node_id_cnt
+ st1 st0 with
+ | Fail -> Fail
+ | Return (st4, node_id_cnt0) ->
+ Return (st4, (BetreeNodeInternal new_node, node_id_cnt0))
+ end
+ end
+ end
+ end
+ else
+ begin match
+ betree_store_leaf_node_fwd node.betree_leaf_id content0 st1
+ with
+ | Fail -> Fail
+ | Return (_, _) ->
+ Return (st0, (BetreeNodeLeaf (Mkbetree_leaf_t
+ node.betree_leaf_id len), node_id_cnt))
+ end
+ end
+ end
+ end
+ end
+ end
+
+(** [betree_main::betree::Node::{5}::apply_messages] *)
+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) :
+ Tot (result (state & unit))
+ (decreases (betree_node_apply_messages_decreases self params node_id_cnt msgs
+ st))
+ =
+ begin match self with
+ | BetreeNodeInternal node ->
+ begin match betree_load_internal_node_fwd node.betree_internal_id st with
+ | Fail -> Fail
+ | Return (st1, content) ->
+ begin match betree_node_apply_messages_to_internal_fwd_back content msgs
+ with
+ | Fail -> Fail
+ | Return content0 ->
+ begin match betree_list_len_fwd (u64 & betree_message_t) content0 with
+ | Fail -> Fail
+ | Return num_msgs ->
+ if num_msgs >= params.betree_params_min_flush_size
+ then
+ begin match
+ betree_internal_flush_fwd node params node_id_cnt content0 st1
+ with
+ | Fail -> Fail
+ | Return (st2, content1) ->
+ begin match
+ betree_internal_flush_back'a node params node_id_cnt content0
+ st1 st2 with
+ | Fail -> Fail
+ | Return (st3, (node0, _)) ->
+ begin match
+ betree_store_internal_node_fwd node0.betree_internal_id
+ content1 st3 with
+ | Fail -> Fail
+ | Return (_, _) ->
+ begin match
+ betree_internal_flush_back1 node params node_id_cnt
+ content0 st1 st0 with
+ | Fail -> Fail
+ | Return (st4, ()) -> Return (st4, ())
+ end
+ end
+ end
+ end
+ else
+ begin match
+ betree_store_internal_node_fwd node.betree_internal_id content0
+ st1 with
+ | Fail -> Fail
+ | Return (_, _) -> Return (st0, ())
+ end
+ end
+ end
+ end
+ | BetreeNodeLeaf node ->
+ begin match betree_load_leaf_node_fwd node.betree_leaf_id st with
+ | Fail -> Fail
+ | Return (st1, content) ->
+ begin match betree_node_apply_messages_to_leaf_fwd_back content msgs with
+ | Fail -> Fail
+ | Return content0 ->
+ begin match betree_list_len_fwd (u64 & u64) content0 with
+ | Fail -> Fail
+ | Return len ->
+ begin match u64_mul 2 params.betree_params_split_size with
+ | Fail -> Fail
+ | Return i ->
+ if len >= i
+ then
+ begin match
+ betree_leaf_split_fwd node content0 params node_id_cnt st1 with
+ | Fail -> Fail
+ | Return (st2, _) ->
+ begin match
+ betree_store_leaf_node_fwd node.betree_leaf_id BetreeListNil
+ st2 with
+ | Fail -> Fail
+ | Return (st3, _) ->
+ begin match
+ betree_leaf_split_back0 node content0 params node_id_cnt
+ st1 st3 with
+ | Fail -> Fail
+ | Return (_, ()) ->
+ begin match
+ betree_leaf_split_back1 node content0 params node_id_cnt
+ st1 st0 with
+ | Fail -> Fail
+ | Return (st4, ()) -> Return (st4, ())
+ end
+ end
+ end
+ end
+ else
+ begin match
+ betree_store_leaf_node_fwd node.betree_leaf_id content0 st1
+ with
+ | Fail -> Fail
+ | Return (_, _) -> Return (st0, ())
+ end
+ end
+ end
+ end
+ end
+ end
+
+(** [betree_main::betree::Internal::{4}::flush] *)
+and 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))))
+ (decreases (betree_internal_flush_decreases self params node_id_cnt content
+ st))
+ =
+ begin match
+ betree_list_partition_at_pivot_fwd betree_message_t content
+ self.betree_internal_pivot with
+ | Fail -> Fail
+ | Return p ->
+ let (msgs_left, msgs_right) = p in
+ begin match betree_list_len_fwd (u64 & betree_message_t) msgs_left with
+ | Fail -> Fail
+ | Return len_left ->
+ if len_left >= params.betree_params_min_flush_size
+ then
+ begin match
+ betree_node_apply_messages_fwd self.betree_internal_left params
+ node_id_cnt msgs_left st with
+ | Fail -> Fail
+ | Return (st0, _) ->
+ begin match
+ betree_node_apply_messages_back'a self.betree_internal_left params
+ node_id_cnt msgs_left st st0 with
+ | Fail -> Fail
+ | Return (st1, (_, node_id_cnt0)) ->
+ begin match
+ betree_node_apply_messages_back1 self.betree_internal_left params
+ node_id_cnt msgs_left st st1 with
+ | Fail -> Fail
+ | Return (st2, ()) ->
+ begin match
+ betree_list_len_fwd (u64 & betree_message_t) msgs_right with
+ | Fail -> Fail
+ | Return len_right ->
+ if len_right >= params.betree_params_min_flush_size
+ then
+ begin match
+ betree_node_apply_messages_fwd self.betree_internal_right
+ params node_id_cnt0 msgs_right st2 with
+ | Fail -> Fail
+ | Return (st3, _) ->
+ begin match
+ betree_node_apply_messages_back'a
+ self.betree_internal_right params node_id_cnt0
+ msgs_right st2 st3 with
+ | Fail -> Fail
+ | Return (st4, (_, _)) ->
+ begin match
+ betree_node_apply_messages_back1
+ self.betree_internal_right params node_id_cnt0
+ msgs_right st2 st4 with
+ | Fail -> Fail
+ | Return (st5, ()) -> Return (st5, BetreeListNil)
+ end
+ end
+ end
+ else Return (st2, msgs_right)
+ end
+ end
+ end
+ end
+ else
+ begin match
+ betree_node_apply_messages_fwd self.betree_internal_right params
+ node_id_cnt msgs_right st with
+ | Fail -> Fail
+ | Return (st0, _) ->
+ begin match
+ betree_node_apply_messages_back'a self.betree_internal_right params
+ node_id_cnt msgs_right st st0 with
+ | Fail -> Fail
+ | Return (st1, (_, _)) ->
+ begin match
+ betree_node_apply_messages_back1 self.betree_internal_right
+ params node_id_cnt msgs_right st st1 with
+ | Fail -> Fail
+ | Return (st2, ()) -> Return (st2, msgs_left)
+ end
+ end
+ end
+ end
+ end
+
+(** [betree_main::betree::Internal::{4}::flush] *)
+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) :
+ Tot (result (state & (betree_internal_t & betree_node_id_counter_t)))
+ (decreases (betree_internal_flush_decreases self params node_id_cnt content
+ st))
+ =
+ begin match
+ betree_list_partition_at_pivot_fwd betree_message_t content
+ self.betree_internal_pivot with
+ | Fail -> Fail
+ | Return p ->
+ let (msgs_left, msgs_right) = p in
+ begin match betree_list_len_fwd (u64 & betree_message_t) msgs_left with
+ | Fail -> Fail
+ | Return len_left ->
+ if len_left >= params.betree_params_min_flush_size
+ then
+ begin match
+ betree_node_apply_messages_fwd self.betree_internal_left params
+ node_id_cnt msgs_left st with
+ | Fail -> Fail
+ | Return (st1, _) ->
+ begin match
+ betree_node_apply_messages_back'a self.betree_internal_left params
+ node_id_cnt msgs_left st st1 with
+ | Fail -> Fail
+ | Return (st2, (n, node_id_cnt0)) ->
+ begin match
+ betree_node_apply_messages_back1 self.betree_internal_left params
+ node_id_cnt msgs_left st st2 with
+ | Fail -> Fail
+ | Return (st3, ()) ->
+ begin match
+ betree_list_len_fwd (u64 & betree_message_t) msgs_right with
+ | Fail -> Fail
+ | Return len_right ->
+ if len_right >= params.betree_params_min_flush_size
+ then
+ begin match
+ betree_node_apply_messages_fwd self.betree_internal_right
+ params node_id_cnt0 msgs_right st3 with
+ | Fail -> Fail
+ | Return (st4, _) ->
+ begin match
+ betree_node_apply_messages_back'a
+ self.betree_internal_right params node_id_cnt0
+ msgs_right st3 st4 with
+ | Fail -> Fail
+ | Return (st5, (n0, node_id_cnt1)) ->
+ begin match
+ betree_node_apply_messages_back1
+ self.betree_internal_right params node_id_cnt0
+ msgs_right st3 st5 with
+ | Fail -> Fail
+ | Return (_, ()) ->
+ Return (st0, (Mkbetree_internal_t
+ self.betree_internal_id self.betree_internal_pivot n
+ n0, node_id_cnt1))
+ end
+ end
+ end
+ else
+ Return (st0, (Mkbetree_internal_t self.betree_internal_id
+ self.betree_internal_pivot n self.betree_internal_right,
+ node_id_cnt0))
+ end
+ end
+ end
+ end
+ else
+ begin match
+ betree_node_apply_messages_fwd self.betree_internal_right params
+ node_id_cnt msgs_right st with
+ | Fail -> Fail
+ | Return (st1, _) ->
+ begin match
+ betree_node_apply_messages_back'a self.betree_internal_right params
+ node_id_cnt msgs_right st st1 with
+ | Fail -> Fail
+ | Return (st2, (n, node_id_cnt0)) ->
+ begin match
+ betree_node_apply_messages_back1 self.betree_internal_right
+ params node_id_cnt msgs_right st st2 with
+ | Fail -> Fail
+ | Return (_, ()) ->
+ Return (st0, (Mkbetree_internal_t self.betree_internal_id
+ self.betree_internal_pivot self.betree_internal_left n,
+ node_id_cnt0))
+ end
+ end
+ end
+ end
+ end
+
+(** [betree_main::betree::Internal::{4}::flush] *)
+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) :
+ Tot (result (state & unit))
+ (decreases (betree_internal_flush_decreases self params node_id_cnt content
+ st))
+ =
+ begin match
+ betree_list_partition_at_pivot_fwd betree_message_t content
+ self.betree_internal_pivot with
+ | Fail -> Fail
+ | Return p ->
+ let (msgs_left, msgs_right) = p in
+ begin match betree_list_len_fwd (u64 & betree_message_t) msgs_left with
+ | Fail -> Fail
+ | Return len_left ->
+ if len_left >= params.betree_params_min_flush_size
+ then
+ begin match
+ betree_node_apply_messages_fwd self.betree_internal_left params
+ node_id_cnt msgs_left st with
+ | Fail -> Fail
+ | Return (st1, _) ->
+ begin match
+ betree_node_apply_messages_back'a self.betree_internal_left params
+ node_id_cnt msgs_left st st1 with
+ | Fail -> Fail
+ | Return (st2, (_, node_id_cnt0)) ->
+ begin match
+ betree_node_apply_messages_back1 self.betree_internal_left params
+ node_id_cnt msgs_left st st2 with
+ | Fail -> Fail
+ | Return (st3, ()) ->
+ begin match
+ betree_list_len_fwd (u64 & betree_message_t) msgs_right with
+ | Fail -> Fail
+ | Return len_right ->
+ if len_right >= params.betree_params_min_flush_size
+ then
+ begin match
+ betree_node_apply_messages_fwd self.betree_internal_right
+ params node_id_cnt0 msgs_right st3 with
+ | Fail -> Fail
+ | Return (st4, _) ->
+ begin match
+ betree_node_apply_messages_back'a
+ self.betree_internal_right params node_id_cnt0
+ msgs_right st3 st4 with
+ | Fail -> Fail
+ | Return (st5, (_, _)) ->
+ begin match
+ betree_node_apply_messages_back1
+ self.betree_internal_right params node_id_cnt0
+ msgs_right st3 st5 with
+ | Fail -> Fail
+ | Return (_, ()) -> Return (st0, ())
+ end
+ end
+ end
+ else Return (st0, ())
+ end
+ end
+ end
+ end
+ else
+ begin match
+ betree_node_apply_messages_fwd self.betree_internal_right params
+ node_id_cnt msgs_right st with
+ | Fail -> Fail
+ | Return (st1, _) ->
+ begin match
+ betree_node_apply_messages_back'a self.betree_internal_right params
+ node_id_cnt msgs_right st st1 with
+ | Fail -> Fail
+ | Return (st2, (_, _)) ->
+ begin match
+ betree_node_apply_messages_back1 self.betree_internal_right
+ params node_id_cnt msgs_right st st2 with
+ | Fail -> Fail
+ | Return (_, ()) -> Return (st0, ())
+ end
+ end
+ end
+ end
+ end
+
+(** [betree_main::betree::Node::{5}::apply] *)
+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) :
+ result (state & unit)
+ =
+ let l = BetreeListNil in
+ begin match
+ betree_node_apply_messages_fwd self params node_id_cnt (BetreeListCons
+ (key, new_msg) l) st with
+ | Fail -> Fail
+ | Return (st0, _) ->
+ begin match
+ betree_node_apply_messages_back'a self params node_id_cnt (BetreeListCons
+ (key, new_msg) l) st st0 with
+ | Fail -> Fail
+ | Return (st1, (_, _)) ->
+ begin match
+ betree_node_apply_messages_back1 self params node_id_cnt
+ (BetreeListCons (key, new_msg) l) st st1 with
+ | Fail -> Fail
+ | Return (st2, ()) -> Return (st2, ())
+ end
+ end
+ end
+
+(** [betree_main::betree::Node::{5}::apply] *)
+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 l = BetreeListNil in
+ begin match
+ betree_node_apply_messages_fwd self params node_id_cnt (BetreeListCons
+ (key, new_msg) l) st with
+ | Fail -> Fail
+ | Return (st1, _) ->
+ begin match
+ betree_node_apply_messages_back'a self params node_id_cnt (BetreeListCons
+ (key, new_msg) l) st st1 with
+ | Fail -> Fail
+ | Return (st2, (self0, node_id_cnt0)) ->
+ begin match
+ betree_node_apply_messages_back1 self params node_id_cnt
+ (BetreeListCons (key, new_msg) l) st st2 with
+ | Fail -> Fail
+ | Return (_, ()) -> Return (st0, (self0, node_id_cnt0))
+ end
+ end
+ end
+
+(** [betree_main::betree::Node::{5}::apply] *)
+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) :
+ result (state & unit)
+ =
+ let l = BetreeListNil in
+ begin match
+ betree_node_apply_messages_fwd self params node_id_cnt (BetreeListCons
+ (key, new_msg) l) st with
+ | Fail -> Fail
+ | Return (st1, _) ->
+ begin match
+ betree_node_apply_messages_back'a self params node_id_cnt (BetreeListCons
+ (key, new_msg) l) st st1 with
+ | Fail -> Fail
+ | Return (st2, (_, _)) ->
+ begin match
+ betree_node_apply_messages_back1 self params node_id_cnt
+ (BetreeListCons (key, new_msg) l) st st2 with
+ | Fail -> Fail
+ | Return (_, ()) -> Return (st0, ())
+ end
+ end
+ end
+
+(** [betree_main::betree::BeTree::{6}::new] *)
+let betree_be_tree_new_fwd
+ (min_flush_size : u64) (split_size : u64) (st : state) :
+ result (state & betree_be_tree_t)
+ =
+ begin match betree_node_id_counter_new_fwd with
+ | Fail -> Fail
+ | Return node_id_cnt ->
+ begin match betree_node_id_counter_fresh_id_fwd node_id_cnt with
+ | Fail -> Fail
+ | Return id ->
+ begin match betree_store_leaf_node_fwd id BetreeListNil st with
+ | Fail -> Fail
+ | Return (st0, _) ->
+ begin match betree_node_id_counter_fresh_id_back node_id_cnt with
+ | Fail -> Fail
+ | Return node_id_cnt0 ->
+ Return (st0, Mkbetree_be_tree_t (Mkbetree_params_t min_flush_size
+ split_size) node_id_cnt0 (BetreeNodeLeaf (Mkbetree_leaf_t id 0)))
+ end
+ end
+ end
+ end
+
+(** [betree_main::betree::BeTree::{6}::apply] *)
+let betree_be_tree_apply_fwd
+ (self : betree_be_tree_t) (key : u64) (msg : betree_message_t) (st : state) :
+ result (state & unit)
+ =
+ begin match
+ betree_node_apply_fwd self.betree_be_tree_root self.betree_be_tree_params
+ self.betree_be_tree_node_id_cnt key msg st with
+ | Fail -> Fail
+ | Return (st0, _) ->
+ begin match
+ 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 with
+ | Fail -> Fail
+ | Return (st1, (_, _)) ->
+ begin match
+ 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 with
+ | Fail -> Fail
+ | Return (st2, ()) -> Return (st2, ())
+ end
+ end
+ end
+
+(** [betree_main::betree::BeTree::{6}::apply] *)
+let betree_be_tree_apply_back
+ (self : betree_be_tree_t) (key : u64) (msg : betree_message_t) (st : state)
+ (st0 : state) :
+ result (state & betree_be_tree_t)
+ =
+ begin match
+ betree_node_apply_fwd self.betree_be_tree_root self.betree_be_tree_params
+ self.betree_be_tree_node_id_cnt key msg st with
+ | Fail -> Fail
+ | Return (st1, _) ->
+ begin match
+ 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 with
+ | Fail -> Fail
+ | Return (st2, (n, nic)) ->
+ begin match
+ 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 with
+ | Fail -> Fail
+ | Return (_, ()) ->
+ Return (st0, Mkbetree_be_tree_t self.betree_be_tree_params nic n)
+ end
+ end
+ end
+
+(** [betree_main::betree::BeTree::{6}::insert] *)
+let betree_be_tree_insert_fwd
+ (self : betree_be_tree_t) (key : u64) (value : u64) (st : state) :
+ result (state & unit)
+ =
+ begin match betree_be_tree_apply_fwd self key (BetreeMessageInsert value) st
+ with
+ | Fail -> Fail
+ | Return (st0, _) ->
+ begin match
+ betree_be_tree_apply_back self key (BetreeMessageInsert value) st st0
+ with
+ | Fail -> Fail
+ | Return (st1, _) -> Return (st1, ())
+ end
+ end
+
+(** [betree_main::betree::BeTree::{6}::insert] *)
+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)
+ =
+ begin match betree_be_tree_apply_fwd self key (BetreeMessageInsert value) st
+ with
+ | Fail -> Fail
+ | Return (st1, _) ->
+ begin match
+ betree_be_tree_apply_back self key (BetreeMessageInsert value) st st1
+ with
+ | Fail -> Fail
+ | Return (_, self0) -> Return (st0, self0)
+ end
+ end
+
+(** [betree_main::betree::BeTree::{6}::delete] *)
+let betree_be_tree_delete_fwd
+ (self : betree_be_tree_t) (key : u64) (st : state) : result (state & unit) =
+ begin match betree_be_tree_apply_fwd self key BetreeMessageDelete st with
+ | Fail -> Fail
+ | Return (st0, _) ->
+ begin match betree_be_tree_apply_back self key BetreeMessageDelete st st0
+ with
+ | Fail -> Fail
+ | Return (st1, _) -> Return (st1, ())
+ end
+ end
+
+(** [betree_main::betree::BeTree::{6}::delete] *)
+let betree_be_tree_delete_back
+ (self : betree_be_tree_t) (key : u64) (st : state) (st0 : state) :
+ result (state & betree_be_tree_t)
+ =
+ begin match betree_be_tree_apply_fwd self key BetreeMessageDelete st with
+ | Fail -> Fail
+ | Return (st1, _) ->
+ begin match betree_be_tree_apply_back self key BetreeMessageDelete st st1
+ with
+ | Fail -> Fail
+ | Return (_, self0) -> Return (st0, self0)
+ end
+ end
+
+(** [betree_main::betree::BeTree::{6}::upsert] *)
+let betree_be_tree_upsert_fwd
+ (self : betree_be_tree_t) (key : u64) (upd : betree_upsert_fun_state_t)
+ (st : state) :
+ result (state & unit)
+ =
+ begin match betree_be_tree_apply_fwd self key (BetreeMessageUpsert upd) st
+ with
+ | Fail -> Fail
+ | Return (st0, _) ->
+ begin match
+ betree_be_tree_apply_back self key (BetreeMessageUpsert upd) st st0 with
+ | Fail -> Fail
+ | Return (st1, _) -> Return (st1, ())
+ end
+ end
+
+(** [betree_main::betree::BeTree::{6}::upsert] *)
+let betree_be_tree_upsert_back
+ (self : betree_be_tree_t) (key : u64) (upd : betree_upsert_fun_state_t)
+ (st : state) (st0 : state) :
+ result (state & betree_be_tree_t)
+ =
+ begin match betree_be_tree_apply_fwd self key (BetreeMessageUpsert upd) st
+ with
+ | Fail -> Fail
+ | Return (st1, _) ->
+ begin match
+ betree_be_tree_apply_back self key (BetreeMessageUpsert upd) st st1 with
+ | Fail -> Fail
+ | Return (_, self0) -> Return (st0, self0)
+ end
+ end
+
+(** [betree_main::betree::BeTree::{6}::lookup] *)
+let betree_be_tree_lookup_fwd
+ (self : betree_be_tree_t) (key : u64) (st : state) :
+ result (state & (option u64))
+ =
+ begin match betree_node_lookup_fwd self.betree_be_tree_root key st with
+ | Fail -> Fail
+ | Return (st0, opt) -> Return (st0, opt)
+ end
+
+(** [betree_main::betree::BeTree::{6}::lookup] *)
+let betree_be_tree_lookup_back
+ (self : betree_be_tree_t) (key : u64) (st : state) (st0 : state) :
+ result (state & betree_be_tree_t)
+ =
+ begin match betree_node_lookup_back self.betree_be_tree_root key st st0 with
+ | Fail -> Fail
+ | Return (st1, n) ->
+ Return (st1, Mkbetree_be_tree_t self.betree_be_tree_params
+ self.betree_be_tree_node_id_cnt n)
+ end
+
+(** [betree_main::main] *)
+let main_fwd : result unit = Return ()
+
+(** Unit test for [betree_main::main] *)
+let _ = assert_norm (main_fwd = Return ())
+