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| -rw-r--r-- | tests/betree_back_stateful/BetreeMain.Funs.fst | 2085 |
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diff --git a/tests/betree_back_stateful/BetreeMain.Funs.fst b/tests/betree_back_stateful/BetreeMain.Funs.fst new file mode 100644 index 00000000..ea8344fa --- /dev/null +++ b/tests/betree_back_stateful/BetreeMain.Funs.fst @@ -0,0 +1,2085 @@ +(** 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 ()) + |