diff options
Diffstat (limited to 'tests/fstar/betree_back_stateful')
| -rw-r--r-- | tests/fstar/betree_back_stateful/BetreeMain.Clauses.Template.fst | 106 | ||||
| -rw-r--r-- | tests/fstar/betree_back_stateful/BetreeMain.Clauses.fst | 210 | ||||
| -rw-r--r-- | tests/fstar/betree_back_stateful/BetreeMain.Funs.fst | 2085 | ||||
| -rw-r--r-- | tests/fstar/betree_back_stateful/BetreeMain.Opaque.fsti | 30 | ||||
| -rw-r--r-- | tests/fstar/betree_back_stateful/BetreeMain.Types.fsti | 64 | ||||
| -rw-r--r-- | tests/fstar/betree_back_stateful/Makefile | 47 | ||||
| -rw-r--r-- | tests/fstar/betree_back_stateful/Primitives.fst | 287 |
7 files changed, 2829 insertions, 0 deletions
diff --git a/tests/fstar/betree_back_stateful/BetreeMain.Clauses.Template.fst b/tests/fstar/betree_back_stateful/BetreeMain.Clauses.Template.fst new file mode 100644 index 00000000..d48213d3 --- /dev/null +++ b/tests/fstar/betree_back_stateful/BetreeMain.Clauses.Template.fst @@ -0,0 +1,106 @@ +(** THIS FILE WAS AUTOMATICALLY GENERATED BY AENEAS *) +(** [betree_main]: templates for the decreases clauses *) +module BetreeMain.Clauses.Template +open Primitives +open BetreeMain.Types + +#set-options "--z3rlimit 50 --fuel 1 --ifuel 1" + +(** [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::List::{1}::len]: decreases clause *) +unfold +let betree_list_len_decreases (t : Type0) (self : betree_list_t t) : nat = + admit () + +(** [betree_main::betree::List::{1}::split_at]: decreases clause *) +unfold +let betree_list_split_at_decreases (t : Type0) (self : betree_list_t t) + (n : u64) : nat = + admit () + +(** [betree_main::betree::List::{2}::partition_at_pivot]: decreases clause *) +unfold +let betree_list_partition_at_pivot_decreases (t : Type0) + (self : betree_list_t (u64 & t)) (pivot : u64) : nat = + admit () + +(** [betree_main::betree::Node::{5}::lookup_in_bindings]: decreases clause *) +unfold +let betree_node_lookup_in_bindings_decreases (key : u64) + (bindings : betree_list_t (u64 & u64)) : nat = + admit () + +(** [betree_main::betree::Node::{5}::lookup_first_message_for_key]: decreases clause *) +unfold +let betree_node_lookup_first_message_for_key_decreases (key : u64) + (msgs : betree_list_t (u64 & betree_message_t)) : nat = + admit () + +(** [betree_main::betree::Node::{5}::apply_upserts]: decreases clause *) +unfold +let betree_node_apply_upserts_decreases + (msgs : betree_list_t (u64 & betree_message_t)) (prev : option u64) + (key : u64) (st : state) : nat = + admit () + +(** [betree_main::betree::Node::{5}::lookup]: decreases clause *) +unfold +let betree_node_lookup_decreases (self : betree_node_t) (key : u64) + (st : state) : nat = + admit () + +(** [betree_main::betree::Internal::{4}::lookup_in_children]: decreases clause *) +unfold +let betree_internal_lookup_in_children_decreases (self : betree_internal_t) + (key : u64) (st : state) : nat = + admit () + +(** [betree_main::betree::Node::{5}::lookup_mut_in_bindings]: decreases clause *) +unfold +let betree_node_lookup_mut_in_bindings_decreases (key : u64) + (bindings : betree_list_t (u64 & u64)) : nat = + admit () + +(** [betree_main::betree::Node::{5}::apply_messages_to_leaf]: decreases clause *) +unfold +let betree_node_apply_messages_to_leaf_decreases + (bindings : betree_list_t (u64 & u64)) + (new_msgs : betree_list_t (u64 & betree_message_t)) : nat = + admit () + +(** [betree_main::betree::Node::{5}::filter_messages_for_key]: decreases clause *) +unfold +let betree_node_filter_messages_for_key_decreases (key : u64) + (msgs : betree_list_t (u64 & betree_message_t)) : nat = + admit () + +(** [betree_main::betree::Node::{5}::lookup_first_message_after_key]: decreases clause *) +unfold +let betree_node_lookup_first_message_after_key_decreases (key : u64) + (msgs : betree_list_t (u64 & betree_message_t)) : nat = + admit () + +(** [betree_main::betree::Node::{5}::apply_messages_to_internal]: decreases clause *) +unfold +let betree_node_apply_messages_to_internal_decreases + (msgs : betree_list_t (u64 & betree_message_t)) + (new_msgs : betree_list_t (u64 & betree_message_t)) : nat = + admit () + +(** [betree_main::betree::Node::{5}::apply_messages]: decreases clause *) +unfold +let betree_node_apply_messages_decreases (self : betree_node_t) + (params : betree_params_t) (node_id_cnt : betree_node_id_counter_t) + (msgs : betree_list_t (u64 & betree_message_t)) (st : state) : nat = + admit () + +(** [betree_main::betree::Internal::{4}::flush]: decreases clause *) +unfold +let betree_internal_flush_decreases (self : betree_internal_t) + (params : betree_params_t) (node_id_cnt : betree_node_id_counter_t) + (content : betree_list_t (u64 & betree_message_t)) (st : state) : nat = + admit () + diff --git a/tests/fstar/betree_back_stateful/BetreeMain.Clauses.fst b/tests/fstar/betree_back_stateful/BetreeMain.Clauses.fst new file mode 100644 index 00000000..07484711 --- /dev/null +++ b/tests/fstar/betree_back_stateful/BetreeMain.Clauses.fst @@ -0,0 +1,210 @@ +(** [betree_main]: templates for the decreases clauses *) +module BetreeMain.Clauses +open Primitives +open BetreeMain.Types + +#set-options "--z3rlimit 50 --fuel 0 --ifuel 1" + +(*** Well-founded relations *) + +(* We had a few issues when proving termination of the mutually recursive functions: + * - betree_internal_flush + * - betree_node_apply_messages + * + * The quantity which effectively decreases is: + * (betree_size, messages_length) + * where messages_length is 0 when there are no messages + * (and where we use the lexicographic ordering, of course) + * + * However, the `%[...]` and `{:well-founded ...} notations are not available outside + * of `decrease` clauses. + * + * We thus resorted to writing and proving correct a well-founded relation over + * pairs of natural numbers. The trick is that `<<` can be used outside of decrease + * clauses, and can be used to trigger SMT patterns. + * + * What follows is adapted from: + * https://www.fstar-lang.org/tutorial/book/part2/part2_well_founded.html + * + * Also, the following PR might make things easier: + * https://github.com/FStarLang/FStar/pull/2561 + *) + +module P = FStar.Preorder +module W = FStar.WellFounded +module L = FStar.LexicographicOrdering + +let lt_nat (x y:nat) : Type = x < y == true +let rec wf_lt_nat (x:nat) + : W.acc lt_nat x + = W.AccIntro (fun y _ -> wf_lt_nat y) + +// A type abbreviation for a pair of nats +let nat_pair = (x:nat & nat) + +// Making a lexicographic ordering from a pair of nat ordering +let lex_order_nat_pair : P.relation nat_pair = + L.lex_t lt_nat (fun _ -> lt_nat) + +// The lex order on nat pairs is well-founded, using our general proof +// of lexicographic composition of well-founded orders +let lex_order_nat_pair_wf : W.well_founded lex_order_nat_pair = + L.lex_t_wf wf_lt_nat (fun _ -> wf_lt_nat) + +// A utility to introduce lt_nat +let mk_lt_nat (x:nat) (y:nat { x < y }) : lt_nat x y = + let _ : equals (x < y) true = Refl in + () + +// A utility to make a lex ordering of nat pairs +let mk_lex_order_nat_pair (xy0:nat_pair) + (xy1:nat_pair { + let (|x0, y0|) = xy0 in + let (|x1, y1|) = xy1 in + x0 < x1 \/ (x0 == x1 /\ y0 < y1) + }) : lex_order_nat_pair xy0 xy1 = + let (|x0, y0|) = xy0 in + let (|x1, y1|) = xy1 in + if x0 < x1 then L.Left_lex x0 x1 y0 y1 (mk_lt_nat x0 x1) + else L.Right_lex x0 y0 y1 (mk_lt_nat y0 y1) + +let rec coerce #a #r #x (p:W.acc #a r x) : Tot (W.acc r x) (decreases p) = + W.AccIntro (fun y r -> coerce (p.access_smaller y r)) + +let coerce_wf #a #r (p: (x:a -> W.acc r x)) : x:a -> W.acc r x = + fun x -> coerce (p x) + +(* We need this axiom, which comes from the following discussion: + * https://github.com/FStarLang/FStar/issues/1916 + * An issue here is that the `{well-founded ... }` notation + *) +assume +val axiom_well_founded (a : Type) (rel : a -> a -> Type0) + (rwf : W.well_founded #a rel) (x y : a) : + Lemma (requires (rel x y)) (ensures (x << y)) + +(* This lemma has a pattern (which makes it work) *) +let wf_nat_pair_lem (p0 p1 : nat_pair) : + Lemma + (requires ( + let (|x0, y0|) = p0 in + let (|x1, y1|) = p1 in + x0 < x1 || (x0 = x1 && y0 < y1))) + (ensures (p0 << p1)) + [SMTPat (p0 << p1)] = + let rel = lex_order_nat_pair in + let rel_wf = lex_order_nat_pair_wf in + let _ = mk_lex_order_nat_pair p0 p1 in + assert(rel p0 p1); + axiom_well_founded nat_pair rel rel_wf p0 p1 + +(*** Decrease clauses *) +/// "Standard" decrease clauses + +(** [betree_main::betree::List::{1}::len]: decreases clause *) +unfold +let betree_list_len_decreases (t : Type0) (self : betree_list_t t) : betree_list_t t = + self + +(** [betree_main::betree::List::{1}::split_at]: decreases clause *) +unfold +let betree_list_split_at_decreases (t : Type0) (self : betree_list_t t) + (n : u64) : nat = + n + +(** [betree_main::betree::List::{2}::partition_at_pivot]: decreases clause *) +unfold +let betree_list_partition_at_pivot_decreases (t : Type0) + (self : betree_list_t (u64 & t)) (pivot : u64) : betree_list_t (u64 & t) = + self + +(** [betree_main::betree::Node::{5}::lookup_in_bindings]: decreases clause *) +unfold +let betree_node_lookup_in_bindings_decreases (key : u64) + (bindings : betree_list_t (u64 & u64)) : betree_list_t (u64 & u64) = + bindings + +(** [betree_main::betree::Node::{5}::lookup_first_message_for_key]: decreases clause *) +unfold +let betree_node_lookup_first_message_for_key_decreases (key : u64) + (msgs : betree_list_t (u64 & betree_message_t)) : betree_list_t (u64 & betree_message_t) = + msgs + +(** [betree_main::betree::Node::{5}::apply_upserts]: decreases clause *) +unfold +let betree_node_apply_upserts_decreases + (msgs : betree_list_t (u64 & betree_message_t)) (prev : option u64) + (key : u64) (st : state) : betree_list_t (u64 & betree_message_t) = + msgs + +(** [betree_main::betree::Internal::{4}::lookup_in_children]: decreases clause *) +unfold +let betree_internal_lookup_in_children_decreases (self : betree_internal_t) + (key : u64) (st : state) : betree_internal_t = + self + +(** [betree_main::betree::Node::{5}::lookup]: decreases clause *) +unfold +let betree_node_lookup_decreases (self : betree_node_t) (key : u64) + (st : state) : betree_node_t = + self + +(** [betree_main::betree::Node::{5}::lookup_mut_in_bindings]: decreases clause *) +unfold +let betree_node_lookup_mut_in_bindings_decreases (key : u64) + (bindings : betree_list_t (u64 & u64)) : betree_list_t (u64 & u64) = + bindings + +unfold +let betree_node_apply_messages_to_leaf_decreases + (bindings : betree_list_t (u64 & u64)) + (new_msgs : betree_list_t (u64 & betree_message_t)) : betree_list_t (u64 & betree_message_t) = + new_msgs + +(** [betree_main::betree::Node::{5}::filter_messages_for_key]: decreases clause *) +unfold +let betree_node_filter_messages_for_key_decreases (key : u64) + (msgs : betree_list_t (u64 & betree_message_t)) : betree_list_t (u64 & betree_message_t) = + msgs + +(** [betree_main::betree::Node::{5}::lookup_first_message_after_key]: decreases clause *) +unfold +let betree_node_lookup_first_message_after_key_decreases (key : u64) + (msgs : betree_list_t (u64 & betree_message_t)) : betree_list_t (u64 & betree_message_t) = + msgs + +let betree_node_apply_messages_to_internal_decreases + (msgs : betree_list_t (u64 & betree_message_t)) + (new_msgs : betree_list_t (u64 & betree_message_t)) : betree_list_t (u64 & betree_message_t) = + new_msgs + +(*** Decrease clauses - nat_pair *) +/// The following decrease clauses use the [nat_pair] definition and the well-founded +/// relation proven above. + +let rec betree_size (bt : betree_node_t) : nat = + match bt with + | BetreeNodeInternal node -> 1 + betree_internal_size node + | BetreeNodeLeaf _ -> 1 + +and betree_internal_size (node : betree_internal_t) : nat = + 1 + betree_size node.betree_internal_left + betree_size node.betree_internal_right + +let rec betree_list_len (#a : Type0) (ls : betree_list_t a) : nat = + match ls with + | BetreeListCons _ tl -> 1 + betree_list_len tl + | BetreeListNil -> 0 + +(** [betree_main::betree::Internal::{4}::flush]: decreases clause *) +unfold +let betree_internal_flush_decreases (self : betree_internal_t) + (params : betree_params_t) (node_id_cnt : betree_node_id_counter_t) + (content : betree_list_t (u64 & betree_message_t)) (st : state) : nat_pair = + (|betree_internal_size self, 0|) + +(** [betree_main::betree::Node::{5}::apply_messages]: decreases clause *) +unfold +let betree_node_apply_messages_decreases (self : betree_node_t) + (params : betree_params_t) (node_id_cnt : betree_node_id_counter_t) + (msgs : betree_list_t (u64 & betree_message_t)) (st : state) : nat_pair = + (|betree_size self, betree_list_len msgs|) diff --git a/tests/fstar/betree_back_stateful/BetreeMain.Funs.fst b/tests/fstar/betree_back_stateful/BetreeMain.Funs.fst new file mode 100644 index 00000000..ea8344fa --- /dev/null +++ b/tests/fstar/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 ()) + diff --git a/tests/fstar/betree_back_stateful/BetreeMain.Opaque.fsti b/tests/fstar/betree_back_stateful/BetreeMain.Opaque.fsti new file mode 100644 index 00000000..dc49601a --- /dev/null +++ b/tests/fstar/betree_back_stateful/BetreeMain.Opaque.fsti @@ -0,0 +1,30 @@ +(** THIS FILE WAS AUTOMATICALLY GENERATED BY AENEAS *) +(** [betree_main]: opaque function definitions *) +module BetreeMain.Opaque +open Primitives +include BetreeMain.Types + +#set-options "--z3rlimit 50 --fuel 1 --ifuel 1" + +(** [betree_main::betree_utils::load_internal_node] *) +val betree_utils_load_internal_node_fwd + : u64 -> state -> result (state & (betree_list_t (u64 & betree_message_t))) + +(** [betree_main::betree_utils::store_internal_node] *) +val betree_utils_store_internal_node_fwd + : + u64 -> betree_list_t (u64 & betree_message_t) -> state -> result (state & + unit) + +(** [betree_main::betree_utils::load_leaf_node] *) +val betree_utils_load_leaf_node_fwd + : u64 -> state -> result (state & (betree_list_t (u64 & u64))) + +(** [betree_main::betree_utils::store_leaf_node] *) +val betree_utils_store_leaf_node_fwd + : u64 -> betree_list_t (u64 & u64) -> state -> result (state & unit) + +(** [core::option::Option::{0}::unwrap] *) +val core_option_option_unwrap_fwd + (t : Type0) : option t -> state -> result (state & t) + diff --git a/tests/fstar/betree_back_stateful/BetreeMain.Types.fsti b/tests/fstar/betree_back_stateful/BetreeMain.Types.fsti new file mode 100644 index 00000000..c81e3302 --- /dev/null +++ b/tests/fstar/betree_back_stateful/BetreeMain.Types.fsti @@ -0,0 +1,64 @@ +(** THIS FILE WAS AUTOMATICALLY GENERATED BY AENEAS *) +(** [betree_main]: type definitions *) +module BetreeMain.Types +open Primitives + +#set-options "--z3rlimit 50 --fuel 1 --ifuel 1" + +(** [betree_main::betree::List] *) +type betree_list_t (t : Type0) = +| BetreeListCons : t -> betree_list_t t -> betree_list_t t +| BetreeListNil : betree_list_t t + +(** [betree_main::betree::UpsertFunState] *) +type betree_upsert_fun_state_t = +| BetreeUpsertFunStateAdd : u64 -> betree_upsert_fun_state_t +| BetreeUpsertFunStateSub : u64 -> betree_upsert_fun_state_t + +(** [betree_main::betree::Message] *) +type betree_message_t = +| BetreeMessageInsert : u64 -> betree_message_t +| BetreeMessageDelete : betree_message_t +| BetreeMessageUpsert : betree_upsert_fun_state_t -> betree_message_t + +(** [betree_main::betree::Leaf] *) +type betree_leaf_t = { betree_leaf_id : u64; betree_leaf_size : u64; } + +(** [betree_main::betree::Node] *) +type betree_node_t = +| BetreeNodeInternal : betree_internal_t -> betree_node_t +| BetreeNodeLeaf : betree_leaf_t -> betree_node_t + +(** [betree_main::betree::Internal] *) +and betree_internal_t = +{ + betree_internal_id : u64; + betree_internal_pivot : u64; + betree_internal_left : betree_node_t; + betree_internal_right : betree_node_t; +} + +(** [betree_main::betree::Params] *) +type betree_params_t = +{ + betree_params_min_flush_size : u64; betree_params_split_size : u64; +} + +(** [betree_main::betree::NodeIdCounter] *) +type betree_node_id_counter_t = { betree_node_id_counter_next_node_id : u64; } + +(** [betree_main::betree::BeTree] *) +type betree_be_tree_t = +{ + betree_be_tree_params : betree_params_t; + betree_be_tree_node_id_cnt : betree_node_id_counter_t; + betree_be_tree_root : betree_node_t; +} + +(** [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 + +(** The state type used in the state-error monad *) +val state : Type0 + diff --git a/tests/fstar/betree_back_stateful/Makefile b/tests/fstar/betree_back_stateful/Makefile new file mode 100644 index 00000000..a16b0edb --- /dev/null +++ b/tests/fstar/betree_back_stateful/Makefile @@ -0,0 +1,47 @@ +INCLUDE_DIRS = . + +FSTAR_INCLUDES = $(addprefix --include ,$(INCLUDE_DIRS)) + +FSTAR_HINTS ?= --use_hints --use_hint_hashes --record_hints + +FSTAR_OPTIONS = $(FSTAR_HINTS) \ + --cache_checked_modules $(FSTAR_INCLUDES) --cmi \ + --warn_error '+241@247+285-274' \ + +FSTAR_NO_FLAGS = fstar.exe --already_cached 'Prims FStar LowStar Steel' --odir obj --cache_dir obj + +FSTAR = $(FSTAR_NO_FLAGS) $(FSTAR_OPTIONS) + +# The F* roots are used to compute the dependency graph, and generate the .depend file +FSTAR_ROOTS ?= $(wildcard *.fst *.fsti) + +# Build all the files +all: $(addprefix obj/,$(addsuffix .checked,$(FSTAR_ROOTS))) + +# This is the right way to ensure the .depend file always gets re-built. +ifeq (,$(filter %-in,$(MAKECMDGOALS))) +ifndef NODEPEND +ifndef MAKE_RESTARTS +.depend: .FORCE + $(FSTAR_NO_FLAGS) --dep full $(notdir $(FSTAR_ROOTS)) > $@ + +.PHONY: .FORCE +.FORCE: +endif +endif + +include .depend +endif + +# For the interactive mode +%.fst-in %.fsti-in: + @echo $(FSTAR_OPTIONS) + +# Generete the .checked files in batch mode +%.checked: + $(FSTAR) $(FSTAR_OPTIONS) $< && \ + touch -c $@ + +.PHONY: clean +clean: + rm -f obj/* diff --git a/tests/fstar/betree_back_stateful/Primitives.fst b/tests/fstar/betree_back_stateful/Primitives.fst new file mode 100644 index 00000000..96138e46 --- /dev/null +++ b/tests/fstar/betree_back_stateful/Primitives.fst @@ -0,0 +1,287 @@ +/// This file lists primitive and assumed functions and types +module Primitives +open FStar.Mul +open FStar.List.Tot + +#set-options "--z3rlimit 15 --fuel 0 --ifuel 1" + +(*** Utilities *) +val list_update (#a : Type0) (ls : list a) (i : nat{i < length ls}) (x : a) : + ls':list a{ + length ls' = length ls /\ + index ls' i == x + } +#push-options "--fuel 1" +let rec list_update #a ls i x = + match ls with + | x' :: ls -> if i = 0 then x :: ls else x' :: list_update ls (i-1) x +#pop-options + +(*** Result *) +type result (a : Type0) : Type0 = +| Return : v:a -> result a +| Fail : result a + +// Monadic bind and return. +// Re-definining those allows us to customize the result of the monadic notations +// like: `y <-- f x;` +let return (#a : Type0) (x:a) : result a = Return x +let bind (#a #b : Type0) (m : result a) (f : a -> result b) : result b = + match m with + | Return x -> f x + | Fail -> Fail + +// Monadic assert(...) +let massert (b:bool) : result unit = if b then Return () else Fail + +// Normalize and unwrap a successful result (used for globals). +let eval_global (#a : Type0) (x : result a{Return? (normalize_term x)}) : a = Return?.v x + +(*** Misc *) +type char = FStar.Char.char +type string = string + +let mem_replace_fwd (a : Type0) (x : a) (y : a) : a = x +let mem_replace_back (a : Type0) (x : a) (y : a) : a = y + +(*** Scalars *) +/// Rk.: most of the following code was at least partially generated + +let isize_min : int = -9223372036854775808 // TODO: should be opaque +let isize_max : int = 9223372036854775807 // TODO: should be opaque +let i8_min : int = -128 +let i8_max : int = 127 +let i16_min : int = -32768 +let i16_max : int = 32767 +let i32_min : int = -2147483648 +let i32_max : int = 2147483647 +let i64_min : int = -9223372036854775808 +let i64_max : int = 9223372036854775807 +let i128_min : int = -170141183460469231731687303715884105728 +let i128_max : int = 170141183460469231731687303715884105727 +let usize_min : int = 0 +let usize_max : int = 4294967295 // TODO: should be opaque +let u8_min : int = 0 +let u8_max : int = 255 +let u16_min : int = 0 +let u16_max : int = 65535 +let u32_min : int = 0 +let u32_max : int = 4294967295 +let u64_min : int = 0 +let u64_max : int = 18446744073709551615 +let u128_min : int = 0 +let u128_max : int = 340282366920938463463374607431768211455 + +type scalar_ty = +| Isize +| I8 +| I16 +| I32 +| I64 +| I128 +| Usize +| U8 +| U16 +| U32 +| U64 +| U128 + +let scalar_min (ty : scalar_ty) : int = + match ty with + | Isize -> isize_min + | I8 -> i8_min + | I16 -> i16_min + | I32 -> i32_min + | I64 -> i64_min + | I128 -> i128_min + | Usize -> usize_min + | U8 -> u8_min + | U16 -> u16_min + | U32 -> u32_min + | U64 -> u64_min + | U128 -> u128_min + +let scalar_max (ty : scalar_ty) : int = + match ty with + | Isize -> isize_max + | I8 -> i8_max + | I16 -> i16_max + | I32 -> i32_max + | I64 -> i64_max + | I128 -> i128_max + | Usize -> usize_max + | U8 -> u8_max + | U16 -> u16_max + | U32 -> u32_max + | U64 -> u64_max + | U128 -> u128_max + +type scalar (ty : scalar_ty) : eqtype = x:int{scalar_min ty <= x && x <= scalar_max ty} + +let mk_scalar (ty : scalar_ty) (x : int) : result (scalar ty) = + if scalar_min ty <= x && scalar_max ty >= x then Return x else Fail + +let scalar_neg (#ty : scalar_ty) (x : scalar ty) : result (scalar ty) = mk_scalar ty (-x) + +let scalar_div (#ty : scalar_ty) (x : scalar ty) (y : scalar ty) : result (scalar ty) = + if y <> 0 then mk_scalar ty (x / y) else Fail + +/// The remainder operation +let int_rem (x : int) (y : int{y <> 0}) : int = + if x >= 0 then (x % y) else -(x % y) + +(* Checking consistency with Rust *) +let _ = assert_norm(int_rem 1 2 = 1) +let _ = assert_norm(int_rem (-1) 2 = -1) +let _ = assert_norm(int_rem 1 (-2) = 1) +let _ = assert_norm(int_rem (-1) (-2) = -1) + +let scalar_rem (#ty : scalar_ty) (x : scalar ty) (y : scalar ty) : result (scalar ty) = + if y <> 0 then mk_scalar ty (int_rem x y) else Fail + +let scalar_add (#ty : scalar_ty) (x : scalar ty) (y : scalar ty) : result (scalar ty) = + mk_scalar ty (x + y) + +let scalar_sub (#ty : scalar_ty) (x : scalar ty) (y : scalar ty) : result (scalar ty) = + mk_scalar ty (x - y) + +let scalar_mul (#ty : scalar_ty) (x : scalar ty) (y : scalar ty) : result (scalar ty) = + mk_scalar ty (x * y) + +(** Cast an integer from a [src_ty] to a [tgt_ty] *) +// TODO: check the semantics of casts in Rust +let scalar_cast (src_ty : scalar_ty) (tgt_ty : scalar_ty) (x : scalar src_ty) : result (scalar tgt_ty) = + mk_scalar tgt_ty x + +/// The scalar types +type isize : eqtype = scalar Isize +type i8 : eqtype = scalar I8 +type i16 : eqtype = scalar I16 +type i32 : eqtype = scalar I32 +type i64 : eqtype = scalar I64 +type i128 : eqtype = scalar I128 +type usize : eqtype = scalar Usize +type u8 : eqtype = scalar U8 +type u16 : eqtype = scalar U16 +type u32 : eqtype = scalar U32 +type u64 : eqtype = scalar U64 +type u128 : eqtype = scalar U128 + +/// Negation +let isize_neg = scalar_neg #Isize +let i8_neg = scalar_neg #I8 +let i16_neg = scalar_neg #I16 +let i32_neg = scalar_neg #I32 +let i64_neg = scalar_neg #I64 +let i128_neg = scalar_neg #I128 + +/// Division +let isize_div = scalar_div #Isize +let i8_div = scalar_div #I8 +let i16_div = scalar_div #I16 +let i32_div = scalar_div #I32 +let i64_div = scalar_div #I64 +let i128_div = scalar_div #I128 +let usize_div = scalar_div #Usize +let u8_div = scalar_div #U8 +let u16_div = scalar_div #U16 +let u32_div = scalar_div #U32 +let u64_div = scalar_div #U64 +let u128_div = scalar_div #U128 + +/// Remainder +let isize_rem = scalar_rem #Isize +let i8_rem = scalar_rem #I8 +let i16_rem = scalar_rem #I16 +let i32_rem = scalar_rem #I32 +let i64_rem = scalar_rem #I64 +let i128_rem = scalar_rem #I128 +let usize_rem = scalar_rem #Usize +let u8_rem = scalar_rem #U8 +let u16_rem = scalar_rem #U16 +let u32_rem = scalar_rem #U32 +let u64_rem = scalar_rem #U64 +let u128_rem = scalar_rem #U128 + +/// Addition +let isize_add = scalar_add #Isize +let i8_add = scalar_add #I8 +let i16_add = scalar_add #I16 +let i32_add = scalar_add #I32 +let i64_add = scalar_add #I64 +let i128_add = scalar_add #I128 +let usize_add = scalar_add #Usize +let u8_add = scalar_add #U8 +let u16_add = scalar_add #U16 +let u32_add = scalar_add #U32 +let u64_add = scalar_add #U64 +let u128_add = scalar_add #U128 + +/// Substraction +let isize_sub = scalar_sub #Isize +let i8_sub = scalar_sub #I8 +let i16_sub = scalar_sub #I16 +let i32_sub = scalar_sub #I32 +let i64_sub = scalar_sub #I64 +let i128_sub = scalar_sub #I128 +let usize_sub = scalar_sub #Usize +let u8_sub = scalar_sub #U8 +let u16_sub = scalar_sub #U16 +let u32_sub = scalar_sub #U32 +let u64_sub = scalar_sub #U64 +let u128_sub = scalar_sub #U128 + +/// Multiplication +let isize_mul = scalar_mul #Isize +let i8_mul = scalar_mul #I8 +let i16_mul = scalar_mul #I16 +let i32_mul = scalar_mul #I32 +let i64_mul = scalar_mul #I64 +let i128_mul = scalar_mul #I128 +let usize_mul = scalar_mul #Usize +let u8_mul = scalar_mul #U8 +let u16_mul = scalar_mul #U16 +let u32_mul = scalar_mul #U32 +let u64_mul = scalar_mul #U64 +let u128_mul = scalar_mul #U128 + +(*** Vector *) +type vec (a : Type0) = v:list a{length v <= usize_max} + +let vec_new (a : Type0) : vec a = assert_norm(length #a [] == 0); [] +let vec_len (a : Type0) (v : vec a) : usize = length v + +// The **forward** function shouldn't be used +let vec_push_fwd (a : Type0) (v : vec a) (x : a) : unit = () +let vec_push_back (a : Type0) (v : vec a) (x : a) : + Pure (result (vec a)) + (requires True) + (ensures (fun res -> + match res with + | Fail -> True + | Return v' -> length v' = length v + 1)) = + if length v < usize_max then begin + (**) assert_norm(length [x] == 1); + (**) append_length v [x]; + (**) assert(length (append v [x]) = length v + 1); + Return (append v [x]) + end + else Fail + +// The **forward** function shouldn't be used +let vec_insert_fwd (a : Type0) (v : vec a) (i : usize) (x : a) : result unit = + if i < length v then Return () else Fail +let vec_insert_back (a : Type0) (v : vec a) (i : usize) (x : a) : result (vec a) = + if i < length v then Return (list_update v i x) else Fail + +// The **backward** function shouldn't be used +let vec_index_fwd (a : Type0) (v : vec a) (i : usize) : result a = + if i < length v then Return (index v i) else Fail +let vec_index_back (a : Type0) (v : vec a) (i : usize) (x : a) : result unit = + if i < length v then Return () else Fail + +let vec_index_mut_fwd (a : Type0) (v : vec a) (i : usize) : result a = + if i < length v then Return (index v i) else Fail +let vec_index_mut_back (a : Type0) (v : vec a) (i : usize) (nx : a) : result (vec a) = + if i < length v then Return (list_update v i nx) else Fail + |