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-rw-r--r--tests/fstar-split/betree/BetreeMain.Clauses.Template.fst117
-rw-r--r--tests/fstar-split/betree/BetreeMain.Clauses.fst210
-rw-r--r--tests/fstar-split/betree/BetreeMain.Funs.fst1006
-rw-r--r--tests/fstar-split/betree/BetreeMain.FunsExternal.fsti35
-rw-r--r--tests/fstar-split/betree/BetreeMain.Types.fst61
-rw-r--r--tests/fstar-split/betree/BetreeMain.TypesExternal.fsti10
-rw-r--r--tests/fstar-split/betree/Makefile49
-rw-r--r--tests/fstar-split/betree/Primitives.fst884
8 files changed, 2372 insertions, 0 deletions
diff --git a/tests/fstar-split/betree/BetreeMain.Clauses.Template.fst b/tests/fstar-split/betree/BetreeMain.Clauses.Template.fst
new file mode 100644
index 00000000..537705c5
--- /dev/null
+++ b/tests/fstar-split/betree/BetreeMain.Clauses.Template.fst
@@ -0,0 +1,117 @@
+(** 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"
+
+(** [betree_main::betree::{betree_main::betree::List<T>#1}::len]: decreases clause
+ Source: 'src/betree.rs', lines 276:4-276:24 *)
+unfold
+let betree_List_len_decreases (t : Type0) (self : betree_List_t t) : nat =
+ admit ()
+
+(** [betree_main::betree::{betree_main::betree::List<T>#1}::split_at]: decreases clause
+ Source: 'src/betree.rs', lines 284:4-284:51 *)
+unfold
+let betree_List_split_at_decreases (t : Type0) (self : betree_List_t t)
+ (n : u64) : nat =
+ admit ()
+
+(** [betree_main::betree::{betree_main::betree::List<(u64, T)>#2}::partition_at_pivot]: decreases clause
+ Source: 'src/betree.rs', lines 339:4-339:73 *)
+unfold
+let betree_ListTupleU64T_partition_at_pivot_decreases (t : Type0)
+ (self : betree_List_t (u64 & t)) (pivot : u64) : nat =
+ admit ()
+
+(** [betree_main::betree::{betree_main::betree::Node#5}::lookup_first_message_for_key]: decreases clause
+ Source: 'src/betree.rs', lines 789:4-792:34 *)
+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::{betree_main::betree::Node#5}::lookup_in_bindings]: decreases clause
+ Source: 'src/betree.rs', lines 636:4-636:80 *)
+unfold
+let betree_Node_lookup_in_bindings_decreases (key : u64)
+ (bindings : betree_List_t (u64 & u64)) : nat =
+ admit ()
+
+(** [betree_main::betree::{betree_main::betree::Node#5}::apply_upserts]: decreases clause
+ Source: 'src/betree.rs', lines 819:4-819:90 *)
+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::{betree_main::betree::Internal#4}::lookup_in_children]: decreases clause
+ Source: 'src/betree.rs', lines 395:4-395:63 *)
+unfold
+let betree_Internal_lookup_in_children_decreases (self : betree_Internal_t)
+ (key : u64) (st : state) : nat =
+ admit ()
+
+(** [betree_main::betree::{betree_main::betree::Node#5}::lookup]: decreases clause
+ Source: 'src/betree.rs', lines 709:4-709:58 *)
+unfold
+let betree_Node_lookup_decreases (self : betree_Node_t) (key : u64)
+ (st : state) : nat =
+ admit ()
+
+(** [betree_main::betree::{betree_main::betree::Node#5}::filter_messages_for_key]: decreases clause
+ Source: 'src/betree.rs', lines 674:4-674:77 *)
+unfold
+let betree_Node_filter_messages_for_key_decreases (key : u64)
+ (msgs : betree_List_t (u64 & betree_Message_t)) : nat =
+ admit ()
+
+(** [betree_main::betree::{betree_main::betree::Node#5}::lookup_first_message_after_key]: decreases clause
+ Source: 'src/betree.rs', lines 689:4-692:34 *)
+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::{betree_main::betree::Node#5}::apply_messages_to_internal]: decreases clause
+ Source: 'src/betree.rs', lines 502:4-505:5 *)
+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::{betree_main::betree::Node#5}::lookup_mut_in_bindings]: decreases clause
+ Source: 'src/betree.rs', lines 653:4-656:32 *)
+unfold
+let betree_Node_lookup_mut_in_bindings_decreases (key : u64)
+ (bindings : betree_List_t (u64 & u64)) : nat =
+ admit ()
+
+(** [betree_main::betree::{betree_main::betree::Node#5}::apply_messages_to_leaf]: decreases clause
+ Source: 'src/betree.rs', lines 444:4-447:5 *)
+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::{betree_main::betree::Internal#4}::flush]: decreases clause
+ Source: 'src/betree.rs', lines 410:4-415:26 *)
+unfold
+let betree_Internal_flush_decreases (self : betree_Internal_t)
+ (params : betree_Params_t) (node_id_cnt : betree_NodeIdCounter_t)
+ (content : betree_List_t (u64 & betree_Message_t)) (st : state) : nat =
+ admit ()
+
+(** [betree_main::betree::{betree_main::betree::Node#5}::apply_messages]: decreases clause
+ Source: 'src/betree.rs', lines 588:4-593:5 *)
+unfold
+let betree_Node_apply_messages_decreases (self : betree_Node_t)
+ (params : betree_Params_t) (node_id_cnt : betree_NodeIdCounter_t)
+ (msgs : betree_List_t (u64 & betree_Message_t)) (st : state) : nat =
+ admit ()
+
diff --git a/tests/fstar-split/betree/BetreeMain.Clauses.fst b/tests/fstar-split/betree/BetreeMain.Clauses.fst
new file mode 100644
index 00000000..21f953d1
--- /dev/null
+++ b/tests/fstar-split/betree/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_ListTupleU64T_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
+ | Betree_Node_Internal node -> 1 + betree_Internal_size node
+ | Betree_Node_Leaf _ -> 1
+
+and betree_Internal_size (node : betree_Internal_t) : nat =
+ 1 + betree_size node.left + betree_size node.right
+
+let rec betree_List_len (#a : Type0) (ls : betree_List_t a) : nat =
+ match ls with
+ | Betree_List_Cons _ tl -> 1 + betree_List_len tl
+ | Betree_List_Nil -> 0
+
+(** [betree_main::betree::Internal::{4}::flush]: decreases clause *)
+unfold
+let betree_Internal_flush_decreases (self : betree_Internal_t)
+ (params : betree_Params_t) (node_id_cnt : betree_NodeIdCounter_t)
+ (content : betree_List_t (u64 & betree_Message_t)) (st : state) : nat_pair =
+ (|betree_Internal_size self, 0|)
+
+(** [betree_main::betree::Node::{5}::apply_messages]: decreases clause *)
+unfold
+let betree_Node_apply_messages_decreases (self : betree_Node_t)
+ (params : betree_Params_t) (node_id_cnt : betree_NodeIdCounter_t)
+ (msgs : betree_List_t (u64 & betree_Message_t)) (st : state) : nat_pair =
+ (|betree_size self, betree_List_len msgs|)
diff --git a/tests/fstar-split/betree/BetreeMain.Funs.fst b/tests/fstar-split/betree/BetreeMain.Funs.fst
new file mode 100644
index 00000000..33133236
--- /dev/null
+++ b/tests/fstar-split/betree/BetreeMain.Funs.fst
@@ -0,0 +1,1006 @@
+(** THIS FILE WAS AUTOMATICALLY GENERATED BY AENEAS *)
+(** [betree_main]: function definitions *)
+module BetreeMain.Funs
+open Primitives
+include BetreeMain.Types
+include BetreeMain.FunsExternal
+include BetreeMain.Clauses
+
+#set-options "--z3rlimit 50 --fuel 1 --ifuel 1"
+
+(** [betree_main::betree::load_internal_node]: forward function
+ Source: 'src/betree.rs', lines 36:0-36:52 *)
+let betree_load_internal_node
+ (id : u64) (st : state) :
+ result (state & (betree_List_t (u64 & betree_Message_t)))
+ =
+ betree_utils_load_internal_node id st
+
+(** [betree_main::betree::store_internal_node]: forward function
+ Source: 'src/betree.rs', lines 41:0-41:60 *)
+let betree_store_internal_node
+ (id : u64) (content : betree_List_t (u64 & betree_Message_t)) (st : state) :
+ result (state & unit)
+ =
+ let* (st1, _) = betree_utils_store_internal_node id content st in
+ Return (st1, ())
+
+(** [betree_main::betree::load_leaf_node]: forward function
+ Source: 'src/betree.rs', lines 46:0-46:44 *)
+let betree_load_leaf_node
+ (id : u64) (st : state) : result (state & (betree_List_t (u64 & u64))) =
+ betree_utils_load_leaf_node id st
+
+(** [betree_main::betree::store_leaf_node]: forward function
+ Source: 'src/betree.rs', lines 51:0-51:52 *)
+let betree_store_leaf_node
+ (id : u64) (content : betree_List_t (u64 & u64)) (st : state) :
+ result (state & unit)
+ =
+ let* (st1, _) = betree_utils_store_leaf_node id content st in
+ Return (st1, ())
+
+(** [betree_main::betree::fresh_node_id]: forward function
+ Source: 'src/betree.rs', lines 55:0-55:48 *)
+let betree_fresh_node_id (counter : u64) : result u64 =
+ let* _ = u64_add counter 1 in Return counter
+
+(** [betree_main::betree::fresh_node_id]: backward function 0
+ Source: 'src/betree.rs', lines 55:0-55:48 *)
+let betree_fresh_node_id_back (counter : u64) : result u64 =
+ u64_add counter 1
+
+(** [betree_main::betree::{betree_main::betree::NodeIdCounter}::new]: forward function
+ Source: 'src/betree.rs', lines 206:4-206:20 *)
+let betree_NodeIdCounter_new : result betree_NodeIdCounter_t =
+ Return { next_node_id = 0 }
+
+(** [betree_main::betree::{betree_main::betree::NodeIdCounter}::fresh_id]: forward function
+ Source: 'src/betree.rs', lines 210:4-210:36 *)
+let betree_NodeIdCounter_fresh_id
+ (self : betree_NodeIdCounter_t) : result u64 =
+ let* _ = u64_add self.next_node_id 1 in Return self.next_node_id
+
+(** [betree_main::betree::{betree_main::betree::NodeIdCounter}::fresh_id]: backward function 0
+ Source: 'src/betree.rs', lines 210:4-210:36 *)
+let betree_NodeIdCounter_fresh_id_back
+ (self : betree_NodeIdCounter_t) : result betree_NodeIdCounter_t =
+ let* i = u64_add self.next_node_id 1 in Return { next_node_id = i }
+
+(** [betree_main::betree::upsert_update]: forward function
+ Source: 'src/betree.rs', lines 234:0-234:70 *)
+let betree_upsert_update
+ (prev : option u64) (st : betree_UpsertFunState_t) : result u64 =
+ begin match prev with
+ | None ->
+ begin match st with
+ | Betree_UpsertFunState_Add v -> Return v
+ | Betree_UpsertFunState_Sub _ -> Return 0
+ end
+ | Some prev1 ->
+ begin match st with
+ | Betree_UpsertFunState_Add v ->
+ let* margin = u64_sub core_u64_max prev1 in
+ if margin >= v then u64_add prev1 v else Return core_u64_max
+ | Betree_UpsertFunState_Sub v ->
+ if prev1 >= v then u64_sub prev1 v else Return 0
+ end
+ end
+
+(** [betree_main::betree::{betree_main::betree::List<T>#1}::len]: forward function
+ Source: 'src/betree.rs', lines 276:4-276:24 *)
+let rec betree_List_len
+ (t : Type0) (self : betree_List_t t) :
+ Tot (result u64) (decreases (betree_List_len_decreases t self))
+ =
+ begin match self with
+ | Betree_List_Cons _ tl -> let* i = betree_List_len t tl in u64_add 1 i
+ | Betree_List_Nil -> Return 0
+ end
+
+(** [betree_main::betree::{betree_main::betree::List<T>#1}::split_at]: forward function
+ Source: 'src/betree.rs', lines 284:4-284:51 *)
+let rec betree_List_split_at
+ (t : Type0) (self : betree_List_t t) (n : u64) :
+ Tot (result ((betree_List_t t) & (betree_List_t t)))
+ (decreases (betree_List_split_at_decreases t self n))
+ =
+ if n = 0
+ then Return (Betree_List_Nil, self)
+ else
+ begin match self with
+ | Betree_List_Cons hd tl ->
+ let* i = u64_sub n 1 in
+ let* p = betree_List_split_at t tl i in
+ let (ls0, ls1) = p in
+ Return (Betree_List_Cons hd ls0, ls1)
+ | Betree_List_Nil -> Fail Failure
+ end
+
+(** [betree_main::betree::{betree_main::betree::List<T>#1}::push_front]: merged forward/backward function
+ (there is a single backward function, and the forward function returns ())
+ Source: 'src/betree.rs', lines 299:4-299:34 *)
+let betree_List_push_front
+ (t : Type0) (self : betree_List_t t) (x : t) : result (betree_List_t t) =
+ let tl = core_mem_replace (betree_List_t t) self Betree_List_Nil in
+ Return (Betree_List_Cons x tl)
+
+(** [betree_main::betree::{betree_main::betree::List<T>#1}::pop_front]: forward function
+ Source: 'src/betree.rs', lines 306:4-306:32 *)
+let betree_List_pop_front (t : Type0) (self : betree_List_t t) : result t =
+ let ls = core_mem_replace (betree_List_t t) self Betree_List_Nil in
+ begin match ls with
+ | Betree_List_Cons x _ -> Return x
+ | Betree_List_Nil -> Fail Failure
+ end
+
+(** [betree_main::betree::{betree_main::betree::List<T>#1}::pop_front]: backward function 0
+ Source: 'src/betree.rs', lines 306:4-306:32 *)
+let betree_List_pop_front_back
+ (t : Type0) (self : betree_List_t t) : result (betree_List_t t) =
+ let ls = core_mem_replace (betree_List_t t) self Betree_List_Nil in
+ begin match ls with
+ | Betree_List_Cons _ tl -> Return tl
+ | Betree_List_Nil -> Fail Failure
+ end
+
+(** [betree_main::betree::{betree_main::betree::List<T>#1}::hd]: forward function
+ Source: 'src/betree.rs', lines 318:4-318:22 *)
+let betree_List_hd (t : Type0) (self : betree_List_t t) : result t =
+ begin match self with
+ | Betree_List_Cons hd _ -> Return hd
+ | Betree_List_Nil -> Fail Failure
+ end
+
+(** [betree_main::betree::{betree_main::betree::List<(u64, T)>#2}::head_has_key]: forward function
+ Source: 'src/betree.rs', lines 327:4-327:44 *)
+let betree_ListTupleU64T_head_has_key
+ (t : Type0) (self : betree_List_t (u64 & t)) (key : u64) : result bool =
+ begin match self with
+ | Betree_List_Cons hd _ -> let (i, _) = hd in Return (i = key)
+ | Betree_List_Nil -> Return false
+ end
+
+(** [betree_main::betree::{betree_main::betree::List<(u64, T)>#2}::partition_at_pivot]: forward function
+ Source: 'src/betree.rs', lines 339:4-339:73 *)
+let rec betree_ListTupleU64T_partition_at_pivot
+ (t : Type0) (self : betree_List_t (u64 & t)) (pivot : u64) :
+ Tot (result ((betree_List_t (u64 & t)) & (betree_List_t (u64 & t))))
+ (decreases (betree_ListTupleU64T_partition_at_pivot_decreases t self pivot))
+ =
+ begin match self with
+ | Betree_List_Cons hd tl ->
+ let (i, x) = hd in
+ if i >= pivot
+ then Return (Betree_List_Nil, Betree_List_Cons (i, x) tl)
+ else
+ let* p = betree_ListTupleU64T_partition_at_pivot t tl pivot in
+ let (ls0, ls1) = p in
+ Return (Betree_List_Cons (i, x) ls0, ls1)
+ | Betree_List_Nil -> Return (Betree_List_Nil, Betree_List_Nil)
+ end
+
+(** [betree_main::betree::{betree_main::betree::Leaf#3}::split]: forward function
+ Source: 'src/betree.rs', lines 359:4-364:17 *)
+let betree_Leaf_split
+ (self : betree_Leaf_t) (content : betree_List_t (u64 & u64))
+ (params : betree_Params_t) (node_id_cnt : betree_NodeIdCounter_t)
+ (st : state) :
+ result (state & betree_Internal_t)
+ =
+ let* p = betree_List_split_at (u64 & u64) content params.split_size in
+ let (content0, content1) = p in
+ let* p1 = betree_List_hd (u64 & u64) content1 in
+ let (pivot, _) = p1 in
+ let* id0 = betree_NodeIdCounter_fresh_id node_id_cnt in
+ let* node_id_cnt1 = betree_NodeIdCounter_fresh_id_back node_id_cnt in
+ let* id1 = betree_NodeIdCounter_fresh_id node_id_cnt1 in
+ let* (st1, _) = betree_store_leaf_node id0 content0 st in
+ let* (st2, _) = betree_store_leaf_node id1 content1 st1 in
+ let n = Betree_Node_Leaf { id = id0; size = params.split_size } in
+ let n1 = Betree_Node_Leaf { id = id1; size = params.split_size } in
+ Return (st2, { id = self.id; pivot = pivot; left = n; right = n1 })
+
+(** [betree_main::betree::{betree_main::betree::Leaf#3}::split]: backward function 2
+ Source: 'src/betree.rs', lines 359:4-364:17 *)
+let betree_Leaf_split_back
+ (self : betree_Leaf_t) (content : betree_List_t (u64 & u64))
+ (params : betree_Params_t) (node_id_cnt : betree_NodeIdCounter_t)
+ (st : state) :
+ result betree_NodeIdCounter_t
+ =
+ let* p = betree_List_split_at (u64 & u64) content params.split_size in
+ let (content0, content1) = p in
+ let* _ = betree_List_hd (u64 & u64) content1 in
+ let* id0 = betree_NodeIdCounter_fresh_id node_id_cnt in
+ let* node_id_cnt1 = betree_NodeIdCounter_fresh_id_back node_id_cnt in
+ let* id1 = betree_NodeIdCounter_fresh_id node_id_cnt1 in
+ let* (st1, _) = betree_store_leaf_node id0 content0 st in
+ let* _ = betree_store_leaf_node id1 content1 st1 in
+ betree_NodeIdCounter_fresh_id_back node_id_cnt1
+
+(** [betree_main::betree::{betree_main::betree::Node#5}::lookup_first_message_for_key]: forward function
+ Source: 'src/betree.rs', lines 789:4-792:34 *)
+let rec betree_Node_lookup_first_message_for_key
+ (key : u64) (msgs : betree_List_t (u64 & betree_Message_t)) :
+ Tot (result (betree_List_t (u64 & betree_Message_t)))
+ (decreases (betree_Node_lookup_first_message_for_key_decreases key msgs))
+ =
+ begin match msgs with
+ | Betree_List_Cons x next_msgs ->
+ let (i, m) = x in
+ if i >= key
+ then Return (Betree_List_Cons (i, m) next_msgs)
+ else betree_Node_lookup_first_message_for_key key next_msgs
+ | Betree_List_Nil -> Return Betree_List_Nil
+ end
+
+(** [betree_main::betree::{betree_main::betree::Node#5}::lookup_first_message_for_key]: backward function 0
+ Source: 'src/betree.rs', lines 789:4-792:34 *)
+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
+ | Betree_List_Cons x next_msgs ->
+ let (i, m) = x in
+ if i >= key
+ then Return ret
+ else
+ let* next_msgs1 =
+ betree_Node_lookup_first_message_for_key_back key next_msgs ret in
+ Return (Betree_List_Cons (i, m) next_msgs1)
+ | Betree_List_Nil -> Return ret
+ end
+
+(** [betree_main::betree::{betree_main::betree::Node#5}::lookup_in_bindings]: forward function
+ Source: 'src/betree.rs', lines 636:4-636:80 *)
+let rec betree_Node_lookup_in_bindings
+ (key : u64) (bindings : betree_List_t (u64 & u64)) :
+ Tot (result (option u64))
+ (decreases (betree_Node_lookup_in_bindings_decreases key bindings))
+ =
+ begin match bindings with
+ | Betree_List_Cons hd tl ->
+ let (i, i1) = hd in
+ if i = key
+ then Return (Some i1)
+ else if i > key then Return None else betree_Node_lookup_in_bindings key tl
+ | Betree_List_Nil -> Return None
+ end
+
+(** [betree_main::betree::{betree_main::betree::Node#5}::apply_upserts]: forward function
+ Source: 'src/betree.rs', lines 819:4-819:90 *)
+let rec betree_Node_apply_upserts
+ (msgs : betree_List_t (u64 & betree_Message_t)) (prev : option u64)
+ (key : u64) (st : state) :
+ Tot (result (state & u64))
+ (decreases (betree_Node_apply_upserts_decreases msgs prev key st))
+ =
+ let* b = betree_ListTupleU64T_head_has_key betree_Message_t msgs key in
+ if b
+ then
+ let* msg = betree_List_pop_front (u64 & betree_Message_t) msgs in
+ let (_, m) = msg in
+ begin match m with
+ | Betree_Message_Insert _ -> Fail Failure
+ | Betree_Message_Delete -> Fail Failure
+ | Betree_Message_Upsert s ->
+ let* v = betree_upsert_update prev s in
+ let* msgs1 = betree_List_pop_front_back (u64 & betree_Message_t) msgs in
+ betree_Node_apply_upserts msgs1 (Some v) key st
+ end
+ else
+ let* (st1, v) = core_option_Option_unwrap u64 prev st in
+ let* _ =
+ betree_List_push_front (u64 & betree_Message_t) msgs (key,
+ Betree_Message_Insert v) in
+ Return (st1, v)
+
+(** [betree_main::betree::{betree_main::betree::Node#5}::apply_upserts]: backward function 0
+ Source: 'src/betree.rs', lines 819:4-819:90 *)
+let rec betree_Node_apply_upserts_back
+ (msgs : betree_List_t (u64 & betree_Message_t)) (prev : option u64)
+ (key : u64) (st : state) :
+ Tot (result (betree_List_t (u64 & betree_Message_t)))
+ (decreases (betree_Node_apply_upserts_decreases msgs prev key st))
+ =
+ let* b = betree_ListTupleU64T_head_has_key betree_Message_t msgs key in
+ if b
+ then
+ let* msg = betree_List_pop_front (u64 & betree_Message_t) msgs in
+ let (_, m) = msg in
+ begin match m with
+ | Betree_Message_Insert _ -> Fail Failure
+ | Betree_Message_Delete -> Fail Failure
+ | Betree_Message_Upsert s ->
+ let* v = betree_upsert_update prev s in
+ let* msgs1 = betree_List_pop_front_back (u64 & betree_Message_t) msgs in
+ betree_Node_apply_upserts_back msgs1 (Some v) key st
+ end
+ else
+ let* (_, v) = core_option_Option_unwrap u64 prev st in
+ betree_List_push_front (u64 & betree_Message_t) msgs (key,
+ Betree_Message_Insert v)
+
+(** [betree_main::betree::{betree_main::betree::Internal#4}::lookup_in_children]: forward function
+ Source: 'src/betree.rs', lines 395:4-395:63 *)
+let rec betree_Internal_lookup_in_children
+ (self : betree_Internal_t) (key : u64) (st : state) :
+ Tot (result (state & (option u64)))
+ (decreases (betree_Internal_lookup_in_children_decreases self key st))
+ =
+ if key < self.pivot
+ then betree_Node_lookup self.left key st
+ else betree_Node_lookup self.right key st
+
+(** [betree_main::betree::{betree_main::betree::Internal#4}::lookup_in_children]: backward function 0
+ Source: 'src/betree.rs', lines 395:4-395:63 *)
+and betree_Internal_lookup_in_children_back
+ (self : betree_Internal_t) (key : u64) (st : state) :
+ Tot (result betree_Internal_t)
+ (decreases (betree_Internal_lookup_in_children_decreases self key st))
+ =
+ if key < self.pivot
+ then
+ let* n = betree_Node_lookup_back self.left key st in
+ Return { self with left = n }
+ else
+ let* n = betree_Node_lookup_back self.right key st in
+ Return { self with right = n }
+
+(** [betree_main::betree::{betree_main::betree::Node#5}::lookup]: forward function
+ Source: 'src/betree.rs', lines 709:4-709:58 *)
+and betree_Node_lookup
+ (self : betree_Node_t) (key : u64) (st : state) :
+ Tot (result (state & (option u64)))
+ (decreases (betree_Node_lookup_decreases self key st))
+ =
+ begin match self with
+ | Betree_Node_Internal node ->
+ let* (st1, msgs) = betree_load_internal_node node.id st in
+ let* pending = betree_Node_lookup_first_message_for_key key msgs in
+ begin match pending with
+ | Betree_List_Cons p l ->
+ let (k, msg) = p in
+ if k <> key
+ then
+ let* (st2, o) = betree_Internal_lookup_in_children node key st1 in
+ let* _ =
+ betree_Node_lookup_first_message_for_key_back key msgs
+ (Betree_List_Cons (k, msg) l) in
+ Return (st2, o)
+ else
+ begin match msg with
+ | Betree_Message_Insert v ->
+ let* _ =
+ betree_Node_lookup_first_message_for_key_back key msgs
+ (Betree_List_Cons (k, Betree_Message_Insert v) l) in
+ Return (st1, Some v)
+ | Betree_Message_Delete ->
+ let* _ =
+ betree_Node_lookup_first_message_for_key_back key msgs
+ (Betree_List_Cons (k, Betree_Message_Delete) l) in
+ Return (st1, None)
+ | Betree_Message_Upsert ufs ->
+ let* (st2, v) = betree_Internal_lookup_in_children node key st1 in
+ let* (st3, v1) =
+ betree_Node_apply_upserts (Betree_List_Cons (k,
+ Betree_Message_Upsert ufs) l) v key st2 in
+ let* node1 = betree_Internal_lookup_in_children_back node key st1 in
+ let* pending1 =
+ betree_Node_apply_upserts_back (Betree_List_Cons (k,
+ Betree_Message_Upsert ufs) l) v key st2 in
+ let* msgs1 =
+ betree_Node_lookup_first_message_for_key_back key msgs pending1 in
+ let* (st4, _) = betree_store_internal_node node1.id msgs1 st3 in
+ Return (st4, Some v1)
+ end
+ | Betree_List_Nil ->
+ let* (st2, o) = betree_Internal_lookup_in_children node key st1 in
+ let* _ =
+ betree_Node_lookup_first_message_for_key_back key msgs Betree_List_Nil
+ in
+ Return (st2, o)
+ end
+ | Betree_Node_Leaf node ->
+ let* (st1, bindings) = betree_load_leaf_node node.id st in
+ let* o = betree_Node_lookup_in_bindings key bindings in
+ Return (st1, o)
+ end
+
+(** [betree_main::betree::{betree_main::betree::Node#5}::lookup]: backward function 0
+ Source: 'src/betree.rs', lines 709:4-709:58 *)
+and betree_Node_lookup_back
+ (self : betree_Node_t) (key : u64) (st : state) :
+ Tot (result betree_Node_t)
+ (decreases (betree_Node_lookup_decreases self key st))
+ =
+ begin match self with
+ | Betree_Node_Internal node ->
+ let* (st1, msgs) = betree_load_internal_node node.id st in
+ let* pending = betree_Node_lookup_first_message_for_key key msgs in
+ begin match pending with
+ | Betree_List_Cons p l ->
+ let (k, msg) = p in
+ if k <> key
+ then
+ let* _ =
+ betree_Node_lookup_first_message_for_key_back key msgs
+ (Betree_List_Cons (k, msg) l) in
+ let* node1 = betree_Internal_lookup_in_children_back node key st1 in
+ Return (Betree_Node_Internal node1)
+ else
+ begin match msg with
+ | Betree_Message_Insert v ->
+ let* _ =
+ betree_Node_lookup_first_message_for_key_back key msgs
+ (Betree_List_Cons (k, Betree_Message_Insert v) l) in
+ Return (Betree_Node_Internal node)
+ | Betree_Message_Delete ->
+ let* _ =
+ betree_Node_lookup_first_message_for_key_back key msgs
+ (Betree_List_Cons (k, Betree_Message_Delete) l) in
+ Return (Betree_Node_Internal node)
+ | Betree_Message_Upsert ufs ->
+ let* (st2, v) = betree_Internal_lookup_in_children node key st1 in
+ let* (st3, _) =
+ betree_Node_apply_upserts (Betree_List_Cons (k,
+ Betree_Message_Upsert ufs) l) v key st2 in
+ let* node1 = betree_Internal_lookup_in_children_back node key st1 in
+ let* pending1 =
+ betree_Node_apply_upserts_back (Betree_List_Cons (k,
+ Betree_Message_Upsert ufs) l) v key st2 in
+ let* msgs1 =
+ betree_Node_lookup_first_message_for_key_back key msgs pending1 in
+ let* _ = betree_store_internal_node node1.id msgs1 st3 in
+ Return (Betree_Node_Internal node1)
+ end
+ | Betree_List_Nil ->
+ let* _ =
+ betree_Node_lookup_first_message_for_key_back key msgs Betree_List_Nil
+ in
+ let* node1 = betree_Internal_lookup_in_children_back node key st1 in
+ Return (Betree_Node_Internal node1)
+ end
+ | Betree_Node_Leaf node ->
+ let* (_, bindings) = betree_load_leaf_node node.id st in
+ let* _ = betree_Node_lookup_in_bindings key bindings in
+ Return (Betree_Node_Leaf node)
+ end
+
+(** [betree_main::betree::{betree_main::betree::Node#5}::filter_messages_for_key]: merged forward/backward function
+ (there is a single backward function, and the forward function returns ())
+ Source: 'src/betree.rs', lines 674:4-674:77 *)
+let rec betree_Node_filter_messages_for_key
+ (key : u64) (msgs : betree_List_t (u64 & betree_Message_t)) :
+ Tot (result (betree_List_t (u64 & betree_Message_t)))
+ (decreases (betree_Node_filter_messages_for_key_decreases key msgs))
+ =
+ begin match msgs with
+ | Betree_List_Cons p l ->
+ let (k, m) = p in
+ if k = key
+ then
+ let* msgs1 =
+ betree_List_pop_front_back (u64 & betree_Message_t) (Betree_List_Cons
+ (k, m) l) in
+ betree_Node_filter_messages_for_key key msgs1
+ else Return (Betree_List_Cons (k, m) l)
+ | Betree_List_Nil -> Return Betree_List_Nil
+ end
+
+(** [betree_main::betree::{betree_main::betree::Node#5}::lookup_first_message_after_key]: forward function
+ Source: 'src/betree.rs', lines 689:4-692:34 *)
+let rec betree_Node_lookup_first_message_after_key
+ (key : u64) (msgs : betree_List_t (u64 & betree_Message_t)) :
+ Tot (result (betree_List_t (u64 & betree_Message_t)))
+ (decreases (betree_Node_lookup_first_message_after_key_decreases key msgs))
+ =
+ begin match msgs with
+ | Betree_List_Cons p next_msgs ->
+ let (k, m) = p in
+ if k = key
+ then betree_Node_lookup_first_message_after_key key next_msgs
+ else Return (Betree_List_Cons (k, m) next_msgs)
+ | Betree_List_Nil -> Return Betree_List_Nil
+ end
+
+(** [betree_main::betree::{betree_main::betree::Node#5}::lookup_first_message_after_key]: backward function 0
+ Source: 'src/betree.rs', lines 689:4-692:34 *)
+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
+ | Betree_List_Cons p next_msgs ->
+ let (k, m) = p in
+ if k = key
+ then
+ let* next_msgs1 =
+ betree_Node_lookup_first_message_after_key_back key next_msgs ret in
+ Return (Betree_List_Cons (k, m) next_msgs1)
+ else Return ret
+ | Betree_List_Nil -> Return ret
+ end
+
+(** [betree_main::betree::{betree_main::betree::Node#5}::apply_to_internal]: merged forward/backward function
+ (there is a single backward function, and the forward function returns ())
+ Source: 'src/betree.rs', lines 521:4-521:89 *)
+let betree_Node_apply_to_internal
+ (msgs : betree_List_t (u64 & betree_Message_t)) (key : u64)
+ (new_msg : betree_Message_t) :
+ result (betree_List_t (u64 & betree_Message_t))
+ =
+ let* msgs1 = betree_Node_lookup_first_message_for_key key msgs in
+ let* b = betree_ListTupleU64T_head_has_key betree_Message_t msgs1 key in
+ if b
+ then
+ begin match new_msg with
+ | Betree_Message_Insert i ->
+ let* msgs2 = betree_Node_filter_messages_for_key key msgs1 in
+ let* msgs3 =
+ betree_List_push_front (u64 & betree_Message_t) msgs2 (key,
+ Betree_Message_Insert i) in
+ betree_Node_lookup_first_message_for_key_back key msgs msgs3
+ | Betree_Message_Delete ->
+ let* msgs2 = betree_Node_filter_messages_for_key key msgs1 in
+ let* msgs3 =
+ betree_List_push_front (u64 & betree_Message_t) msgs2 (key,
+ Betree_Message_Delete) in
+ betree_Node_lookup_first_message_for_key_back key msgs msgs3
+ | Betree_Message_Upsert s ->
+ let* p = betree_List_hd (u64 & betree_Message_t) msgs1 in
+ let (_, m) = p in
+ begin match m with
+ | Betree_Message_Insert prev ->
+ let* v = betree_upsert_update (Some prev) s in
+ let* msgs2 = betree_List_pop_front_back (u64 & betree_Message_t) msgs1
+ in
+ let* msgs3 =
+ betree_List_push_front (u64 & betree_Message_t) msgs2 (key,
+ Betree_Message_Insert v) in
+ betree_Node_lookup_first_message_for_key_back key msgs msgs3
+ | Betree_Message_Delete ->
+ let* v = betree_upsert_update None s in
+ let* msgs2 = betree_List_pop_front_back (u64 & betree_Message_t) msgs1
+ in
+ let* msgs3 =
+ betree_List_push_front (u64 & betree_Message_t) msgs2 (key,
+ Betree_Message_Insert v) in
+ betree_Node_lookup_first_message_for_key_back key msgs msgs3
+ | Betree_Message_Upsert _ ->
+ let* msgs2 = betree_Node_lookup_first_message_after_key key msgs1 in
+ let* msgs3 =
+ betree_List_push_front (u64 & betree_Message_t) msgs2 (key,
+ Betree_Message_Upsert s) in
+ let* msgs4 =
+ betree_Node_lookup_first_message_after_key_back key msgs1 msgs3 in
+ betree_Node_lookup_first_message_for_key_back key msgs msgs4
+ end
+ end
+ else
+ let* msgs2 =
+ betree_List_push_front (u64 & betree_Message_t) msgs1 (key, new_msg) in
+ betree_Node_lookup_first_message_for_key_back key msgs msgs2
+
+(** [betree_main::betree::{betree_main::betree::Node#5}::apply_messages_to_internal]: merged forward/backward function
+ (there is a single backward function, and the forward function returns ())
+ Source: 'src/betree.rs', lines 502:4-505:5 *)
+let rec betree_Node_apply_messages_to_internal
+ (msgs : betree_List_t (u64 & betree_Message_t))
+ (new_msgs : betree_List_t (u64 & betree_Message_t)) :
+ Tot (result (betree_List_t (u64 & betree_Message_t)))
+ (decreases (betree_Node_apply_messages_to_internal_decreases msgs new_msgs))
+ =
+ begin match new_msgs with
+ | Betree_List_Cons new_msg new_msgs_tl ->
+ let (i, m) = new_msg in
+ let* msgs1 = betree_Node_apply_to_internal msgs i m in
+ betree_Node_apply_messages_to_internal msgs1 new_msgs_tl
+ | Betree_List_Nil -> Return msgs
+ end
+
+(** [betree_main::betree::{betree_main::betree::Node#5}::lookup_mut_in_bindings]: forward function
+ Source: 'src/betree.rs', lines 653:4-656:32 *)
+let rec betree_Node_lookup_mut_in_bindings
+ (key : u64) (bindings : betree_List_t (u64 & u64)) :
+ Tot (result (betree_List_t (u64 & u64)))
+ (decreases (betree_Node_lookup_mut_in_bindings_decreases key bindings))
+ =
+ begin match bindings with
+ | Betree_List_Cons hd tl ->
+ let (i, i1) = hd in
+ if i >= key
+ then Return (Betree_List_Cons (i, i1) tl)
+ else betree_Node_lookup_mut_in_bindings key tl
+ | Betree_List_Nil -> Return Betree_List_Nil
+ end
+
+(** [betree_main::betree::{betree_main::betree::Node#5}::lookup_mut_in_bindings]: backward function 0
+ Source: 'src/betree.rs', lines 653:4-656:32 *)
+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
+ | Betree_List_Cons hd tl ->
+ let (i, i1) = hd in
+ if i >= key
+ then Return ret
+ else
+ let* tl1 = betree_Node_lookup_mut_in_bindings_back key tl ret in
+ Return (Betree_List_Cons (i, i1) tl1)
+ | Betree_List_Nil -> Return ret
+ end
+
+(** [betree_main::betree::{betree_main::betree::Node#5}::apply_to_leaf]: merged forward/backward function
+ (there is a single backward function, and the forward function returns ())
+ Source: 'src/betree.rs', lines 460:4-460:87 *)
+let betree_Node_apply_to_leaf
+ (bindings : betree_List_t (u64 & u64)) (key : u64)
+ (new_msg : betree_Message_t) :
+ result (betree_List_t (u64 & u64))
+ =
+ let* bindings1 = betree_Node_lookup_mut_in_bindings key bindings in
+ let* b = betree_ListTupleU64T_head_has_key u64 bindings1 key in
+ if b
+ then
+ let* hd = betree_List_pop_front (u64 & u64) bindings1 in
+ begin match new_msg with
+ | Betree_Message_Insert v ->
+ let* bindings2 = betree_List_pop_front_back (u64 & u64) bindings1 in
+ let* bindings3 = betree_List_push_front (u64 & u64) bindings2 (key, v) in
+ betree_Node_lookup_mut_in_bindings_back key bindings bindings3
+ | Betree_Message_Delete ->
+ let* bindings2 = betree_List_pop_front_back (u64 & u64) bindings1 in
+ betree_Node_lookup_mut_in_bindings_back key bindings bindings2
+ | Betree_Message_Upsert s ->
+ let (_, i) = hd in
+ let* v = betree_upsert_update (Some i) s in
+ let* bindings2 = betree_List_pop_front_back (u64 & u64) bindings1 in
+ let* bindings3 = betree_List_push_front (u64 & u64) bindings2 (key, v) in
+ betree_Node_lookup_mut_in_bindings_back key bindings bindings3
+ end
+ else
+ begin match new_msg with
+ | Betree_Message_Insert v ->
+ let* bindings2 = betree_List_push_front (u64 & u64) bindings1 (key, v) in
+ betree_Node_lookup_mut_in_bindings_back key bindings bindings2
+ | Betree_Message_Delete ->
+ betree_Node_lookup_mut_in_bindings_back key bindings bindings1
+ | Betree_Message_Upsert s ->
+ let* v = betree_upsert_update None s in
+ let* bindings2 = betree_List_push_front (u64 & u64) bindings1 (key, v) in
+ betree_Node_lookup_mut_in_bindings_back key bindings bindings2
+ end
+
+(** [betree_main::betree::{betree_main::betree::Node#5}::apply_messages_to_leaf]: merged forward/backward function
+ (there is a single backward function, and the forward function returns ())
+ Source: 'src/betree.rs', lines 444:4-447:5 *)
+let rec betree_Node_apply_messages_to_leaf
+ (bindings : betree_List_t (u64 & u64))
+ (new_msgs : betree_List_t (u64 & betree_Message_t)) :
+ Tot (result (betree_List_t (u64 & u64)))
+ (decreases (betree_Node_apply_messages_to_leaf_decreases bindings new_msgs))
+ =
+ begin match new_msgs with
+ | Betree_List_Cons new_msg new_msgs_tl ->
+ let (i, m) = new_msg in
+ let* bindings1 = betree_Node_apply_to_leaf bindings i m in
+ betree_Node_apply_messages_to_leaf bindings1 new_msgs_tl
+ | Betree_List_Nil -> Return bindings
+ end
+
+(** [betree_main::betree::{betree_main::betree::Internal#4}::flush]: forward function
+ Source: 'src/betree.rs', lines 410:4-415:26 *)
+let rec betree_Internal_flush
+ (self : betree_Internal_t) (params : betree_Params_t)
+ (node_id_cnt : betree_NodeIdCounter_t)
+ (content : betree_List_t (u64 & betree_Message_t)) (st : state) :
+ Tot (result (state & (betree_List_t (u64 & betree_Message_t))))
+ (decreases (
+ betree_Internal_flush_decreases self params node_id_cnt content st))
+ =
+ let* p =
+ betree_ListTupleU64T_partition_at_pivot betree_Message_t content self.pivot
+ in
+ let (msgs_left, msgs_right) = p in
+ let* len_left = betree_List_len (u64 & betree_Message_t) msgs_left in
+ if len_left >= params.min_flush_size
+ then
+ let* (st1, _) =
+ betree_Node_apply_messages self.left params node_id_cnt msgs_left st in
+ let* (_, node_id_cnt1) =
+ betree_Node_apply_messages_back self.left params node_id_cnt msgs_left st
+ in
+ let* len_right = betree_List_len (u64 & betree_Message_t) msgs_right in
+ if len_right >= params.min_flush_size
+ then
+ let* (st2, _) =
+ betree_Node_apply_messages self.right params node_id_cnt1 msgs_right
+ st1 in
+ let* _ =
+ betree_Node_apply_messages_back self.right params node_id_cnt1
+ msgs_right st1 in
+ Return (st2, Betree_List_Nil)
+ else Return (st1, msgs_right)
+ else
+ let* (st1, _) =
+ betree_Node_apply_messages self.right params node_id_cnt msgs_right st in
+ let* _ =
+ betree_Node_apply_messages_back self.right params node_id_cnt msgs_right
+ st in
+ Return (st1, msgs_left)
+
+(** [betree_main::betree::{betree_main::betree::Internal#4}::flush]: backward function 0
+ Source: 'src/betree.rs', lines 410:4-415:26 *)
+and betree_Internal_flush_back
+ (self : betree_Internal_t) (params : betree_Params_t)
+ (node_id_cnt : betree_NodeIdCounter_t)
+ (content : betree_List_t (u64 & betree_Message_t)) (st : state) :
+ Tot (result (betree_Internal_t & betree_NodeIdCounter_t))
+ (decreases (
+ betree_Internal_flush_decreases self params node_id_cnt content st))
+ =
+ let* p =
+ betree_ListTupleU64T_partition_at_pivot betree_Message_t content self.pivot
+ in
+ let (msgs_left, msgs_right) = p in
+ let* len_left = betree_List_len (u64 & betree_Message_t) msgs_left in
+ if len_left >= params.min_flush_size
+ then
+ let* (st1, _) =
+ betree_Node_apply_messages self.left params node_id_cnt msgs_left st in
+ let* (n, node_id_cnt1) =
+ betree_Node_apply_messages_back self.left params node_id_cnt msgs_left st
+ in
+ let* len_right = betree_List_len (u64 & betree_Message_t) msgs_right in
+ if len_right >= params.min_flush_size
+ then
+ let* (n1, node_id_cnt2) =
+ betree_Node_apply_messages_back self.right params node_id_cnt1
+ msgs_right st1 in
+ Return ({ self with left = n; right = n1 }, node_id_cnt2)
+ else Return ({ self with left = n }, node_id_cnt1)
+ else
+ let* (n, node_id_cnt1) =
+ betree_Node_apply_messages_back self.right params node_id_cnt msgs_right
+ st in
+ Return ({ self with right = n }, node_id_cnt1)
+
+(** [betree_main::betree::{betree_main::betree::Node#5}::apply_messages]: forward function
+ Source: 'src/betree.rs', lines 588:4-593:5 *)
+and betree_Node_apply_messages
+ (self : betree_Node_t) (params : betree_Params_t)
+ (node_id_cnt : betree_NodeIdCounter_t)
+ (msgs : betree_List_t (u64 & betree_Message_t)) (st : state) :
+ Tot (result (state & unit))
+ (decreases (
+ betree_Node_apply_messages_decreases self params node_id_cnt msgs st))
+ =
+ begin match self with
+ | Betree_Node_Internal node ->
+ let* (st1, content) = betree_load_internal_node node.id st in
+ let* content1 = betree_Node_apply_messages_to_internal content msgs in
+ let* num_msgs = betree_List_len (u64 & betree_Message_t) content1 in
+ if num_msgs >= params.min_flush_size
+ then
+ let* (st2, content2) =
+ betree_Internal_flush node params node_id_cnt content1 st1 in
+ let* (node1, _) =
+ betree_Internal_flush_back node params node_id_cnt content1 st1 in
+ let* (st3, _) = betree_store_internal_node node1.id content2 st2 in
+ Return (st3, ())
+ else
+ let* (st2, _) = betree_store_internal_node node.id content1 st1 in
+ Return (st2, ())
+ | Betree_Node_Leaf node ->
+ let* (st1, content) = betree_load_leaf_node node.id st in
+ let* content1 = betree_Node_apply_messages_to_leaf content msgs in
+ let* len = betree_List_len (u64 & u64) content1 in
+ let* i = u64_mul 2 params.split_size in
+ if len >= i
+ then
+ let* (st2, _) = betree_Leaf_split node content1 params node_id_cnt st1 in
+ let* (st3, _) = betree_store_leaf_node node.id Betree_List_Nil st2 in
+ Return (st3, ())
+ else
+ let* (st2, _) = betree_store_leaf_node node.id content1 st1 in
+ Return (st2, ())
+ end
+
+(** [betree_main::betree::{betree_main::betree::Node#5}::apply_messages]: backward function 0
+ Source: 'src/betree.rs', lines 588:4-593:5 *)
+and betree_Node_apply_messages_back
+ (self : betree_Node_t) (params : betree_Params_t)
+ (node_id_cnt : betree_NodeIdCounter_t)
+ (msgs : betree_List_t (u64 & betree_Message_t)) (st : state) :
+ Tot (result (betree_Node_t & betree_NodeIdCounter_t))
+ (decreases (
+ betree_Node_apply_messages_decreases self params node_id_cnt msgs st))
+ =
+ begin match self with
+ | Betree_Node_Internal node ->
+ let* (st1, content) = betree_load_internal_node node.id st in
+ let* content1 = betree_Node_apply_messages_to_internal content msgs in
+ let* num_msgs = betree_List_len (u64 & betree_Message_t) content1 in
+ if num_msgs >= params.min_flush_size
+ then
+ let* (st2, content2) =
+ betree_Internal_flush node params node_id_cnt content1 st1 in
+ let* (node1, node_id_cnt1) =
+ betree_Internal_flush_back node params node_id_cnt content1 st1 in
+ let* _ = betree_store_internal_node node1.id content2 st2 in
+ Return (Betree_Node_Internal node1, node_id_cnt1)
+ else
+ let* _ = betree_store_internal_node node.id content1 st1 in
+ Return (Betree_Node_Internal node, node_id_cnt)
+ | Betree_Node_Leaf node ->
+ let* (st1, content) = betree_load_leaf_node node.id st in
+ let* content1 = betree_Node_apply_messages_to_leaf content msgs in
+ let* len = betree_List_len (u64 & u64) content1 in
+ let* i = u64_mul 2 params.split_size in
+ if len >= i
+ then
+ let* (st2, new_node) =
+ betree_Leaf_split node content1 params node_id_cnt st1 in
+ let* _ = betree_store_leaf_node node.id Betree_List_Nil st2 in
+ let* node_id_cnt1 =
+ betree_Leaf_split_back node content1 params node_id_cnt st1 in
+ Return (Betree_Node_Internal new_node, node_id_cnt1)
+ else
+ let* _ = betree_store_leaf_node node.id content1 st1 in
+ Return (Betree_Node_Leaf { node with size = len }, node_id_cnt)
+ end
+
+(** [betree_main::betree::{betree_main::betree::Node#5}::apply]: forward function
+ Source: 'src/betree.rs', lines 576:4-582:5 *)
+let betree_Node_apply
+ (self : betree_Node_t) (params : betree_Params_t)
+ (node_id_cnt : betree_NodeIdCounter_t) (key : u64)
+ (new_msg : betree_Message_t) (st : state) :
+ result (state & unit)
+ =
+ let* (st1, _) =
+ betree_Node_apply_messages self params node_id_cnt (Betree_List_Cons (key,
+ new_msg) Betree_List_Nil) st in
+ let* _ =
+ betree_Node_apply_messages_back self params node_id_cnt (Betree_List_Cons
+ (key, new_msg) Betree_List_Nil) st in
+ Return (st1, ())
+
+(** [betree_main::betree::{betree_main::betree::Node#5}::apply]: backward function 0
+ Source: 'src/betree.rs', lines 576:4-582:5 *)
+let betree_Node_apply_back
+ (self : betree_Node_t) (params : betree_Params_t)
+ (node_id_cnt : betree_NodeIdCounter_t) (key : u64)
+ (new_msg : betree_Message_t) (st : state) :
+ result (betree_Node_t & betree_NodeIdCounter_t)
+ =
+ betree_Node_apply_messages_back self params node_id_cnt (Betree_List_Cons
+ (key, new_msg) Betree_List_Nil) st
+
+(** [betree_main::betree::{betree_main::betree::BeTree#6}::new]: forward function
+ Source: 'src/betree.rs', lines 849:4-849:60 *)
+let betree_BeTree_new
+ (min_flush_size : u64) (split_size : u64) (st : state) :
+ result (state & betree_BeTree_t)
+ =
+ let* node_id_cnt = betree_NodeIdCounter_new in
+ let* id = betree_NodeIdCounter_fresh_id node_id_cnt in
+ let* (st1, _) = betree_store_leaf_node id Betree_List_Nil st in
+ let* node_id_cnt1 = betree_NodeIdCounter_fresh_id_back node_id_cnt in
+ Return (st1,
+ {
+ params = { min_flush_size = min_flush_size; split_size = split_size };
+ node_id_cnt = node_id_cnt1;
+ root = (Betree_Node_Leaf { id = id; size = 0 })
+ })
+
+(** [betree_main::betree::{betree_main::betree::BeTree#6}::apply]: forward function
+ Source: 'src/betree.rs', lines 868:4-868:47 *)
+let betree_BeTree_apply
+ (self : betree_BeTree_t) (key : u64) (msg : betree_Message_t) (st : state) :
+ result (state & unit)
+ =
+ let* (st1, _) =
+ betree_Node_apply self.root self.params self.node_id_cnt key msg st in
+ let* _ =
+ betree_Node_apply_back self.root self.params self.node_id_cnt key msg st in
+ Return (st1, ())
+
+(** [betree_main::betree::{betree_main::betree::BeTree#6}::apply]: backward function 0
+ Source: 'src/betree.rs', lines 868:4-868:47 *)
+let betree_BeTree_apply_back
+ (self : betree_BeTree_t) (key : u64) (msg : betree_Message_t) (st : state) :
+ result betree_BeTree_t
+ =
+ let* (n, nic) =
+ betree_Node_apply_back self.root self.params self.node_id_cnt key msg st in
+ Return { self with node_id_cnt = nic; root = n }
+
+(** [betree_main::betree::{betree_main::betree::BeTree#6}::insert]: forward function
+ Source: 'src/betree.rs', lines 874:4-874:52 *)
+let betree_BeTree_insert
+ (self : betree_BeTree_t) (key : u64) (value : u64) (st : state) :
+ result (state & unit)
+ =
+ let* (st1, _) = betree_BeTree_apply self key (Betree_Message_Insert value) st
+ in
+ let* _ = betree_BeTree_apply_back self key (Betree_Message_Insert value) st
+ in
+ Return (st1, ())
+
+(** [betree_main::betree::{betree_main::betree::BeTree#6}::insert]: backward function 0
+ Source: 'src/betree.rs', lines 874:4-874:52 *)
+let betree_BeTree_insert_back
+ (self : betree_BeTree_t) (key : u64) (value : u64) (st : state) :
+ result betree_BeTree_t
+ =
+ betree_BeTree_apply_back self key (Betree_Message_Insert value) st
+
+(** [betree_main::betree::{betree_main::betree::BeTree#6}::delete]: forward function
+ Source: 'src/betree.rs', lines 880:4-880:38 *)
+let betree_BeTree_delete
+ (self : betree_BeTree_t) (key : u64) (st : state) : result (state & unit) =
+ let* (st1, _) = betree_BeTree_apply self key Betree_Message_Delete st in
+ let* _ = betree_BeTree_apply_back self key Betree_Message_Delete st in
+ Return (st1, ())
+
+(** [betree_main::betree::{betree_main::betree::BeTree#6}::delete]: backward function 0
+ Source: 'src/betree.rs', lines 880:4-880:38 *)
+let betree_BeTree_delete_back
+ (self : betree_BeTree_t) (key : u64) (st : state) : result betree_BeTree_t =
+ betree_BeTree_apply_back self key Betree_Message_Delete st
+
+(** [betree_main::betree::{betree_main::betree::BeTree#6}::upsert]: forward function
+ Source: 'src/betree.rs', lines 886:4-886:59 *)
+let betree_BeTree_upsert
+ (self : betree_BeTree_t) (key : u64) (upd : betree_UpsertFunState_t)
+ (st : state) :
+ result (state & unit)
+ =
+ let* (st1, _) = betree_BeTree_apply self key (Betree_Message_Upsert upd) st
+ in
+ let* _ = betree_BeTree_apply_back self key (Betree_Message_Upsert upd) st in
+ Return (st1, ())
+
+(** [betree_main::betree::{betree_main::betree::BeTree#6}::upsert]: backward function 0
+ Source: 'src/betree.rs', lines 886:4-886:59 *)
+let betree_BeTree_upsert_back
+ (self : betree_BeTree_t) (key : u64) (upd : betree_UpsertFunState_t)
+ (st : state) :
+ result betree_BeTree_t
+ =
+ betree_BeTree_apply_back self key (Betree_Message_Upsert upd) st
+
+(** [betree_main::betree::{betree_main::betree::BeTree#6}::lookup]: forward function
+ Source: 'src/betree.rs', lines 895:4-895:62 *)
+let betree_BeTree_lookup
+ (self : betree_BeTree_t) (key : u64) (st : state) :
+ result (state & (option u64))
+ =
+ betree_Node_lookup self.root key st
+
+(** [betree_main::betree::{betree_main::betree::BeTree#6}::lookup]: backward function 0
+ Source: 'src/betree.rs', lines 895:4-895:62 *)
+let betree_BeTree_lookup_back
+ (self : betree_BeTree_t) (key : u64) (st : state) : result betree_BeTree_t =
+ let* n = betree_Node_lookup_back self.root key st in
+ Return { self with root = n }
+
+(** [betree_main::main]: forward function
+ Source: 'src/betree_main.rs', lines 5:0-5:9 *)
+let main : result unit =
+ Return ()
+
+(** Unit test for [betree_main::main] *)
+let _ = assert_norm (main = Return ())
+
diff --git a/tests/fstar-split/betree/BetreeMain.FunsExternal.fsti b/tests/fstar-split/betree/BetreeMain.FunsExternal.fsti
new file mode 100644
index 00000000..cd2f956f
--- /dev/null
+++ b/tests/fstar-split/betree/BetreeMain.FunsExternal.fsti
@@ -0,0 +1,35 @@
+(** THIS FILE WAS AUTOMATICALLY GENERATED BY AENEAS *)
+(** [betree_main]: external function declarations *)
+module BetreeMain.FunsExternal
+open Primitives
+include BetreeMain.Types
+
+#set-options "--z3rlimit 50 --fuel 1 --ifuel 1"
+
+(** [betree_main::betree_utils::load_internal_node]: forward function
+ Source: 'src/betree_utils.rs', lines 98:0-98:63 *)
+val betree_utils_load_internal_node
+ : u64 -> state -> result (state & (betree_List_t (u64 & betree_Message_t)))
+
+(** [betree_main::betree_utils::store_internal_node]: forward function
+ Source: 'src/betree_utils.rs', lines 115:0-115:71 *)
+val betree_utils_store_internal_node
+ :
+ u64 -> betree_List_t (u64 & betree_Message_t) -> state -> result (state &
+ unit)
+
+(** [betree_main::betree_utils::load_leaf_node]: forward function
+ Source: 'src/betree_utils.rs', lines 132:0-132:55 *)
+val betree_utils_load_leaf_node
+ : u64 -> state -> result (state & (betree_List_t (u64 & u64)))
+
+(** [betree_main::betree_utils::store_leaf_node]: forward function
+ Source: 'src/betree_utils.rs', lines 145:0-145:63 *)
+val betree_utils_store_leaf_node
+ : u64 -> betree_List_t (u64 & u64) -> state -> result (state & unit)
+
+(** [core::option::{core::option::Option<T>}::unwrap]: forward function
+ Source: '/rustc/d59363ad0b6391b7fc5bbb02c9ccf9300eef3753/library/core/src/option.rs', lines 932:4-932:34 *)
+val core_option_Option_unwrap
+ (t : Type0) : option t -> state -> result (state & t)
+
diff --git a/tests/fstar-split/betree/BetreeMain.Types.fst b/tests/fstar-split/betree/BetreeMain.Types.fst
new file mode 100644
index 00000000..b87219b2
--- /dev/null
+++ b/tests/fstar-split/betree/BetreeMain.Types.fst
@@ -0,0 +1,61 @@
+(** THIS FILE WAS AUTOMATICALLY GENERATED BY AENEAS *)
+(** [betree_main]: type definitions *)
+module BetreeMain.Types
+open Primitives
+include BetreeMain.TypesExternal
+
+#set-options "--z3rlimit 50 --fuel 1 --ifuel 1"
+
+(** [betree_main::betree::List]
+ Source: 'src/betree.rs', lines 17:0-17:23 *)
+type betree_List_t (t : Type0) =
+| Betree_List_Cons : t -> betree_List_t t -> betree_List_t t
+| Betree_List_Nil : betree_List_t t
+
+(** [betree_main::betree::UpsertFunState]
+ Source: 'src/betree.rs', lines 63:0-63:23 *)
+type betree_UpsertFunState_t =
+| Betree_UpsertFunState_Add : u64 -> betree_UpsertFunState_t
+| Betree_UpsertFunState_Sub : u64 -> betree_UpsertFunState_t
+
+(** [betree_main::betree::Message]
+ Source: 'src/betree.rs', lines 69:0-69:23 *)
+type betree_Message_t =
+| Betree_Message_Insert : u64 -> betree_Message_t
+| Betree_Message_Delete : betree_Message_t
+| Betree_Message_Upsert : betree_UpsertFunState_t -> betree_Message_t
+
+(** [betree_main::betree::Leaf]
+ Source: 'src/betree.rs', lines 167:0-167:11 *)
+type betree_Leaf_t = { id : u64; size : u64; }
+
+(** [betree_main::betree::Internal]
+ Source: 'src/betree.rs', lines 156:0-156:15 *)
+type betree_Internal_t =
+{
+ id : u64; pivot : u64; left : betree_Node_t; right : betree_Node_t;
+}
+
+(** [betree_main::betree::Node]
+ Source: 'src/betree.rs', lines 179:0-179:9 *)
+and betree_Node_t =
+| Betree_Node_Internal : betree_Internal_t -> betree_Node_t
+| Betree_Node_Leaf : betree_Leaf_t -> betree_Node_t
+
+(** [betree_main::betree::Params]
+ Source: 'src/betree.rs', lines 187:0-187:13 *)
+type betree_Params_t = { min_flush_size : u64; split_size : u64; }
+
+(** [betree_main::betree::NodeIdCounter]
+ Source: 'src/betree.rs', lines 201:0-201:20 *)
+type betree_NodeIdCounter_t = { next_node_id : u64; }
+
+(** [betree_main::betree::BeTree]
+ Source: 'src/betree.rs', lines 218:0-218:17 *)
+type betree_BeTree_t =
+{
+ params : betree_Params_t;
+ node_id_cnt : betree_NodeIdCounter_t;
+ root : betree_Node_t;
+}
+
diff --git a/tests/fstar-split/betree/BetreeMain.TypesExternal.fsti b/tests/fstar-split/betree/BetreeMain.TypesExternal.fsti
new file mode 100644
index 00000000..1b2c53a6
--- /dev/null
+++ b/tests/fstar-split/betree/BetreeMain.TypesExternal.fsti
@@ -0,0 +1,10 @@
+(** THIS FILE WAS AUTOMATICALLY GENERATED BY AENEAS *)
+(** [betree_main]: external type declarations *)
+module BetreeMain.TypesExternal
+open Primitives
+
+#set-options "--z3rlimit 50 --fuel 1 --ifuel 1"
+
+(** The state type used in the state-error monad *)
+val state : Type0
+
diff --git a/tests/fstar-split/betree/Makefile b/tests/fstar-split/betree/Makefile
new file mode 100644
index 00000000..fa7d1f36
--- /dev/null
+++ b/tests/fstar-split/betree/Makefile
@@ -0,0 +1,49 @@
+# This file was automatically generated - modify ../Makefile.template instead
+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_EXE ?= fstar.exe
+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-split/betree/Primitives.fst b/tests/fstar-split/betree/Primitives.fst
new file mode 100644
index 00000000..a3ffbde4
--- /dev/null
+++ b/tests/fstar-split/betree/Primitives.fst
@@ -0,0 +1,884 @@
+/// 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 error : Type0 =
+| Failure
+| OutOfFuel
+
+type result (a : Type0) : Type0 =
+| Return : v:a -> result a
+| Fail : e:error -> result a
+
+// Monadic return operator
+unfold let return (#a : Type0) (x : a) : result a = Return x
+
+// Monadic bind operator.
+// Allows to use the notation:
+// ```
+// let* x = y in
+// ...
+// ```
+unfold let (let*) (#a #b : Type0) (m: result a)
+ (f: (x:a) -> Pure (result b) (requires (m == Return x)) (ensures fun _ -> True)) :
+ result b =
+ match m with
+ | Return x -> f x
+ | Fail e -> Fail e
+
+// Monadic assert(...)
+let massert (b:bool) : result unit = if b then Return () else Fail Failure
+
+// 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 is_zero (n: nat) : bool = n = 0
+let decrease (n: nat{n > 0}) : nat = n - 1
+
+let core_mem_replace (a : Type0) (x : a) (y : a) : a = x
+let core_mem_replace_back (a : Type0) (x : a) (y : a) : a = y
+
+// We don't really use raw pointers for now
+type mut_raw_ptr (t : Type0) = { v : t }
+type const_raw_ptr (t : Type0) = { v : t }
+
+(*** Scalars *)
+/// Rem.: most of the following code was partially generated
+
+assume val size_numbits : pos
+
+// TODO: we could use FStar.Int.int_t and FStar.UInt.int_t
+
+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 is_unsigned = function
+ | Isize | I8 | I16 | I32 | I64 | I128 -> false
+ | Usize | U8 | U16 | U32 | U64 | U128 -> true
+
+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 Failure
+
+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 Failure
+
+/// 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 Failure
+
+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)
+
+let scalar_xor (#ty : scalar_ty)
+ (x : scalar ty) (y : scalar ty) : scalar ty =
+ match ty with
+ | U8 -> FStar.UInt.logxor #8 x y
+ | U16 -> FStar.UInt.logxor #16 x y
+ | U32 -> FStar.UInt.logxor #32 x y
+ | U64 -> FStar.UInt.logxor #64 x y
+ | U128 -> FStar.UInt.logxor #128 x y
+ | Usize -> admit() // TODO
+ | I8 ->
+ // Encoding issues...
+ normalize_spec (FStar.Int.int_t 8);
+ normalize_spec (scalar I8);
+ FStar.Int.logxor #8 x y
+ | I16 ->
+ // Encoding issues...
+ normalize_spec (FStar.Int.int_t 16);
+ normalize_spec (scalar I16);
+ FStar.Int.logxor #16 x y
+ | I32 -> FStar.Int.logxor #32 x y
+ | I64 -> FStar.Int.logxor #64 x y
+ | I128 ->
+ // Encoding issues...
+ normalize_spec (FStar.Int.int_t 128);
+ normalize_spec (scalar I128);
+ FStar.Int.logxor #128 x y
+ | Isize -> admit() // TODO
+
+let scalar_or (#ty : scalar_ty)
+ (x : scalar ty) (y : scalar ty) : scalar ty =
+ match ty with
+ | U8 -> FStar.UInt.logor #8 x y
+ | U16 -> FStar.UInt.logor #16 x y
+ | U32 -> FStar.UInt.logor #32 x y
+ | U64 -> FStar.UInt.logor #64 x y
+ | U128 -> FStar.UInt.logor #128 x y
+ | Usize -> admit() // TODO
+ | I8 ->
+ // Encoding issues...
+ normalize_spec (FStar.Int.int_t 8);
+ normalize_spec (scalar I8);
+ FStar.Int.logor #8 x y
+ | I16 ->
+ // Encoding issues...
+ normalize_spec (FStar.Int.int_t 16);
+ normalize_spec (scalar I16);
+ FStar.Int.logor #16 x y
+ | I32 -> FStar.Int.logor #32 x y
+ | I64 -> FStar.Int.logor #64 x y
+ | I128 ->
+ // Encoding issues...
+ normalize_spec (FStar.Int.int_t 128);
+ normalize_spec (scalar I128);
+ FStar.Int.logor #128 x y
+ | Isize -> admit() // TODO
+
+let scalar_and (#ty : scalar_ty)
+ (x : scalar ty) (y : scalar ty) : scalar ty =
+ match ty with
+ | U8 -> FStar.UInt.logand #8 x y
+ | U16 -> FStar.UInt.logand #16 x y
+ | U32 -> FStar.UInt.logand #32 x y
+ | U64 -> FStar.UInt.logand #64 x y
+ | U128 -> FStar.UInt.logand #128 x y
+ | Usize -> admit() // TODO
+ | I8 ->
+ // Encoding issues...
+ normalize_spec (FStar.Int.int_t 8);
+ normalize_spec (scalar I8);
+ FStar.Int.logand #8 x y
+ | I16 ->
+ // Encoding issues...
+ normalize_spec (FStar.Int.int_t 16);
+ normalize_spec (scalar I16);
+ FStar.Int.logand #16 x y
+ | I32 -> FStar.Int.logand #32 x y
+ | I64 -> FStar.Int.logand #64 x y
+ | I128 ->
+ // Encoding issues...
+ normalize_spec (FStar.Int.int_t 128);
+ normalize_spec (scalar I128);
+ FStar.Int.logand #128 x y
+ | Isize -> admit() // TODO
+
+// Shift left
+let scalar_shl (#ty0 #ty1 : scalar_ty)
+ (x : scalar ty0) (y : scalar ty1) : result (scalar ty0) =
+ admit()
+
+// Shift right
+let scalar_shr (#ty0 #ty1 : scalar_ty)
+ (x : scalar ty0) (y : scalar ty1) : result (scalar ty0) =
+ admit()
+
+(** 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
+
+// This can't fail, but for now we make all casts faillible (easier for the translation)
+let scalar_cast_bool (tgt_ty : scalar_ty) (x : bool) : result (scalar tgt_ty) =
+ mk_scalar tgt_ty (if x then 1 else 0)
+
+/// 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
+
+
+let core_isize_min : isize = isize_min
+let core_isize_max : isize = isize_max
+let core_i8_min : i8 = i8_min
+let core_i8_max : i8 = i8_max
+let core_i16_min : i16 = i16_min
+let core_i16_max : i16 = i16_max
+let core_i32_min : i32 = i32_min
+let core_i32_max : i32 = i32_max
+let core_i64_min : i64 = i64_min
+let core_i64_max : i64 = i64_max
+let core_i128_min : i128 = i128_min
+let core_i128_max : i128 = i128_max
+
+let core_usize_min : usize = usize_min
+let core_usize_max : usize = usize_max
+let core_u8_min : u8 = u8_min
+let core_u8_max : u8 = u8_max
+let core_u16_min : u16 = u16_min
+let core_u16_max : u16 = u16_max
+let core_u32_min : u32 = u32_min
+let core_u32_max : u32 = u32_max
+let core_u64_min : u64 = u64_min
+let core_u64_max : u64 = u64_max
+let core_u128_min : u128 = u128_min
+let core_u128_max : u128 = u128_max
+
+/// 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
+
+/// Subtraction
+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
+
+/// Xor
+let u8_xor = scalar_xor #U8
+let u16_xor = scalar_xor #U16
+let u32_xor = scalar_xor #U32
+let u64_xor = scalar_xor #U64
+let u128_xor = scalar_xor #U128
+let usize_xor = scalar_xor #Usize
+let i8_xor = scalar_xor #I8
+let i16_xor = scalar_xor #I16
+let i32_xor = scalar_xor #I32
+let i64_xor = scalar_xor #I64
+let i128_xor = scalar_xor #I128
+let isize_xor = scalar_xor #Isize
+
+/// Or
+let u8_or = scalar_or #U8
+let u16_or = scalar_or #U16
+let u32_or = scalar_or #U32
+let u64_or = scalar_or #U64
+let u128_or = scalar_or #U128
+let usize_or = scalar_or #Usize
+let i8_or = scalar_or #I8
+let i16_or = scalar_or #I16
+let i32_or = scalar_or #I32
+let i64_or = scalar_or #I64
+let i128_or = scalar_or #I128
+let isize_or = scalar_or #Isize
+
+/// And
+let u8_and = scalar_and #U8
+let u16_and = scalar_and #U16
+let u32_and = scalar_and #U32
+let u64_and = scalar_and #U64
+let u128_and = scalar_and #U128
+let usize_and = scalar_and #Usize
+let i8_and = scalar_and #I8
+let i16_and = scalar_and #I16
+let i32_and = scalar_and #I32
+let i64_and = scalar_and #I64
+let i128_and = scalar_and #I128
+let isize_and = scalar_and #Isize
+
+/// Shift left
+let u8_shl #ty = scalar_shl #U8 #ty
+let u16_shl #ty = scalar_shl #U16 #ty
+let u32_shl #ty = scalar_shl #U32 #ty
+let u64_shl #ty = scalar_shl #U64 #ty
+let u128_shl #ty = scalar_shl #U128 #ty
+let usize_shl #ty = scalar_shl #Usize #ty
+let i8_shl #ty = scalar_shl #I8 #ty
+let i16_shl #ty = scalar_shl #I16 #ty
+let i32_shl #ty = scalar_shl #I32 #ty
+let i64_shl #ty = scalar_shl #I64 #ty
+let i128_shl #ty = scalar_shl #I128 #ty
+let isize_shl #ty = scalar_shl #Isize #ty
+
+/// Shift right
+let u8_shr #ty = scalar_shr #U8 #ty
+let u16_shr #ty = scalar_shr #U16 #ty
+let u32_shr #ty = scalar_shr #U32 #ty
+let u64_shr #ty = scalar_shr #U64 #ty
+let u128_shr #ty = scalar_shr #U128 #ty
+let usize_shr #ty = scalar_shr #Usize #ty
+let i8_shr #ty = scalar_shr #I8 #ty
+let i16_shr #ty = scalar_shr #I16 #ty
+let i32_shr #ty = scalar_shr #I32 #ty
+let i64_shr #ty = scalar_shr #I64 #ty
+let i128_shr #ty = scalar_shr #I128 #ty
+let isize_shr #ty = scalar_shr #Isize #ty
+
+(*** core::ops *)
+
+// Trait declaration: [core::ops::index::Index]
+noeq type core_ops_index_Index (self idx : Type0) = {
+ output : Type0;
+ index : self → idx → result output
+}
+
+// Trait declaration: [core::ops::index::IndexMut]
+noeq type core_ops_index_IndexMut (self idx : Type0) = {
+ indexInst : core_ops_index_Index self idx;
+ index_mut : self → idx → result indexInst.output;
+ index_mut_back : self → idx → indexInst.output → result self;
+}
+
+// Trait declaration [core::ops::deref::Deref]
+noeq type core_ops_deref_Deref (self : Type0) = {
+ target : Type0;
+ deref : self → result target;
+}
+
+// Trait declaration [core::ops::deref::DerefMut]
+noeq type core_ops_deref_DerefMut (self : Type0) = {
+ derefInst : core_ops_deref_Deref self;
+ deref_mut : self → result derefInst.target;
+ deref_mut_back : self → derefInst.target → result self;
+}
+
+type core_ops_range_Range (a : Type0) = {
+ start : a;
+ end_ : a;
+}
+
+(*** [alloc] *)
+
+let alloc_boxed_Box_deref (t : Type0) (x : t) : result t = Return x
+let alloc_boxed_Box_deref_mut (t : Type0) (x : t) : result t = Return x
+let alloc_boxed_Box_deref_mut_back (t : Type) (_ : t) (x : t) : result t = Return x
+
+// Trait instance
+let alloc_boxed_Box_coreopsDerefInst (self : Type0) : core_ops_deref_Deref self = {
+ target = self;
+ deref = alloc_boxed_Box_deref self;
+}
+
+// Trait instance
+let alloc_boxed_Box_coreopsDerefMutInst (self : Type0) : core_ops_deref_DerefMut self = {
+ derefInst = alloc_boxed_Box_coreopsDerefInst self;
+ deref_mut = alloc_boxed_Box_deref_mut self;
+ deref_mut_back = alloc_boxed_Box_deref_mut_back self;
+}
+
+(*** Array *)
+type array (a : Type0) (n : usize) = s:list a{length s = n}
+
+// We tried putting the normalize_term condition as a refinement on the list
+// but it didn't work. It works with the requires clause.
+let mk_array (a : Type0) (n : usize)
+ (l : list a) :
+ Pure (array a n)
+ (requires (normalize_term(FStar.List.Tot.length l) = n))
+ (ensures (fun _ -> True)) =
+ normalize_term_spec (FStar.List.Tot.length l);
+ l
+
+let array_index_usize (a : Type0) (n : usize) (x : array a n) (i : usize) : result a =
+ if i < length x then Return (index x i)
+ else Fail Failure
+
+let array_update_usize (a : Type0) (n : usize) (x : array a n) (i : usize) (nx : a) : result (array a n) =
+ if i < length x then Return (list_update x i nx)
+ else Fail Failure
+
+(*** Slice *)
+type slice (a : Type0) = s:list a{length s <= usize_max}
+
+let slice_len (a : Type0) (s : slice a) : usize = length s
+
+let slice_index_usize (a : Type0) (x : slice a) (i : usize) : result a =
+ if i < length x then Return (index x i)
+ else Fail Failure
+
+let slice_update_usize (a : Type0) (x : slice a) (i : usize) (nx : a) : result (slice a) =
+ if i < length x then Return (list_update x i nx)
+ else Fail Failure
+
+(*** Subslices *)
+
+let array_to_slice (a : Type0) (n : usize) (x : array a n) : result (slice a) = Return x
+let array_from_slice (a : Type0) (n : usize) (x : array a n) (s : slice a) : result (array a n) =
+ if length s = n then Return s
+ else Fail Failure
+
+// TODO: finish the definitions below (there lacks [List.drop] and [List.take] in the standard library *)
+let array_subslice (a : Type0) (n : usize) (x : array a n) (r : core_ops_range_Range usize) : result (slice a) =
+ admit()
+
+let array_update_subslice (a : Type0) (n : usize) (x : array a n) (r : core_ops_range_Range usize) (ns : slice a) : result (array a n) =
+ admit()
+
+let array_repeat (a : Type0) (n : usize) (x : a) : array a n =
+ admit()
+
+let slice_subslice (a : Type0) (x : slice a) (r : core_ops_range_Range usize) : result (slice a) =
+ admit()
+
+let slice_update_subslice (a : Type0) (x : slice a) (r : core_ops_range_Range usize) (ns : slice a) : result (slice a) =
+ admit()
+
+(*** Vector *)
+type alloc_vec_Vec (a : Type0) = v:list a{length v <= usize_max}
+
+let alloc_vec_Vec_new (a : Type0) : alloc_vec_Vec a = assert_norm(length #a [] == 0); []
+let alloc_vec_Vec_len (a : Type0) (v : alloc_vec_Vec a) : usize = length v
+
+// Helper
+let alloc_vec_Vec_index_usize (#a : Type0) (v : alloc_vec_Vec a) (i : usize) : result a =
+ if i < length v then Return (index v i) else Fail Failure
+// Helper
+let alloc_vec_Vec_update_usize (#a : Type0) (v : alloc_vec_Vec a) (i : usize) (x : a) : result (alloc_vec_Vec a) =
+ if i < length v then Return (list_update v i x) else Fail Failure
+
+// The **forward** function shouldn't be used
+let alloc_vec_Vec_push_fwd (a : Type0) (v : alloc_vec_Vec a) (x : a) : unit = ()
+let alloc_vec_Vec_push (a : Type0) (v : alloc_vec_Vec a) (x : a) :
+ Pure (result (alloc_vec_Vec a))
+ (requires True)
+ (ensures (fun res ->
+ match res with
+ | Fail e -> e == Failure
+ | 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 Failure
+
+// The **forward** function shouldn't be used
+let alloc_vec_Vec_insert_fwd (a : Type0) (v : alloc_vec_Vec a) (i : usize) (x : a) : result unit =
+ if i < length v then Return () else Fail Failure
+let alloc_vec_Vec_insert (a : Type0) (v : alloc_vec_Vec a) (i : usize) (x : a) : result (alloc_vec_Vec a) =
+ if i < length v then Return (list_update v i x) else Fail Failure
+
+// Trait declaration: [core::slice::index::private_slice_index::Sealed]
+type core_slice_index_private_slice_index_Sealed (self : Type0) = unit
+
+// Trait declaration: [core::slice::index::SliceIndex]
+noeq type core_slice_index_SliceIndex (self t : Type0) = {
+ sealedInst : core_slice_index_private_slice_index_Sealed self;
+ output : Type0;
+ get : self → t → result (option output);
+ get_mut : self → t → result (option output);
+ get_mut_back : self → t → option output → result t;
+ get_unchecked : self → const_raw_ptr t → result (const_raw_ptr output);
+ get_unchecked_mut : self → mut_raw_ptr t → result (mut_raw_ptr output);
+ index : self → t → result output;
+ index_mut : self → t → result output;
+ index_mut_back : self → t → output → result t;
+}
+
+// [core::slice::index::[T]::index]: forward function
+let core_slice_index_Slice_index
+ (t idx : Type0) (inst : core_slice_index_SliceIndex idx (slice t))
+ (s : slice t) (i : idx) : result inst.output =
+ let* x = inst.get i s in
+ match x with
+ | None -> Fail Failure
+ | Some x -> Return x
+
+// [core::slice::index::Range:::get]: forward function
+let core_slice_index_RangeUsize_get (t : Type0) (i : core_ops_range_Range usize) (s : slice t) :
+ result (option (slice t)) =
+ admit () // TODO
+
+// [core::slice::index::Range::get_mut]: forward function
+let core_slice_index_RangeUsize_get_mut
+ (t : Type0) : core_ops_range_Range usize → slice t → result (option (slice t)) =
+ admit () // TODO
+
+// [core::slice::index::Range::get_mut]: backward function 0
+let core_slice_index_RangeUsize_get_mut_back
+ (t : Type0) :
+ core_ops_range_Range usize → slice t → option (slice t) → result (slice t) =
+ admit () // TODO
+
+// [core::slice::index::Range::get_unchecked]: forward function
+let core_slice_index_RangeUsize_get_unchecked
+ (t : Type0) :
+ core_ops_range_Range usize → const_raw_ptr (slice t) → result (const_raw_ptr (slice t)) =
+ // Don't know what the model should be - for now we always fail to make
+ // sure code which uses it fails
+ fun _ _ -> Fail Failure
+
+// [core::slice::index::Range::get_unchecked_mut]: forward function
+let core_slice_index_RangeUsize_get_unchecked_mut
+ (t : Type0) :
+ core_ops_range_Range usize → mut_raw_ptr (slice t) → result (mut_raw_ptr (slice t)) =
+ // Don't know what the model should be - for now we always fail to make
+ // sure code which uses it fails
+ fun _ _ -> Fail Failure
+
+// [core::slice::index::Range::index]: forward function
+let core_slice_index_RangeUsize_index
+ (t : Type0) : core_ops_range_Range usize → slice t → result (slice t) =
+ admit () // TODO
+
+// [core::slice::index::Range::index_mut]: forward function
+let core_slice_index_RangeUsize_index_mut
+ (t : Type0) : core_ops_range_Range usize → slice t → result (slice t) =
+ admit () // TODO
+
+// [core::slice::index::Range::index_mut]: backward function 0
+let core_slice_index_RangeUsize_index_mut_back
+ (t : Type0) : core_ops_range_Range usize → slice t → slice t → result (slice t) =
+ admit () // TODO
+
+// [core::slice::index::[T]::index_mut]: forward function
+let core_slice_index_Slice_index_mut
+ (t idx : Type0) (inst : core_slice_index_SliceIndex idx (slice t)) :
+ slice t → idx → result inst.output =
+ admit () //
+
+// [core::slice::index::[T]::index_mut]: backward function 0
+let core_slice_index_Slice_index_mut_back
+ (t idx : Type0) (inst : core_slice_index_SliceIndex idx (slice t)) :
+ slice t → idx → inst.output → result (slice t) =
+ admit () // TODO
+
+// [core::array::[T; N]::index]: forward function
+let core_array_Array_index
+ (t idx : Type0) (n : usize) (inst : core_ops_index_Index (slice t) idx)
+ (a : array t n) (i : idx) : result inst.output =
+ admit () // TODO
+
+// [core::array::[T; N]::index_mut]: forward function
+let core_array_Array_index_mut
+ (t idx : Type0) (n : usize) (inst : core_ops_index_IndexMut (slice t) idx)
+ (a : array t n) (i : idx) : result inst.indexInst.output =
+ admit () // TODO
+
+// [core::array::[T; N]::index_mut]: backward function 0
+let core_array_Array_index_mut_back
+ (t idx : Type0) (n : usize) (inst : core_ops_index_IndexMut (slice t) idx)
+ (a : array t n) (i : idx) (x : inst.indexInst.output) : result (array t n) =
+ admit () // TODO
+
+// Trait implementation: [core::slice::index::private_slice_index::Range]
+let core_slice_index_private_slice_index_SealedRangeUsizeInst
+ : core_slice_index_private_slice_index_Sealed (core_ops_range_Range usize) = ()
+
+// Trait implementation: [core::slice::index::Range]
+let core_slice_index_SliceIndexRangeUsizeSliceTInst (t : Type0) :
+ core_slice_index_SliceIndex (core_ops_range_Range usize) (slice t) = {
+ sealedInst = core_slice_index_private_slice_index_SealedRangeUsizeInst;
+ output = slice t;
+ get = core_slice_index_RangeUsize_get t;
+ get_mut = core_slice_index_RangeUsize_get_mut t;
+ get_mut_back = core_slice_index_RangeUsize_get_mut_back t;
+ get_unchecked = core_slice_index_RangeUsize_get_unchecked t;
+ get_unchecked_mut = core_slice_index_RangeUsize_get_unchecked_mut t;
+ index = core_slice_index_RangeUsize_index t;
+ index_mut = core_slice_index_RangeUsize_index_mut t;
+ index_mut_back = core_slice_index_RangeUsize_index_mut_back t;
+}
+
+// Trait implementation: [core::slice::index::[T]]
+let core_ops_index_IndexSliceTIInst (t idx : Type0)
+ (inst : core_slice_index_SliceIndex idx (slice t)) :
+ core_ops_index_Index (slice t) idx = {
+ output = inst.output;
+ index = core_slice_index_Slice_index t idx inst;
+}
+
+// Trait implementation: [core::slice::index::[T]]
+let core_ops_index_IndexMutSliceTIInst (t idx : Type0)
+ (inst : core_slice_index_SliceIndex idx (slice t)) :
+ core_ops_index_IndexMut (slice t) idx = {
+ indexInst = core_ops_index_IndexSliceTIInst t idx inst;
+ index_mut = core_slice_index_Slice_index_mut t idx inst;
+ index_mut_back = core_slice_index_Slice_index_mut_back t idx inst;
+}
+
+// Trait implementation: [core::array::[T; N]]
+let core_ops_index_IndexArrayInst (t idx : Type0) (n : usize)
+ (inst : core_ops_index_Index (slice t) idx) :
+ core_ops_index_Index (array t n) idx = {
+ output = inst.output;
+ index = core_array_Array_index t idx n inst;
+}
+
+// Trait implementation: [core::array::[T; N]]
+let core_ops_index_IndexMutArrayIInst (t idx : Type0) (n : usize)
+ (inst : core_ops_index_IndexMut (slice t) idx) :
+ core_ops_index_IndexMut (array t n) idx = {
+ indexInst = core_ops_index_IndexArrayInst t idx n inst.indexInst;
+ index_mut = core_array_Array_index_mut t idx n inst;
+ index_mut_back = core_array_Array_index_mut_back t idx n inst;
+}
+
+// [core::slice::index::usize::get]: forward function
+let core_slice_index_usize_get
+ (t : Type0) : usize → slice t → result (option t) =
+ admit () // TODO
+
+// [core::slice::index::usize::get_mut]: forward function
+let core_slice_index_usize_get_mut
+ (t : Type0) : usize → slice t → result (option t) =
+ admit () // TODO
+
+// [core::slice::index::usize::get_mut]: backward function 0
+let core_slice_index_usize_get_mut_back
+ (t : Type0) : usize → slice t → option t → result (slice t) =
+ admit () // TODO
+
+// [core::slice::index::usize::get_unchecked]: forward function
+let core_slice_index_usize_get_unchecked
+ (t : Type0) : usize → const_raw_ptr (slice t) → result (const_raw_ptr t) =
+ admit () // TODO
+
+// [core::slice::index::usize::get_unchecked_mut]: forward function
+let core_slice_index_usize_get_unchecked_mut
+ (t : Type0) : usize → mut_raw_ptr (slice t) → result (mut_raw_ptr t) =
+ admit () // TODO
+
+// [core::slice::index::usize::index]: forward function
+let core_slice_index_usize_index (t : Type0) : usize → slice t → result t =
+ admit () // TODO
+
+// [core::slice::index::usize::index_mut]: forward function
+let core_slice_index_usize_index_mut (t : Type0) : usize → slice t → result t =
+ admit () // TODO
+
+// [core::slice::index::usize::index_mut]: backward function 0
+let core_slice_index_usize_index_mut_back
+ (t : Type0) : usize → slice t → t → result (slice t) =
+ admit () // TODO
+
+// Trait implementation: [core::slice::index::private_slice_index::usize]
+let core_slice_index_private_slice_index_SealedUsizeInst
+ : core_slice_index_private_slice_index_Sealed usize = ()
+
+// Trait implementation: [core::slice::index::usize]
+let core_slice_index_SliceIndexUsizeSliceTInst (t : Type0) :
+ core_slice_index_SliceIndex usize (slice t) = {
+ sealedInst = core_slice_index_private_slice_index_SealedUsizeInst;
+ output = t;
+ get = core_slice_index_usize_get t;
+ get_mut = core_slice_index_usize_get_mut t;
+ get_mut_back = core_slice_index_usize_get_mut_back t;
+ get_unchecked = core_slice_index_usize_get_unchecked t;
+ get_unchecked_mut = core_slice_index_usize_get_unchecked_mut t;
+ index = core_slice_index_usize_index t;
+ index_mut = core_slice_index_usize_index_mut t;
+ index_mut_back = core_slice_index_usize_index_mut_back t;
+}
+
+// [alloc::vec::Vec::index]: forward function
+let alloc_vec_Vec_index (t idx : Type0) (inst : core_slice_index_SliceIndex idx (slice t))
+ (self : alloc_vec_Vec t) (i : idx) : result inst.output =
+ admit () // TODO
+
+// [alloc::vec::Vec::index_mut]: forward function
+let alloc_vec_Vec_index_mut (t idx : Type0) (inst : core_slice_index_SliceIndex idx (slice t))
+ (self : alloc_vec_Vec t) (i : idx) : result inst.output =
+ admit () // TODO
+
+// [alloc::vec::Vec::index_mut]: backward function 0
+let alloc_vec_Vec_index_mut_back
+ (t idx : Type0) (inst : core_slice_index_SliceIndex idx (slice t))
+ (self : alloc_vec_Vec t) (i : idx) (x : inst.output) : result (alloc_vec_Vec t) =
+ admit () // TODO
+
+// Trait implementation: [alloc::vec::Vec]
+let alloc_vec_Vec_coreopsindexIndexInst (t idx : Type0)
+ (inst : core_slice_index_SliceIndex idx (slice t)) :
+ core_ops_index_Index (alloc_vec_Vec t) idx = {
+ output = inst.output;
+ index = alloc_vec_Vec_index t idx inst;
+}
+
+// Trait implementation: [alloc::vec::Vec]
+let alloc_vec_Vec_coreopsindexIndexMutInst (t idx : Type0)
+ (inst : core_slice_index_SliceIndex idx (slice t)) :
+ core_ops_index_IndexMut (alloc_vec_Vec t) idx = {
+ indexInst = alloc_vec_Vec_coreopsindexIndexInst t idx inst;
+ index_mut = alloc_vec_Vec_index_mut t idx inst;
+ index_mut_back = alloc_vec_Vec_index_mut_back t idx inst;
+}
+
+(*** Theorems *)
+
+let alloc_vec_Vec_index_eq (#a : Type0) (v : alloc_vec_Vec a) (i : usize) :
+ Lemma (
+ alloc_vec_Vec_index a usize (core_slice_index_SliceIndexUsizeSliceTInst a) v i ==
+ alloc_vec_Vec_index_usize v i)
+ [SMTPat (alloc_vec_Vec_index a usize (core_slice_index_SliceIndexUsizeSliceTInst a) v i)]
+ =
+ admit()
+
+let alloc_vec_Vec_index_mut_eq (#a : Type0) (v : alloc_vec_Vec a) (i : usize) :
+ Lemma (
+ alloc_vec_Vec_index_mut a usize (core_slice_index_SliceIndexUsizeSliceTInst a) v i ==
+ alloc_vec_Vec_index_usize v i)
+ [SMTPat (alloc_vec_Vec_index_mut a usize (core_slice_index_SliceIndexUsizeSliceTInst a) v i)]
+ =
+ admit()
+
+let alloc_vec_Vec_index_mut_back_eq (#a : Type0) (v : alloc_vec_Vec a) (i : usize) (x : a) :
+ Lemma (
+ alloc_vec_Vec_index_mut_back a usize (core_slice_index_SliceIndexUsizeSliceTInst a) v i x ==
+ alloc_vec_Vec_update_usize v i x)
+ [SMTPat (alloc_vec_Vec_index_mut_back a usize (core_slice_index_SliceIndexUsizeSliceTInst a) v i x)]
+ =
+ admit()
generated by cgit v1.2.3 (git 2.25.1) at 2024-12-30 21:43:27 +0000