From f77e3f9cbe2ea7abeb4be815bdbf33d0c98076c2 Mon Sep 17 00:00:00 2001
From: Nadrieril
Date: Mon, 27 May 2024 13:28:28 +0200
Subject: tests: Rename betree_main -> betree

---
 tests/lean/Betree/Funs.lean | 699 ++++++++++++++++++++++++++++++++++++++++++++
 1 file changed, 699 insertions(+)
 create mode 100644 tests/lean/Betree/Funs.lean

(limited to 'tests/lean/Betree/Funs.lean')

diff --git a/tests/lean/Betree/Funs.lean b/tests/lean/Betree/Funs.lean
new file mode 100644
index 00000000..8612ccbc
--- /dev/null
+++ b/tests/lean/Betree/Funs.lean
@@ -0,0 +1,699 @@
+-- THIS FILE WAS AUTOMATICALLY GENERATED BY AENEAS
+-- [betree]: function definitions
+import Base
+import Betree.Types
+import Betree.FunsExternal
+open Primitives
+
+namespace betree
+
+/- [betree::betree::load_internal_node]:
+   Source: 'src/betree.rs', lines 36:0-36:52 -/
+def betree.load_internal_node
+  (id : U64) (st : State) :
+  Result (State × (betree.List (U64 × betree.Message)))
+  :=
+  betree_utils.load_internal_node id st
+
+/- [betree::betree::store_internal_node]:
+   Source: 'src/betree.rs', lines 41:0-41:60 -/
+def betree.store_internal_node
+  (id : U64) (content : betree.List (U64 × betree.Message)) (st : State) :
+  Result (State × Unit)
+  :=
+  betree_utils.store_internal_node id content st
+
+/- [betree::betree::load_leaf_node]:
+   Source: 'src/betree.rs', lines 46:0-46:44 -/
+def betree.load_leaf_node
+  (id : U64) (st : State) : Result (State × (betree.List (U64 × U64))) :=
+  betree_utils.load_leaf_node id st
+
+/- [betree::betree::store_leaf_node]:
+   Source: 'src/betree.rs', lines 51:0-51:52 -/
+def betree.store_leaf_node
+  (id : U64) (content : betree.List (U64 × U64)) (st : State) :
+  Result (State × Unit)
+  :=
+  betree_utils.store_leaf_node id content st
+
+/- [betree::betree::fresh_node_id]:
+   Source: 'src/betree.rs', lines 55:0-55:48 -/
+def betree.fresh_node_id (counter : U64) : Result (U64 × U64) :=
+  do
+  let counter1 ← counter + 1#u64
+  Result.ok (counter, counter1)
+
+/- [betree::betree::{betree::betree::NodeIdCounter}::new]:
+   Source: 'src/betree.rs', lines 206:4-206:20 -/
+def betree.NodeIdCounter.new : Result betree.NodeIdCounter :=
+  Result.ok { next_node_id := 0#u64 }
+
+/- [betree::betree::{betree::betree::NodeIdCounter}::fresh_id]:
+   Source: 'src/betree.rs', lines 210:4-210:36 -/
+def betree.NodeIdCounter.fresh_id
+  (self : betree.NodeIdCounter) : Result (U64 × betree.NodeIdCounter) :=
+  do
+  let i ← self.next_node_id + 1#u64
+  Result.ok (self.next_node_id, { next_node_id := i })
+
+/- [betree::betree::upsert_update]:
+   Source: 'src/betree.rs', lines 234:0-234:70 -/
+def betree.upsert_update
+  (prev : Option U64) (st : betree.UpsertFunState) : Result U64 :=
+  match prev with
+  | none =>
+    match st with
+    | betree.UpsertFunState.Add v => Result.ok v
+    | betree.UpsertFunState.Sub _ => Result.ok 0#u64
+  | some prev1 =>
+    match st with
+    | betree.UpsertFunState.Add v =>
+      do
+      let margin ← core_u64_max - prev1
+      if margin >= v
+      then prev1 + v
+      else Result.ok core_u64_max
+    | betree.UpsertFunState.Sub v =>
+      if prev1 >= v
+      then prev1 - v
+      else Result.ok 0#u64
+
+/- [betree::betree::{betree::betree::List<T>#1}::len]:
+   Source: 'src/betree.rs', lines 276:4-276:24 -/
+divergent def betree.List.len (T : Type) (self : betree.List T) : Result U64 :=
+  match self with
+  | betree.List.Cons _ tl => do
+                             let i ← betree.List.len T tl
+                             1#u64 + i
+  | betree.List.Nil => Result.ok 0#u64
+
+/- [betree::betree::{betree::betree::List<T>#1}::split_at]:
+   Source: 'src/betree.rs', lines 284:4-284:51 -/
+divergent def betree.List.split_at
+  (T : Type) (self : betree.List T) (n : U64) :
+  Result ((betree.List T) × (betree.List T))
+  :=
+  if n = 0#u64
+  then Result.ok (betree.List.Nil, self)
+  else
+    match self with
+    | betree.List.Cons hd tl =>
+      do
+      let i ← n - 1#u64
+      let p ← betree.List.split_at T tl i
+      let (ls0, ls1) := p
+      Result.ok (betree.List.Cons hd ls0, ls1)
+    | betree.List.Nil => Result.fail .panic
+
+/- [betree::betree::{betree::betree::List<T>#1}::push_front]:
+   Source: 'src/betree.rs', lines 299:4-299:34 -/
+def betree.List.push_front
+  (T : Type) (self : betree.List T) (x : T) : Result (betree.List T) :=
+  let (tl, _) := core.mem.replace (betree.List T) self betree.List.Nil
+  Result.ok (betree.List.Cons x tl)
+
+/- [betree::betree::{betree::betree::List<T>#1}::pop_front]:
+   Source: 'src/betree.rs', lines 306:4-306:32 -/
+def betree.List.pop_front
+  (T : Type) (self : betree.List T) : Result (T × (betree.List T)) :=
+  let (ls, _) := core.mem.replace (betree.List T) self betree.List.Nil
+  match ls with
+  | betree.List.Cons x tl => Result.ok (x, tl)
+  | betree.List.Nil => Result.fail .panic
+
+/- [betree::betree::{betree::betree::List<T>#1}::hd]:
+   Source: 'src/betree.rs', lines 318:4-318:22 -/
+def betree.List.hd (T : Type) (self : betree.List T) : Result T :=
+  match self with
+  | betree.List.Cons hd _ => Result.ok hd
+  | betree.List.Nil => Result.fail .panic
+
+/- [betree::betree::{betree::betree::List<(u64, T)>#2}::head_has_key]:
+   Source: 'src/betree.rs', lines 327:4-327:44 -/
+def betree.ListPairU64T.head_has_key
+  (T : Type) (self : betree.List (U64 × T)) (key : U64) : Result Bool :=
+  match self with
+  | betree.List.Cons hd _ => let (i, _) := hd
+                             Result.ok (i = key)
+  | betree.List.Nil => Result.ok false
+
+/- [betree::betree::{betree::betree::List<(u64, T)>#2}::partition_at_pivot]:
+   Source: 'src/betree.rs', lines 339:4-339:73 -/
+divergent def betree.ListPairU64T.partition_at_pivot
+  (T : Type) (self : betree.List (U64 × T)) (pivot : U64) :
+  Result ((betree.List (U64 × T)) × (betree.List (U64 × T)))
+  :=
+  match self with
+  | betree.List.Cons hd tl =>
+    let (i, t) := hd
+    if i >= pivot
+    then Result.ok (betree.List.Nil, betree.List.Cons (i, t) tl)
+    else
+      do
+      let p ← betree.ListPairU64T.partition_at_pivot T tl pivot
+      let (ls0, ls1) := p
+      Result.ok (betree.List.Cons (i, t) ls0, ls1)
+  | betree.List.Nil => Result.ok (betree.List.Nil, betree.List.Nil)
+
+/- [betree::betree::{betree::betree::Leaf#3}::split]:
+   Source: 'src/betree.rs', lines 359:4-364:17 -/
+def betree.Leaf.split
+  (self : betree.Leaf) (content : betree.List (U64 × U64))
+  (params : betree.Params) (node_id_cnt : betree.NodeIdCounter) (st : State) :
+  Result (State × (betree.Internal × betree.NodeIdCounter))
+  :=
+  do
+  let p ← betree.List.split_at (U64 × U64) content params.split_size
+  let (content0, content1) := p
+  let p1 ← betree.List.hd (U64 × U64) content1
+  let (pivot, _) := p1
+  let (id0, node_id_cnt1) ← betree.NodeIdCounter.fresh_id node_id_cnt
+  let (id1, node_id_cnt2) ← betree.NodeIdCounter.fresh_id node_id_cnt1
+  let (st1, _) ← betree.store_leaf_node id0 content0 st
+  let (st2, _) ← betree.store_leaf_node id1 content1 st1
+  let n := betree.Node.Leaf { id := id0, size := params.split_size }
+  let n1 := betree.Node.Leaf { id := id1, size := params.split_size }
+  Result.ok (st2, (betree.Internal.mk self.id pivot n n1, node_id_cnt2))
+
+/- [betree::betree::{betree::betree::Node#5}::lookup_first_message_for_key]:
+   Source: 'src/betree.rs', lines 789:4-792:34 -/
+divergent def betree.Node.lookup_first_message_for_key
+  (key : U64) (msgs : betree.List (U64 × betree.Message)) :
+  Result ((betree.List (U64 × betree.Message)) × (betree.List (U64 ×
+    betree.Message) → Result (betree.List (U64 × betree.Message))))
+  :=
+  match msgs with
+  | betree.List.Cons x next_msgs =>
+    let (i, m) := x
+    if i >= key
+    then Result.ok (betree.List.Cons (i, m) next_msgs, Result.ok)
+    else
+      do
+      let (l, lookup_first_message_for_key_back) ←
+        betree.Node.lookup_first_message_for_key key next_msgs
+      let back :=
+        fun ret =>
+          do
+          let next_msgs1 ← lookup_first_message_for_key_back ret
+          Result.ok (betree.List.Cons (i, m) next_msgs1)
+      Result.ok (l, back)
+  | betree.List.Nil => Result.ok (betree.List.Nil, Result.ok)
+
+/- [betree::betree::{betree::betree::Node#5}::lookup_in_bindings]:
+   Source: 'src/betree.rs', lines 636:4-636:80 -/
+divergent def betree.Node.lookup_in_bindings
+  (key : U64) (bindings : betree.List (U64 × U64)) : Result (Option U64) :=
+  match bindings with
+  | betree.List.Cons hd tl =>
+    let (i, i1) := hd
+    if i = key
+    then Result.ok (some i1)
+    else
+      if i > key
+      then Result.ok none
+      else betree.Node.lookup_in_bindings key tl
+  | betree.List.Nil => Result.ok none
+
+/- [betree::betree::{betree::betree::Node#5}::apply_upserts]:
+   Source: 'src/betree.rs', lines 819:4-819:90 -/
+divergent def betree.Node.apply_upserts
+  (msgs : betree.List (U64 × betree.Message)) (prev : Option U64) (key : U64)
+  :
+  Result (U64 × (betree.List (U64 × betree.Message)))
+  :=
+  do
+  let b ← betree.ListPairU64T.head_has_key betree.Message msgs key
+  if b
+  then
+    do
+    let (msg, msgs1) ← betree.List.pop_front (U64 × betree.Message) msgs
+    let (_, m) := msg
+    match m with
+    | betree.Message.Insert _ => Result.fail .panic
+    | betree.Message.Delete => Result.fail .panic
+    | betree.Message.Upsert s =>
+      do
+      let v ← betree.upsert_update prev s
+      betree.Node.apply_upserts msgs1 (some v) key
+  else
+    do
+    let v ← core.option.Option.unwrap U64 prev
+    let msgs1 ←
+      betree.List.push_front (U64 × betree.Message) msgs (key,
+        betree.Message.Insert v)
+    Result.ok (v, msgs1)
+
+/- [betree::betree::{betree::betree::Internal#4}::lookup_in_children]:
+   Source: 'src/betree.rs', lines 395:4-395:63 -/
+mutual divergent def betree.Internal.lookup_in_children
+  (self : betree.Internal) (key : U64) (st : State) :
+  Result (State × ((Option U64) × betree.Internal))
+  :=
+  if key < self.pivot
+  then
+    do
+    let (st1, (o, n)) ← betree.Node.lookup self.left key st
+    Result.ok (st1, (o, betree.Internal.mk self.id self.pivot n self.right))
+  else
+    do
+    let (st1, (o, n)) ← betree.Node.lookup self.right key st
+    Result.ok (st1, (o, betree.Internal.mk self.id self.pivot self.left n))
+
+/- [betree::betree::{betree::betree::Node#5}::lookup]:
+   Source: 'src/betree.rs', lines 709:4-709:58 -/
+divergent def betree.Node.lookup
+  (self : betree.Node) (key : U64) (st : State) :
+  Result (State × ((Option U64) × betree.Node))
+  :=
+  match self with
+  | betree.Node.Internal node =>
+    do
+    let (st1, msgs) ← betree.load_internal_node node.id st
+    let (pending, lookup_first_message_for_key_back) ←
+      betree.Node.lookup_first_message_for_key key msgs
+    match pending with
+    | betree.List.Cons p l =>
+      let (k, msg) := p
+      if k != key
+      then
+        do
+        let (st2, (o, node1)) ←
+          betree.Internal.lookup_in_children node key st1
+        let _ ←
+          lookup_first_message_for_key_back (betree.List.Cons (k, msg) l)
+        Result.ok (st2, (o, betree.Node.Internal node1))
+      else
+        match msg with
+        | betree.Message.Insert v =>
+          do
+          let _ ←
+            lookup_first_message_for_key_back (betree.List.Cons (k,
+              betree.Message.Insert v) l)
+          Result.ok (st1, (some v, betree.Node.Internal node))
+        | betree.Message.Delete =>
+          do
+          let _ ←
+            lookup_first_message_for_key_back (betree.List.Cons (k,
+              betree.Message.Delete) l)
+          Result.ok (st1, (none, betree.Node.Internal node))
+        | betree.Message.Upsert ufs =>
+          do
+          let (st2, (v, node1)) ←
+            betree.Internal.lookup_in_children node key st1
+          let (v1, pending1) ←
+            betree.Node.apply_upserts (betree.List.Cons (k,
+              betree.Message.Upsert ufs) l) v key
+          let msgs1 ← lookup_first_message_for_key_back pending1
+          let (st3, _) ← betree.store_internal_node node1.id msgs1 st2
+          Result.ok (st3, (some v1, betree.Node.Internal node1))
+    | betree.List.Nil =>
+      do
+      let (st2, (o, node1)) ← betree.Internal.lookup_in_children node key st1
+      let _ ← lookup_first_message_for_key_back betree.List.Nil
+      Result.ok (st2, (o, betree.Node.Internal node1))
+  | betree.Node.Leaf node =>
+    do
+    let (st1, bindings) ← betree.load_leaf_node node.id st
+    let o ← betree.Node.lookup_in_bindings key bindings
+    Result.ok (st1, (o, betree.Node.Leaf node))
+
+end
+
+/- [betree::betree::{betree::betree::Node#5}::filter_messages_for_key]:
+   Source: 'src/betree.rs', lines 674:4-674:77 -/
+divergent def betree.Node.filter_messages_for_key
+  (key : U64) (msgs : betree.List (U64 × betree.Message)) :
+  Result (betree.List (U64 × betree.Message))
+  :=
+  match msgs with
+  | betree.List.Cons p l =>
+    let (k, m) := p
+    if k = key
+    then
+      do
+      let (_, msgs1) ←
+        betree.List.pop_front (U64 × betree.Message) (betree.List.Cons (k, m)
+          l)
+      betree.Node.filter_messages_for_key key msgs1
+    else Result.ok (betree.List.Cons (k, m) l)
+  | betree.List.Nil => Result.ok betree.List.Nil
+
+/- [betree::betree::{betree::betree::Node#5}::lookup_first_message_after_key]:
+   Source: 'src/betree.rs', lines 689:4-692:34 -/
+divergent def betree.Node.lookup_first_message_after_key
+  (key : U64) (msgs : betree.List (U64 × betree.Message)) :
+  Result ((betree.List (U64 × betree.Message)) × (betree.List (U64 ×
+    betree.Message) → Result (betree.List (U64 × betree.Message))))
+  :=
+  match msgs with
+  | betree.List.Cons p next_msgs =>
+    let (k, m) := p
+    if k = key
+    then
+      do
+      let (l, lookup_first_message_after_key_back) ←
+        betree.Node.lookup_first_message_after_key key next_msgs
+      let back :=
+        fun ret =>
+          do
+          let next_msgs1 ← lookup_first_message_after_key_back ret
+          Result.ok (betree.List.Cons (k, m) next_msgs1)
+      Result.ok (l, back)
+    else Result.ok (betree.List.Cons (k, m) next_msgs, Result.ok)
+  | betree.List.Nil => Result.ok (betree.List.Nil, Result.ok)
+
+/- [betree::betree::{betree::betree::Node#5}::apply_to_internal]:
+   Source: 'src/betree.rs', lines 521:4-521:89 -/
+def betree.Node.apply_to_internal
+  (msgs : betree.List (U64 × betree.Message)) (key : U64)
+  (new_msg : betree.Message) :
+  Result (betree.List (U64 × betree.Message))
+  :=
+  do
+  let (msgs1, lookup_first_message_for_key_back) ←
+    betree.Node.lookup_first_message_for_key key msgs
+  let b ← betree.ListPairU64T.head_has_key betree.Message msgs1 key
+  if b
+  then
+    match new_msg with
+    | betree.Message.Insert i =>
+      do
+      let msgs2 ← betree.Node.filter_messages_for_key key msgs1
+      let msgs3 ←
+        betree.List.push_front (U64 × betree.Message) msgs2 (key,
+          betree.Message.Insert i)
+      lookup_first_message_for_key_back msgs3
+    | betree.Message.Delete =>
+      do
+      let msgs2 ← betree.Node.filter_messages_for_key key msgs1
+      let msgs3 ←
+        betree.List.push_front (U64 × betree.Message) msgs2 (key,
+          betree.Message.Delete)
+      lookup_first_message_for_key_back msgs3
+    | betree.Message.Upsert s =>
+      do
+      let p ← betree.List.hd (U64 × betree.Message) msgs1
+      let (_, m) := p
+      match m with
+      | betree.Message.Insert prev =>
+        do
+        let v ← betree.upsert_update (some prev) s
+        let (_, msgs2) ← betree.List.pop_front (U64 × betree.Message) msgs1
+        let msgs3 ←
+          betree.List.push_front (U64 × betree.Message) msgs2 (key,
+            betree.Message.Insert v)
+        lookup_first_message_for_key_back msgs3
+      | betree.Message.Delete =>
+        do
+        let (_, msgs2) ← betree.List.pop_front (U64 × betree.Message) msgs1
+        let v ← betree.upsert_update none s
+        let msgs3 ←
+          betree.List.push_front (U64 × betree.Message) msgs2 (key,
+            betree.Message.Insert v)
+        lookup_first_message_for_key_back msgs3
+      | betree.Message.Upsert _ =>
+        do
+        let (msgs2, lookup_first_message_after_key_back) ←
+          betree.Node.lookup_first_message_after_key key msgs1
+        let msgs3 ←
+          betree.List.push_front (U64 × betree.Message) msgs2 (key,
+            betree.Message.Upsert s)
+        let msgs4 ← lookup_first_message_after_key_back msgs3
+        lookup_first_message_for_key_back msgs4
+  else
+    do
+    let msgs2 ←
+      betree.List.push_front (U64 × betree.Message) msgs1 (key, new_msg)
+    lookup_first_message_for_key_back msgs2
+
+/- [betree::betree::{betree::betree::Node#5}::apply_messages_to_internal]:
+   Source: 'src/betree.rs', lines 502:4-505:5 -/
+divergent def betree.Node.apply_messages_to_internal
+  (msgs : betree.List (U64 × betree.Message))
+  (new_msgs : betree.List (U64 × betree.Message)) :
+  Result (betree.List (U64 × betree.Message))
+  :=
+  match new_msgs with
+  | betree.List.Cons new_msg new_msgs_tl =>
+    do
+    let (i, m) := new_msg
+    let msgs1 ← betree.Node.apply_to_internal msgs i m
+    betree.Node.apply_messages_to_internal msgs1 new_msgs_tl
+  | betree.List.Nil => Result.ok msgs
+
+/- [betree::betree::{betree::betree::Node#5}::lookup_mut_in_bindings]:
+   Source: 'src/betree.rs', lines 653:4-656:32 -/
+divergent def betree.Node.lookup_mut_in_bindings
+  (key : U64) (bindings : betree.List (U64 × U64)) :
+  Result ((betree.List (U64 × U64)) × (betree.List (U64 × U64) → Result
+    (betree.List (U64 × U64))))
+  :=
+  match bindings with
+  | betree.List.Cons hd tl =>
+    let (i, i1) := hd
+    if i >= key
+    then Result.ok (betree.List.Cons (i, i1) tl, Result.ok)
+    else
+      do
+      let (l, lookup_mut_in_bindings_back) ←
+        betree.Node.lookup_mut_in_bindings key tl
+      let back :=
+        fun ret =>
+          do
+          let tl1 ← lookup_mut_in_bindings_back ret
+          Result.ok (betree.List.Cons (i, i1) tl1)
+      Result.ok (l, back)
+  | betree.List.Nil => Result.ok (betree.List.Nil, Result.ok)
+
+/- [betree::betree::{betree::betree::Node#5}::apply_to_leaf]:
+   Source: 'src/betree.rs', lines 460:4-460:87 -/
+def betree.Node.apply_to_leaf
+  (bindings : betree.List (U64 × U64)) (key : U64) (new_msg : betree.Message)
+  :
+  Result (betree.List (U64 × U64))
+  :=
+  do
+  let (bindings1, lookup_mut_in_bindings_back) ←
+    betree.Node.lookup_mut_in_bindings key bindings
+  let b ← betree.ListPairU64T.head_has_key U64 bindings1 key
+  if b
+  then
+    do
+    let (hd, bindings2) ← betree.List.pop_front (U64 × U64) bindings1
+    match new_msg with
+    | betree.Message.Insert v =>
+      do
+      let bindings3 ← betree.List.push_front (U64 × U64) bindings2 (key, v)
+      lookup_mut_in_bindings_back bindings3
+    | betree.Message.Delete => lookup_mut_in_bindings_back bindings2
+    | betree.Message.Upsert s =>
+      do
+      let (_, i) := hd
+      let v ← betree.upsert_update (some i) s
+      let bindings3 ← betree.List.push_front (U64 × U64) bindings2 (key, v)
+      lookup_mut_in_bindings_back bindings3
+  else
+    match new_msg with
+    | betree.Message.Insert v =>
+      do
+      let bindings2 ← betree.List.push_front (U64 × U64) bindings1 (key, v)
+      lookup_mut_in_bindings_back bindings2
+    | betree.Message.Delete => lookup_mut_in_bindings_back bindings1
+    | betree.Message.Upsert s =>
+      do
+      let v ← betree.upsert_update none s
+      let bindings2 ← betree.List.push_front (U64 × U64) bindings1 (key, v)
+      lookup_mut_in_bindings_back bindings2
+
+/- [betree::betree::{betree::betree::Node#5}::apply_messages_to_leaf]:
+   Source: 'src/betree.rs', lines 444:4-447:5 -/
+divergent def betree.Node.apply_messages_to_leaf
+  (bindings : betree.List (U64 × U64))
+  (new_msgs : betree.List (U64 × betree.Message)) :
+  Result (betree.List (U64 × U64))
+  :=
+  match new_msgs with
+  | betree.List.Cons new_msg new_msgs_tl =>
+    do
+    let (i, m) := new_msg
+    let bindings1 ← betree.Node.apply_to_leaf bindings i m
+    betree.Node.apply_messages_to_leaf bindings1 new_msgs_tl
+  | betree.List.Nil => Result.ok bindings
+
+/- [betree::betree::{betree::betree::Internal#4}::flush]:
+   Source: 'src/betree.rs', lines 410:4-415:26 -/
+mutual divergent def betree.Internal.flush
+  (self : betree.Internal) (params : betree.Params)
+  (node_id_cnt : betree.NodeIdCounter)
+  (content : betree.List (U64 × betree.Message)) (st : State) :
+  Result (State × ((betree.List (U64 × betree.Message)) × (betree.Internal
+    × betree.NodeIdCounter)))
+  :=
+  do
+  let p ←
+    betree.ListPairU64T.partition_at_pivot betree.Message content self.pivot
+  let (msgs_left, msgs_right) := p
+  let len_left ← betree.List.len (U64 × betree.Message) msgs_left
+  if len_left >= params.min_flush_size
+  then
+    do
+    let (st1, p1) ←
+      betree.Node.apply_messages self.left params node_id_cnt msgs_left st
+    let (n, node_id_cnt1) := p1
+    let len_right ← betree.List.len (U64 × betree.Message) msgs_right
+    if len_right >= params.min_flush_size
+    then
+      do
+      let (st2, p2) ←
+        betree.Node.apply_messages self.right params node_id_cnt1 msgs_right
+          st1
+      let (n1, node_id_cnt2) := p2
+      Result.ok (st2, (betree.List.Nil, (betree.Internal.mk self.id self.pivot
+        n n1, node_id_cnt2)))
+    else
+      Result.ok (st1, (msgs_right, (betree.Internal.mk self.id self.pivot n
+        self.right, node_id_cnt1)))
+  else
+    do
+    let (st1, p1) ←
+      betree.Node.apply_messages self.right params node_id_cnt msgs_right st
+    let (n, node_id_cnt1) := p1
+    Result.ok (st1, (msgs_left, (betree.Internal.mk self.id self.pivot
+      self.left n, node_id_cnt1)))
+
+/- [betree::betree::{betree::betree::Node#5}::apply_messages]:
+   Source: 'src/betree.rs', lines 588:4-593:5 -/
+divergent def betree.Node.apply_messages
+  (self : betree.Node) (params : betree.Params)
+  (node_id_cnt : betree.NodeIdCounter)
+  (msgs : betree.List (U64 × betree.Message)) (st : State) :
+  Result (State × (betree.Node × betree.NodeIdCounter))
+  :=
+  match self with
+  | betree.Node.Internal node =>
+    do
+    let (st1, content) ← betree.load_internal_node node.id st
+    let content1 ← betree.Node.apply_messages_to_internal content msgs
+    let num_msgs ← betree.List.len (U64 × betree.Message) content1
+    if num_msgs >= params.min_flush_size
+    then
+      do
+      let (st2, (content2, p)) ←
+        betree.Internal.flush node params node_id_cnt content1 st1
+      let (node1, node_id_cnt1) := p
+      let (st3, _) ← betree.store_internal_node node1.id content2 st2
+      Result.ok (st3, (betree.Node.Internal node1, node_id_cnt1))
+    else
+      do
+      let (st2, _) ← betree.store_internal_node node.id content1 st1
+      Result.ok (st2, (betree.Node.Internal node, node_id_cnt))
+  | betree.Node.Leaf node =>
+    do
+    let (st1, content) ← betree.load_leaf_node node.id st
+    let content1 ← betree.Node.apply_messages_to_leaf content msgs
+    let len ← betree.List.len (U64 × U64) content1
+    let i ← 2#u64 * params.split_size
+    if len >= i
+    then
+      do
+      let (st2, (new_node, node_id_cnt1)) ←
+        betree.Leaf.split node content1 params node_id_cnt st1
+      let (st3, _) ← betree.store_leaf_node node.id betree.List.Nil st2
+      Result.ok (st3, (betree.Node.Internal new_node, node_id_cnt1))
+    else
+      do
+      let (st2, _) ← betree.store_leaf_node node.id content1 st1
+      Result.ok (st2, (betree.Node.Leaf { node with size := len },
+        node_id_cnt))
+
+end
+
+/- [betree::betree::{betree::betree::Node#5}::apply]:
+   Source: 'src/betree.rs', lines 576:4-582:5 -/
+def betree.Node.apply
+  (self : betree.Node) (params : betree.Params)
+  (node_id_cnt : betree.NodeIdCounter) (key : U64) (new_msg : betree.Message)
+  (st : State) :
+  Result (State × (betree.Node × betree.NodeIdCounter))
+  :=
+  do
+  let (st1, p) ←
+    betree.Node.apply_messages self params node_id_cnt (betree.List.Cons (key,
+      new_msg) betree.List.Nil) st
+  let (self1, node_id_cnt1) := p
+  Result.ok (st1, (self1, node_id_cnt1))
+
+/- [betree::betree::{betree::betree::BeTree#6}::new]:
+   Source: 'src/betree.rs', lines 849:4-849:60 -/
+def betree.BeTree.new
+  (min_flush_size : U64) (split_size : U64) (st : State) :
+  Result (State × betree.BeTree)
+  :=
+  do
+  let node_id_cnt ← betree.NodeIdCounter.new
+  let (id, node_id_cnt1) ← betree.NodeIdCounter.fresh_id node_id_cnt
+  let (st1, _) ← betree.store_leaf_node id betree.List.Nil st
+  Result.ok (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#u64 })
+    })
+
+/- [betree::betree::{betree::betree::BeTree#6}::apply]:
+   Source: 'src/betree.rs', lines 868:4-868:47 -/
+def betree.BeTree.apply
+  (self : betree.BeTree) (key : U64) (msg : betree.Message) (st : State) :
+  Result (State × betree.BeTree)
+  :=
+  do
+  let (st1, p) ←
+    betree.Node.apply self.root self.params self.node_id_cnt key msg st
+  let (n, nic) := p
+  Result.ok (st1, { self with node_id_cnt := nic, root := n })
+
+/- [betree::betree::{betree::betree::BeTree#6}::insert]:
+   Source: 'src/betree.rs', lines 874:4-874:52 -/
+def betree.BeTree.insert
+  (self : betree.BeTree) (key : U64) (value : U64) (st : State) :
+  Result (State × betree.BeTree)
+  :=
+  betree.BeTree.apply self key (betree.Message.Insert value) st
+
+/- [betree::betree::{betree::betree::BeTree#6}::delete]:
+   Source: 'src/betree.rs', lines 880:4-880:38 -/
+def betree.BeTree.delete
+  (self : betree.BeTree) (key : U64) (st : State) :
+  Result (State × betree.BeTree)
+  :=
+  betree.BeTree.apply self key betree.Message.Delete st
+
+/- [betree::betree::{betree::betree::BeTree#6}::upsert]:
+   Source: 'src/betree.rs', lines 886:4-886:59 -/
+def betree.BeTree.upsert
+  (self : betree.BeTree) (key : U64) (upd : betree.UpsertFunState) (st : State)
+  :
+  Result (State × betree.BeTree)
+  :=
+  betree.BeTree.apply self key (betree.Message.Upsert upd) st
+
+/- [betree::betree::{betree::betree::BeTree#6}::lookup]:
+   Source: 'src/betree.rs', lines 895:4-895:62 -/
+def betree.BeTree.lookup
+  (self : betree.BeTree) (key : U64) (st : State) :
+  Result (State × ((Option U64) × betree.BeTree))
+  :=
+  do
+  let (st1, (o, n)) ← betree.Node.lookup self.root key st
+  Result.ok (st1, (o, { self with root := n }))
+
+/- [betree::main]:
+   Source: 'src/main.rs', lines 4:0-4:9 -/
+def main : Result Unit :=
+  Result.ok ()
+
+/- Unit test for [betree::main] -/
+#assert (main == Result.ok ())
+
+end betree
-- 
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