Reorganize the Lean tests

1 files changed, 1071 insertions, 0 deletions

diff --git a/tests/lean/BetreeMain/Funs.lean b/tests/lean/BetreeMain/Funs.lean
new file mode 100644
index 00000000..fb48b3a6
--- /dev/null
+++ b/tests/lean/BetreeMain/Funs.lean
@@ -0,0 +1,1071 @@
+-- THIS FILE WAS AUTOMATICALLY GENERATED BY AENEAS
+-- [betree_main]: function definitions
+import Base
+import BetreeMain.Types
+import BetreeMain.ExternalFuns
+open Primitives
+
+/- [betree_main::betree::load_internal_node] -/
+def betree_load_internal_node_fwd
+  (id : U64) (st : State) :
+  Result (State × (betree_list_t (U64 × betree_message_t)))
+  :=
+  opaque_defs.betree_utils_load_internal_node_fwd id st
+
+/- [betree_main::betree::store_internal_node] -/
+def betree_store_internal_node_fwd
+  (id : U64) (content : betree_list_t (U64 × betree_message_t)) (st : State) :
+  Result (State × Unit)
+  :=
+  do
+    let (st0, _) ←
+      opaque_defs.betree_utils_store_internal_node_fwd id content st
+    Result.ret (st0, ())
+
+/- [betree_main::betree::load_leaf_node] -/
+def betree_load_leaf_node_fwd
+  (id : U64) (st : State) : Result (State × (betree_list_t (U64 × U64))) :=
+  opaque_defs.betree_utils_load_leaf_node_fwd id st
+
+/- [betree_main::betree::store_leaf_node] -/
+def betree_store_leaf_node_fwd
+  (id : U64) (content : betree_list_t (U64 × U64)) (st : State) :
+  Result (State × Unit)
+  :=
+  do
+    let (st0, _) ← opaque_defs.betree_utils_store_leaf_node_fwd id content st
+    Result.ret (st0, ())
+
+/- [betree_main::betree::fresh_node_id] -/
+def betree_fresh_node_id_fwd (counter : U64) : Result U64 :=
+  do
+    let _ ← counter + (U64.ofInt 1 (by intlit))
+    Result.ret counter
+
+/- [betree_main::betree::fresh_node_id] -/
+def betree_fresh_node_id_back (counter : U64) : Result U64 :=
+  counter + (U64.ofInt 1 (by intlit))
+
+/- [betree_main::betree::NodeIdCounter::{0}::new] -/
+def betree_node_id_counter_new_fwd : Result betree_node_id_counter_t :=
+  Result.ret
+  { betree_node_id_counter_next_node_id := (U64.ofInt 0 (by intlit)) }
+
+/- [betree_main::betree::NodeIdCounter::{0}::fresh_id] -/
+def betree_node_id_counter_fresh_id_fwd
+  (self : betree_node_id_counter_t) : Result U64 :=
+  do
+    let _ ← self.betree_node_id_counter_next_node_id +
+      (U64.ofInt 1 (by intlit))
+    Result.ret self.betree_node_id_counter_next_node_id
+
+/- [betree_main::betree::NodeIdCounter::{0}::fresh_id] -/
+def betree_node_id_counter_fresh_id_back
+  (self : betree_node_id_counter_t) : Result betree_node_id_counter_t :=
+  do
+    let i ← self.betree_node_id_counter_next_node_id +
+      (U64.ofInt 1 (by intlit))
+    Result.ret { betree_node_id_counter_next_node_id := i }
+
+/- [core::num::u64::{10}::MAX] -/
+def core_num_u64_max_body : Result U64 :=
+  Result.ret (U64.ofInt 18446744073709551615 (by intlit))
+def core_num_u64_max_c : U64 := eval_global core_num_u64_max_body (by simp)
+
+/- [betree_main::betree::upsert_update] -/
+def betree_upsert_update_fwd
+  (prev : Option U64) (st : betree_upsert_fun_state_t) : Result U64 :=
+  match h: prev with
+  | Option.none =>
+    match h: st with
+    | betree_upsert_fun_state_t.Add v => Result.ret v
+    | betree_upsert_fun_state_t.Sub i => Result.ret (U64.ofInt 0 (by intlit))
+  | Option.some prev0 =>
+    match h: st with
+    | betree_upsert_fun_state_t.Add v =>
+      do
+        let margin ← core_num_u64_max_c - prev0
+        if margin >= v
+        then prev0 + v
+        else Result.ret core_num_u64_max_c
+    | betree_upsert_fun_state_t.Sub v =>
+      if prev0 >= v
+      then prev0 - v
+      else Result.ret (U64.ofInt 0 (by intlit))
+
+/- [betree_main::betree::List::{1}::len] -/
+divergent def betree_list_len_fwd
+  (T : Type) (self : betree_list_t T) : Result U64 :=
+  match h: self with
+  | betree_list_t.Cons t tl =>
+    do
+      let i ← betree_list_len_fwd T tl
+      (U64.ofInt 1 (by intlit)) + i
+  | betree_list_t.Nil => Result.ret (U64.ofInt 0 (by intlit))
+
+/- [betree_main::betree::List::{1}::split_at] -/
+divergent def betree_list_split_at_fwd
+  (T : Type) (self : betree_list_t T) (n : U64) :
+  Result ((betree_list_t T) × (betree_list_t T))
+  :=
+  if n = (U64.ofInt 0 (by intlit))
+  then Result.ret (betree_list_t.Nil, self)
+  else
+    match h: self with
+    | betree_list_t.Cons hd tl =>
+      do
+        let i ← n - (U64.ofInt 1 (by intlit))
+        let p ← betree_list_split_at_fwd T tl i
+        let (ls0, ls1) := p
+        let l := ls0
+        Result.ret (betree_list_t.Cons hd l, ls1)
+    | betree_list_t.Nil => Result.fail Error.panic
+
+/- [betree_main::betree::List::{1}::push_front] -/
+def betree_list_push_front_fwd_back
+  (T : Type) (self : betree_list_t T) (x : T) : Result (betree_list_t T) :=
+  let tl := mem_replace_fwd (betree_list_t T) self betree_list_t.Nil
+  let l := tl
+  Result.ret (betree_list_t.Cons x l)
+
+/- [betree_main::betree::List::{1}::pop_front] -/
+def betree_list_pop_front_fwd (T : Type) (self : betree_list_t T) : Result T :=
+  let ls := mem_replace_fwd (betree_list_t T) self betree_list_t.Nil
+  match h: ls with
+  | betree_list_t.Cons x tl => Result.ret x
+  | betree_list_t.Nil => Result.fail Error.panic
+
+/- [betree_main::betree::List::{1}::pop_front] -/
+def betree_list_pop_front_back
+  (T : Type) (self : betree_list_t T) : Result (betree_list_t T) :=
+  let ls := mem_replace_fwd (betree_list_t T) self betree_list_t.Nil
+  match h: ls with
+  | betree_list_t.Cons x tl => Result.ret tl
+  | betree_list_t.Nil => Result.fail Error.panic
+
+/- [betree_main::betree::List::{1}::hd] -/
+def betree_list_hd_fwd (T : Type) (self : betree_list_t T) : Result T :=
+  match h: self with
+  | betree_list_t.Cons hd l => Result.ret hd
+  | betree_list_t.Nil => Result.fail Error.panic
+
+/- [betree_main::betree::List::{2}::head_has_key] -/
+def betree_list_head_has_key_fwd
+  (T : Type) (self : betree_list_t (U64 × T)) (key : U64) : Result Bool :=
+  match h: self with
+  | betree_list_t.Cons hd l => let (i, _) := hd
+                               Result.ret (i = key)
+  | betree_list_t.Nil => Result.ret false
+
+/- [betree_main::betree::List::{2}::partition_at_pivot] -/
+divergent def betree_list_partition_at_pivot_fwd
+  (T : Type) (self : betree_list_t (U64 × T)) (pivot : U64) :
+  Result ((betree_list_t (U64 × T)) × (betree_list_t (U64 × T)))
+  :=
+  match h: self with
+  | betree_list_t.Cons hd tl =>
+    let (i, t) := hd
+    if i >= pivot
+    then Result.ret (betree_list_t.Nil, betree_list_t.Cons (i, t) tl)
+    else
+      do
+        let p ← betree_list_partition_at_pivot_fwd T tl pivot
+        let (ls0, ls1) := p
+        let l := ls0
+        Result.ret (betree_list_t.Cons (i, t) l, ls1)
+  | betree_list_t.Nil => Result.ret (betree_list_t.Nil, betree_list_t.Nil)
+
+/- [betree_main::betree::Leaf::{3}::split] -/
+def betree_leaf_split_fwd
+  (self : betree_leaf_t) (content : betree_list_t (U64 × U64))
+  (params : betree_params_t) (node_id_cnt : betree_node_id_counter_t)
+  (st : State) :
+  Result (State × betree_internal_t)
+  :=
+  do
+    let p ←
+      betree_list_split_at_fwd (U64 × U64) content
+        params.betree_params_split_size
+    let (content0, content1) := p
+    let p0 ← betree_list_hd_fwd (U64 × U64) content1
+    let (pivot, _) := p0
+    let id0 ← betree_node_id_counter_fresh_id_fwd node_id_cnt
+    let node_id_cnt0 ← betree_node_id_counter_fresh_id_back node_id_cnt
+    let id1 ← betree_node_id_counter_fresh_id_fwd node_id_cnt0
+    let (st0, _) ← betree_store_leaf_node_fwd id0 content0 st
+    let (st1, _) ← betree_store_leaf_node_fwd id1 content1 st0
+    let n := betree_node_t.Leaf
+      {
+        betree_leaf_id := id0,
+        betree_leaf_size := params.betree_params_split_size
+      }
+    let n0 := betree_node_t.Leaf
+      {
+        betree_leaf_id := id1,
+        betree_leaf_size := params.betree_params_split_size
+      }
+    Result.ret (st1, mkbetree_internal_t self.betree_leaf_id pivot n n0)
+
+/- [betree_main::betree::Leaf::{3}::split] -/
+def betree_leaf_split_back
+  (self : betree_leaf_t) (content : betree_list_t (U64 × U64))
+  (params : betree_params_t) (node_id_cnt : betree_node_id_counter_t)
+  (st : State) :
+  Result betree_node_id_counter_t
+  :=
+  do
+    let p ←
+      betree_list_split_at_fwd (U64 × U64) content
+        params.betree_params_split_size
+    let (content0, content1) := p
+    let _ ← betree_list_hd_fwd (U64 × U64) content1
+    let id0 ← betree_node_id_counter_fresh_id_fwd node_id_cnt
+    let node_id_cnt0 ← betree_node_id_counter_fresh_id_back node_id_cnt
+    let id1 ← betree_node_id_counter_fresh_id_fwd node_id_cnt0
+    let (st0, _) ← betree_store_leaf_node_fwd id0 content0 st
+    let _ ← betree_store_leaf_node_fwd id1 content1 st0
+    betree_node_id_counter_fresh_id_back node_id_cnt0
+
+/- [betree_main::betree::Node::{5}::lookup_in_bindings] -/
+divergent def betree_node_lookup_in_bindings_fwd
+  (key : U64) (bindings : betree_list_t (U64 × U64)) : Result (Option U64) :=
+  match h: bindings with
+  | betree_list_t.Cons hd tl =>
+    let (i, i0) := hd
+    if i = key
+    then Result.ret (Option.some i0)
+    else
+      if i > key
+      then Result.ret Option.none
+      else betree_node_lookup_in_bindings_fwd key tl
+  | betree_list_t.Nil => Result.ret Option.none
+
+/- [betree_main::betree::Node::{5}::lookup_first_message_for_key] -/
+divergent def betree_node_lookup_first_message_for_key_fwd
+  (key : U64) (msgs : betree_list_t (U64 × betree_message_t)) :
+  Result (betree_list_t (U64 × betree_message_t))
+  :=
+  match h: msgs with
+  | betree_list_t.Cons x next_msgs =>
+    let (i, m) := x
+    if i >= key
+    then Result.ret (betree_list_t.Cons (i, m) next_msgs)
+    else betree_node_lookup_first_message_for_key_fwd key next_msgs
+  | betree_list_t.Nil => Result.ret betree_list_t.Nil
+
+/- [betree_main::betree::Node::{5}::lookup_first_message_for_key] -/
+divergent def betree_node_lookup_first_message_for_key_back
+  (key : U64) (msgs : betree_list_t (U64 × betree_message_t))
+  (ret0 : betree_list_t (U64 × betree_message_t)) :
+  Result (betree_list_t (U64 × betree_message_t))
+  :=
+  match h: msgs with
+  | betree_list_t.Cons x next_msgs =>
+    let (i, m) := x
+    if i >= key
+    then Result.ret ret0
+    else
+      do
+        let next_msgs0 ←
+          betree_node_lookup_first_message_for_key_back key next_msgs ret0
+        Result.ret (betree_list_t.Cons (i, m) next_msgs0)
+  | betree_list_t.Nil => Result.ret ret0
+
+/- [betree_main::betree::Node::{5}::apply_upserts] -/
+divergent def betree_node_apply_upserts_fwd
+  (msgs : betree_list_t (U64 × betree_message_t)) (prev : Option U64)
+  (key : U64) (st : State) :
+  Result (State × U64)
+  :=
+  do
+    let b ← betree_list_head_has_key_fwd betree_message_t msgs key
+    if b
+    then
+      do
+        let msg ← betree_list_pop_front_fwd (U64 × betree_message_t) msgs
+        let (_, m) := msg
+        match h: m with
+        | betree_message_t.Insert i => Result.fail Error.panic
+        | betree_message_t.Delete => Result.fail Error.panic
+        | betree_message_t.Upsert s =>
+          do
+            let v ← betree_upsert_update_fwd prev s
+            let msgs0 ←
+              betree_list_pop_front_back (U64 × betree_message_t) msgs
+            betree_node_apply_upserts_fwd msgs0 (Option.some v) key st
+    else
+      do
+        let (st0, v) ← opaque_defs.core_option_option_unwrap_fwd U64 prev st
+        let _ ←
+          betree_list_push_front_fwd_back (U64 × betree_message_t) msgs (key,
+            betree_message_t.Insert v)
+        Result.ret (st0, v)
+
+/- [betree_main::betree::Node::{5}::apply_upserts] -/
+divergent def betree_node_apply_upserts_back
+  (msgs : betree_list_t (U64 × betree_message_t)) (prev : Option U64)
+  (key : U64) (st : State) :
+  Result (betree_list_t (U64 × betree_message_t))
+  :=
+  do
+    let b ← betree_list_head_has_key_fwd betree_message_t msgs key
+    if b
+    then
+      do
+        let msg ← betree_list_pop_front_fwd (U64 × betree_message_t) msgs
+        let (_, m) := msg
+        match h: m with
+        | betree_message_t.Insert i => Result.fail Error.panic
+        | betree_message_t.Delete => Result.fail Error.panic
+        | betree_message_t.Upsert s =>
+          do
+            let v ← betree_upsert_update_fwd prev s
+            let msgs0 ←
+              betree_list_pop_front_back (U64 × betree_message_t) msgs
+            betree_node_apply_upserts_back msgs0 (Option.some v) key st
+    else
+      do
+        let (_, v) ← opaque_defs.core_option_option_unwrap_fwd U64 prev st
+        betree_list_push_front_fwd_back (U64 × betree_message_t) msgs (key,
+          betree_message_t.Insert v)
+
+/- [betree_main::betree::Node::{5}::lookup] -/
+mutual divergent def betree_node_lookup_fwd
+  (self : betree_node_t) (key : U64) (st : State) :
+  Result (State × (Option U64))
+  :=
+  match h: self with
+  | betree_node_t.Internal node =>
+    do
+      let (mkbetree_internal_t i i0 n n0) := node
+      let (st0, msgs) ← betree_load_internal_node_fwd i st
+      let pending ← betree_node_lookup_first_message_for_key_fwd key msgs
+      match h: pending with
+      | betree_list_t.Cons p l =>
+        let (k, msg) := p
+        if k != key
+        then
+          do
+            let (st1, opt) ←
+              betree_internal_lookup_in_children_fwd (mkbetree_internal_t i i0
+                n n0) key st0
+            let _ ←
+              betree_node_lookup_first_message_for_key_back key msgs
+                (betree_list_t.Cons (k, msg) l)
+            Result.ret (st1, opt)
+        else
+          match h: msg with
+          | betree_message_t.Insert v =>
+            do
+              let _ ←
+                betree_node_lookup_first_message_for_key_back key msgs
+                  (betree_list_t.Cons (k, betree_message_t.Insert v) l)
+              Result.ret (st0, Option.some v)
+          | betree_message_t.Delete =>
+            do
+              let _ ←
+                betree_node_lookup_first_message_for_key_back key msgs
+                  (betree_list_t.Cons (k, betree_message_t.Delete) l)
+              Result.ret (st0, Option.none)
+          | betree_message_t.Upsert ufs =>
+            do
+              let (st1, v) ←
+                betree_internal_lookup_in_children_fwd (mkbetree_internal_t i
+                  i0 n n0) key st0
+              let (st2, v0) ←
+                betree_node_apply_upserts_fwd (betree_list_t.Cons (k,
+                  betree_message_t.Upsert ufs) l) v key st1
+              let node0 ←
+                betree_internal_lookup_in_children_back (mkbetree_internal_t i
+                  i0 n n0) key st0
+              let (mkbetree_internal_t i1 _ _ _) := node0
+              let pending0 ←
+                betree_node_apply_upserts_back (betree_list_t.Cons (k,
+                  betree_message_t.Upsert ufs) l) v key st1
+              let msgs0 ←
+                betree_node_lookup_first_message_for_key_back key msgs pending0
+              let (st3, _) ← betree_store_internal_node_fwd i1 msgs0 st2
+              Result.ret (st3, Option.some v0)
+      | betree_list_t.Nil =>
+        do
+          let (st1, opt) ←
+            betree_internal_lookup_in_children_fwd (mkbetree_internal_t i i0 n
+              n0) key st0
+          let _ ←
+            betree_node_lookup_first_message_for_key_back key msgs
+              betree_list_t.Nil
+          Result.ret (st1, opt)
+  | betree_node_t.Leaf node =>
+    do
+      let (st0, bindings) ← betree_load_leaf_node_fwd node.betree_leaf_id st
+      let opt ← betree_node_lookup_in_bindings_fwd key bindings
+      Result.ret (st0, opt)
+
+/- [betree_main::betree::Node::{5}::lookup] -/
+divergent def betree_node_lookup_back
+  (self : betree_node_t) (key : U64) (st : State) : Result betree_node_t :=
+  match h: self with
+  | betree_node_t.Internal node =>
+    do
+      let (mkbetree_internal_t i i0 n n0) := node
+      let (st0, msgs) ← betree_load_internal_node_fwd i st
+      let pending ← betree_node_lookup_first_message_for_key_fwd key msgs
+      match h: pending with
+      | betree_list_t.Cons p l =>
+        let (k, msg) := p
+        if k != key
+        then
+          do
+            let _ ←
+              betree_node_lookup_first_message_for_key_back key msgs
+                (betree_list_t.Cons (k, msg) l)
+            let node0 ←
+              betree_internal_lookup_in_children_back (mkbetree_internal_t i i0
+                n n0) key st0
+            Result.ret (betree_node_t.Internal node0)
+        else
+          match h: msg with
+          | betree_message_t.Insert v =>
+            do
+              let _ ←
+                betree_node_lookup_first_message_for_key_back key msgs
+                  (betree_list_t.Cons (k, betree_message_t.Insert v) l)
+              Result.ret (betree_node_t.Internal (mkbetree_internal_t i i0 n
+                n0))
+          | betree_message_t.Delete =>
+            do
+              let _ ←
+                betree_node_lookup_first_message_for_key_back key msgs
+                  (betree_list_t.Cons (k, betree_message_t.Delete) l)
+              Result.ret (betree_node_t.Internal (mkbetree_internal_t i i0 n
+                n0))
+          | betree_message_t.Upsert ufs =>
+            do
+              let (st1, v) ←
+                betree_internal_lookup_in_children_fwd (mkbetree_internal_t i
+                  i0 n n0) key st0
+              let (st2, _) ←
+                betree_node_apply_upserts_fwd (betree_list_t.Cons (k,
+                  betree_message_t.Upsert ufs) l) v key st1
+              let node0 ←
+                betree_internal_lookup_in_children_back (mkbetree_internal_t i
+                  i0 n n0) key st0
+              let (mkbetree_internal_t i1 i2 n1 n2) := node0
+              let pending0 ←
+                betree_node_apply_upserts_back (betree_list_t.Cons (k,
+                  betree_message_t.Upsert ufs) l) v key st1
+              let msgs0 ←
+                betree_node_lookup_first_message_for_key_back key msgs pending0
+              let _ ← betree_store_internal_node_fwd i1 msgs0 st2
+              Result.ret (betree_node_t.Internal (mkbetree_internal_t i1 i2 n1
+                n2))
+      | betree_list_t.Nil =>
+        do
+          let _ ←
+            betree_node_lookup_first_message_for_key_back key msgs
+              betree_list_t.Nil
+          let node0 ←
+            betree_internal_lookup_in_children_back (mkbetree_internal_t i i0 n
+              n0) key st0
+          Result.ret (betree_node_t.Internal node0)
+  | betree_node_t.Leaf node =>
+    do
+      let (_, bindings) ← betree_load_leaf_node_fwd node.betree_leaf_id st
+      let _ ← betree_node_lookup_in_bindings_fwd key bindings
+      Result.ret (betree_node_t.Leaf node)
+
+/- [betree_main::betree::Internal::{4}::lookup_in_children] -/
+divergent def betree_internal_lookup_in_children_fwd
+  (self : betree_internal_t) (key : U64) (st : State) :
+  Result (State × (Option U64))
+  :=
+  let (mkbetree_internal_t _ i n n0) := self
+  if key < i
+  then betree_node_lookup_fwd n key st
+  else betree_node_lookup_fwd n0 key st
+
+/- [betree_main::betree::Internal::{4}::lookup_in_children] -/
+divergent def betree_internal_lookup_in_children_back
+  (self : betree_internal_t) (key : U64) (st : State) :
+  Result betree_internal_t
+  :=
+  let (mkbetree_internal_t i i0 n n0) := self
+  if key < i0
+  then
+    do
+      let n1 ← betree_node_lookup_back n key st
+      Result.ret (mkbetree_internal_t i i0 n1 n0)
+  else
+    do
+      let n1 ← betree_node_lookup_back n0 key st
+      Result.ret (mkbetree_internal_t i i0 n n1)
+
+end
+
+/- [betree_main::betree::Node::{5}::lookup_mut_in_bindings] -/
+divergent def betree_node_lookup_mut_in_bindings_fwd
+  (key : U64) (bindings : betree_list_t (U64 × U64)) :
+  Result (betree_list_t (U64 × U64))
+  :=
+  match h: bindings with
+  | betree_list_t.Cons hd tl =>
+    let (i, i0) := hd
+    if i >= key
+    then Result.ret (betree_list_t.Cons (i, i0) tl)
+    else betree_node_lookup_mut_in_bindings_fwd key tl
+  | betree_list_t.Nil => Result.ret betree_list_t.Nil
+
+/- [betree_main::betree::Node::{5}::lookup_mut_in_bindings] -/
+divergent def betree_node_lookup_mut_in_bindings_back
+  (key : U64) (bindings : betree_list_t (U64 × U64))
+  (ret0 : betree_list_t (U64 × U64)) :
+  Result (betree_list_t (U64 × U64))
+  :=
+  match h: bindings with
+  | betree_list_t.Cons hd tl =>
+    let (i, i0) := hd
+    if i >= key
+    then Result.ret ret0
+    else
+      do
+        let tl0 ← betree_node_lookup_mut_in_bindings_back key tl ret0
+        Result.ret (betree_list_t.Cons (i, i0) tl0)
+  | betree_list_t.Nil => Result.ret ret0
+
+/- [betree_main::betree::Node::{5}::apply_to_leaf] -/
+def betree_node_apply_to_leaf_fwd_back
+  (bindings : betree_list_t (U64 × U64)) (key : U64)
+  (new_msg : betree_message_t) :
+  Result (betree_list_t (U64 × U64))
+  :=
+  do
+    let bindings0 ← betree_node_lookup_mut_in_bindings_fwd key bindings
+    let b ← betree_list_head_has_key_fwd U64 bindings0 key
+    if b
+    then
+      do
+        let hd ← betree_list_pop_front_fwd (U64 × U64) bindings0
+        match h: new_msg with
+        | betree_message_t.Insert v =>
+          do
+            let bindings1 ← betree_list_pop_front_back (U64 × U64) bindings0
+            let bindings2 ←
+              betree_list_push_front_fwd_back (U64 × U64) bindings1 (key, v)
+            betree_node_lookup_mut_in_bindings_back key bindings bindings2
+        | betree_message_t.Delete =>
+          do
+            let bindings1 ← betree_list_pop_front_back (U64 × U64) bindings0
+            betree_node_lookup_mut_in_bindings_back key bindings bindings1
+        | betree_message_t.Upsert s =>
+          do
+            let (_, i) := hd
+            let v ← betree_upsert_update_fwd (Option.some i) s
+            let bindings1 ← betree_list_pop_front_back (U64 × U64) bindings0
+            let bindings2 ←
+              betree_list_push_front_fwd_back (U64 × U64) bindings1 (key, v)
+            betree_node_lookup_mut_in_bindings_back key bindings bindings2
+    else
+      match h: new_msg with
+      | betree_message_t.Insert v =>
+        do
+          let bindings1 ←
+            betree_list_push_front_fwd_back (U64 × U64) bindings0 (key, v)
+          betree_node_lookup_mut_in_bindings_back key bindings bindings1
+      | betree_message_t.Delete =>
+        betree_node_lookup_mut_in_bindings_back key bindings bindings0
+      | betree_message_t.Upsert s =>
+        do
+          let v ← betree_upsert_update_fwd Option.none s
+          let bindings1 ←
+            betree_list_push_front_fwd_back (U64 × U64) bindings0 (key, v)
+          betree_node_lookup_mut_in_bindings_back key bindings bindings1
+
+/- [betree_main::betree::Node::{5}::apply_messages_to_leaf] -/
+divergent def betree_node_apply_messages_to_leaf_fwd_back
+  (bindings : betree_list_t (U64 × U64))
+  (new_msgs : betree_list_t (U64 × betree_message_t)) :
+  Result (betree_list_t (U64 × U64))
+  :=
+  match h: new_msgs with
+  | betree_list_t.Cons new_msg new_msgs_tl =>
+    do
+      let (i, m) := new_msg
+      let bindings0 ← betree_node_apply_to_leaf_fwd_back bindings i m
+      betree_node_apply_messages_to_leaf_fwd_back bindings0 new_msgs_tl
+  | betree_list_t.Nil => Result.ret bindings
+
+/- [betree_main::betree::Node::{5}::filter_messages_for_key] -/
+divergent def betree_node_filter_messages_for_key_fwd_back
+  (key : U64) (msgs : betree_list_t (U64 × betree_message_t)) :
+  Result (betree_list_t (U64 × betree_message_t))
+  :=
+  match h: msgs with
+  | betree_list_t.Cons p l =>
+    let (k, m) := p
+    if k = key
+    then
+      do
+        let msgs0 ←
+          betree_list_pop_front_back (U64 × betree_message_t)
+            (betree_list_t.Cons (k, m) l)
+        betree_node_filter_messages_for_key_fwd_back key msgs0
+    else Result.ret (betree_list_t.Cons (k, m) l)
+  | betree_list_t.Nil => Result.ret betree_list_t.Nil
+
+/- [betree_main::betree::Node::{5}::lookup_first_message_after_key] -/
+divergent def betree_node_lookup_first_message_after_key_fwd
+  (key : U64) (msgs : betree_list_t (U64 × betree_message_t)) :
+  Result (betree_list_t (U64 × betree_message_t))
+  :=
+  match h: msgs with
+  | betree_list_t.Cons p next_msgs =>
+    let (k, m) := p
+    if k = key
+    then betree_node_lookup_first_message_after_key_fwd key next_msgs
+    else Result.ret (betree_list_t.Cons (k, m) next_msgs)
+  | betree_list_t.Nil => Result.ret betree_list_t.Nil
+
+/- [betree_main::betree::Node::{5}::lookup_first_message_after_key] -/
+divergent def betree_node_lookup_first_message_after_key_back
+  (key : U64) (msgs : betree_list_t (U64 × betree_message_t))
+  (ret0 : betree_list_t (U64 × betree_message_t)) :
+  Result (betree_list_t (U64 × betree_message_t))
+  :=
+  match h: msgs with
+  | betree_list_t.Cons p next_msgs =>
+    let (k, m) := p
+    if k = key
+    then
+      do
+        let next_msgs0 ←
+          betree_node_lookup_first_message_after_key_back key next_msgs ret0
+        Result.ret (betree_list_t.Cons (k, m) next_msgs0)
+    else Result.ret ret0
+  | betree_list_t.Nil => Result.ret ret0
+
+/- [betree_main::betree::Node::{5}::apply_to_internal] -/
+def betree_node_apply_to_internal_fwd_back
+  (msgs : betree_list_t (U64 × betree_message_t)) (key : U64)
+  (new_msg : betree_message_t) :
+  Result (betree_list_t (U64 × betree_message_t))
+  :=
+  do
+    let msgs0 ← betree_node_lookup_first_message_for_key_fwd key msgs
+    let b ← betree_list_head_has_key_fwd betree_message_t msgs0 key
+    if b
+    then
+      match h: new_msg with
+      | betree_message_t.Insert i =>
+        do
+          let msgs1 ← betree_node_filter_messages_for_key_fwd_back key msgs0
+          let msgs2 ←
+            betree_list_push_front_fwd_back (U64 × betree_message_t) msgs1
+              (key, betree_message_t.Insert i)
+          betree_node_lookup_first_message_for_key_back key msgs msgs2
+      | betree_message_t.Delete =>
+        do
+          let msgs1 ← betree_node_filter_messages_for_key_fwd_back key msgs0
+          let msgs2 ←
+            betree_list_push_front_fwd_back (U64 × betree_message_t) msgs1
+              (key, betree_message_t.Delete)
+          betree_node_lookup_first_message_for_key_back key msgs msgs2
+      | betree_message_t.Upsert s =>
+        do
+          let p ← betree_list_hd_fwd (U64 × betree_message_t) msgs0
+          let (_, m) := p
+          match h: m with
+          | betree_message_t.Insert prev =>
+            do
+              let v ← betree_upsert_update_fwd (Option.some prev) s
+              let msgs1 ←
+                betree_list_pop_front_back (U64 × betree_message_t) msgs0
+              let msgs2 ←
+                betree_list_push_front_fwd_back (U64 × betree_message_t) msgs1
+                  (key, betree_message_t.Insert v)
+              betree_node_lookup_first_message_for_key_back key msgs msgs2
+          | betree_message_t.Delete =>
+            do
+              let v ← betree_upsert_update_fwd Option.none s
+              let msgs1 ←
+                betree_list_pop_front_back (U64 × betree_message_t) msgs0
+              let msgs2 ←
+                betree_list_push_front_fwd_back (U64 × betree_message_t) msgs1
+                  (key, betree_message_t.Insert v)
+              betree_node_lookup_first_message_for_key_back key msgs msgs2
+          | betree_message_t.Upsert ufs =>
+            do
+              let msgs1 ←
+                betree_node_lookup_first_message_after_key_fwd key msgs0
+              let msgs2 ←
+                betree_list_push_front_fwd_back (U64 × betree_message_t) msgs1
+                  (key, betree_message_t.Upsert s)
+              let msgs3 ←
+                betree_node_lookup_first_message_after_key_back key msgs0 msgs2
+              betree_node_lookup_first_message_for_key_back key msgs msgs3
+    else
+      do
+        let msgs1 ←
+          betree_list_push_front_fwd_back (U64 × betree_message_t) msgs0 (key,
+            new_msg)
+        betree_node_lookup_first_message_for_key_back key msgs msgs1
+
+/- [betree_main::betree::Node::{5}::apply_messages_to_internal] -/
+divergent def betree_node_apply_messages_to_internal_fwd_back
+  (msgs : betree_list_t (U64 × betree_message_t))
+  (new_msgs : betree_list_t (U64 × betree_message_t)) :
+  Result (betree_list_t (U64 × betree_message_t))
+  :=
+  match h: new_msgs with
+  | betree_list_t.Cons new_msg new_msgs_tl =>
+    do
+      let (i, m) := new_msg
+      let msgs0 ← betree_node_apply_to_internal_fwd_back msgs i m
+      betree_node_apply_messages_to_internal_fwd_back msgs0 new_msgs_tl
+  | betree_list_t.Nil => Result.ret msgs
+
+/- [betree_main::betree::Node::{5}::apply_messages] -/
+mutual divergent def betree_node_apply_messages_fwd
+  (self : betree_node_t) (params : betree_params_t)
+  (node_id_cnt : betree_node_id_counter_t)
+  (msgs : betree_list_t (U64 × betree_message_t)) (st : State) :
+  Result (State × Unit)
+  :=
+  match h: self with
+  | betree_node_t.Internal node =>
+    do
+      let (mkbetree_internal_t i i0 n n0) := node
+      let (st0, content) ← betree_load_internal_node_fwd i st
+      let content0 ←
+        betree_node_apply_messages_to_internal_fwd_back content msgs
+      let num_msgs ← betree_list_len_fwd (U64 × betree_message_t) content0
+      if num_msgs >= params.betree_params_min_flush_size
+      then
+        do
+          let (st1, content1) ←
+            betree_internal_flush_fwd (mkbetree_internal_t i i0 n n0) params
+              node_id_cnt content0 st0
+          let (node0, _) ←
+            betree_internal_flush_back (mkbetree_internal_t i i0 n n0) params
+              node_id_cnt content0 st0
+          let (mkbetree_internal_t i1 _ _ _) := node0
+          let (st2, _) ← betree_store_internal_node_fwd i1 content1 st1
+          Result.ret (st2, ())
+      else
+        do
+          let (st1, _) ← betree_store_internal_node_fwd i content0 st0
+          Result.ret (st1, ())
+  | betree_node_t.Leaf node =>
+    do
+      let (st0, content) ← betree_load_leaf_node_fwd node.betree_leaf_id st
+      let content0 ← betree_node_apply_messages_to_leaf_fwd_back content msgs
+      let len ← betree_list_len_fwd (U64 × U64) content0
+      let i ← (U64.ofInt 2 (by intlit)) * params.betree_params_split_size
+      if len >= i
+      then
+        do
+          let (st1, _) ←
+            betree_leaf_split_fwd node content0 params node_id_cnt st0
+          let (st2, _) ←
+            betree_store_leaf_node_fwd node.betree_leaf_id betree_list_t.Nil
+              st1
+          Result.ret (st2, ())
+      else
+        do
+          let (st1, _) ←
+            betree_store_leaf_node_fwd node.betree_leaf_id content0 st0
+          Result.ret (st1, ())
+
+/- [betree_main::betree::Node::{5}::apply_messages] -/
+divergent def betree_node_apply_messages_back
+  (self : betree_node_t) (params : betree_params_t)
+  (node_id_cnt : betree_node_id_counter_t)
+  (msgs : betree_list_t (U64 × betree_message_t)) (st : State) :
+  Result (betree_node_t × betree_node_id_counter_t)
+  :=
+  match h: self with
+  | betree_node_t.Internal node =>
+    do
+      let (mkbetree_internal_t i i0 n n0) := node
+      let (st0, content) ← betree_load_internal_node_fwd i st
+      let content0 ←
+        betree_node_apply_messages_to_internal_fwd_back content msgs
+      let num_msgs ← betree_list_len_fwd (U64 × betree_message_t) content0
+      if num_msgs >= params.betree_params_min_flush_size
+      then
+        do
+          let (st1, content1) ←
+            betree_internal_flush_fwd (mkbetree_internal_t i i0 n n0) params
+              node_id_cnt content0 st0
+          let (node0, node_id_cnt0) ←
+            betree_internal_flush_back (mkbetree_internal_t i i0 n n0) params
+              node_id_cnt content0 st0
+          let (mkbetree_internal_t i1 i2 n1 n2) := node0
+          let _ ← betree_store_internal_node_fwd i1 content1 st1
+          Result.ret (betree_node_t.Internal (mkbetree_internal_t i1 i2 n1 n2),
+            node_id_cnt0)
+      else
+        do
+          let _ ← betree_store_internal_node_fwd i content0 st0
+          Result.ret (betree_node_t.Internal (mkbetree_internal_t i i0 n n0),
+            node_id_cnt)
+  | betree_node_t.Leaf node =>
+    do
+      let (st0, content) ← betree_load_leaf_node_fwd node.betree_leaf_id st
+      let content0 ← betree_node_apply_messages_to_leaf_fwd_back content msgs
+      let len ← betree_list_len_fwd (U64 × U64) content0
+      let i ← (U64.ofInt 2 (by intlit)) * params.betree_params_split_size
+      if len >= i
+      then
+        do
+          let (st1, new_node) ←
+            betree_leaf_split_fwd node content0 params node_id_cnt st0
+          let _ ←
+            betree_store_leaf_node_fwd node.betree_leaf_id betree_list_t.Nil
+              st1
+          let node_id_cnt0 ←
+            betree_leaf_split_back node content0 params node_id_cnt st0
+          Result.ret (betree_node_t.Internal new_node, node_id_cnt0)
+      else
+        do
+          let _ ← betree_store_leaf_node_fwd node.betree_leaf_id content0 st0
+          Result.ret (betree_node_t.Leaf { node with betree_leaf_size := len },
+            node_id_cnt)
+
+/- [betree_main::betree::Internal::{4}::flush] -/
+divergent def betree_internal_flush_fwd
+  (self : betree_internal_t) (params : betree_params_t)
+  (node_id_cnt : betree_node_id_counter_t)
+  (content : betree_list_t (U64 × betree_message_t)) (st : State) :
+  Result (State × (betree_list_t (U64 × betree_message_t)))
+  :=
+  do
+    let (mkbetree_internal_t _ i n n0) := self
+    let p ← betree_list_partition_at_pivot_fwd betree_message_t content i
+    let (msgs_left, msgs_right) := p
+    let len_left ← betree_list_len_fwd (U64 × betree_message_t) msgs_left
+    if len_left >= params.betree_params_min_flush_size
+    then
+      do
+        let (st0, _) ←
+          betree_node_apply_messages_fwd n params node_id_cnt msgs_left st
+        let (_, node_id_cnt0) ←
+          betree_node_apply_messages_back n params node_id_cnt msgs_left st
+        let len_right ←
+          betree_list_len_fwd (U64 × betree_message_t) msgs_right
+        if len_right >= params.betree_params_min_flush_size
+        then
+          do
+            let (st1, _) ←
+              betree_node_apply_messages_fwd n0 params node_id_cnt0 msgs_right
+                st0
+            let _ ←
+              betree_node_apply_messages_back n0 params node_id_cnt0 msgs_right
+                st0
+            Result.ret (st1, betree_list_t.Nil)
+        else Result.ret (st0, msgs_right)
+    else
+      do
+        let (st0, _) ←
+          betree_node_apply_messages_fwd n0 params node_id_cnt msgs_right st
+        let _ ←
+          betree_node_apply_messages_back n0 params node_id_cnt msgs_right st
+        Result.ret (st0, msgs_left)
+
+/- [betree_main::betree::Internal::{4}::flush] -/
+divergent def betree_internal_flush_back
+  (self : betree_internal_t) (params : betree_params_t)
+  (node_id_cnt : betree_node_id_counter_t)
+  (content : betree_list_t (U64 × betree_message_t)) (st : State) :
+  Result (betree_internal_t × betree_node_id_counter_t)
+  :=
+  do
+    let (mkbetree_internal_t i i0 n n0) := self
+    let p ← betree_list_partition_at_pivot_fwd betree_message_t content i0
+    let (msgs_left, msgs_right) := p
+    let len_left ← betree_list_len_fwd (U64 × betree_message_t) msgs_left
+    if len_left >= params.betree_params_min_flush_size
+    then
+      do
+        let (st0, _) ←
+          betree_node_apply_messages_fwd n params node_id_cnt msgs_left st
+        let (n1, node_id_cnt0) ←
+          betree_node_apply_messages_back n params node_id_cnt msgs_left st
+        let len_right ←
+          betree_list_len_fwd (U64 × betree_message_t) msgs_right
+        if len_right >= params.betree_params_min_flush_size
+        then
+          do
+            let (n2, node_id_cnt1) ←
+              betree_node_apply_messages_back n0 params node_id_cnt0 msgs_right
+                st0
+            Result.ret (mkbetree_internal_t i i0 n1 n2, node_id_cnt1)
+        else Result.ret (mkbetree_internal_t i i0 n1 n0, node_id_cnt0)
+    else
+      do
+        let (n1, node_id_cnt0) ←
+          betree_node_apply_messages_back n0 params node_id_cnt msgs_right st
+        Result.ret (mkbetree_internal_t i i0 n n1, node_id_cnt0)
+
+end
+
+/- [betree_main::betree::Node::{5}::apply] -/
+def betree_node_apply_fwd
+  (self : betree_node_t) (params : betree_params_t)
+  (node_id_cnt : betree_node_id_counter_t) (key : U64)
+  (new_msg : betree_message_t) (st : State) :
+  Result (State × Unit)
+  :=
+  do
+    let l := betree_list_t.Nil
+    let (st0, _) ←
+      betree_node_apply_messages_fwd self params node_id_cnt
+        (betree_list_t.Cons (key, new_msg) l) st
+    let _ ←
+      betree_node_apply_messages_back self params node_id_cnt
+        (betree_list_t.Cons (key, new_msg) l) st
+    Result.ret (st0, ())
+
+/- [betree_main::betree::Node::{5}::apply] -/
+def betree_node_apply_back
+  (self : betree_node_t) (params : betree_params_t)
+  (node_id_cnt : betree_node_id_counter_t) (key : U64)
+  (new_msg : betree_message_t) (st : State) :
+  Result (betree_node_t × betree_node_id_counter_t)
+  :=
+  let l := betree_list_t.Nil
+  betree_node_apply_messages_back self params node_id_cnt (betree_list_t.Cons
+    (key, new_msg) l) st
+
+/- [betree_main::betree::BeTree::{6}::new] -/
+def betree_be_tree_new_fwd
+  (min_flush_size : U64) (split_size : U64) (st : State) :
+  Result (State × betree_be_tree_t)
+  :=
+  do
+    let node_id_cnt ← betree_node_id_counter_new_fwd
+    let id ← betree_node_id_counter_fresh_id_fwd node_id_cnt
+    let (st0, _) ← betree_store_leaf_node_fwd id betree_list_t.Nil st
+    let node_id_cnt0 ← betree_node_id_counter_fresh_id_back node_id_cnt
+    Result.ret (st0,
+      {
+        betree_be_tree_params :=
+          {
+            betree_params_min_flush_size := min_flush_size,
+            betree_params_split_size := split_size
+          },
+        betree_be_tree_node_id_cnt := node_id_cnt0,
+        betree_be_tree_root :=
+          (betree_node_t.Leaf
+            {
+              betree_leaf_id := id,
+              betree_leaf_size := (U64.ofInt 0 (by intlit))
+            })
+      })
+
+/- [betree_main::betree::BeTree::{6}::apply] -/
+def betree_be_tree_apply_fwd
+  (self : betree_be_tree_t) (key : U64) (msg : betree_message_t) (st : State) :
+  Result (State × Unit)
+  :=
+  do
+    let (st0, _) ←
+      betree_node_apply_fwd self.betree_be_tree_root self.betree_be_tree_params
+        self.betree_be_tree_node_id_cnt key msg st
+    let _ ←
+      betree_node_apply_back self.betree_be_tree_root
+        self.betree_be_tree_params self.betree_be_tree_node_id_cnt key msg st
+    Result.ret (st0, ())
+
+/- [betree_main::betree::BeTree::{6}::apply] -/
+def betree_be_tree_apply_back
+  (self : betree_be_tree_t) (key : U64) (msg : betree_message_t) (st : State) :
+  Result betree_be_tree_t
+  :=
+  do
+    let (n, nic) ←
+      betree_node_apply_back self.betree_be_tree_root
+        self.betree_be_tree_params self.betree_be_tree_node_id_cnt key msg st
+    Result.ret
+      { self with betree_be_tree_node_id_cnt := nic, betree_be_tree_root := n }
+
+/- [betree_main::betree::BeTree::{6}::insert] -/
+def betree_be_tree_insert_fwd
+  (self : betree_be_tree_t) (key : U64) (value : U64) (st : State) :
+  Result (State × Unit)
+  :=
+  do
+    let (st0, _) ←
+      betree_be_tree_apply_fwd self key (betree_message_t.Insert value) st
+    let _ ←
+      betree_be_tree_apply_back self key (betree_message_t.Insert value) st
+    Result.ret (st0, ())
+
+/- [betree_main::betree::BeTree::{6}::insert] -/
+def betree_be_tree_insert_back
+  (self : betree_be_tree_t) (key : U64) (value : U64) (st : State) :
+  Result betree_be_tree_t
+  :=
+  betree_be_tree_apply_back self key (betree_message_t.Insert value) st
+
+/- [betree_main::betree::BeTree::{6}::delete] -/
+def betree_be_tree_delete_fwd
+  (self : betree_be_tree_t) (key : U64) (st : State) :
+  Result (State × Unit)
+  :=
+  do
+    let (st0, _) ←
+      betree_be_tree_apply_fwd self key betree_message_t.Delete st
+    let _ ← betree_be_tree_apply_back self key betree_message_t.Delete st
+    Result.ret (st0, ())
+
+/- [betree_main::betree::BeTree::{6}::delete] -/
+def betree_be_tree_delete_back
+  (self : betree_be_tree_t) (key : U64) (st : State) :
+  Result betree_be_tree_t
+  :=
+  betree_be_tree_apply_back self key betree_message_t.Delete st
+
+/- [betree_main::betree::BeTree::{6}::upsert] -/
+def betree_be_tree_upsert_fwd
+  (self : betree_be_tree_t) (key : U64) (upd : betree_upsert_fun_state_t)
+  (st : State) :
+  Result (State × Unit)
+  :=
+  do
+    let (st0, _) ←
+      betree_be_tree_apply_fwd self key (betree_message_t.Upsert upd) st
+    let _ ←
+      betree_be_tree_apply_back self key (betree_message_t.Upsert upd) st
+    Result.ret (st0, ())
+
+/- [betree_main::betree::BeTree::{6}::upsert] -/
+def betree_be_tree_upsert_back
+  (self : betree_be_tree_t) (key : U64) (upd : betree_upsert_fun_state_t)
+  (st : State) :
+  Result betree_be_tree_t
+  :=
+  betree_be_tree_apply_back self key (betree_message_t.Upsert upd) st
+
+/- [betree_main::betree::BeTree::{6}::lookup] -/
+def betree_be_tree_lookup_fwd
+  (self : betree_be_tree_t) (key : U64) (st : State) :
+  Result (State × (Option U64))
+  :=
+  betree_node_lookup_fwd self.betree_be_tree_root key st
+
+/- [betree_main::betree::BeTree::{6}::lookup] -/
+def betree_be_tree_lookup_back
+  (self : betree_be_tree_t) (key : U64) (st : State) :
+  Result betree_be_tree_t
+  :=
+  do
+    let n ← betree_node_lookup_back self.betree_be_tree_root key st
+    Result.ret { self with betree_be_tree_root := n }
+
+/- [betree_main::main] -/
+def main_fwd : Result Unit :=
+  Result.ret ()
+
+/- Unit test for [betree_main::main] -/
+#assert (main_fwd == .ret ())
+