Improve the generated comments

15 files changed, 916 insertions, 920 deletions

diff --git a/tests/lean/BetreeMain/Funs.lean b/tests/lean/BetreeMain/Funs.lean
index 074fff5e..41e4349e 100644
--- a/tests/lean/BetreeMain/Funs.lean
+++ b/tests/lean/BetreeMain/Funs.lean
@@ -6,60 +6,59 @@ import BetreeMain.FunsExternal
 open Primitives
 namespace betree_main
 
-/- [betree_main::betree::load_internal_node] -/
-def betree.load_internal_node_fwd
+/- [betree_main::betree::load_internal_node]: forward function -/
+def betree.load_internal_node
   (id : U64) (st : State) :
   Result (State × (betree.List (U64 × betree.Message)))
   :=
-  betree_utils.load_internal_node_fwd id st
+  betree_utils.load_internal_node id st
 
-/- [betree_main::betree::store_internal_node] -/
-def betree.store_internal_node_fwd
+/- [betree_main::betree::store_internal_node]: forward function -/
+def betree.store_internal_node
   (id : U64) (content : betree.List (U64 × betree.Message)) (st : State) :
   Result (State × Unit)
   :=
   do
-    let (st0, _) ← betree_utils.store_internal_node_fwd id content st
+    let (st0, _) ← betree_utils.store_internal_node id content st
     Result.ret (st0, ())
 
-/- [betree_main::betree::load_leaf_node] -/
-def betree.load_leaf_node_fwd
+/- [betree_main::betree::load_leaf_node]: forward function -/
+def betree.load_leaf_node
   (id : U64) (st : State) : Result (State × (betree.List (U64 × U64))) :=
-  betree_utils.load_leaf_node_fwd id st
+  betree_utils.load_leaf_node id st
 
-/- [betree_main::betree::store_leaf_node] -/
-def betree.store_leaf_node_fwd
+/- [betree_main::betree::store_leaf_node]: forward function -/
+def betree.store_leaf_node
   (id : U64) (content : betree.List (U64 × U64)) (st : State) :
   Result (State × Unit)
   :=
   do
-    let (st0, _) ← betree_utils.store_leaf_node_fwd id content st
+    let (st0, _) ← betree_utils.store_leaf_node id content st
     Result.ret (st0, ())
 
-/- [betree_main::betree::fresh_node_id] -/
-def betree.fresh_node_id_fwd (counter : U64) : Result U64 :=
+/- [betree_main::betree::fresh_node_id]: forward function -/
+def betree.fresh_node_id (counter : U64) : Result U64 :=
   do
     let _ ← counter + (U64.ofInt 1 (by intlit))
     Result.ret counter
 
-/- [betree_main::betree::fresh_node_id] -/
+/- [betree_main::betree::fresh_node_id]: backward function 0 -/
 def betree.fresh_node_id_back (counter : U64) : Result U64 :=
   counter + (U64.ofInt 1 (by intlit))
 
-/- [betree_main::betree::NodeIdCounter::{0}::new] -/
-def betree.NodeIdCounter.new_fwd : Result betree.NodeIdCounter :=
+/- [betree_main::betree::NodeIdCounter::{0}::new]: forward function -/
+def betree.NodeIdCounter.new : Result betree.NodeIdCounter :=
   Result.ret
   { betree_node_id_counter_next_node_id := (U64.ofInt 0 (by intlit)) }
 
-/- [betree_main::betree::NodeIdCounter::{0}::fresh_id] -/
-def betree.NodeIdCounter.fresh_id_fwd
-  (self : betree.NodeIdCounter) : Result U64 :=
+/- [betree_main::betree::NodeIdCounter::{0}::fresh_id]: forward function -/
+def betree.NodeIdCounter.fresh_id (self : betree.NodeIdCounter) : 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] -/
+/- [betree_main::betree::NodeIdCounter::{0}::fresh_id]: backward function 0 -/
 def betree.NodeIdCounter.fresh_id_back
   (self : betree.NodeIdCounter) : Result betree.NodeIdCounter :=
   do
@@ -72,8 +71,8 @@ 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
+/- [betree_main::betree::upsert_update]: forward function -/
+def betree.upsert_update
   (prev : Option U64) (st : betree.UpsertFunState) : Result U64 :=
   match prev with
   | Option.none =>
@@ -93,18 +92,17 @@ def betree.upsert_update_fwd
       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) : Result U64 :=
+/- [betree_main::betree::List::{1}::len]: forward function -/
+divergent def betree.List.len (T : Type) (self : betree.List T) : Result U64 :=
   match self with
   | betree.List.Cons t tl =>
     do
-      let i ← betree.List.len_fwd T tl
+      let i ← betree.List.len T tl
       (U64.ofInt 1 (by intlit)) + i
   | betree.List.Nil => Result.ret (U64.ofInt 0 (by intlit))
 
-/- [betree_main::betree::List::{1}::split_at] -/
-divergent def betree.List.split_at_fwd
+/- [betree_main::betree::List::{1}::split_at]: forward function -/
+divergent def betree.List.split_at
   (T : Type) (self : betree.List T) (n : U64) :
   Result ((betree.List T) × (betree.List T))
   :=
@@ -115,50 +113,51 @@ divergent def betree.List.split_at_fwd
     | betree.List.Cons hd tl =>
       do
         let i ← n - (U64.ofInt 1 (by intlit))
-        let p ← betree.List.split_at_fwd T tl i
+        let p ← betree.List.split_at T tl i
         let (ls0, ls1) := p
         let l := ls0
         Result.ret (betree.List.Cons hd l, ls1)
     | betree.List.Nil => Result.fail Error.panic
 
-/- [betree_main::betree::List::{1}::push_front] -/
-def betree.List.push_front_fwd_back
+/- [betree_main::betree::List::{1}::push_front]: merged forward/backward function
+   (there is a single backward function, and the forward function returns ()) -/
+def betree.List.push_front
   (T : Type) (self : betree.List T) (x : T) : Result (betree.List T) :=
-  let tl := mem.replace_fwd (betree.List T) self betree.List.Nil
+  let tl := mem.replace (betree.List T) self betree.List.Nil
   let l := tl
   Result.ret (betree.List.Cons x l)
 
-/- [betree_main::betree::List::{1}::pop_front] -/
-def betree.List.pop_front_fwd (T : Type) (self : betree.List T) : Result T :=
-  let ls := mem.replace_fwd (betree.List T) self betree.List.Nil
+/- [betree_main::betree::List::{1}::pop_front]: forward function -/
+def betree.List.pop_front (T : Type) (self : betree.List T) : Result T :=
+  let ls := mem.replace (betree.List T) self betree.List.Nil
   match ls with
   | betree.List.Cons x tl => Result.ret x
   | betree.List.Nil => Result.fail Error.panic
 
-/- [betree_main::betree::List::{1}::pop_front] -/
+/- [betree_main::betree::List::{1}::pop_front]: backward function 0 -/
 def betree.List.pop_front_back
   (T : Type) (self : betree.List T) : Result (betree.List T) :=
-  let ls := mem.replace_fwd (betree.List T) self betree.List.Nil
+  let ls := mem.replace (betree.List T) self betree.List.Nil
   match ls with
   | betree.List.Cons x tl => Result.ret tl
   | betree.List.Nil => Result.fail Error.panic
 
-/- [betree_main::betree::List::{1}::hd] -/
-def betree.List.hd_fwd (T : Type) (self : betree.List T) : Result T :=
+/- [betree_main::betree::List::{1}::hd]: forward function -/
+def betree.List.hd (T : Type) (self : betree.List T) : Result T :=
   match self with
   | betree.List.Cons hd l => Result.ret hd
   | betree.List.Nil => Result.fail Error.panic
 
-/- [betree_main::betree::List::{2}::head_has_key] -/
-def betree.List.head_has_key_fwd
+/- [betree_main::betree::List::{2}::head_has_key]: forward function -/
+def betree.List.head_has_key
   (T : Type) (self : betree.List (U64 × T)) (key : U64) : Result Bool :=
   match self with
   | betree.List.Cons hd l => let (i, _) := hd
                              Result.ret (i = key)
   | betree.List.Nil => Result.ret false
 
-/- [betree_main::betree::List::{2}::partition_at_pivot] -/
-divergent def betree.List.partition_at_pivot_fwd
+/- [betree_main::betree::List::{2}::partition_at_pivot]: forward function -/
+divergent def betree.List.partition_at_pivot
   (T : Type) (self : betree.List (U64 × T)) (pivot : U64) :
   Result ((betree.List (U64 × T)) × (betree.List (U64 × T)))
   :=
@@ -169,30 +168,29 @@ divergent def betree.List.partition_at_pivot_fwd
     then Result.ret (betree.List.Nil, betree.List.Cons (i, t) tl)
     else
       do
-        let p ← betree.List.partition_at_pivot_fwd T tl pivot
+        let p ← betree.List.partition_at_pivot T tl pivot
         let (ls0, ls1) := p
         let l := ls0
         Result.ret (betree.List.Cons (i, t) l, ls1)
   | betree.List.Nil => Result.ret (betree.List.Nil, betree.List.Nil)
 
-/- [betree_main::betree::Leaf::{3}::split] -/
-def betree.Leaf.split_fwd
+/- [betree_main::betree::Leaf::{3}::split]: forward function -/
+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)
   :=
   do
     let p ←
-      betree.List.split_at_fwd (U64 × U64) content
-        params.betree_params_split_size
+      betree.List.split_at (U64 × U64) content params.betree_params_split_size
     let (content0, content1) := p
-    let p0 ← betree.List.hd_fwd (U64 × U64) content1
+    let p0 ← betree.List.hd (U64 × U64) content1
     let (pivot, _) := p0
-    let id0 ← betree.NodeIdCounter.fresh_id_fwd node_id_cnt
+    let id0 ← betree.NodeIdCounter.fresh_id node_id_cnt
     let node_id_cnt0 ← betree.NodeIdCounter.fresh_id_back node_id_cnt
-    let id1 ← betree.NodeIdCounter.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 id1 ← betree.NodeIdCounter.fresh_id node_id_cnt0
+    let (st0, _) ← betree.store_leaf_node id0 content0 st
+    let (st1, _) ← betree.store_leaf_node id1 content1 st0
     let n := betree.Node.Leaf
       {
         betree_leaf_id := id0,
@@ -205,7 +203,7 @@ def betree.Leaf.split_fwd
       }
     Result.ret (st1, betree.Internal.mk self.betree_leaf_id pivot n n0)
 
-/- [betree_main::betree::Leaf::{3}::split] -/
+/- [betree_main::betree::Leaf::{3}::split]: backward function 2 -/
 def betree.Leaf.split_back
   (self : betree.Leaf) (content : betree.List (U64 × U64))
   (params : betree.Params) (node_id_cnt : betree.NodeIdCounter) (st : State) :
@@ -213,19 +211,18 @@ def betree.Leaf.split_back
   :=
   do
     let p ←
-      betree.List.split_at_fwd (U64 × U64) content
-        params.betree_params_split_size
+      betree.List.split_at (U64 × U64) content params.betree_params_split_size
     let (content0, content1) := p
-    let _ ← betree.List.hd_fwd (U64 × U64) content1
-    let id0 ← betree.NodeIdCounter.fresh_id_fwd node_id_cnt
+    let _ ← betree.List.hd (U64 × U64) content1
+    let id0 ← betree.NodeIdCounter.fresh_id node_id_cnt
     let node_id_cnt0 ← betree.NodeIdCounter.fresh_id_back node_id_cnt
-    let id1 ← betree.NodeIdCounter.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
+    let id1 ← betree.NodeIdCounter.fresh_id node_id_cnt0
+    let (st0, _) ← betree.store_leaf_node id0 content0 st
+    let _ ← betree.store_leaf_node id1 content1 st0
     betree.NodeIdCounter.fresh_id_back node_id_cnt0
 
-/- [betree_main::betree::Node::{5}::lookup_in_bindings] -/
-divergent def betree.Node.lookup_in_bindings_fwd
+/- [betree_main::betree::Node::{5}::lookup_in_bindings]: forward function -/
+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 =>
@@ -235,11 +232,11 @@ divergent def betree.Node.lookup_in_bindings_fwd
     else
       if i > key
       then Result.ret Option.none
-      else betree.Node.lookup_in_bindings_fwd key tl
+      else betree.Node.lookup_in_bindings key tl
   | betree.List.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
+/- [betree_main::betree::Node::{5}::lookup_first_message_for_key]: forward function -/
+divergent def betree.Node.lookup_first_message_for_key
   (key : U64) (msgs : betree.List (U64 × betree.Message)) :
   Result (betree.List (U64 × betree.Message))
   :=
@@ -248,10 +245,10 @@ divergent def betree.Node.lookup_first_message_for_key_fwd
     let (i, m) := x
     if i >= key
     then Result.ret (betree.List.Cons (i, m) next_msgs)
-    else betree.Node.lookup_first_message_for_key_fwd key next_msgs
+    else betree.Node.lookup_first_message_for_key key next_msgs
   | betree.List.Nil => Result.ret betree.List.Nil
 
-/- [betree_main::betree::Node::{5}::lookup_first_message_for_key] -/
+/- [betree_main::betree::Node::{5}::lookup_first_message_for_key]: backward function 0 -/
 divergent def betree.Node.lookup_first_message_for_key_back
   (key : U64) (msgs : betree.List (U64 × betree.Message))
   (ret0 : betree.List (U64 × betree.Message)) :
@@ -269,66 +266,66 @@ divergent def betree.Node.lookup_first_message_for_key_back
         Result.ret (betree.List.Cons (i, m) next_msgs0)
   | betree.List.Nil => Result.ret ret0
 
-/- [betree_main::betree::Node::{5}::apply_upserts] -/
-divergent def betree.Node.apply_upserts_fwd
+/- [betree_main::betree::Node::{5}::apply_upserts]: forward function -/
+divergent def betree.Node.apply_upserts
   (msgs : betree.List (U64 × betree.Message)) (prev : Option U64) (key : U64)
   (st : State) :
   Result (State × U64)
   :=
   do
-    let b ← betree.List.head_has_key_fwd betree.Message msgs key
+    let b ← betree.List.head_has_key betree.Message msgs key
     if b
     then
       do
-        let msg ← betree.List.pop_front_fwd (U64 × betree.Message) msgs
+        let msg ← betree.List.pop_front (U64 × betree.Message) msgs
         let (_, m) := msg
         match m with
         | betree.Message.Insert i => Result.fail Error.panic
         | betree.Message.Delete => Result.fail Error.panic
         | betree.Message.Upsert s =>
           do
-            let v ← betree.upsert_update_fwd prev s
+            let v ← betree.upsert_update prev s
             let msgs0 ←
               betree.List.pop_front_back (U64 × betree.Message) msgs
-            betree.Node.apply_upserts_fwd msgs0 (Option.some v) key st
+            betree.Node.apply_upserts msgs0 (Option.some v) key st
     else
       do
-        let (st0, v) ← core.option.Option.unwrap_fwd U64 prev st
+        let (st0, v) ← core.option.Option.unwrap U64 prev st
         let _ ←
-          betree.List.push_front_fwd_back (U64 × betree.Message) msgs (key,
+          betree.List.push_front (U64 × betree.Message) msgs (key,
             betree.Message.Insert v)
         Result.ret (st0, v)
 
-/- [betree_main::betree::Node::{5}::apply_upserts] -/
+/- [betree_main::betree::Node::{5}::apply_upserts]: backward function 0 -/
 divergent def betree.Node.apply_upserts_back
   (msgs : betree.List (U64 × betree.Message)) (prev : Option U64) (key : U64)
   (st : State) :
   Result (betree.List (U64 × betree.Message))
   :=
   do
-    let b ← betree.List.head_has_key_fwd betree.Message msgs key
+    let b ← betree.List.head_has_key betree.Message msgs key
     if b
     then
       do
-        let msg ← betree.List.pop_front_fwd (U64 × betree.Message) msgs
+        let msg ← betree.List.pop_front (U64 × betree.Message) msgs
         let (_, m) := msg
         match m with
         | betree.Message.Insert i => Result.fail Error.panic
         | betree.Message.Delete => Result.fail Error.panic
         | betree.Message.Upsert s =>
           do
-            let v ← betree.upsert_update_fwd prev s
+            let v ← betree.upsert_update prev s
             let msgs0 ←
               betree.List.pop_front_back (U64 × betree.Message) msgs
             betree.Node.apply_upserts_back msgs0 (Option.some v) key st
     else
       do
-        let (_, v) ← core.option.Option.unwrap_fwd U64 prev st
-        betree.List.push_front_fwd_back (U64 × betree.Message) msgs (key,
+        let (_, v) ← core.option.Option.unwrap U64 prev st
+        betree.List.push_front (U64 × betree.Message) msgs (key,
           betree.Message.Insert v)
 
-/- [betree_main::betree::Node::{5}::lookup] -/
-mutual divergent def betree.Node.lookup_fwd
+/- [betree_main::betree::Node::{5}::lookup]: forward function -/
+mutual divergent def betree.Node.lookup
   (self : betree.Node) (key : U64) (st : State) :
   Result (State × (Option U64))
   :=
@@ -336,8 +333,8 @@ mutual divergent def betree.Node.lookup_fwd
   | betree.Node.Internal node =>
     do
       let ⟨ 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
+      let (st0, msgs) ← betree.load_internal_node i st
+      let pending ← betree.Node.lookup_first_message_for_key key msgs
       match pending with
       | betree.List.Cons p l =>
         let (k, msg) := p
@@ -345,8 +342,8 @@ mutual divergent def betree.Node.lookup_fwd
         then
           do
             let (st1, opt) ←
-              betree.Internal.lookup_in_children_fwd (betree.Internal.mk i i0 n
-                n0) key st0
+              betree.Internal.lookup_in_children (betree.Internal.mk i i0 n n0)
+                key st0
             let _ ←
               betree.Node.lookup_first_message_for_key_back key msgs
                 (betree.List.Cons (k, msg) l)
@@ -368,10 +365,10 @@ mutual divergent def betree.Node.lookup_fwd
           | betree.Message.Upsert ufs =>
             do
               let (st1, v) ←
-                betree.Internal.lookup_in_children_fwd (betree.Internal.mk i i0
-                  n n0) key st0
+                betree.Internal.lookup_in_children (betree.Internal.mk i i0 n
+                  n0) key st0
               let (st2, v0) ←
-                betree.Node.apply_upserts_fwd (betree.List.Cons (k,
+                betree.Node.apply_upserts (betree.List.Cons (k,
                   betree.Message.Upsert ufs) l) v key st1
               let node0 ←
                 betree.Internal.lookup_in_children_back (betree.Internal.mk i
@@ -382,32 +379,32 @@ mutual divergent def betree.Node.lookup_fwd
                   betree.Message.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
+              let (st3, _) ← betree.store_internal_node i1 msgs0 st2
               Result.ret (st3, Option.some v0)
       | betree.List.Nil =>
         do
           let (st1, opt) ←
-            betree.Internal.lookup_in_children_fwd (betree.Internal.mk i i0 n
-              n0) key st0
+            betree.Internal.lookup_in_children (betree.Internal.mk i i0 n n0)
+              key st0
           let _ ←
             betree.Node.lookup_first_message_for_key_back key msgs
               betree.List.Nil
           Result.ret (st1, opt)
   | betree.Node.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
+      let (st0, bindings) ← betree.load_leaf_node node.betree_leaf_id st
+      let opt ← betree.Node.lookup_in_bindings key bindings
       Result.ret (st0, opt)
 
-/- [betree_main::betree::Node::{5}::lookup] -/
+/- [betree_main::betree::Node::{5}::lookup]: backward function 0 -/
 divergent def betree.Node.lookup_back
   (self : betree.Node) (key : U64) (st : State) : Result betree.Node :=
   match self with
   | betree.Node.Internal node =>
     do
       let ⟨ 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
+      let (st0, msgs) ← betree.load_internal_node i st
+      let pending ← betree.Node.lookup_first_message_for_key key msgs
       match pending with
       | betree.List.Cons p l =>
         let (k, msg) := p
@@ -438,10 +435,10 @@ divergent def betree.Node.lookup_back
           | betree.Message.Upsert ufs =>
             do
               let (st1, v) ←
-                betree.Internal.lookup_in_children_fwd (betree.Internal.mk i i0
-                  n n0) key st0
+                betree.Internal.lookup_in_children (betree.Internal.mk i i0 n
+                  n0) key st0
               let (st2, _) ←
-                betree.Node.apply_upserts_fwd (betree.List.Cons (k,
+                betree.Node.apply_upserts (betree.List.Cons (k,
                   betree.Message.Upsert ufs) l) v key st1
               let node0 ←
                 betree.Internal.lookup_in_children_back (betree.Internal.mk i
@@ -452,7 +449,7 @@ divergent def betree.Node.lookup_back
                   betree.Message.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
+              let _ ← betree.store_internal_node i1 msgs0 st2
               Result.ret (betree.Node.Internal (betree.Internal.mk i1 i2 n1
                 n2))
       | betree.List.Nil =>
@@ -466,21 +463,21 @@ divergent def betree.Node.lookup_back
           Result.ret (betree.Node.Internal node0)
   | betree.Node.Leaf node =>
     do
-      let (_, bindings) ← betree.load_leaf_node_fwd node.betree_leaf_id st
-      let _ ← betree.Node.lookup_in_bindings_fwd key bindings
+      let (_, bindings) ← betree.load_leaf_node node.betree_leaf_id st
+      let _ ← betree.Node.lookup_in_bindings key bindings
       Result.ret (betree.Node.Leaf node)
 
-/- [betree_main::betree::Internal::{4}::lookup_in_children] -/
-divergent def betree.Internal.lookup_in_children_fwd
+/- [betree_main::betree::Internal::{4}::lookup_in_children]: forward function -/
+divergent def betree.Internal.lookup_in_children
   (self : betree.Internal) (key : U64) (st : State) :
   Result (State × (Option U64))
   :=
   let ⟨ _, i, n, n0 ⟩ := self
   if key < i
-  then betree.Node.lookup_fwd n key st
-  else betree.Node.lookup_fwd n0 key st
+  then betree.Node.lookup n key st
+  else betree.Node.lookup n0 key st
 
-/- [betree_main::betree::Internal::{4}::lookup_in_children] -/
+/- [betree_main::betree::Internal::{4}::lookup_in_children]: backward function 0 -/
 divergent def betree.Internal.lookup_in_children_back
   (self : betree.Internal) (key : U64) (st : State) : Result betree.Internal :=
   let ⟨ i, i0, n, n0 ⟩ := self
@@ -496,8 +493,8 @@ divergent def betree.Internal.lookup_in_children_back
 
 end
 
-/- [betree_main::betree::Node::{5}::lookup_mut_in_bindings] -/
-divergent def betree.Node.lookup_mut_in_bindings_fwd
+/- [betree_main::betree::Node::{5}::lookup_mut_in_bindings]: forward function -/
+divergent def betree.Node.lookup_mut_in_bindings
   (key : U64) (bindings : betree.List (U64 × U64)) :
   Result (betree.List (U64 × U64))
   :=
@@ -506,10 +503,10 @@ divergent def betree.Node.lookup_mut_in_bindings_fwd
     let (i, i0) := hd
     if i >= key
     then Result.ret (betree.List.Cons (i, i0) tl)
-    else betree.Node.lookup_mut_in_bindings_fwd key tl
+    else betree.Node.lookup_mut_in_bindings key tl
   | betree.List.Nil => Result.ret betree.List.Nil
 
-/- [betree_main::betree::Node::{5}::lookup_mut_in_bindings] -/
+/- [betree_main::betree::Node::{5}::lookup_mut_in_bindings]: backward function 0 -/
 divergent def betree.Node.lookup_mut_in_bindings_back
   (key : U64) (bindings : betree.List (U64 × U64))
   (ret0 : betree.List (U64 × U64)) :
@@ -526,25 +523,26 @@ divergent def betree.Node.lookup_mut_in_bindings_back
         Result.ret (betree.List.Cons (i, i0) tl0)
   | betree.List.Nil => Result.ret ret0
 
-/- [betree_main::betree::Node::{5}::apply_to_leaf] -/
-def betree.Node.apply_to_leaf_fwd_back
+/- [betree_main::betree::Node::{5}::apply_to_leaf]: merged forward/backward function
+   (there is a single backward function, and the forward function returns ()) -/
+def betree.Node.apply_to_leaf
   (bindings : betree.List (U64 × U64)) (key : U64) (new_msg : betree.Message)
   :
   Result (betree.List (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
+    let bindings0 ← betree.Node.lookup_mut_in_bindings key bindings
+    let b ← betree.List.head_has_key U64 bindings0 key
     if b
     then
       do
-        let hd ← betree.List.pop_front_fwd (U64 × U64) bindings0
+        let hd ← betree.List.pop_front (U64 × U64) bindings0
         match new_msg with
         | betree.Message.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.List.push_front (U64 × U64) bindings1 (key, v)
             betree.Node.lookup_mut_in_bindings_back key bindings bindings2
         | betree.Message.Delete =>
           do
@@ -553,29 +551,30 @@ def betree.Node.apply_to_leaf_fwd_back
         | betree.Message.Upsert s =>
           do
             let (_, i) := hd
-            let v ← betree.upsert_update_fwd (Option.some i) s
+            let v ← betree.upsert_update (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.List.push_front (U64 × U64) bindings1 (key, v)
             betree.Node.lookup_mut_in_bindings_back key bindings bindings2
     else
       match new_msg with
       | betree.Message.Insert v =>
         do
           let bindings1 ←
-            betree.List.push_front_fwd_back (U64 × U64) bindings0 (key, v)
+            betree.List.push_front (U64 × U64) bindings0 (key, v)
           betree.Node.lookup_mut_in_bindings_back key bindings bindings1
       | betree.Message.Delete =>
         betree.Node.lookup_mut_in_bindings_back key bindings bindings0
       | betree.Message.Upsert s =>
         do
-          let v ← betree.upsert_update_fwd Option.none s
+          let v ← betree.upsert_update Option.none s
           let bindings1 ←
-            betree.List.push_front_fwd_back (U64 × U64) bindings0 (key, v)
+            betree.List.push_front (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
+/- [betree_main::betree::Node::{5}::apply_messages_to_leaf]: merged forward/backward function
+   (there is a single backward function, and the forward function returns ()) -/
+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))
@@ -584,12 +583,13 @@ divergent def betree.Node.apply_messages_to_leaf_fwd_back
   | betree.List.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
+      let bindings0 ← betree.Node.apply_to_leaf bindings i m
+      betree.Node.apply_messages_to_leaf bindings0 new_msgs_tl
   | betree.List.Nil => Result.ret bindings
 
-/- [betree_main::betree::Node::{5}::filter_messages_for_key] -/
-divergent def betree.Node.filter_messages_for_key_fwd_back
+/- [betree_main::betree::Node::{5}::filter_messages_for_key]: merged forward/backward function
+   (there is a single backward function, and the forward function returns ()) -/
+divergent def betree.Node.filter_messages_for_key
   (key : U64) (msgs : betree.List (U64 × betree.Message)) :
   Result (betree.List (U64 × betree.Message))
   :=
@@ -602,12 +602,12 @@ divergent def betree.Node.filter_messages_for_key_fwd_back
         let msgs0 ←
           betree.List.pop_front_back (U64 × betree.Message) (betree.List.Cons
             (k, m) l)
-        betree.Node.filter_messages_for_key_fwd_back key msgs0
+        betree.Node.filter_messages_for_key key msgs0
     else Result.ret (betree.List.Cons (k, m) l)
   | betree.List.Nil => Result.ret betree.List.Nil
 
-/- [betree_main::betree::Node::{5}::lookup_first_message_after_key] -/
-divergent def betree.Node.lookup_first_message_after_key_fwd
+/- [betree_main::betree::Node::{5}::lookup_first_message_after_key]: forward function -/
+divergent def betree.Node.lookup_first_message_after_key
   (key : U64) (msgs : betree.List (U64 × betree.Message)) :
   Result (betree.List (U64 × betree.Message))
   :=
@@ -615,11 +615,11 @@ divergent def betree.Node.lookup_first_message_after_key_fwd
   | betree.List.Cons p next_msgs =>
     let (k, m) := p
     if k = key
-    then betree.Node.lookup_first_message_after_key_fwd key next_msgs
+    then betree.Node.lookup_first_message_after_key key next_msgs
     else Result.ret (betree.List.Cons (k, m) next_msgs)
   | betree.List.Nil => Result.ret betree.List.Nil
 
-/- [betree_main::betree::Node::{5}::lookup_first_message_after_key] -/
+/- [betree_main::betree::Node::{5}::lookup_first_message_after_key]: backward function 0 -/
 divergent def betree.Node.lookup_first_message_after_key_back
   (key : U64) (msgs : betree.List (U64 × betree.Message))
   (ret0 : betree.List (U64 × betree.Message)) :
@@ -637,74 +637,75 @@ divergent def betree.Node.lookup_first_message_after_key_back
     else Result.ret ret0
   | betree.List.Nil => Result.ret ret0
 
-/- [betree_main::betree::Node::{5}::apply_to_internal] -/
-def betree.Node.apply_to_internal_fwd_back
+/- [betree_main::betree::Node::{5}::apply_to_internal]: merged forward/backward function
+   (there is a single backward function, and the forward function returns ()) -/
+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 msgs0 ← betree.Node.lookup_first_message_for_key_fwd key msgs
-    let b ← betree.List.head_has_key_fwd betree.Message msgs0 key
+    let msgs0 ← betree.Node.lookup_first_message_for_key key msgs
+    let b ← betree.List.head_has_key betree.Message msgs0 key
     if b
     then
       match new_msg with
       | betree.Message.Insert i =>
         do
-          let msgs1 ← betree.Node.filter_messages_for_key_fwd_back key msgs0
+          let msgs1 ← betree.Node.filter_messages_for_key key msgs0
           let msgs2 ←
-            betree.List.push_front_fwd_back (U64 × betree.Message) msgs1 (key,
+            betree.List.push_front (U64 × betree.Message) msgs1 (key,
               betree.Message.Insert i)
           betree.Node.lookup_first_message_for_key_back key msgs msgs2
       | betree.Message.Delete =>
         do
-          let msgs1 ← betree.Node.filter_messages_for_key_fwd_back key msgs0
+          let msgs1 ← betree.Node.filter_messages_for_key key msgs0
           let msgs2 ←
-            betree.List.push_front_fwd_back (U64 × betree.Message) msgs1 (key,
+            betree.List.push_front (U64 × betree.Message) msgs1 (key,
               betree.Message.Delete)
           betree.Node.lookup_first_message_for_key_back key msgs msgs2
       | betree.Message.Upsert s =>
         do
-          let p ← betree.List.hd_fwd (U64 × betree.Message) msgs0
+          let p ← betree.List.hd (U64 × betree.Message) msgs0
           let (_, m) := p
           match m with
           | betree.Message.Insert prev =>
             do
-              let v ← betree.upsert_update_fwd (Option.some prev) s
+              let v ← betree.upsert_update (Option.some prev) s
               let msgs1 ←
                 betree.List.pop_front_back (U64 × betree.Message) msgs0
               let msgs2 ←
-                betree.List.push_front_fwd_back (U64 × betree.Message) msgs1
-                  (key, betree.Message.Insert v)
+                betree.List.push_front (U64 × betree.Message) msgs1 (key,
+                  betree.Message.Insert v)
               betree.Node.lookup_first_message_for_key_back key msgs msgs2
           | betree.Message.Delete =>
             do
-              let v ← betree.upsert_update_fwd Option.none s
+              let v ← betree.upsert_update Option.none s
               let msgs1 ←
                 betree.List.pop_front_back (U64 × betree.Message) msgs0
               let msgs2 ←
-                betree.List.push_front_fwd_back (U64 × betree.Message) msgs1
-                  (key, betree.Message.Insert v)
+                betree.List.push_front (U64 × betree.Message) msgs1 (key,
+                  betree.Message.Insert v)
               betree.Node.lookup_first_message_for_key_back key msgs msgs2
           | betree.Message.Upsert ufs =>
             do
               let msgs1 ←
-                betree.Node.lookup_first_message_after_key_fwd key msgs0
+                betree.Node.lookup_first_message_after_key key msgs0
               let msgs2 ←
-                betree.List.push_front_fwd_back (U64 × betree.Message) msgs1
-                  (key, betree.Message.Upsert s)
+                betree.List.push_front (U64 × betree.Message) msgs1 (key,
+                  betree.Message.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) msgs0 (key,
-            new_msg)
+          betree.List.push_front (U64 × betree.Message) 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
+/- [betree_main::betree::Node::{5}::apply_messages_to_internal]: merged forward/backward function
+   (there is a single backward function, and the forward function returns ()) -/
+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))
@@ -713,12 +714,12 @@ divergent def betree.Node.apply_messages_to_internal_fwd_back
   | betree.List.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
+      let msgs0 ← betree.Node.apply_to_internal msgs i m
+      betree.Node.apply_messages_to_internal msgs0 new_msgs_tl
   | betree.List.Nil => Result.ret msgs
 
-/- [betree_main::betree::Node::{5}::apply_messages] -/
-mutual divergent def betree.Node.apply_messages_fwd
+/- [betree_main::betree::Node::{5}::apply_messages]: forward function -/
+mutual 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) :
@@ -728,47 +729,46 @@ mutual divergent def betree.Node.apply_messages_fwd
   | betree.Node.Internal node =>
     do
       let ⟨ 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) content0
+      let (st0, content) ← betree.load_internal_node i st
+      let content0 ← betree.Node.apply_messages_to_internal content msgs
+      let num_msgs ← betree.List.len (U64 × betree.Message) content0
       if num_msgs >= params.betree_params_min_flush_size
       then
         do
           let (st1, content1) ←
-            betree.Internal.flush_fwd (betree.Internal.mk i i0 n n0) params
+            betree.Internal.flush (betree.Internal.mk i i0 n n0) params
               node_id_cnt content0 st0
           let (node0, _) ←
             betree.Internal.flush_back (betree.Internal.mk i i0 n n0) params
               node_id_cnt content0 st0
           let ⟨ i1, _, _, _ ⟩ := node0
-          let (st2, _) ← betree.store_internal_node_fwd i1 content1 st1
+          let (st2, _) ← betree.store_internal_node i1 content1 st1
           Result.ret (st2, ())
       else
         do
-          let (st1, _) ← betree.store_internal_node_fwd i content0 st0
+          let (st1, _) ← betree.store_internal_node i content0 st0
           Result.ret (st1, ())
   | betree.Node.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 (st0, content) ← betree.load_leaf_node node.betree_leaf_id st
+      let content0 ← betree.Node.apply_messages_to_leaf content msgs
+      let len ← betree.List.len (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
+            betree.Leaf.split node content0 params node_id_cnt st0
           let (st2, _) ←
-            betree.store_leaf_node_fwd node.betree_leaf_id betree.List.Nil st1
+            betree.store_leaf_node node.betree_leaf_id betree.List.Nil st1
           Result.ret (st2, ())
       else
         do
           let (st1, _) ←
-            betree.store_leaf_node_fwd node.betree_leaf_id content0 st0
+            betree.store_leaf_node node.betree_leaf_id content0 st0
           Result.ret (st1, ())
 
-/- [betree_main::betree::Node::{5}::apply_messages] -/
+/- [betree_main::betree::Node::{5}::apply_messages]: backward function 0 -/
 divergent def betree.Node.apply_messages_back
   (self : betree.Node) (params : betree.Params)
   (node_id_cnt : betree.NodeIdCounter)
@@ -779,52 +779,51 @@ divergent def betree.Node.apply_messages_back
   | betree.Node.Internal node =>
     do
       let ⟨ 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) content0
+      let (st0, content) ← betree.load_internal_node i st
+      let content0 ← betree.Node.apply_messages_to_internal content msgs
+      let num_msgs ← betree.List.len (U64 × betree.Message) content0
       if num_msgs >= params.betree_params_min_flush_size
       then
         do
           let (st1, content1) ←
-            betree.Internal.flush_fwd (betree.Internal.mk i i0 n n0) params
+            betree.Internal.flush (betree.Internal.mk i i0 n n0) params
               node_id_cnt content0 st0
           let (node0, node_id_cnt0) ←
             betree.Internal.flush_back (betree.Internal.mk i i0 n n0) params
               node_id_cnt content0 st0
           let ⟨ i1, i2, n1, n2 ⟩ := node0
-          let _ ← betree.store_internal_node_fwd i1 content1 st1
+          let _ ← betree.store_internal_node i1 content1 st1
           Result.ret (betree.Node.Internal (betree.Internal.mk i1 i2 n1 n2),
             node_id_cnt0)
       else
         do
-          let _ ← betree.store_internal_node_fwd i content0 st0
+          let _ ← betree.store_internal_node i content0 st0
           Result.ret (betree.Node.Internal (betree.Internal.mk i i0 n n0),
             node_id_cnt)
   | betree.Node.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 (st0, content) ← betree.load_leaf_node node.betree_leaf_id st
+      let content0 ← betree.Node.apply_messages_to_leaf content msgs
+      let len ← betree.List.len (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
+            betree.Leaf.split node content0 params node_id_cnt st0
           let _ ←
-            betree.store_leaf_node_fwd node.betree_leaf_id betree.List.Nil st1
+            betree.store_leaf_node node.betree_leaf_id betree.List.Nil st1
           let node_id_cnt0 ←
             betree.Leaf.split_back node content0 params node_id_cnt st0
           Result.ret (betree.Node.Internal new_node, node_id_cnt0)
       else
         do
-          let _ ← betree.store_leaf_node_fwd node.betree_leaf_id content0 st0
+          let _ ← betree.store_leaf_node node.betree_leaf_id content0 st0
           Result.ret (betree.Node.Leaf { node with betree_leaf_size := len },
             node_id_cnt)
 
-/- [betree_main::betree::Internal::{4}::flush] -/
-divergent def betree.Internal.flush_fwd
+/- [betree_main::betree::Internal::{4}::flush]: forward function -/
+divergent def betree.Internal.flush
   (self : betree.Internal) (params : betree.Params)
   (node_id_cnt : betree.NodeIdCounter)
   (content : betree.List (U64 × betree.Message)) (st : State) :
@@ -832,24 +831,22 @@ divergent def betree.Internal.flush_fwd
   :=
   do
     let ⟨ _, i, n, n0 ⟩ := self
-    let p ← betree.List.partition_at_pivot_fwd betree.Message content i
+    let p ← betree.List.partition_at_pivot betree.Message content i
     let (msgs_left, msgs_right) := p
-    let len_left ← betree.List.len_fwd (U64 × betree.Message) msgs_left
+    let len_left ← betree.List.len (U64 × betree.Message) 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
+          betree.Node.apply_messages 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) msgs_right
+        let len_right ← betree.List.len (U64 × betree.Message) 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
+              betree.Node.apply_messages n0 params node_id_cnt0 msgs_right st0
             let _ ←
               betree.Node.apply_messages_back n0 params node_id_cnt0 msgs_right
                 st0
@@ -858,12 +855,12 @@ divergent def betree.Internal.flush_fwd
     else
       do
         let (st0, _) ←
-          betree.Node.apply_messages_fwd n0 params node_id_cnt msgs_right st
+          betree.Node.apply_messages 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] -/
+/- [betree_main::betree::Internal::{4}::flush]: backward function 0 -/
 divergent def betree.Internal.flush_back
   (self : betree.Internal) (params : betree.Params)
   (node_id_cnt : betree.NodeIdCounter)
@@ -872,18 +869,17 @@ divergent def betree.Internal.flush_back
   :=
   do
     let ⟨ i, i0, n, n0 ⟩ := self
-    let p ← betree.List.partition_at_pivot_fwd betree.Message content i0
+    let p ← betree.List.partition_at_pivot betree.Message content i0
     let (msgs_left, msgs_right) := p
-    let len_left ← betree.List.len_fwd (U64 × betree.Message) msgs_left
+    let len_left ← betree.List.len (U64 × betree.Message) 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
+          betree.Node.apply_messages 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) msgs_right
+        let len_right ← betree.List.len (U64 × betree.Message) msgs_right
         if len_right >= params.betree_params_min_flush_size
         then
           do
@@ -900,8 +896,8 @@ divergent def betree.Internal.flush_back
 
 end
 
-/- [betree_main::betree::Node::{5}::apply] -/
-def betree.Node.apply_fwd
+/- [betree_main::betree::Node::{5}::apply]: forward function -/
+def betree.Node.apply
   (self : betree.Node) (params : betree.Params)
   (node_id_cnt : betree.NodeIdCounter) (key : U64) (new_msg : betree.Message)
   (st : State) :
@@ -910,14 +906,14 @@ def betree.Node.apply_fwd
   do
     let l := betree.List.Nil
     let (st0, _) ←
-      betree.Node.apply_messages_fwd self params node_id_cnt (betree.List.Cons
+      betree.Node.apply_messages self params node_id_cnt (betree.List.Cons
         (key, new_msg) l) st
     let _ ←
       betree.Node.apply_messages_back self params node_id_cnt (betree.List.Cons
         (key, new_msg) l) st
     Result.ret (st0, ())
 
-/- [betree_main::betree::Node::{5}::apply] -/
+/- [betree_main::betree::Node::{5}::apply]: backward function 0 -/
 def betree.Node.apply_back
   (self : betree.Node) (params : betree.Params)
   (node_id_cnt : betree.NodeIdCounter) (key : U64) (new_msg : betree.Message)
@@ -928,15 +924,15 @@ def betree.Node.apply_back
   betree.Node.apply_messages_back self params node_id_cnt (betree.List.Cons
     (key, new_msg) l) st
 
-/- [betree_main::betree::BeTree::{6}::new] -/
-def betree.BeTree.new_fwd
+/- [betree_main::betree::BeTree::{6}::new]: forward function -/
+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_fwd
-    let id ← betree.NodeIdCounter.fresh_id_fwd node_id_cnt
-    let (st0, _) ← betree.store_leaf_node_fwd id betree.List.Nil st
+    let node_id_cnt ← betree.NodeIdCounter.new
+    let id ← betree.NodeIdCounter.fresh_id node_id_cnt
+    let (st0, _) ← betree.store_leaf_node id betree.List.Nil st
     let node_id_cnt0 ← betree.NodeIdCounter.fresh_id_back node_id_cnt
     Result.ret (st0,
       {
@@ -954,21 +950,21 @@ def betree.BeTree.new_fwd
             })
       })
 
-/- [betree_main::betree::BeTree::{6}::apply] -/
-def betree.BeTree.apply_fwd
+/- [betree_main::betree::BeTree::{6}::apply]: forward function -/
+def betree.BeTree.apply
   (self : betree.BeTree) (key : U64) (msg : betree.Message) (st : State) :
   Result (State × Unit)
   :=
   do
     let (st0, _) ←
-      betree.Node.apply_fwd self.betree_be_tree_root self.betree_be_tree_params
+      betree.Node.apply 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] -/
+/- [betree_main::betree::BeTree::{6}::apply]: backward function 0 -/
 def betree.BeTree.apply_back
   (self : betree.BeTree) (key : U64) (msg : betree.Message) (st : State) :
   Result betree.BeTree
@@ -980,51 +976,51 @@ def betree.BeTree.apply_back
     Result.ret
       { self with betree_be_tree_node_id_cnt := nic, betree_be_tree_root := n }
 
-/- [betree_main::betree::BeTree::{6}::insert] -/
-def betree.BeTree.insert_fwd
+/- [betree_main::betree::BeTree::{6}::insert]: forward function -/
+def betree.BeTree.insert
   (self : betree.BeTree) (key : U64) (value : U64) (st : State) :
   Result (State × Unit)
   :=
   do
     let (st0, _) ←
-      betree.BeTree.apply_fwd self key (betree.Message.Insert value) st
+      betree.BeTree.apply self key (betree.Message.Insert value) st
     let _ ←
       betree.BeTree.apply_back self key (betree.Message.Insert value) st
     Result.ret (st0, ())
 
-/- [betree_main::betree::BeTree::{6}::insert] -/
+/- [betree_main::betree::BeTree::{6}::insert]: backward function 0 -/
 def betree.BeTree.insert_back
   (self : betree.BeTree) (key : U64) (value : U64) (st : State) :
   Result betree.BeTree
   :=
   betree.BeTree.apply_back self key (betree.Message.Insert value) st
 
-/- [betree_main::betree::BeTree::{6}::delete] -/
-def betree.BeTree.delete_fwd
+/- [betree_main::betree::BeTree::{6}::delete]: forward function -/
+def betree.BeTree.delete
   (self : betree.BeTree) (key : U64) (st : State) : Result (State × Unit) :=
   do
-    let (st0, _) ← betree.BeTree.apply_fwd self key betree.Message.Delete st
+    let (st0, _) ← betree.BeTree.apply self key betree.Message.Delete st
     let _ ← betree.BeTree.apply_back self key betree.Message.Delete st
     Result.ret (st0, ())
 
-/- [betree_main::betree::BeTree::{6}::delete] -/
+/- [betree_main::betree::BeTree::{6}::delete]: backward function 0 -/
 def betree.BeTree.delete_back
   (self : betree.BeTree) (key : U64) (st : State) : Result betree.BeTree :=
   betree.BeTree.apply_back self key betree.Message.Delete st
 
-/- [betree_main::betree::BeTree::{6}::upsert] -/
-def betree.BeTree.upsert_fwd
+/- [betree_main::betree::BeTree::{6}::upsert]: forward function -/
+def betree.BeTree.upsert
   (self : betree.BeTree) (key : U64) (upd : betree.UpsertFunState) (st : State)
   :
   Result (State × Unit)
   :=
   do
     let (st0, _) ←
-      betree.BeTree.apply_fwd self key (betree.Message.Upsert upd) st
+      betree.BeTree.apply self key (betree.Message.Upsert upd) st
     let _ ← betree.BeTree.apply_back self key (betree.Message.Upsert upd) st
     Result.ret (st0, ())
 
-/- [betree_main::betree::BeTree::{6}::upsert] -/
+/- [betree_main::betree::BeTree::{6}::upsert]: backward function 0 -/
 def betree.BeTree.upsert_back
   (self : betree.BeTree) (key : U64) (upd : betree.UpsertFunState) (st : State)
   :
@@ -1032,25 +1028,25 @@ def betree.BeTree.upsert_back
   :=
   betree.BeTree.apply_back self key (betree.Message.Upsert upd) st
 
-/- [betree_main::betree::BeTree::{6}::lookup] -/
-def betree.BeTree.lookup_fwd
+/- [betree_main::betree::BeTree::{6}::lookup]: forward function -/
+def betree.BeTree.lookup
   (self : betree.BeTree) (key : U64) (st : State) :
   Result (State × (Option U64))
   :=
-  betree.Node.lookup_fwd self.betree_be_tree_root key st
+  betree.Node.lookup self.betree_be_tree_root key st
 
-/- [betree_main::betree::BeTree::{6}::lookup] -/
+/- [betree_main::betree::BeTree::{6}::lookup]: backward function 0 -/
 def betree.BeTree.lookup_back
   (self : betree.BeTree) (key : U64) (st : State) : Result betree.BeTree :=
   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 :=
+/- [betree_main::main]: forward function -/
+def main : Result Unit :=
   Result.ret ()
 
 /- Unit test for [betree_main::main] -/
-#assert (main_fwd == .ret ())
+#assert (main == .ret ())
 
 end betree_main
diff --git a/tests/lean/BetreeMain/FunsExternal.lean b/tests/lean/BetreeMain/FunsExternal.lean
index 7bcba380..71d26da4 100644
--- a/tests/lean/BetreeMain/FunsExternal.lean
+++ b/tests/lean/BetreeMain/FunsExternal.lean
@@ -7,29 +7,29 @@ open betree_main
 -- TODO: fill those bodies
 
 /- [betree_main::betree_utils::load_internal_node] -/
-def betree_utils.load_internal_node_fwd
+def betree_utils.load_internal_node
   :
   U64 → State → Result (State × (betree.List (U64 × betree.Message))) :=
   fun _ _ => .fail .panic
 
 /- [betree_main::betree_utils::store_internal_node] -/
-def betree_utils.store_internal_node_fwd
+def betree_utils.store_internal_node
   :
   U64 → betree.List (U64 × betree.Message) → State → Result (State
     × Unit) :=
   fun _ _ _ => .fail .panic
 
 /- [betree_main::betree_utils::load_leaf_node] -/
-def betree_utils.load_leaf_node_fwd
+def betree_utils.load_leaf_node
   : U64 → State → Result (State × (betree.List (U64 × U64))) :=
   fun _ _ => .fail .panic
 
 /- [betree_main::betree_utils::store_leaf_node] -/
-def betree_utils.store_leaf_node_fwd
+def betree_utils.store_leaf_node
   : U64 → betree.List (U64 × U64) → State → Result (State × Unit) :=
   fun _ _ _ => .fail .panic
 
 /- [core::option::Option::{0}::unwrap] -/
-def core.option.Option.unwrap_fwd
+def core.option.Option.unwrap
   (T : Type) : Option T → State → Result (State × T) :=
   fun _ _ => .fail .panic
diff --git a/tests/lean/BetreeMain/FunsExternal_Template.lean b/tests/lean/BetreeMain/FunsExternal_Template.lean
index d768bb20..430d2dda 100644
--- a/tests/lean/BetreeMain/FunsExternal_Template.lean
+++ b/tests/lean/BetreeMain/FunsExternal_Template.lean
@@ -6,25 +6,25 @@ import BetreeMain.Types
 open Primitives
 open betree_main
 
-/- [betree_main::betree_utils::load_internal_node] -/
-axiom betree_utils.load_internal_node_fwd
+/- [betree_main::betree_utils::load_internal_node]: forward function -/
+axiom betree_utils.load_internal_node
   : U64 → State → Result (State × (betree.List (U64 × betree.Message)))
 
-/- [betree_main::betree_utils::store_internal_node] -/
-axiom betree_utils.store_internal_node_fwd
+/- [betree_main::betree_utils::store_internal_node]: forward function -/
+axiom betree_utils.store_internal_node
   :
   U64 → betree.List (U64 × betree.Message) → State → Result (State ×
     Unit)
 
-/- [betree_main::betree_utils::load_leaf_node] -/
-axiom betree_utils.load_leaf_node_fwd
+/- [betree_main::betree_utils::load_leaf_node]: forward function -/
+axiom betree_utils.load_leaf_node
   : U64 → State → Result (State × (betree.List (U64 × U64)))
 
-/- [betree_main::betree_utils::store_leaf_node] -/
-axiom betree_utils.store_leaf_node_fwd
+/- [betree_main::betree_utils::store_leaf_node]: forward function -/
+axiom betree_utils.store_leaf_node
   : U64 → betree.List (U64 × U64) → State → Result (State × Unit)
 
-/- [core::option::Option::{0}::unwrap] -/
-axiom core.option.Option.unwrap_fwd
+/- [core::option::Option::{0}::unwrap]: forward function -/
+axiom core.option.Option.unwrap
   (T : Type) : Option T → State → Result (State × T)
 
diff --git a/tests/lean/Constants.lean b/tests/lean/Constants.lean
index 7014b0d8..f37c9204 100644
--- a/tests/lean/Constants.lean
+++ b/tests/lean/Constants.lean
@@ -21,16 +21,16 @@ def x1_c : U32 := eval_global x1_body (by simp)
 def x2_body : Result U32 := Result.ret (U32.ofInt 3 (by intlit))
 def x2_c : U32 := eval_global x2_body (by simp)
 
-/- [constants::incr] -/
-def incr_fwd (n : U32) : Result U32 :=
+/- [constants::incr]: forward function -/
+def incr (n : U32) : Result U32 :=
   n + (U32.ofInt 1 (by intlit))
 
 /- [constants::X3] -/
-def x3_body : Result U32 := incr_fwd (U32.ofInt 32 (by intlit))
+def x3_body : Result U32 := incr (U32.ofInt 32 (by intlit))
 def x3_c : U32 := eval_global x3_body (by simp)
 
-/- [constants::mk_pair0] -/
-def mk_pair0_fwd (x : U32) (y : U32) : Result (U32 × U32) :=
+/- [constants::mk_pair0]: forward function -/
+def mk_pair0 (x : U32) (y : U32) : Result (U32 × U32) :=
   Result.ret (x, y)
 
 /- [constants::Pair] -/
@@ -38,18 +38,18 @@ structure Pair (T1 T2 : Type) where
   pair_x : T1
   pair_y : T2
 
-/- [constants::mk_pair1] -/
-def mk_pair1_fwd (x : U32) (y : U32) : Result (Pair U32 U32) :=
+/- [constants::mk_pair1]: forward function -/
+def mk_pair1 (x : U32) (y : U32) : Result (Pair U32 U32) :=
   Result.ret { pair_x := x, pair_y := y }
 
 /- [constants::P0] -/
 def p0_body : Result (U32 × U32) :=
-  mk_pair0_fwd (U32.ofInt 0 (by intlit)) (U32.ofInt 1 (by intlit))
+  mk_pair0 (U32.ofInt 0 (by intlit)) (U32.ofInt 1 (by intlit))
 def p0_c : (U32 × U32) := eval_global p0_body (by simp)
 
 /- [constants::P1] -/
 def p1_body : Result (Pair U32 U32) :=
-  mk_pair1_fwd (U32.ofInt 0 (by intlit)) (U32.ofInt 1 (by intlit))
+  mk_pair1 (U32.ofInt 0 (by intlit)) (U32.ofInt 1 (by intlit))
 def p1_c : Pair U32 U32 := eval_global p1_body (by simp)
 
 /- [constants::P2] -/
@@ -67,32 +67,32 @@ def p3_c : Pair U32 U32 := eval_global p3_body (by simp)
 structure Wrap (T : Type) where
   wrap_val : T
 
-/- [constants::Wrap::{0}::new] -/
-def Wrap.new_fwd (T : Type) (val : T) : Result (Wrap T) :=
+/- [constants::Wrap::{0}::new]: forward function -/
+def Wrap.new (T : Type) (val : T) : Result (Wrap T) :=
   Result.ret { wrap_val := val }
 
 /- [constants::Y] -/
-def y_body : Result (Wrap I32) := Wrap.new_fwd I32 (I32.ofInt 2 (by intlit))
+def y_body : Result (Wrap I32) := Wrap.new I32 (I32.ofInt 2 (by intlit))
 def y_c : Wrap I32 := eval_global y_body (by simp)
 
-/- [constants::unwrap_y] -/
-def unwrap_y_fwd : Result I32 :=
+/- [constants::unwrap_y]: forward function -/
+def unwrap_y : Result I32 :=
   Result.ret y_c.wrap_val
 
 /- [constants::YVAL] -/
-def yval_body : Result I32 := unwrap_y_fwd
+def yval_body : Result I32 := unwrap_y
 def yval_c : I32 := eval_global yval_body (by simp)
 
 /- [constants::get_z1::Z1] -/
 def get_z1_z1_body : Result I32 := Result.ret (I32.ofInt 3 (by intlit))
 def get_z1_z1_c : I32 := eval_global get_z1_z1_body (by simp)
 
-/- [constants::get_z1] -/
-def get_z1_fwd : Result I32 :=
+/- [constants::get_z1]: forward function -/
+def get_z1 : Result I32 :=
   Result.ret get_z1_z1_c
 
-/- [constants::add] -/
-def add_fwd (a : I32) (b : I32) : Result I32 :=
+/- [constants::add]: forward function -/
+def add (a : I32) (b : I32) : Result I32 :=
   a + b
 
 /- [constants::Q1] -/
@@ -104,22 +104,22 @@ def q2_body : Result I32 := Result.ret q1_c
 def q2_c : I32 := eval_global q2_body (by simp)
 
 /- [constants::Q3] -/
-def q3_body : Result I32 := add_fwd q2_c (I32.ofInt 3 (by intlit))
+def q3_body : Result I32 := add q2_c (I32.ofInt 3 (by intlit))
 def q3_c : I32 := eval_global q3_body (by simp)
 
-/- [constants::get_z2] -/
-def get_z2_fwd : Result I32 :=
+/- [constants::get_z2]: forward function -/
+def get_z2 : Result I32 :=
   do
-    let i ← get_z1_fwd
-    let i0 ← add_fwd i q3_c
-    add_fwd q1_c i0
+    let i ← get_z1
+    let i0 ← add i q3_c
+    add q1_c i0
 
 /- [constants::S1] -/
 def s1_body : Result U32 := Result.ret (U32.ofInt 6 (by intlit))
 def s1_c : U32 := eval_global s1_body (by simp)
 
 /- [constants::S2] -/
-def s2_body : Result U32 := incr_fwd s1_c
+def s2_body : Result U32 := incr s1_c
 def s2_c : U32 := eval_global s2_body (by simp)
 
 /- [constants::S3] -/
@@ -128,7 +128,7 @@ def s3_c : Pair U32 U32 := eval_global s3_body (by simp)
 
 /- [constants::S4] -/
 def s4_body : Result (Pair U32 U32) :=
-  mk_pair1_fwd (U32.ofInt 7 (by intlit)) (U32.ofInt 8 (by intlit))
+  mk_pair1 (U32.ofInt 7 (by intlit)) (U32.ofInt 8 (by intlit))
 def s4_c : Pair U32 U32 := eval_global s4_body (by simp)
 
 end constants
diff --git a/tests/lean/External/Funs.lean b/tests/lean/External/Funs.lean
index 3fc21d91..122f94da 100644
--- a/tests/lean/External/Funs.lean
+++ b/tests/lean/External/Funs.lean
@@ -6,81 +6,80 @@ import External.FunsExternal
 open Primitives
 namespace external
 
-/- [external::swap] -/
-def swap_fwd
-  (T : Type) (x : T) (y : T) (st : State) : Result (State × Unit) :=
+/- [external::swap]: forward function -/
+def swap (T : Type) (x : T) (y : T) (st : State) : Result (State × Unit) :=
   do
-    let (st0, _) ← core.mem.swap_fwd T x y st
+    let (st0, _) ← core.mem.swap T x y st
     let (st1, _) ← core.mem.swap_back0 T x y st st0
     let (st2, _) ← core.mem.swap_back1 T x y st st1
     Result.ret (st2, ())
 
-/- [external::swap] -/
+/- [external::swap]: backward function 0 -/
 def swap_back
   (T : Type) (x : T) (y : T) (st : State) (st0 : State) :
   Result (State × (T × T))
   :=
   do
-    let (st1, _) ← core.mem.swap_fwd T x y st
+    let (st1, _) ← core.mem.swap T x y st
     let (st2, x0) ← core.mem.swap_back0 T x y st st1
     let (_, y0) ← core.mem.swap_back1 T x y st st2
     Result.ret (st0, (x0, y0))
 
-/- [external::test_new_non_zero_u32] -/
-def test_new_non_zero_u32_fwd
+/- [external::test_new_non_zero_u32]: forward function -/
+def test_new_non_zero_u32
   (x : U32) (st : State) : Result (State × core.num.nonzero.NonZeroU32) :=
   do
-    let (st0, opt) ← core.num.nonzero.NonZeroU32.new_fwd x st
-    core.option.Option.unwrap_fwd core.num.nonzero.NonZeroU32 opt st0
+    let (st0, opt) ← core.num.nonzero.NonZeroU32.new x st
+    core.option.Option.unwrap core.num.nonzero.NonZeroU32 opt st0
 
-/- [external::test_vec] -/
-def test_vec_fwd : Result Unit :=
+/- [external::test_vec]: forward function -/
+def test_vec : Result Unit :=
   do
     let v := Vec.new U32
     let _ ← Vec.push U32 v (U32.ofInt 0 (by intlit))
     Result.ret ()
 
 /- Unit test for [external::test_vec] -/
-#assert (test_vec_fwd == .ret ())
+#assert (test_vec == .ret ())
 
-/- [external::custom_swap] -/
-def custom_swap_fwd
+/- [external::custom_swap]: forward function -/
+def custom_swap
   (T : Type) (x : T) (y : T) (st : State) : Result (State × T) :=
   do
-    let (st0, _) ← core.mem.swap_fwd T x y st
+    let (st0, _) ← core.mem.swap T x y st
     let (st1, x0) ← core.mem.swap_back0 T x y st st0
     let (st2, _) ← core.mem.swap_back1 T x y st st1
     Result.ret (st2, x0)
 
-/- [external::custom_swap] -/
+/- [external::custom_swap]: backward function 0 -/
 def custom_swap_back
   (T : Type) (x : T) (y : T) (st : State) (ret0 : T) (st0 : State) :
   Result (State × (T × T))
   :=
   do
-    let (st1, _) ← core.mem.swap_fwd T x y st
+    let (st1, _) ← core.mem.swap T x y st
     let (st2, _) ← core.mem.swap_back0 T x y st st1
     let (_, y0) ← core.mem.swap_back1 T x y st st2
     Result.ret (st0, (ret0, y0))
 
-/- [external::test_custom_swap] -/
-def test_custom_swap_fwd
+/- [external::test_custom_swap]: forward function -/
+def test_custom_swap
   (x : U32) (y : U32) (st : State) : Result (State × Unit) :=
   do
-    let (st0, _) ← custom_swap_fwd U32 x y st
+    let (st0, _) ← custom_swap U32 x y st
     Result.ret (st0, ())
 
-/- [external::test_custom_swap] -/
+/- [external::test_custom_swap]: backward function 0 -/
 def test_custom_swap_back
   (x : U32) (y : U32) (st : State) (st0 : State) :
   Result (State × (U32 × U32))
   :=
   custom_swap_back U32 x y st (U32.ofInt 1 (by intlit)) st0
 
-/- [external::test_swap_non_zero] -/
-def test_swap_non_zero_fwd (x : U32) (st : State) : Result (State × U32) :=
+/- [external::test_swap_non_zero]: forward function -/
+def test_swap_non_zero (x : U32) (st : State) : Result (State × U32) :=
   do
-    let (st0, _) ← swap_fwd U32 x (U32.ofInt 0 (by intlit)) st
+    let (st0, _) ← swap U32 x (U32.ofInt 0 (by intlit)) st
     let (st1, (x0, _)) ← swap_back U32 x (U32.ofInt 0 (by intlit)) st st0
     if x0 = (U32.ofInt 0 (by intlit))
     then Result.fail Error.panic
diff --git a/tests/lean/External/FunsExternal.lean b/tests/lean/External/FunsExternal.lean
index 5326dd77..aae11ba1 100644
--- a/tests/lean/External/FunsExternal.lean
+++ b/tests/lean/External/FunsExternal.lean
@@ -7,7 +7,7 @@ open external
 -- TODO: fill those bodies
 
 /- [core::mem::swap] -/
-def core.mem.swap_fwd
+def core.mem.swap
   (T : Type) : T → T → State → Result (State × Unit) :=
   fun _x _y s => .ret (s, ())
 
@@ -22,12 +22,12 @@ def core.mem.swap_back1
   fun x _y _s0 s1 => .ret (s1, x)
 
 /- [core::num::nonzero::NonZeroU32::{14}::new] -/
-def core.num.nonzero.NonZeroU32.new_fwd
+def core.num.nonzero.NonZeroU32.new
   :
   U32 → State → Result (State × (Option core_num_nonzero_non_zero_u32_t)) :=
   fun _ _ => .fail .panic
 
 /- [core::option::Option::{0}::unwrap] -/
-def core.option.Option.unwrap_fwd
+def core.option.Option.unwrap
   (T : Type) : Option T → State → Result (State × T) :=
   fun _ _ => .fail .panic
diff --git a/tests/lean/External/FunsExternal_Template.lean b/tests/lean/External/FunsExternal_Template.lean
index 669fe91b..c8bc397f 100644
--- a/tests/lean/External/FunsExternal_Template.lean
+++ b/tests/lean/External/FunsExternal_Template.lean
@@ -6,23 +6,22 @@ import External.Types
 open Primitives
 open external
 
-/- [core::mem::swap] -/
-axiom core.mem.swap_fwd
-  (T : Type) : T → T → State → Result (State × Unit)
+/- [core::mem::swap]: forward function -/
+axiom core.mem.swap (T : Type) : T → T → State → Result (State × Unit)
 
-/- [core::mem::swap] -/
+/- [core::mem::swap]: backward function 0 -/
 axiom core.mem.swap_back0
   (T : Type) : T → T → State → State → Result (State × T)
 
-/- [core::mem::swap] -/
+/- [core::mem::swap]: backward function 1 -/
 axiom core.mem.swap_back1
   (T : Type) : T → T → State → State → Result (State × T)
 
-/- [core::num::nonzero::NonZeroU32::{14}::new] -/
-axiom core.num.nonzero.NonZeroU32.new_fwd
+/- [core::num::nonzero::NonZeroU32::{14}::new]: forward function -/
+axiom core.num.nonzero.NonZeroU32.new
   : U32 → State → Result (State × (Option core.num.nonzero.NonZeroU32))
 
-/- [core::option::Option::{0}::unwrap] -/
-axiom core.option.Option.unwrap_fwd
+/- [core::option::Option::{0}::unwrap]: forward function -/
+axiom core.option.Option.unwrap
   (T : Type) : Option T → State → Result (State × T)
 
diff --git a/tests/lean/Hashmap/Funs.lean b/tests/lean/Hashmap/Funs.lean
index 48038bfb..34ff1379 100644
--- a/tests/lean/Hashmap/Funs.lean
+++ b/tests/lean/Hashmap/Funs.lean
@@ -5,35 +5,35 @@ import Hashmap.Types
 open Primitives
 namespace hashmap
 
-/- [hashmap::hash_key] -/
-def hash_key_fwd (k : Usize) : Result Usize :=
+/- [hashmap::hash_key]: forward function -/
+def hash_key (k : Usize) : Result Usize :=
   Result.ret k
 
-/- [hashmap::HashMap::{0}::allocate_slots] -/
-divergent def HashMap.allocate_slots_loop_fwd
+/- [hashmap::HashMap::{0}::allocate_slots]: loop 0: forward function -/
+divergent def HashMap.allocate_slots_loop
   (T : Type) (slots : Vec (List T)) (n : Usize) : Result (Vec (List T)) :=
   if n > (Usize.ofInt 0 (by intlit))
   then
     do
       let slots0 ← Vec.push (List T) slots List.Nil
       let n0 ← n - (Usize.ofInt 1 (by intlit))
-      HashMap.allocate_slots_loop_fwd T slots0 n0
+      HashMap.allocate_slots_loop T slots0 n0
   else Result.ret slots
 
-/- [hashmap::HashMap::{0}::allocate_slots] -/
-def HashMap.allocate_slots_fwd
+/- [hashmap::HashMap::{0}::allocate_slots]: forward function -/
+def HashMap.allocate_slots
   (T : Type) (slots : Vec (List T)) (n : Usize) : Result (Vec (List T)) :=
-  HashMap.allocate_slots_loop_fwd T slots n
+  HashMap.allocate_slots_loop T slots n
 
-/- [hashmap::HashMap::{0}::new_with_capacity] -/
-def HashMap.new_with_capacity_fwd
+/- [hashmap::HashMap::{0}::new_with_capacity]: forward function -/
+def HashMap.new_with_capacity
   (T : Type) (capacity : Usize) (max_load_dividend : Usize)
   (max_load_divisor : Usize) :
   Result (HashMap T)
   :=
   do
     let v := Vec.new (List T)
-    let slots ← HashMap.allocate_slots_fwd T v capacity
+    let slots ← HashMap.allocate_slots T v capacity
     let i ← capacity * max_load_dividend
     let i0 ← i / max_load_divisor
     Result.ret
@@ -44,13 +44,14 @@ def HashMap.new_with_capacity_fwd
         hash_map_slots := slots
       }
 
-/- [hashmap::HashMap::{0}::new] -/
-def HashMap.new_fwd (T : Type) : Result (HashMap T) :=
-  HashMap.new_with_capacity_fwd T (Usize.ofInt 32 (by intlit))
+/- [hashmap::HashMap::{0}::new]: forward function -/
+def HashMap.new (T : Type) : Result (HashMap T) :=
+  HashMap.new_with_capacity T (Usize.ofInt 32 (by intlit))
     (Usize.ofInt 4 (by intlit)) (Usize.ofInt 5 (by intlit))
 
-/- [hashmap::HashMap::{0}::clear] -/
-divergent def HashMap.clear_loop_fwd_back
+/- [hashmap::HashMap::{0}::clear]: loop 0: merged forward/backward function
+   (there is a single backward function, and the forward function returns ()) -/
+divergent def HashMap.clear_loop
   (T : Type) (slots : Vec (List T)) (i : Usize) : Result (Vec (List T)) :=
   let i0 := Vec.len (List T) slots
   if i < i0
@@ -58,16 +59,15 @@ divergent def HashMap.clear_loop_fwd_back
     do
       let i1 ← i + (Usize.ofInt 1 (by intlit))
       let slots0 ← Vec.index_mut_back (List T) slots i List.Nil
-      HashMap.clear_loop_fwd_back T slots0 i1
+      HashMap.clear_loop T slots0 i1
   else Result.ret slots
 
-/- [hashmap::HashMap::{0}::clear] -/
-def HashMap.clear_fwd_back
-  (T : Type) (self : HashMap T) : Result (HashMap T) :=
+/- [hashmap::HashMap::{0}::clear]: merged forward/backward function
+   (there is a single backward function, and the forward function returns ()) -/
+def HashMap.clear (T : Type) (self : HashMap T) : Result (HashMap T) :=
   do
     let v ←
-      HashMap.clear_loop_fwd_back T self.hash_map_slots
-        (Usize.ofInt 0 (by intlit))
+      HashMap.clear_loop T self.hash_map_slots (Usize.ofInt 0 (by intlit))
     Result.ret
       {
         self
@@ -76,26 +76,26 @@ def HashMap.clear_fwd_back
           hash_map_slots := v
       }
 
-/- [hashmap::HashMap::{0}::len] -/
-def HashMap.len_fwd (T : Type) (self : HashMap T) : Result Usize :=
+/- [hashmap::HashMap::{0}::len]: forward function -/
+def HashMap.len (T : Type) (self : HashMap T) : Result Usize :=
   Result.ret self.hash_map_num_entries
 
-/- [hashmap::HashMap::{0}::insert_in_list] -/
-divergent def HashMap.insert_in_list_loop_fwd
+/- [hashmap::HashMap::{0}::insert_in_list]: loop 0: forward function -/
+divergent def HashMap.insert_in_list_loop
   (T : Type) (key : Usize) (value : T) (ls : List T) : Result Bool :=
   match ls with
   | List.Cons ckey cvalue tl =>
     if ckey = key
     then Result.ret false
-    else HashMap.insert_in_list_loop_fwd T key value tl
+    else HashMap.insert_in_list_loop T key value tl
   | List.Nil => Result.ret true
 
-/- [hashmap::HashMap::{0}::insert_in_list] -/
-def HashMap.insert_in_list_fwd
+/- [hashmap::HashMap::{0}::insert_in_list]: forward function -/
+def HashMap.insert_in_list
   (T : Type) (key : Usize) (value : T) (ls : List T) : Result Bool :=
-  HashMap.insert_in_list_loop_fwd T key value ls
+  HashMap.insert_in_list_loop T key value ls
 
-/- [hashmap::HashMap::{0}::insert_in_list] -/
+/- [hashmap::HashMap::{0}::insert_in_list]: loop 0: backward function 0 -/
 divergent def HashMap.insert_in_list_loop_back
   (T : Type) (key : Usize) (value : T) (ls : List T) : Result (List T) :=
   match ls with
@@ -109,22 +109,23 @@ divergent def HashMap.insert_in_list_loop_back
   | List.Nil => let l := List.Nil
                 Result.ret (List.Cons key value l)
 
-/- [hashmap::HashMap::{0}::insert_in_list] -/
+/- [hashmap::HashMap::{0}::insert_in_list]: backward function 0 -/
 def HashMap.insert_in_list_back
   (T : Type) (key : Usize) (value : T) (ls : List T) : Result (List T) :=
   HashMap.insert_in_list_loop_back T key value ls
 
-/- [hashmap::HashMap::{0}::insert_no_resize] -/
-def HashMap.insert_no_resize_fwd_back
+/- [hashmap::HashMap::{0}::insert_no_resize]: merged forward/backward function
+   (there is a single backward function, and the forward function returns ()) -/
+def HashMap.insert_no_resize
   (T : Type) (self : HashMap T) (key : Usize) (value : T) :
   Result (HashMap T)
   :=
   do
-    let hash ← hash_key_fwd key
+    let hash ← hash_key key
     let i := Vec.len (List T) self.hash_map_slots
     let hash_mod ← hash % i
     let l ← Vec.index_mut (List T) self.hash_map_slots hash_mod
-    let inserted ← HashMap.insert_in_list_fwd T key value l
+    let inserted ← HashMap.insert_in_list T key value l
     if inserted
     then
       do
@@ -144,23 +145,26 @@ def core_num_u32_max_body : Result U32 :=
   Result.ret (U32.ofInt 4294967295 (by intlit))
 def core_num_u32_max_c : U32 := eval_global core_num_u32_max_body (by simp)
 
-/- [hashmap::HashMap::{0}::move_elements_from_list] -/
-divergent def HashMap.move_elements_from_list_loop_fwd_back
+/- [hashmap::HashMap::{0}::move_elements_from_list]: loop 0: merged forward/backward function
+   (there is a single backward function, and the forward function returns ()) -/
+divergent def HashMap.move_elements_from_list_loop
   (T : Type) (ntable : HashMap T) (ls : List T) : Result (HashMap T) :=
   match ls with
   | List.Cons k v tl =>
     do
-      let ntable0 ← HashMap.insert_no_resize_fwd_back T ntable k v
-      HashMap.move_elements_from_list_loop_fwd_back T ntable0 tl
+      let ntable0 ← HashMap.insert_no_resize T ntable k v
+      HashMap.move_elements_from_list_loop T ntable0 tl
   | List.Nil => Result.ret ntable
 
-/- [hashmap::HashMap::{0}::move_elements_from_list] -/
-def HashMap.move_elements_from_list_fwd_back
+/- [hashmap::HashMap::{0}::move_elements_from_list]: merged forward/backward function
+   (there is a single backward function, and the forward function returns ()) -/
+def HashMap.move_elements_from_list
   (T : Type) (ntable : HashMap T) (ls : List T) : Result (HashMap T) :=
-  HashMap.move_elements_from_list_loop_fwd_back T ntable ls
+  HashMap.move_elements_from_list_loop T ntable ls
 
-/- [hashmap::HashMap::{0}::move_elements] -/
-divergent def HashMap.move_elements_loop_fwd_back
+/- [hashmap::HashMap::{0}::move_elements]: loop 0: merged forward/backward function
+   (there is a single backward function, and the forward function returns ()) -/
+divergent def HashMap.move_elements_loop
   (T : Type) (ntable : HashMap T) (slots : Vec (List T)) (i : Usize) :
   Result ((HashMap T) × (Vec (List T)))
   :=
@@ -169,24 +173,25 @@ divergent def HashMap.move_elements_loop_fwd_back
   then
     do
       let l ← Vec.index_mut (List T) slots i
-      let ls := mem.replace_fwd (List T) l List.Nil
-      let ntable0 ← HashMap.move_elements_from_list_fwd_back T ntable ls
+      let ls := mem.replace (List T) l List.Nil
+      let ntable0 ← HashMap.move_elements_from_list T ntable ls
       let i1 ← i + (Usize.ofInt 1 (by intlit))
       let l0 := mem.replace_back (List T) l List.Nil
       let slots0 ← Vec.index_mut_back (List T) slots i l0
-      HashMap.move_elements_loop_fwd_back T ntable0 slots0 i1
+      HashMap.move_elements_loop T ntable0 slots0 i1
   else Result.ret (ntable, slots)
 
-/- [hashmap::HashMap::{0}::move_elements] -/
-def HashMap.move_elements_fwd_back
+/- [hashmap::HashMap::{0}::move_elements]: merged forward/backward function
+   (there is a single backward function, and the forward function returns ()) -/
+def HashMap.move_elements
   (T : Type) (ntable : HashMap T) (slots : Vec (List T)) (i : Usize) :
   Result ((HashMap T) × (Vec (List T)))
   :=
-  HashMap.move_elements_loop_fwd_back T ntable slots i
+  HashMap.move_elements_loop T ntable slots i
 
-/- [hashmap::HashMap::{0}::try_resize] -/
-def HashMap.try_resize_fwd_back
-  (T : Type) (self : HashMap T) : Result (HashMap T) :=
+/- [hashmap::HashMap::{0}::try_resize]: merged forward/backward function
+   (there is a single backward function, and the forward function returns ()) -/
+def HashMap.try_resize (T : Type) (self : HashMap T) : Result (HashMap T) :=
   do
     let max_usize ← Scalar.cast .Usize core_num_u32_max_c
     let capacity := Vec.len (List T) self.hash_map_slots
@@ -197,9 +202,9 @@ def HashMap.try_resize_fwd_back
     then
       do
         let i2 ← capacity * (Usize.ofInt 2 (by intlit))
-        let ntable ← HashMap.new_with_capacity_fwd T i2 i i0
+        let ntable ← HashMap.new_with_capacity T i2 i i0
         let (ntable0, _) ←
-          HashMap.move_elements_fwd_back T ntable self.hash_map_slots
+          HashMap.move_elements T ntable self.hash_map_slots
             (Usize.ofInt 0 (by intlit))
         Result.ret
           {
@@ -210,83 +215,83 @@ def HashMap.try_resize_fwd_back
           }
     else Result.ret { self with hash_map_max_load_factor := (i, i0) }
 
-/- [hashmap::HashMap::{0}::insert] -/
-def HashMap.insert_fwd_back
+/- [hashmap::HashMap::{0}::insert]: merged forward/backward function
+   (there is a single backward function, and the forward function returns ()) -/
+def HashMap.insert
   (T : Type) (self : HashMap T) (key : Usize) (value : T) :
   Result (HashMap T)
   :=
   do
-    let self0 ← HashMap.insert_no_resize_fwd_back T self key value
-    let i ← HashMap.len_fwd T self0
+    let self0 ← HashMap.insert_no_resize T self key value
+    let i ← HashMap.len T self0
     if i > self0.hash_map_max_load
-    then HashMap.try_resize_fwd_back T self0
+    then HashMap.try_resize T self0
     else Result.ret self0
 
-/- [hashmap::HashMap::{0}::contains_key_in_list] -/
-divergent def HashMap.contains_key_in_list_loop_fwd
+/- [hashmap::HashMap::{0}::contains_key_in_list]: loop 0: forward function -/
+divergent def HashMap.contains_key_in_list_loop
   (T : Type) (key : Usize) (ls : List T) : Result Bool :=
   match ls with
   | List.Cons ckey t tl =>
     if ckey = key
     then Result.ret true
-    else HashMap.contains_key_in_list_loop_fwd T key tl
+    else HashMap.contains_key_in_list_loop T key tl
   | List.Nil => Result.ret false
 
-/- [hashmap::HashMap::{0}::contains_key_in_list] -/
-def HashMap.contains_key_in_list_fwd
+/- [hashmap::HashMap::{0}::contains_key_in_list]: forward function -/
+def HashMap.contains_key_in_list
   (T : Type) (key : Usize) (ls : List T) : Result Bool :=
-  HashMap.contains_key_in_list_loop_fwd T key ls
+  HashMap.contains_key_in_list_loop T key ls
 
-/- [hashmap::HashMap::{0}::contains_key] -/
-def HashMap.contains_key_fwd
+/- [hashmap::HashMap::{0}::contains_key]: forward function -/
+def HashMap.contains_key
   (T : Type) (self : HashMap T) (key : Usize) : Result Bool :=
   do
-    let hash ← hash_key_fwd key
+    let hash ← hash_key key
     let i := Vec.len (List T) self.hash_map_slots
     let hash_mod ← hash % i
     let l ← Vec.index (List T) self.hash_map_slots hash_mod
-    HashMap.contains_key_in_list_fwd T key l
+    HashMap.contains_key_in_list T key l
 
-/- [hashmap::HashMap::{0}::get_in_list] -/
-divergent def HashMap.get_in_list_loop_fwd
+/- [hashmap::HashMap::{0}::get_in_list]: loop 0: forward function -/
+divergent def HashMap.get_in_list_loop
   (T : Type) (key : Usize) (ls : List T) : Result T :=
   match ls with
   | List.Cons ckey cvalue tl =>
     if ckey = key
     then Result.ret cvalue
-    else HashMap.get_in_list_loop_fwd T key tl
+    else HashMap.get_in_list_loop T key tl
   | List.Nil => Result.fail Error.panic
 
-/- [hashmap::HashMap::{0}::get_in_list] -/
-def HashMap.get_in_list_fwd
-  (T : Type) (key : Usize) (ls : List T) : Result T :=
-  HashMap.get_in_list_loop_fwd T key ls
+/- [hashmap::HashMap::{0}::get_in_list]: forward function -/
+def HashMap.get_in_list (T : Type) (key : Usize) (ls : List T) : Result T :=
+  HashMap.get_in_list_loop T key ls
 
-/- [hashmap::HashMap::{0}::get] -/
-def HashMap.get_fwd (T : Type) (self : HashMap T) (key : Usize) : Result T :=
+/- [hashmap::HashMap::{0}::get]: forward function -/
+def HashMap.get (T : Type) (self : HashMap T) (key : Usize) : Result T :=
   do
-    let hash ← hash_key_fwd key
+    let hash ← hash_key key
     let i := Vec.len (List T) self.hash_map_slots
     let hash_mod ← hash % i
     let l ← Vec.index (List T) self.hash_map_slots hash_mod
-    HashMap.get_in_list_fwd T key l
+    HashMap.get_in_list T key l
 
-/- [hashmap::HashMap::{0}::get_mut_in_list] -/
-divergent def HashMap.get_mut_in_list_loop_fwd
+/- [hashmap::HashMap::{0}::get_mut_in_list]: loop 0: forward function -/
+divergent def HashMap.get_mut_in_list_loop
   (T : Type) (ls : List T) (key : Usize) : Result T :=
   match ls with
   | List.Cons ckey cvalue tl =>
     if ckey = key
     then Result.ret cvalue
-    else HashMap.get_mut_in_list_loop_fwd T tl key
+    else HashMap.get_mut_in_list_loop T tl key
   | List.Nil => Result.fail Error.panic
 
-/- [hashmap::HashMap::{0}::get_mut_in_list] -/
-def HashMap.get_mut_in_list_fwd
+/- [hashmap::HashMap::{0}::get_mut_in_list]: forward function -/
+def HashMap.get_mut_in_list
   (T : Type) (ls : List T) (key : Usize) : Result T :=
-  HashMap.get_mut_in_list_loop_fwd T ls key
+  HashMap.get_mut_in_list_loop T ls key
 
-/- [hashmap::HashMap::{0}::get_mut_in_list] -/
+/- [hashmap::HashMap::{0}::get_mut_in_list]: loop 0: backward function 0 -/
 divergent def HashMap.get_mut_in_list_loop_back
   (T : Type) (ls : List T) (key : Usize) (ret0 : T) : Result (List T) :=
   match ls with
@@ -299,28 +304,27 @@ divergent def HashMap.get_mut_in_list_loop_back
         Result.ret (List.Cons ckey cvalue tl0)
   | List.Nil => Result.fail Error.panic
 
-/- [hashmap::HashMap::{0}::get_mut_in_list] -/
+/- [hashmap::HashMap::{0}::get_mut_in_list]: backward function 0 -/
 def HashMap.get_mut_in_list_back
   (T : Type) (ls : List T) (key : Usize) (ret0 : T) : Result (List T) :=
   HashMap.get_mut_in_list_loop_back T ls key ret0
 
-/- [hashmap::HashMap::{0}::get_mut] -/
-def HashMap.get_mut_fwd
-  (T : Type) (self : HashMap T) (key : Usize) : Result T :=
+/- [hashmap::HashMap::{0}::get_mut]: forward function -/
+def HashMap.get_mut (T : Type) (self : HashMap T) (key : Usize) : Result T :=
   do
-    let hash ← hash_key_fwd key
+    let hash ← hash_key key
     let i := Vec.len (List T) self.hash_map_slots
     let hash_mod ← hash % i
     let l ← Vec.index_mut (List T) self.hash_map_slots hash_mod
-    HashMap.get_mut_in_list_fwd T l key
+    HashMap.get_mut_in_list T l key
 
-/- [hashmap::HashMap::{0}::get_mut] -/
+/- [hashmap::HashMap::{0}::get_mut]: backward function 0 -/
 def HashMap.get_mut_back
   (T : Type) (self : HashMap T) (key : Usize) (ret0 : T) :
   Result (HashMap T)
   :=
   do
-    let hash ← hash_key_fwd key
+    let hash ← hash_key key
     let i := Vec.len (List T) self.hash_map_slots
     let hash_mod ← hash % i
     let l ← Vec.index_mut (List T) self.hash_map_slots hash_mod
@@ -328,33 +332,33 @@ def HashMap.get_mut_back
     let v ← Vec.index_mut_back (List T) self.hash_map_slots hash_mod l0
     Result.ret { self with hash_map_slots := v }
 
-/- [hashmap::HashMap::{0}::remove_from_list] -/
-divergent def HashMap.remove_from_list_loop_fwd
+/- [hashmap::HashMap::{0}::remove_from_list]: loop 0: forward function -/
+divergent def HashMap.remove_from_list_loop
   (T : Type) (key : Usize) (ls : List T) : Result (Option T) :=
   match ls with
   | List.Cons ckey t tl =>
     if ckey = key
     then
-      let mv_ls := mem.replace_fwd (List T) (List.Cons ckey t tl) List.Nil
+      let mv_ls := mem.replace (List T) (List.Cons ckey t tl) List.Nil
       match mv_ls with
       | List.Cons i cvalue tl0 => Result.ret (Option.some cvalue)
       | List.Nil => Result.fail Error.panic
-    else HashMap.remove_from_list_loop_fwd T key tl
+    else HashMap.remove_from_list_loop T key tl
   | List.Nil => Result.ret Option.none
 
-/- [hashmap::HashMap::{0}::remove_from_list] -/
-def HashMap.remove_from_list_fwd
+/- [hashmap::HashMap::{0}::remove_from_list]: forward function -/
+def HashMap.remove_from_list
   (T : Type) (key : Usize) (ls : List T) : Result (Option T) :=
-  HashMap.remove_from_list_loop_fwd T key ls
+  HashMap.remove_from_list_loop T key ls
 
-/- [hashmap::HashMap::{0}::remove_from_list] -/
+/- [hashmap::HashMap::{0}::remove_from_list]: loop 0: backward function 1 -/
 divergent def HashMap.remove_from_list_loop_back
   (T : Type) (key : Usize) (ls : List T) : Result (List T) :=
   match ls with
   | List.Cons ckey t tl =>
     if ckey = key
     then
-      let mv_ls := mem.replace_fwd (List T) (List.Cons ckey t tl) List.Nil
+      let mv_ls := mem.replace (List T) (List.Cons ckey t tl) List.Nil
       match mv_ls with
       | List.Cons i cvalue tl0 => Result.ret tl0
       | List.Nil => Result.fail Error.panic
@@ -364,20 +368,20 @@ divergent def HashMap.remove_from_list_loop_back
         Result.ret (List.Cons ckey t tl0)
   | List.Nil => Result.ret List.Nil
 
-/- [hashmap::HashMap::{0}::remove_from_list] -/
+/- [hashmap::HashMap::{0}::remove_from_list]: backward function 1 -/
 def HashMap.remove_from_list_back
   (T : Type) (key : Usize) (ls : List T) : Result (List T) :=
   HashMap.remove_from_list_loop_back T key ls
 
-/- [hashmap::HashMap::{0}::remove] -/
-def HashMap.remove_fwd
+/- [hashmap::HashMap::{0}::remove]: forward function -/
+def HashMap.remove
   (T : Type) (self : HashMap T) (key : Usize) : Result (Option T) :=
   do
-    let hash ← hash_key_fwd key
+    let hash ← hash_key key
     let i := Vec.len (List T) self.hash_map_slots
     let hash_mod ← hash % i
     let l ← Vec.index_mut (List T) self.hash_map_slots hash_mod
-    let x ← HashMap.remove_from_list_fwd T key l
+    let x ← HashMap.remove_from_list T key l
     match x with
     | Option.none => Result.ret Option.none
     | Option.some x0 =>
@@ -385,15 +389,15 @@ def HashMap.remove_fwd
         let _ ← self.hash_map_num_entries - (Usize.ofInt 1 (by intlit))
         Result.ret (Option.some x0)
 
-/- [hashmap::HashMap::{0}::remove] -/
+/- [hashmap::HashMap::{0}::remove]: backward function 0 -/
 def HashMap.remove_back
   (T : Type) (self : HashMap T) (key : Usize) : Result (HashMap T) :=
   do
-    let hash ← hash_key_fwd key
+    let hash ← hash_key key
     let i := Vec.len (List T) self.hash_map_slots
     let hash_mod ← hash % i
     let l ← Vec.index_mut (List T) self.hash_map_slots hash_mod
-    let x ← HashMap.remove_from_list_fwd T key l
+    let x ← HashMap.remove_from_list T key l
     match x with
     | Option.none =>
       do
@@ -408,23 +412,23 @@ def HashMap.remove_back
         Result.ret
           { self with hash_map_num_entries := i0, hash_map_slots := v }
 
-/- [hashmap::test1] -/
-def test1_fwd : Result Unit :=
+/- [hashmap::test1]: forward function -/
+def test1 : Result Unit :=
   do
-    let hm ← HashMap.new_fwd U64
+    let hm ← HashMap.new U64
     let hm0 ←
-      HashMap.insert_fwd_back U64 hm (Usize.ofInt 0 (by intlit))
+      HashMap.insert U64 hm (Usize.ofInt 0 (by intlit))
         (U64.ofInt 42 (by intlit))
     let hm1 ←
-      HashMap.insert_fwd_back U64 hm0 (Usize.ofInt 128 (by intlit))
+      HashMap.insert U64 hm0 (Usize.ofInt 128 (by intlit))
         (U64.ofInt 18 (by intlit))
     let hm2 ←
-      HashMap.insert_fwd_back U64 hm1 (Usize.ofInt 1024 (by intlit))
+      HashMap.insert U64 hm1 (Usize.ofInt 1024 (by intlit))
         (U64.ofInt 138 (by intlit))
     let hm3 ←
-      HashMap.insert_fwd_back U64 hm2 (Usize.ofInt 1056 (by intlit))
+      HashMap.insert U64 hm2 (Usize.ofInt 1056 (by intlit))
         (U64.ofInt 256 (by intlit))
-    let i ← HashMap.get_fwd U64 hm3 (Usize.ofInt 128 (by intlit))
+    let i ← HashMap.get U64 hm3 (Usize.ofInt 128 (by intlit))
     if not (i = (U64.ofInt 18 (by intlit)))
     then Result.fail Error.panic
     else
@@ -432,12 +436,12 @@ def test1_fwd : Result Unit :=
         let hm4 ←
           HashMap.get_mut_back U64 hm3 (Usize.ofInt 1024 (by intlit))
             (U64.ofInt 56 (by intlit))
-        let i0 ← HashMap.get_fwd U64 hm4 (Usize.ofInt 1024 (by intlit))
+        let i0 ← HashMap.get U64 hm4 (Usize.ofInt 1024 (by intlit))
         if not (i0 = (U64.ofInt 56 (by intlit)))
         then Result.fail Error.panic
         else
           do
-            let x ← HashMap.remove_fwd U64 hm4 (Usize.ofInt 1024 (by intlit))
+            let x ← HashMap.remove U64 hm4 (Usize.ofInt 1024 (by intlit))
             match x with
             | Option.none => Result.fail Error.panic
             | Option.some x0 =>
@@ -447,26 +451,24 @@ def test1_fwd : Result Unit :=
                 do
                   let hm5 ←
                     HashMap.remove_back U64 hm4 (Usize.ofInt 1024 (by intlit))
-                  let i1 ←
-                    HashMap.get_fwd U64 hm5 (Usize.ofInt 0 (by intlit))
+                  let i1 ← HashMap.get U64 hm5 (Usize.ofInt 0 (by intlit))
                   if not (i1 = (U64.ofInt 42 (by intlit)))
                   then Result.fail Error.panic
                   else
                     do
                       let i2 ←
-                        HashMap.get_fwd U64 hm5 (Usize.ofInt 128 (by intlit))
+                        HashMap.get U64 hm5 (Usize.ofInt 128 (by intlit))
                       if not (i2 = (U64.ofInt 18 (by intlit)))
                       then Result.fail Error.panic
                       else
                         do
                           let i3 ←
-                            HashMap.get_fwd U64 hm5
-                              (Usize.ofInt 1056 (by intlit))
+                            HashMap.get U64 hm5 (Usize.ofInt 1056 (by intlit))
                           if not (i3 = (U64.ofInt 256 (by intlit)))
                           then Result.fail Error.panic
                           else Result.ret ()
 
 /- Unit test for [hashmap::test1] -/
-#assert (test1_fwd == .ret ())
+#assert (test1 == .ret ())
 
 end hashmap
diff --git a/tests/lean/HashmapMain/Funs.lean b/tests/lean/HashmapMain/Funs.lean
index 1a741a2d..b1afcd44 100644
--- a/tests/lean/HashmapMain/Funs.lean
+++ b/tests/lean/HashmapMain/Funs.lean
@@ -6,12 +6,12 @@ import HashmapMain.FunsExternal
 open Primitives
 namespace hashmap_main
 
-/- [hashmap_main::hashmap::hash_key] -/
-def hashmap.hash_key_fwd (k : Usize) : Result Usize :=
+/- [hashmap_main::hashmap::hash_key]: forward function -/
+def hashmap.hash_key (k : Usize) : Result Usize :=
   Result.ret k
 
-/- [hashmap_main::hashmap::HashMap::{0}::allocate_slots] -/
-divergent def hashmap.HashMap.allocate_slots_loop_fwd
+/- [hashmap_main::hashmap::HashMap::{0}::allocate_slots]: loop 0: forward function -/
+divergent def hashmap.HashMap.allocate_slots_loop
   (T : Type) (slots : Vec (hashmap.List T)) (n : Usize) :
   Result (Vec (hashmap.List T))
   :=
@@ -20,25 +20,25 @@ divergent def hashmap.HashMap.allocate_slots_loop_fwd
     do
       let slots0 ← Vec.push (hashmap.List T) slots hashmap.List.Nil
       let n0 ← n - (Usize.ofInt 1 (by intlit))
-      hashmap.HashMap.allocate_slots_loop_fwd T slots0 n0
+      hashmap.HashMap.allocate_slots_loop T slots0 n0
   else Result.ret slots
 
-/- [hashmap_main::hashmap::HashMap::{0}::allocate_slots] -/
-def hashmap.HashMap.allocate_slots_fwd
+/- [hashmap_main::hashmap::HashMap::{0}::allocate_slots]: forward function -/
+def hashmap.HashMap.allocate_slots
   (T : Type) (slots : Vec (hashmap.List T)) (n : Usize) :
   Result (Vec (hashmap.List T))
   :=
-  hashmap.HashMap.allocate_slots_loop_fwd T slots n
+  hashmap.HashMap.allocate_slots_loop T slots n
 
-/- [hashmap_main::hashmap::HashMap::{0}::new_with_capacity] -/
-def hashmap.HashMap.new_with_capacity_fwd
+/- [hashmap_main::hashmap::HashMap::{0}::new_with_capacity]: forward function -/
+def hashmap.HashMap.new_with_capacity
   (T : Type) (capacity : Usize) (max_load_dividend : Usize)
   (max_load_divisor : Usize) :
   Result (hashmap.HashMap T)
   :=
   do
     let v := Vec.new (hashmap.List T)
-    let slots ← hashmap.HashMap.allocate_slots_fwd T v capacity
+    let slots ← hashmap.HashMap.allocate_slots T v capacity
     let i ← capacity * max_load_dividend
     let i0 ← i / max_load_divisor
     Result.ret
@@ -50,13 +50,14 @@ def hashmap.HashMap.new_with_capacity_fwd
         hashmap_hash_map_slots := slots
       }
 
-/- [hashmap_main::hashmap::HashMap::{0}::new] -/
-def hashmap.HashMap.new_fwd (T : Type) : Result (hashmap.HashMap T) :=
-  hashmap.HashMap.new_with_capacity_fwd T (Usize.ofInt 32 (by intlit))
+/- [hashmap_main::hashmap::HashMap::{0}::new]: forward function -/
+def hashmap.HashMap.new (T : Type) : Result (hashmap.HashMap T) :=
+  hashmap.HashMap.new_with_capacity T (Usize.ofInt 32 (by intlit))
     (Usize.ofInt 4 (by intlit)) (Usize.ofInt 5 (by intlit))
 
-/- [hashmap_main::hashmap::HashMap::{0}::clear] -/
-divergent def hashmap.HashMap.clear_loop_fwd_back
+/- [hashmap_main::hashmap::HashMap::{0}::clear]: loop 0: merged forward/backward function
+   (there is a single backward function, and the forward function returns ()) -/
+divergent def hashmap.HashMap.clear_loop
   (T : Type) (slots : Vec (hashmap.List T)) (i : Usize) :
   Result (Vec (hashmap.List T))
   :=
@@ -67,15 +68,16 @@ divergent def hashmap.HashMap.clear_loop_fwd_back
       let i1 ← i + (Usize.ofInt 1 (by intlit))
       let slots0 ←
         Vec.index_mut_back (hashmap.List T) slots i hashmap.List.Nil
-      hashmap.HashMap.clear_loop_fwd_back T slots0 i1
+      hashmap.HashMap.clear_loop T slots0 i1
   else Result.ret slots
 
-/- [hashmap_main::hashmap::HashMap::{0}::clear] -/
-def hashmap.HashMap.clear_fwd_back
+/- [hashmap_main::hashmap::HashMap::{0}::clear]: merged forward/backward function
+   (there is a single backward function, and the forward function returns ()) -/
+def hashmap.HashMap.clear
   (T : Type) (self : hashmap.HashMap T) : Result (hashmap.HashMap T) :=
   do
     let v ←
-      hashmap.HashMap.clear_loop_fwd_back T self.hashmap_hash_map_slots
+      hashmap.HashMap.clear_loop T self.hashmap_hash_map_slots
         (Usize.ofInt 0 (by intlit))
     Result.ret
       {
@@ -85,27 +87,26 @@ def hashmap.HashMap.clear_fwd_back
           hashmap_hash_map_slots := v
       }
 
-/- [hashmap_main::hashmap::HashMap::{0}::len] -/
-def hashmap.HashMap.len_fwd
-  (T : Type) (self : hashmap.HashMap T) : Result Usize :=
+/- [hashmap_main::hashmap::HashMap::{0}::len]: forward function -/
+def hashmap.HashMap.len (T : Type) (self : hashmap.HashMap T) : Result Usize :=
   Result.ret self.hashmap_hash_map_num_entries
 
-/- [hashmap_main::hashmap::HashMap::{0}::insert_in_list] -/
-divergent def hashmap.HashMap.insert_in_list_loop_fwd
+/- [hashmap_main::hashmap::HashMap::{0}::insert_in_list]: loop 0: forward function -/
+divergent def hashmap.HashMap.insert_in_list_loop
   (T : Type) (key : Usize) (value : T) (ls : hashmap.List T) : Result Bool :=
   match ls with
   | hashmap.List.Cons ckey cvalue tl =>
     if ckey = key
     then Result.ret false
-    else hashmap.HashMap.insert_in_list_loop_fwd T key value tl
+    else hashmap.HashMap.insert_in_list_loop T key value tl
   | hashmap.List.Nil => Result.ret true
 
-/- [hashmap_main::hashmap::HashMap::{0}::insert_in_list] -/
-def hashmap.HashMap.insert_in_list_fwd
+/- [hashmap_main::hashmap::HashMap::{0}::insert_in_list]: forward function -/
+def hashmap.HashMap.insert_in_list
   (T : Type) (key : Usize) (value : T) (ls : hashmap.List T) : Result Bool :=
-  hashmap.HashMap.insert_in_list_loop_fwd T key value ls
+  hashmap.HashMap.insert_in_list_loop T key value ls
 
-/- [hashmap_main::hashmap::HashMap::{0}::insert_in_list] -/
+/- [hashmap_main::hashmap::HashMap::{0}::insert_in_list]: loop 0: backward function 0 -/
 divergent def hashmap.HashMap.insert_in_list_loop_back
   (T : Type) (key : Usize) (value : T) (ls : hashmap.List T) :
   Result (hashmap.List T)
@@ -122,25 +123,26 @@ divergent def hashmap.HashMap.insert_in_list_loop_back
     let l := hashmap.List.Nil
     Result.ret (hashmap.List.Cons key value l)
 
-/- [hashmap_main::hashmap::HashMap::{0}::insert_in_list] -/
+/- [hashmap_main::hashmap::HashMap::{0}::insert_in_list]: backward function 0 -/
 def hashmap.HashMap.insert_in_list_back
   (T : Type) (key : Usize) (value : T) (ls : hashmap.List T) :
   Result (hashmap.List T)
   :=
   hashmap.HashMap.insert_in_list_loop_back T key value ls
 
-/- [hashmap_main::hashmap::HashMap::{0}::insert_no_resize] -/
-def hashmap.HashMap.insert_no_resize_fwd_back
+/- [hashmap_main::hashmap::HashMap::{0}::insert_no_resize]: merged forward/backward function
+   (there is a single backward function, and the forward function returns ()) -/
+def hashmap.HashMap.insert_no_resize
   (T : Type) (self : hashmap.HashMap T) (key : Usize) (value : T) :
   Result (hashmap.HashMap T)
   :=
   do
-    let hash ← hashmap.hash_key_fwd key
+    let hash ← hashmap.hash_key key
     let i := Vec.len (hashmap.List T) self.hashmap_hash_map_slots
     let hash_mod ← hash % i
     let l ←
       Vec.index_mut (hashmap.List T) self.hashmap_hash_map_slots hash_mod
-    let inserted ← hashmap.HashMap.insert_in_list_fwd T key value l
+    let inserted ← hashmap.HashMap.insert_in_list T key value l
     if inserted
     then
       do
@@ -169,27 +171,30 @@ def core_num_u32_max_body : Result U32 :=
   Result.ret (U32.ofInt 4294967295 (by intlit))
 def core_num_u32_max_c : U32 := eval_global core_num_u32_max_body (by simp)
 
-/- [hashmap_main::hashmap::HashMap::{0}::move_elements_from_list] -/
-divergent def hashmap.HashMap.move_elements_from_list_loop_fwd_back
+/- [hashmap_main::hashmap::HashMap::{0}::move_elements_from_list]: loop 0: merged forward/backward function
+   (there is a single backward function, and the forward function returns ()) -/
+divergent def hashmap.HashMap.move_elements_from_list_loop
   (T : Type) (ntable : hashmap.HashMap T) (ls : hashmap.List T) :
   Result (hashmap.HashMap T)
   :=
   match ls with
   | hashmap.List.Cons k v tl =>
     do
-      let ntable0 ← hashmap.HashMap.insert_no_resize_fwd_back T ntable k v
-      hashmap.HashMap.move_elements_from_list_loop_fwd_back T ntable0 tl
+      let ntable0 ← hashmap.HashMap.insert_no_resize T ntable k v
+      hashmap.HashMap.move_elements_from_list_loop T ntable0 tl
   | hashmap.List.Nil => Result.ret ntable
 
-/- [hashmap_main::hashmap::HashMap::{0}::move_elements_from_list] -/
-def hashmap.HashMap.move_elements_from_list_fwd_back
+/- [hashmap_main::hashmap::HashMap::{0}::move_elements_from_list]: merged forward/backward function
+   (there is a single backward function, and the forward function returns ()) -/
+def hashmap.HashMap.move_elements_from_list
   (T : Type) (ntable : hashmap.HashMap T) (ls : hashmap.List T) :
   Result (hashmap.HashMap T)
   :=
-  hashmap.HashMap.move_elements_from_list_loop_fwd_back T ntable ls
+  hashmap.HashMap.move_elements_from_list_loop T ntable ls
 
-/- [hashmap_main::hashmap::HashMap::{0}::move_elements] -/
-divergent def hashmap.HashMap.move_elements_loop_fwd_back
+/- [hashmap_main::hashmap::HashMap::{0}::move_elements]: loop 0: merged forward/backward function
+   (there is a single backward function, and the forward function returns ()) -/
+divergent def hashmap.HashMap.move_elements_loop
   (T : Type) (ntable : hashmap.HashMap T) (slots : Vec (hashmap.List T))
   (i : Usize) :
   Result ((hashmap.HashMap T) × (Vec (hashmap.List T)))
@@ -199,25 +204,26 @@ divergent def hashmap.HashMap.move_elements_loop_fwd_back
   then
     do
       let l ← Vec.index_mut (hashmap.List T) slots i
-      let ls := mem.replace_fwd (hashmap.List T) l hashmap.List.Nil
-      let ntable0 ←
-        hashmap.HashMap.move_elements_from_list_fwd_back T ntable ls
+      let ls := mem.replace (hashmap.List T) l hashmap.List.Nil
+      let ntable0 ← hashmap.HashMap.move_elements_from_list T ntable ls
       let i1 ← i + (Usize.ofInt 1 (by intlit))
       let l0 := mem.replace_back (hashmap.List T) l hashmap.List.Nil
       let slots0 ← Vec.index_mut_back (hashmap.List T) slots i l0
-      hashmap.HashMap.move_elements_loop_fwd_back T ntable0 slots0 i1
+      hashmap.HashMap.move_elements_loop T ntable0 slots0 i1
   else Result.ret (ntable, slots)
 
-/- [hashmap_main::hashmap::HashMap::{0}::move_elements] -/
-def hashmap.HashMap.move_elements_fwd_back
+/- [hashmap_main::hashmap::HashMap::{0}::move_elements]: merged forward/backward function
+   (there is a single backward function, and the forward function returns ()) -/
+def hashmap.HashMap.move_elements
   (T : Type) (ntable : hashmap.HashMap T) (slots : Vec (hashmap.List T))
   (i : Usize) :
   Result ((hashmap.HashMap T) × (Vec (hashmap.List T)))
   :=
-  hashmap.HashMap.move_elements_loop_fwd_back T ntable slots i
+  hashmap.HashMap.move_elements_loop T ntable slots i
 
-/- [hashmap_main::hashmap::HashMap::{0}::try_resize] -/
-def hashmap.HashMap.try_resize_fwd_back
+/- [hashmap_main::hashmap::HashMap::{0}::try_resize]: merged forward/backward function
+   (there is a single backward function, and the forward function returns ()) -/
+def hashmap.HashMap.try_resize
   (T : Type) (self : hashmap.HashMap T) : Result (hashmap.HashMap T) :=
   do
     let max_usize ← Scalar.cast .Usize core_num_u32_max_c
@@ -229,10 +235,10 @@ def hashmap.HashMap.try_resize_fwd_back
     then
       do
         let i2 ← capacity * (Usize.ofInt 2 (by intlit))
-        let ntable ← hashmap.HashMap.new_with_capacity_fwd T i2 i i0
+        let ntable ← hashmap.HashMap.new_with_capacity T i2 i i0
         let (ntable0, _) ←
-          hashmap.HashMap.move_elements_fwd_back T ntable
-            self.hashmap_hash_map_slots (Usize.ofInt 0 (by intlit))
+          hashmap.HashMap.move_elements T ntable self.hashmap_hash_map_slots
+            (Usize.ofInt 0 (by intlit))
         Result.ret
           {
             ntable0
@@ -242,84 +248,85 @@ def hashmap.HashMap.try_resize_fwd_back
           }
     else Result.ret { self with hashmap_hash_map_max_load_factor := (i, i0) }
 
-/- [hashmap_main::hashmap::HashMap::{0}::insert] -/
-def hashmap.HashMap.insert_fwd_back
+/- [hashmap_main::hashmap::HashMap::{0}::insert]: merged forward/backward function
+   (there is a single backward function, and the forward function returns ()) -/
+def hashmap.HashMap.insert
   (T : Type) (self : hashmap.HashMap T) (key : Usize) (value : T) :
   Result (hashmap.HashMap T)
   :=
   do
-    let self0 ← hashmap.HashMap.insert_no_resize_fwd_back T self key value
-    let i ← hashmap.HashMap.len_fwd T self0
+    let self0 ← hashmap.HashMap.insert_no_resize T self key value
+    let i ← hashmap.HashMap.len T self0
     if i > self0.hashmap_hash_map_max_load
-    then hashmap.HashMap.try_resize_fwd_back T self0
+    then hashmap.HashMap.try_resize T self0
     else Result.ret self0
 
-/- [hashmap_main::hashmap::HashMap::{0}::contains_key_in_list] -/
-divergent def hashmap.HashMap.contains_key_in_list_loop_fwd
+/- [hashmap_main::hashmap::HashMap::{0}::contains_key_in_list]: loop 0: forward function -/
+divergent def hashmap.HashMap.contains_key_in_list_loop
   (T : Type) (key : Usize) (ls : hashmap.List T) : Result Bool :=
   match ls with
   | hashmap.List.Cons ckey t tl =>
     if ckey = key
     then Result.ret true
-    else hashmap.HashMap.contains_key_in_list_loop_fwd T key tl
+    else hashmap.HashMap.contains_key_in_list_loop T key tl
   | hashmap.List.Nil => Result.ret false
 
-/- [hashmap_main::hashmap::HashMap::{0}::contains_key_in_list] -/
-def hashmap.HashMap.contains_key_in_list_fwd
+/- [hashmap_main::hashmap::HashMap::{0}::contains_key_in_list]: forward function -/
+def hashmap.HashMap.contains_key_in_list
   (T : Type) (key : Usize) (ls : hashmap.List T) : Result Bool :=
-  hashmap.HashMap.contains_key_in_list_loop_fwd T key ls
+  hashmap.HashMap.contains_key_in_list_loop T key ls
 
-/- [hashmap_main::hashmap::HashMap::{0}::contains_key] -/
-def hashmap.HashMap.contains_key_fwd
+/- [hashmap_main::hashmap::HashMap::{0}::contains_key]: forward function -/
+def hashmap.HashMap.contains_key
   (T : Type) (self : hashmap.HashMap T) (key : Usize) : Result Bool :=
   do
-    let hash ← hashmap.hash_key_fwd key
+    let hash ← hashmap.hash_key key
     let i := Vec.len (hashmap.List T) self.hashmap_hash_map_slots
     let hash_mod ← hash % i
     let l ← Vec.index (hashmap.List T) self.hashmap_hash_map_slots hash_mod
-    hashmap.HashMap.contains_key_in_list_fwd T key l
+    hashmap.HashMap.contains_key_in_list T key l
 
-/- [hashmap_main::hashmap::HashMap::{0}::get_in_list] -/
-divergent def hashmap.HashMap.get_in_list_loop_fwd
+/- [hashmap_main::hashmap::HashMap::{0}::get_in_list]: loop 0: forward function -/
+divergent def hashmap.HashMap.get_in_list_loop
   (T : Type) (key : Usize) (ls : hashmap.List T) : Result T :=
   match ls with
   | hashmap.List.Cons ckey cvalue tl =>
     if ckey = key
     then Result.ret cvalue
-    else hashmap.HashMap.get_in_list_loop_fwd T key tl
+    else hashmap.HashMap.get_in_list_loop T key tl
   | hashmap.List.Nil => Result.fail Error.panic
 
-/- [hashmap_main::hashmap::HashMap::{0}::get_in_list] -/
-def hashmap.HashMap.get_in_list_fwd
+/- [hashmap_main::hashmap::HashMap::{0}::get_in_list]: forward function -/
+def hashmap.HashMap.get_in_list
   (T : Type) (key : Usize) (ls : hashmap.List T) : Result T :=
-  hashmap.HashMap.get_in_list_loop_fwd T key ls
+  hashmap.HashMap.get_in_list_loop T key ls
 
-/- [hashmap_main::hashmap::HashMap::{0}::get] -/
-def hashmap.HashMap.get_fwd
+/- [hashmap_main::hashmap::HashMap::{0}::get]: forward function -/
+def hashmap.HashMap.get
   (T : Type) (self : hashmap.HashMap T) (key : Usize) : Result T :=
   do
-    let hash ← hashmap.hash_key_fwd key
+    let hash ← hashmap.hash_key key
     let i := Vec.len (hashmap.List T) self.hashmap_hash_map_slots
     let hash_mod ← hash % i
     let l ← Vec.index (hashmap.List T) self.hashmap_hash_map_slots hash_mod
-    hashmap.HashMap.get_in_list_fwd T key l
+    hashmap.HashMap.get_in_list T key l
 
-/- [hashmap_main::hashmap::HashMap::{0}::get_mut_in_list] -/
-divergent def hashmap.HashMap.get_mut_in_list_loop_fwd
+/- [hashmap_main::hashmap::HashMap::{0}::get_mut_in_list]: loop 0: forward function -/
+divergent def hashmap.HashMap.get_mut_in_list_loop
   (T : Type) (ls : hashmap.List T) (key : Usize) : Result T :=
   match ls with
   | hashmap.List.Cons ckey cvalue tl =>
     if ckey = key
     then Result.ret cvalue
-    else hashmap.HashMap.get_mut_in_list_loop_fwd T tl key
+    else hashmap.HashMap.get_mut_in_list_loop T tl key
   | hashmap.List.Nil => Result.fail Error.panic
 
-/- [hashmap_main::hashmap::HashMap::{0}::get_mut_in_list] -/
-def hashmap.HashMap.get_mut_in_list_fwd
+/- [hashmap_main::hashmap::HashMap::{0}::get_mut_in_list]: forward function -/
+def hashmap.HashMap.get_mut_in_list
   (T : Type) (ls : hashmap.List T) (key : Usize) : Result T :=
-  hashmap.HashMap.get_mut_in_list_loop_fwd T ls key
+  hashmap.HashMap.get_mut_in_list_loop T ls key
 
-/- [hashmap_main::hashmap::HashMap::{0}::get_mut_in_list] -/
+/- [hashmap_main::hashmap::HashMap::{0}::get_mut_in_list]: loop 0: backward function 0 -/
 divergent def hashmap.HashMap.get_mut_in_list_loop_back
   (T : Type) (ls : hashmap.List T) (key : Usize) (ret0 : T) :
   Result (hashmap.List T)
@@ -334,31 +341,31 @@ divergent def hashmap.HashMap.get_mut_in_list_loop_back
         Result.ret (hashmap.List.Cons ckey cvalue tl0)
   | hashmap.List.Nil => Result.fail Error.panic
 
-/- [hashmap_main::hashmap::HashMap::{0}::get_mut_in_list] -/
+/- [hashmap_main::hashmap::HashMap::{0}::get_mut_in_list]: backward function 0 -/
 def hashmap.HashMap.get_mut_in_list_back
   (T : Type) (ls : hashmap.List T) (key : Usize) (ret0 : T) :
   Result (hashmap.List T)
   :=
   hashmap.HashMap.get_mut_in_list_loop_back T ls key ret0
 
-/- [hashmap_main::hashmap::HashMap::{0}::get_mut] -/
-def hashmap.HashMap.get_mut_fwd
+/- [hashmap_main::hashmap::HashMap::{0}::get_mut]: forward function -/
+def hashmap.HashMap.get_mut
   (T : Type) (self : hashmap.HashMap T) (key : Usize) : Result T :=
   do
-    let hash ← hashmap.hash_key_fwd key
+    let hash ← hashmap.hash_key key
     let i := Vec.len (hashmap.List T) self.hashmap_hash_map_slots
     let hash_mod ← hash % i
     let l ←
       Vec.index_mut (hashmap.List T) self.hashmap_hash_map_slots hash_mod
-    hashmap.HashMap.get_mut_in_list_fwd T l key
+    hashmap.HashMap.get_mut_in_list T l key
 
-/- [hashmap_main::hashmap::HashMap::{0}::get_mut] -/
+/- [hashmap_main::hashmap::HashMap::{0}::get_mut]: backward function 0 -/
 def hashmap.HashMap.get_mut_back
   (T : Type) (self : hashmap.HashMap T) (key : Usize) (ret0 : T) :
   Result (hashmap.HashMap T)
   :=
   do
-    let hash ← hashmap.hash_key_fwd key
+    let hash ← hashmap.hash_key key
     let i := Vec.len (hashmap.List T) self.hashmap_hash_map_slots
     let hash_mod ← hash % i
     let l ←
@@ -369,28 +376,28 @@ def hashmap.HashMap.get_mut_back
         l0
     Result.ret { self with hashmap_hash_map_slots := v }
 
-/- [hashmap_main::hashmap::HashMap::{0}::remove_from_list] -/
-divergent def hashmap.HashMap.remove_from_list_loop_fwd
+/- [hashmap_main::hashmap::HashMap::{0}::remove_from_list]: loop 0: forward function -/
+divergent def hashmap.HashMap.remove_from_list_loop
   (T : Type) (key : Usize) (ls : hashmap.List T) : Result (Option T) :=
   match ls with
   | hashmap.List.Cons ckey t tl =>
     if ckey = key
     then
       let mv_ls :=
-        mem.replace_fwd (hashmap.List T) (hashmap.List.Cons ckey t tl)
+        mem.replace (hashmap.List T) (hashmap.List.Cons ckey t tl)
           hashmap.List.Nil
       match mv_ls with
       | hashmap.List.Cons i cvalue tl0 => Result.ret (Option.some cvalue)
       | hashmap.List.Nil => Result.fail Error.panic
-    else hashmap.HashMap.remove_from_list_loop_fwd T key tl
+    else hashmap.HashMap.remove_from_list_loop T key tl
   | hashmap.List.Nil => Result.ret Option.none
 
-/- [hashmap_main::hashmap::HashMap::{0}::remove_from_list] -/
-def hashmap.HashMap.remove_from_list_fwd
+/- [hashmap_main::hashmap::HashMap::{0}::remove_from_list]: forward function -/
+def hashmap.HashMap.remove_from_list
   (T : Type) (key : Usize) (ls : hashmap.List T) : Result (Option T) :=
-  hashmap.HashMap.remove_from_list_loop_fwd T key ls
+  hashmap.HashMap.remove_from_list_loop T key ls
 
-/- [hashmap_main::hashmap::HashMap::{0}::remove_from_list] -/
+/- [hashmap_main::hashmap::HashMap::{0}::remove_from_list]: loop 0: backward function 1 -/
 divergent def hashmap.HashMap.remove_from_list_loop_back
   (T : Type) (key : Usize) (ls : hashmap.List T) : Result (hashmap.List T) :=
   match ls with
@@ -398,7 +405,7 @@ divergent def hashmap.HashMap.remove_from_list_loop_back
     if ckey = key
     then
       let mv_ls :=
-        mem.replace_fwd (hashmap.List T) (hashmap.List.Cons ckey t tl)
+        mem.replace (hashmap.List T) (hashmap.List.Cons ckey t tl)
           hashmap.List.Nil
       match mv_ls with
       | hashmap.List.Cons i cvalue tl0 => Result.ret tl0
@@ -409,21 +416,21 @@ divergent def hashmap.HashMap.remove_from_list_loop_back
         Result.ret (hashmap.List.Cons ckey t tl0)
   | hashmap.List.Nil => Result.ret hashmap.List.Nil
 
-/- [hashmap_main::hashmap::HashMap::{0}::remove_from_list] -/
+/- [hashmap_main::hashmap::HashMap::{0}::remove_from_list]: backward function 1 -/
 def hashmap.HashMap.remove_from_list_back
   (T : Type) (key : Usize) (ls : hashmap.List T) : Result (hashmap.List T) :=
   hashmap.HashMap.remove_from_list_loop_back T key ls
 
-/- [hashmap_main::hashmap::HashMap::{0}::remove] -/
-def hashmap.HashMap.remove_fwd
+/- [hashmap_main::hashmap::HashMap::{0}::remove]: forward function -/
+def hashmap.HashMap.remove
   (T : Type) (self : hashmap.HashMap T) (key : Usize) : Result (Option T) :=
   do
-    let hash ← hashmap.hash_key_fwd key
+    let hash ← hashmap.hash_key key
     let i := Vec.len (hashmap.List T) self.hashmap_hash_map_slots
     let hash_mod ← hash % i
     let l ←
       Vec.index_mut (hashmap.List T) self.hashmap_hash_map_slots hash_mod
-    let x ← hashmap.HashMap.remove_from_list_fwd T key l
+    let x ← hashmap.HashMap.remove_from_list T key l
     match x with
     | Option.none => Result.ret Option.none
     | Option.some x0 =>
@@ -432,18 +439,18 @@ def hashmap.HashMap.remove_fwd
           (Usize.ofInt 1 (by intlit))
         Result.ret (Option.some x0)
 
-/- [hashmap_main::hashmap::HashMap::{0}::remove] -/
+/- [hashmap_main::hashmap::HashMap::{0}::remove]: backward function 0 -/
 def hashmap.HashMap.remove_back
   (T : Type) (self : hashmap.HashMap T) (key : Usize) :
   Result (hashmap.HashMap T)
   :=
   do
-    let hash ← hashmap.hash_key_fwd key
+    let hash ← hashmap.hash_key key
     let i := Vec.len (hashmap.List T) self.hashmap_hash_map_slots
     let hash_mod ← hash % i
     let l ←
       Vec.index_mut (hashmap.List T) self.hashmap_hash_map_slots hash_mod
-    let x ← hashmap.HashMap.remove_from_list_fwd T key l
+    let x ← hashmap.HashMap.remove_from_list T key l
     match x with
     | Option.none =>
       do
@@ -467,23 +474,23 @@ def hashmap.HashMap.remove_back
               hashmap_hash_map_num_entries := i0, hashmap_hash_map_slots := v
           }
 
-/- [hashmap_main::hashmap::test1] -/
-def hashmap.test1_fwd : Result Unit :=
+/- [hashmap_main::hashmap::test1]: forward function -/
+def hashmap.test1 : Result Unit :=
   do
-    let hm ← hashmap.HashMap.new_fwd U64
+    let hm ← hashmap.HashMap.new U64
     let hm0 ←
-      hashmap.HashMap.insert_fwd_back U64 hm (Usize.ofInt 0 (by intlit))
+      hashmap.HashMap.insert U64 hm (Usize.ofInt 0 (by intlit))
         (U64.ofInt 42 (by intlit))
     let hm1 ←
-      hashmap.HashMap.insert_fwd_back U64 hm0 (Usize.ofInt 128 (by intlit))
+      hashmap.HashMap.insert U64 hm0 (Usize.ofInt 128 (by intlit))
         (U64.ofInt 18 (by intlit))
     let hm2 ←
-      hashmap.HashMap.insert_fwd_back U64 hm1 (Usize.ofInt 1024 (by intlit))
+      hashmap.HashMap.insert U64 hm1 (Usize.ofInt 1024 (by intlit))
         (U64.ofInt 138 (by intlit))
     let hm3 ←
-      hashmap.HashMap.insert_fwd_back U64 hm2 (Usize.ofInt 1056 (by intlit))
+      hashmap.HashMap.insert U64 hm2 (Usize.ofInt 1056 (by intlit))
         (U64.ofInt 256 (by intlit))
-    let i ← hashmap.HashMap.get_fwd U64 hm3 (Usize.ofInt 128 (by intlit))
+    let i ← hashmap.HashMap.get U64 hm3 (Usize.ofInt 128 (by intlit))
     if not (i = (U64.ofInt 18 (by intlit)))
     then Result.fail Error.panic
     else
@@ -491,14 +498,13 @@ def hashmap.test1_fwd : Result Unit :=
         let hm4 ←
           hashmap.HashMap.get_mut_back U64 hm3 (Usize.ofInt 1024 (by intlit))
             (U64.ofInt 56 (by intlit))
-        let i0 ←
-          hashmap.HashMap.get_fwd U64 hm4 (Usize.ofInt 1024 (by intlit))
+        let i0 ← hashmap.HashMap.get U64 hm4 (Usize.ofInt 1024 (by intlit))
         if not (i0 = (U64.ofInt 56 (by intlit)))
         then Result.fail Error.panic
         else
           do
             let x ←
-              hashmap.HashMap.remove_fwd U64 hm4 (Usize.ofInt 1024 (by intlit))
+              hashmap.HashMap.remove U64 hm4 (Usize.ofInt 1024 (by intlit))
             match x with
             | Option.none => Result.fail Error.panic
             | Option.some x0 =>
@@ -510,42 +516,42 @@ def hashmap.test1_fwd : Result Unit :=
                     hashmap.HashMap.remove_back U64 hm4
                       (Usize.ofInt 1024 (by intlit))
                   let i1 ←
-                    hashmap.HashMap.get_fwd U64 hm5 (Usize.ofInt 0 (by intlit))
+                    hashmap.HashMap.get U64 hm5 (Usize.ofInt 0 (by intlit))
                   if not (i1 = (U64.ofInt 42 (by intlit)))
                   then Result.fail Error.panic
                   else
                     do
                       let i2 ←
-                        hashmap.HashMap.get_fwd U64 hm5
+                        hashmap.HashMap.get U64 hm5
                           (Usize.ofInt 128 (by intlit))
                       if not (i2 = (U64.ofInt 18 (by intlit)))
                       then Result.fail Error.panic
                       else
                         do
                           let i3 ←
-                            hashmap.HashMap.get_fwd U64 hm5
+                            hashmap.HashMap.get U64 hm5
                               (Usize.ofInt 1056 (by intlit))
                           if not (i3 = (U64.ofInt 256 (by intlit)))
                           then Result.fail Error.panic
                           else Result.ret ()
 
 /- Unit test for [hashmap_main::hashmap::test1] -/
-#assert (hashmap.test1_fwd == .ret ())
+#assert (hashmap.test1 == .ret ())
 
-/- [hashmap_main::insert_on_disk] -/
-def insert_on_disk_fwd
+/- [hashmap_main::insert_on_disk]: forward function -/
+def insert_on_disk
   (key : Usize) (value : U64) (st : State) : Result (State × Unit) :=
   do
-    let (st0, hm) ← hashmap_utils.deserialize_fwd st
-    let hm0 ← hashmap.HashMap.insert_fwd_back U64 hm key value
-    let (st1, _) ← hashmap_utils.serialize_fwd hm0 st0
+    let (st0, hm) ← hashmap_utils.deserialize st
+    let hm0 ← hashmap.HashMap.insert U64 hm key value
+    let (st1, _) ← hashmap_utils.serialize hm0 st0
     Result.ret (st1, ())
 
-/- [hashmap_main::main] -/
-def main_fwd : Result Unit :=
+/- [hashmap_main::main]: forward function -/
+def main : Result Unit :=
   Result.ret ()
 
 /- Unit test for [hashmap_main::main] -/
-#assert (main_fwd == .ret ())
+#assert (main == .ret ())
 
 end hashmap_main
diff --git a/tests/lean/HashmapMain/FunsExternal.lean b/tests/lean/HashmapMain/FunsExternal.lean
index 3689dd45..b394b32b 100644
--- a/tests/lean/HashmapMain/FunsExternal.lean
+++ b/tests/lean/HashmapMain/FunsExternal.lean
@@ -7,11 +7,11 @@ open hashmap_main
 -- TODO: fill those bodies
 
 /- [hashmap_main::hashmap_utils::deserialize] -/
-def hashmap_utils.deserialize_fwd
+def hashmap_utils.deserialize
   : State → Result (State × (hashmap.HashMap U64)) :=
   fun _ => .fail .panic
 
 /- [hashmap_main::hashmap_utils::serialize] -/
-def hashmap_utils.serialize_fwd
+def hashmap_utils.serialize
   : hashmap.HashMap U64 → State → Result (State × Unit) :=
   fun _ _ => .fail .panic
diff --git a/tests/lean/HashmapMain/FunsExternal_Template.lean b/tests/lean/HashmapMain/FunsExternal_Template.lean
index 8853b7fc..f537fc8f 100644
--- a/tests/lean/HashmapMain/FunsExternal_Template.lean
+++ b/tests/lean/HashmapMain/FunsExternal_Template.lean
@@ -6,11 +6,11 @@ import HashmapMain.Types
 open Primitives
 open hashmap_main
 
-/- [hashmap_main::hashmap_utils::deserialize] -/
-axiom hashmap_utils.deserialize_fwd
+/- [hashmap_main::hashmap_utils::deserialize]: forward function -/
+axiom hashmap_utils.deserialize
   : State → Result (State × (hashmap.HashMap U64))
 
-/- [hashmap_main::hashmap_utils::serialize] -/
-axiom hashmap_utils.serialize_fwd
+/- [hashmap_main::hashmap_utils::serialize]: forward function -/
+axiom hashmap_utils.serialize
   : hashmap.HashMap U64 → State → Result (State × Unit)
 
diff --git a/tests/lean/Loops/Funs.lean b/tests/lean/Loops/Funs.lean
index 6e6eef3b..8cac7ac0 100644
--- a/tests/lean/Loops/Funs.lean
+++ b/tests/lean/Loops/Funs.lean
@@ -5,82 +5,83 @@ import Loops.Types
 open Primitives
 namespace loops
 
-/- [loops::sum] -/
-divergent def sum_loop_fwd (max : U32) (i : U32) (s : U32) : Result U32 :=
+/- [loops::sum]: loop 0: forward function -/
+divergent def sum_loop (max : U32) (i : U32) (s : U32) : Result U32 :=
   if i < max
   then
     do
       let s0 ← s + i
       let i0 ← i + (U32.ofInt 1 (by intlit))
-      sum_loop_fwd max i0 s0
+      sum_loop max i0 s0
   else s * (U32.ofInt 2 (by intlit))
 
-/- [loops::sum] -/
-def sum_fwd (max : U32) : Result U32 :=
-  sum_loop_fwd max (U32.ofInt 0 (by intlit)) (U32.ofInt 0 (by intlit))
+/- [loops::sum]: forward function -/
+def sum (max : U32) : Result U32 :=
+  sum_loop max (U32.ofInt 0 (by intlit)) (U32.ofInt 0 (by intlit))
 
-/- [loops::sum_with_mut_borrows] -/
-divergent def sum_with_mut_borrows_loop_fwd
+/- [loops::sum_with_mut_borrows]: loop 0: forward function -/
+divergent def sum_with_mut_borrows_loop
   (max : U32) (mi : U32) (ms : U32) : Result U32 :=
   if mi < max
   then
     do
       let ms0 ← ms + mi
       let mi0 ← mi + (U32.ofInt 1 (by intlit))
-      sum_with_mut_borrows_loop_fwd max mi0 ms0
+      sum_with_mut_borrows_loop max mi0 ms0
   else ms * (U32.ofInt 2 (by intlit))
 
-/- [loops::sum_with_mut_borrows] -/
-def sum_with_mut_borrows_fwd (max : U32) : Result U32 :=
-  sum_with_mut_borrows_loop_fwd max (U32.ofInt 0 (by intlit))
+/- [loops::sum_with_mut_borrows]: forward function -/
+def sum_with_mut_borrows (max : U32) : Result U32 :=
+  sum_with_mut_borrows_loop max (U32.ofInt 0 (by intlit))
     (U32.ofInt 0 (by intlit))
 
-/- [loops::sum_with_shared_borrows] -/
-divergent def sum_with_shared_borrows_loop_fwd
+/- [loops::sum_with_shared_borrows]: loop 0: forward function -/
+divergent def sum_with_shared_borrows_loop
   (max : U32) (i : U32) (s : U32) : Result U32 :=
   if i < max
   then
     do
       let i0 ← i + (U32.ofInt 1 (by intlit))
       let s0 ← s + i0
-      sum_with_shared_borrows_loop_fwd max i0 s0
+      sum_with_shared_borrows_loop max i0 s0
   else s * (U32.ofInt 2 (by intlit))
 
-/- [loops::sum_with_shared_borrows] -/
-def sum_with_shared_borrows_fwd (max : U32) : Result U32 :=
-  sum_with_shared_borrows_loop_fwd max (U32.ofInt 0 (by intlit))
+/- [loops::sum_with_shared_borrows]: forward function -/
+def sum_with_shared_borrows (max : U32) : Result U32 :=
+  sum_with_shared_borrows_loop max (U32.ofInt 0 (by intlit))
     (U32.ofInt 0 (by intlit))
 
-/- [loops::clear] -/
-divergent def clear_loop_fwd_back
-  (v : Vec U32) (i : Usize) : Result (Vec U32) :=
+/- [loops::clear]: loop 0: merged forward/backward function
+   (there is a single backward function, and the forward function returns ()) -/
+divergent def clear_loop (v : Vec U32) (i : Usize) : Result (Vec U32) :=
   let i0 := Vec.len U32 v
   if i < i0
   then
     do
       let i1 ← i + (Usize.ofInt 1 (by intlit))
       let v0 ← Vec.index_mut_back U32 v i (U32.ofInt 0 (by intlit))
-      clear_loop_fwd_back v0 i1
+      clear_loop v0 i1
   else Result.ret v
 
-/- [loops::clear] -/
-def clear_fwd_back (v : Vec U32) : Result (Vec U32) :=
-  clear_loop_fwd_back v (Usize.ofInt 0 (by intlit))
+/- [loops::clear]: merged forward/backward function
+   (there is a single backward function, and the forward function returns ()) -/
+def clear (v : Vec U32) : Result (Vec U32) :=
+  clear_loop v (Usize.ofInt 0 (by intlit))
 
-/- [loops::list_mem] -/
-divergent def list_mem_loop_fwd (x : U32) (ls : List U32) : Result Bool :=
+/- [loops::list_mem]: loop 0: forward function -/
+divergent def list_mem_loop (x : U32) (ls : List U32) : Result Bool :=
   match ls with
   | List.Cons y tl => if y = x
                       then Result.ret true
-                      else list_mem_loop_fwd x tl
+                      else list_mem_loop x tl
   | List.Nil => Result.ret false
 
-/- [loops::list_mem] -/
-def list_mem_fwd (x : U32) (ls : List U32) : Result Bool :=
-  list_mem_loop_fwd x ls
+/- [loops::list_mem]: forward function -/
+def list_mem (x : U32) (ls : List U32) : Result Bool :=
+  list_mem_loop x ls
 
-/- [loops::list_nth_mut_loop] -/
-divergent def list_nth_mut_loop_loop_fwd
+/- [loops::list_nth_mut_loop]: loop 0: forward function -/
+divergent def list_nth_mut_loop_loop
   (T : Type) (ls : List T) (i : U32) : Result T :=
   match ls with
   | List.Cons x tl =>
@@ -89,14 +90,14 @@ divergent def list_nth_mut_loop_loop_fwd
     else
       do
         let i0 ← i - (U32.ofInt 1 (by intlit))
-        list_nth_mut_loop_loop_fwd T tl i0
+        list_nth_mut_loop_loop T tl i0
   | List.Nil => Result.fail Error.panic
 
-/- [loops::list_nth_mut_loop] -/
-def list_nth_mut_loop_fwd (T : Type) (ls : List T) (i : U32) : Result T :=
-  list_nth_mut_loop_loop_fwd T ls i
+/- [loops::list_nth_mut_loop]: forward function -/
+def list_nth_mut_loop (T : Type) (ls : List T) (i : U32) : Result T :=
+  list_nth_mut_loop_loop T ls i
 
-/- [loops::list_nth_mut_loop] -/
+/- [loops::list_nth_mut_loop]: loop 0: backward function 0 -/
 divergent def list_nth_mut_loop_loop_back
   (T : Type) (ls : List T) (i : U32) (ret0 : T) : Result (List T) :=
   match ls with
@@ -110,13 +111,13 @@ divergent def list_nth_mut_loop_loop_back
         Result.ret (List.Cons x tl0)
   | List.Nil => Result.fail Error.panic
 
-/- [loops::list_nth_mut_loop] -/
+/- [loops::list_nth_mut_loop]: backward function 0 -/
 def list_nth_mut_loop_back
   (T : Type) (ls : List T) (i : U32) (ret0 : T) : Result (List T) :=
   list_nth_mut_loop_loop_back T ls i ret0
 
-/- [loops::list_nth_shared_loop] -/
-divergent def list_nth_shared_loop_loop_fwd
+/- [loops::list_nth_shared_loop]: loop 0: forward function -/
+divergent def list_nth_shared_loop_loop
   (T : Type) (ls : List T) (i : U32) : Result T :=
   match ls with
   | List.Cons x tl =>
@@ -125,30 +126,28 @@ divergent def list_nth_shared_loop_loop_fwd
     else
       do
         let i0 ← i - (U32.ofInt 1 (by intlit))
-        list_nth_shared_loop_loop_fwd T tl i0
+        list_nth_shared_loop_loop T tl i0
   | List.Nil => Result.fail Error.panic
 
-/- [loops::list_nth_shared_loop] -/
-def list_nth_shared_loop_fwd (T : Type) (ls : List T) (i : U32) : Result T :=
-  list_nth_shared_loop_loop_fwd T ls i
+/- [loops::list_nth_shared_loop]: forward function -/
+def list_nth_shared_loop (T : Type) (ls : List T) (i : U32) : Result T :=
+  list_nth_shared_loop_loop T ls i
 
-/- [loops::get_elem_mut] -/
-divergent def get_elem_mut_loop_fwd
-  (x : Usize) (ls : List Usize) : Result Usize :=
+/- [loops::get_elem_mut]: loop 0: forward function -/
+divergent def get_elem_mut_loop (x : Usize) (ls : List Usize) : Result Usize :=
   match ls with
-  | List.Cons y tl =>
-    if y = x
-    then Result.ret y
-    else get_elem_mut_loop_fwd x tl
+  | List.Cons y tl => if y = x
+                      then Result.ret y
+                      else get_elem_mut_loop x tl
   | List.Nil => Result.fail Error.panic
 
-/- [loops::get_elem_mut] -/
-def get_elem_mut_fwd (slots : Vec (List Usize)) (x : Usize) : Result Usize :=
+/- [loops::get_elem_mut]: forward function -/
+def get_elem_mut (slots : Vec (List Usize)) (x : Usize) : Result Usize :=
   do
     let l ← Vec.index_mut (List Usize) slots (Usize.ofInt 0 (by intlit))
-    get_elem_mut_loop_fwd x l
+    get_elem_mut_loop x l
 
-/- [loops::get_elem_mut] -/
+/- [loops::get_elem_mut]: loop 0: backward function 0 -/
 divergent def get_elem_mut_loop_back
   (x : Usize) (ls : List Usize) (ret0 : Usize) : Result (List Usize) :=
   match ls with
@@ -161,7 +160,7 @@ divergent def get_elem_mut_loop_back
         Result.ret (List.Cons y tl0)
   | List.Nil => Result.fail Error.panic
 
-/- [loops::get_elem_mut] -/
+/- [loops::get_elem_mut]: backward function 0 -/
 def get_elem_mut_back
   (slots : Vec (List Usize)) (x : Usize) (ret0 : Usize) :
   Result (Vec (List Usize))
@@ -171,37 +170,35 @@ def get_elem_mut_back
     let l0 ← get_elem_mut_loop_back x l ret0
     Vec.index_mut_back (List Usize) slots (Usize.ofInt 0 (by intlit)) l0
 
-/- [loops::get_elem_shared] -/
-divergent def get_elem_shared_loop_fwd
+/- [loops::get_elem_shared]: loop 0: forward function -/
+divergent def get_elem_shared_loop
   (x : Usize) (ls : List Usize) : Result Usize :=
   match ls with
-  | List.Cons y tl =>
-    if y = x
-    then Result.ret y
-    else get_elem_shared_loop_fwd x tl
+  | List.Cons y tl => if y = x
+                      then Result.ret y
+                      else get_elem_shared_loop x tl
   | List.Nil => Result.fail Error.panic
 
-/- [loops::get_elem_shared] -/
-def get_elem_shared_fwd
-  (slots : Vec (List Usize)) (x : Usize) : Result Usize :=
+/- [loops::get_elem_shared]: forward function -/
+def get_elem_shared (slots : Vec (List Usize)) (x : Usize) : Result Usize :=
   do
     let l ← Vec.index (List Usize) slots (Usize.ofInt 0 (by intlit))
-    get_elem_shared_loop_fwd x l
+    get_elem_shared_loop x l
 
-/- [loops::id_mut] -/
-def id_mut_fwd (T : Type) (ls : List T) : Result (List T) :=
+/- [loops::id_mut]: forward function -/
+def id_mut (T : Type) (ls : List T) : Result (List T) :=
   Result.ret ls
 
-/- [loops::id_mut] -/
+/- [loops::id_mut]: backward function 0 -/
 def id_mut_back (T : Type) (ls : List T) (ret0 : List T) : Result (List T) :=
   Result.ret ret0
 
-/- [loops::id_shared] -/
-def id_shared_fwd (T : Type) (ls : List T) : Result (List T) :=
+/- [loops::id_shared]: forward function -/
+def id_shared (T : Type) (ls : List T) : Result (List T) :=
   Result.ret ls
 
-/- [loops::list_nth_mut_loop_with_id] -/
-divergent def list_nth_mut_loop_with_id_loop_fwd
+/- [loops::list_nth_mut_loop_with_id]: loop 0: forward function -/
+divergent def list_nth_mut_loop_with_id_loop
   (T : Type) (i : U32) (ls : List T) : Result T :=
   match ls with
   | List.Cons x tl =>
@@ -210,17 +207,16 @@ divergent def list_nth_mut_loop_with_id_loop_fwd
     else
       do
         let i0 ← i - (U32.ofInt 1 (by intlit))
-        list_nth_mut_loop_with_id_loop_fwd T i0 tl
+        list_nth_mut_loop_with_id_loop T i0 tl
   | List.Nil => Result.fail Error.panic
 
-/- [loops::list_nth_mut_loop_with_id] -/
-def list_nth_mut_loop_with_id_fwd
-  (T : Type) (ls : List T) (i : U32) : Result T :=
+/- [loops::list_nth_mut_loop_with_id]: forward function -/
+def list_nth_mut_loop_with_id (T : Type) (ls : List T) (i : U32) : Result T :=
   do
-    let ls0 ← id_mut_fwd T ls
-    list_nth_mut_loop_with_id_loop_fwd T i ls0
+    let ls0 ← id_mut T ls
+    list_nth_mut_loop_with_id_loop T i ls0
 
-/- [loops::list_nth_mut_loop_with_id] -/
+/- [loops::list_nth_mut_loop_with_id]: loop 0: backward function 0 -/
 divergent def list_nth_mut_loop_with_id_loop_back
   (T : Type) (i : U32) (ls : List T) (ret0 : T) : Result (List T) :=
   match ls with
@@ -234,16 +230,16 @@ divergent def list_nth_mut_loop_with_id_loop_back
         Result.ret (List.Cons x tl0)
   | List.Nil => Result.fail Error.panic
 
-/- [loops::list_nth_mut_loop_with_id] -/
+/- [loops::list_nth_mut_loop_with_id]: backward function 0 -/
 def list_nth_mut_loop_with_id_back
   (T : Type) (ls : List T) (i : U32) (ret0 : T) : Result (List T) :=
   do
-    let ls0 ← id_mut_fwd T ls
+    let ls0 ← id_mut T ls
     let l ← list_nth_mut_loop_with_id_loop_back T i ls0 ret0
     id_mut_back T ls l
 
-/- [loops::list_nth_shared_loop_with_id] -/
-divergent def list_nth_shared_loop_with_id_loop_fwd
+/- [loops::list_nth_shared_loop_with_id]: loop 0: forward function -/
+divergent def list_nth_shared_loop_with_id_loop
   (T : Type) (i : U32) (ls : List T) : Result T :=
   match ls with
   | List.Cons x tl =>
@@ -252,18 +248,18 @@ divergent def list_nth_shared_loop_with_id_loop_fwd
     else
       do
         let i0 ← i - (U32.ofInt 1 (by intlit))
-        list_nth_shared_loop_with_id_loop_fwd T i0 tl
+        list_nth_shared_loop_with_id_loop T i0 tl
   | List.Nil => Result.fail Error.panic
 
-/- [loops::list_nth_shared_loop_with_id] -/
-def list_nth_shared_loop_with_id_fwd
+/- [loops::list_nth_shared_loop_with_id]: forward function -/
+def list_nth_shared_loop_with_id
   (T : Type) (ls : List T) (i : U32) : Result T :=
   do
-    let ls0 ← id_shared_fwd T ls
-    list_nth_shared_loop_with_id_loop_fwd T i ls0
+    let ls0 ← id_shared T ls
+    list_nth_shared_loop_with_id_loop T i ls0
 
-/- [loops::list_nth_mut_loop_pair] -/
-divergent def list_nth_mut_loop_pair_loop_fwd
+/- [loops::list_nth_mut_loop_pair]: loop 0: forward function -/
+divergent def list_nth_mut_loop_pair_loop
   (T : Type) (ls0 : List T) (ls1 : List T) (i : U32) : Result (T × T) :=
   match ls0 with
   | List.Cons x0 tl0 =>
@@ -274,16 +270,16 @@ divergent def list_nth_mut_loop_pair_loop_fwd
       else
         do
           let i0 ← i - (U32.ofInt 1 (by intlit))
-          list_nth_mut_loop_pair_loop_fwd T tl0 tl1 i0
+          list_nth_mut_loop_pair_loop T tl0 tl1 i0
     | List.Nil => Result.fail Error.panic
   | List.Nil => Result.fail Error.panic
 
-/- [loops::list_nth_mut_loop_pair] -/
-def list_nth_mut_loop_pair_fwd
+/- [loops::list_nth_mut_loop_pair]: forward function -/
+def list_nth_mut_loop_pair
   (T : Type) (ls0 : List T) (ls1 : List T) (i : U32) : Result (T × T) :=
-  list_nth_mut_loop_pair_loop_fwd T ls0 ls1 i
+  list_nth_mut_loop_pair_loop T ls0 ls1 i
 
-/- [loops::list_nth_mut_loop_pair] -/
+/- [loops::list_nth_mut_loop_pair]: loop 0: backward function 0 -/
 divergent def list_nth_mut_loop_pair_loop_back'a
   (T : Type) (ls0 : List T) (ls1 : List T) (i : U32) (ret0 : T) :
   Result (List T)
@@ -302,14 +298,14 @@ divergent def list_nth_mut_loop_pair_loop_back'a
     | List.Nil => Result.fail Error.panic
   | List.Nil => Result.fail Error.panic
 
-/- [loops::list_nth_mut_loop_pair] -/
+/- [loops::list_nth_mut_loop_pair]: backward function 0 -/
 def list_nth_mut_loop_pair_back'a
   (T : Type) (ls0 : List T) (ls1 : List T) (i : U32) (ret0 : T) :
   Result (List T)
   :=
   list_nth_mut_loop_pair_loop_back'a T ls0 ls1 i ret0
 
-/- [loops::list_nth_mut_loop_pair] -/
+/- [loops::list_nth_mut_loop_pair]: loop 0: backward function 1 -/
 divergent def list_nth_mut_loop_pair_loop_back'b
   (T : Type) (ls0 : List T) (ls1 : List T) (i : U32) (ret0 : T) :
   Result (List T)
@@ -328,15 +324,15 @@ divergent def list_nth_mut_loop_pair_loop_back'b
     | List.Nil => Result.fail Error.panic
   | List.Nil => Result.fail Error.panic
 
-/- [loops::list_nth_mut_loop_pair] -/
+/- [loops::list_nth_mut_loop_pair]: backward function 1 -/
 def list_nth_mut_loop_pair_back'b
   (T : Type) (ls0 : List T) (ls1 : List T) (i : U32) (ret0 : T) :
   Result (List T)
   :=
   list_nth_mut_loop_pair_loop_back'b T ls0 ls1 i ret0
 
-/- [loops::list_nth_shared_loop_pair] -/
-divergent def list_nth_shared_loop_pair_loop_fwd
+/- [loops::list_nth_shared_loop_pair]: loop 0: forward function -/
+divergent def list_nth_shared_loop_pair_loop
   (T : Type) (ls0 : List T) (ls1 : List T) (i : U32) : Result (T × T) :=
   match ls0 with
   | List.Cons x0 tl0 =>
@@ -347,17 +343,17 @@ divergent def list_nth_shared_loop_pair_loop_fwd
       else
         do
           let i0 ← i - (U32.ofInt 1 (by intlit))
-          list_nth_shared_loop_pair_loop_fwd T tl0 tl1 i0
+          list_nth_shared_loop_pair_loop T tl0 tl1 i0
     | List.Nil => Result.fail Error.panic
   | List.Nil => Result.fail Error.panic
 
-/- [loops::list_nth_shared_loop_pair] -/
-def list_nth_shared_loop_pair_fwd
+/- [loops::list_nth_shared_loop_pair]: forward function -/
+def list_nth_shared_loop_pair
   (T : Type) (ls0 : List T) (ls1 : List T) (i : U32) : Result (T × T) :=
-  list_nth_shared_loop_pair_loop_fwd T ls0 ls1 i
+  list_nth_shared_loop_pair_loop T ls0 ls1 i
 
-/- [loops::list_nth_mut_loop_pair_merge] -/
-divergent def list_nth_mut_loop_pair_merge_loop_fwd
+/- [loops::list_nth_mut_loop_pair_merge]: loop 0: forward function -/
+divergent def list_nth_mut_loop_pair_merge_loop
   (T : Type) (ls0 : List T) (ls1 : List T) (i : U32) : Result (T × T) :=
   match ls0 with
   | List.Cons x0 tl0 =>
@@ -368,16 +364,16 @@ divergent def list_nth_mut_loop_pair_merge_loop_fwd
       else
         do
           let i0 ← i - (U32.ofInt 1 (by intlit))
-          list_nth_mut_loop_pair_merge_loop_fwd T tl0 tl1 i0
+          list_nth_mut_loop_pair_merge_loop T tl0 tl1 i0
     | List.Nil => Result.fail Error.panic
   | List.Nil => Result.fail Error.panic
 
-/- [loops::list_nth_mut_loop_pair_merge] -/
-def list_nth_mut_loop_pair_merge_fwd
+/- [loops::list_nth_mut_loop_pair_merge]: forward function -/
+def list_nth_mut_loop_pair_merge
   (T : Type) (ls0 : List T) (ls1 : List T) (i : U32) : Result (T × T) :=
-  list_nth_mut_loop_pair_merge_loop_fwd T ls0 ls1 i
+  list_nth_mut_loop_pair_merge_loop T ls0 ls1 i
 
-/- [loops::list_nth_mut_loop_pair_merge] -/
+/- [loops::list_nth_mut_loop_pair_merge]: loop 0: backward function 0 -/
 divergent def list_nth_mut_loop_pair_merge_loop_back
   (T : Type) (ls0 : List T) (ls1 : List T) (i : U32) (ret0 : (T × T)) :
   Result ((List T) × (List T))
@@ -398,15 +394,15 @@ divergent def list_nth_mut_loop_pair_merge_loop_back
     | List.Nil => Result.fail Error.panic
   | List.Nil => Result.fail Error.panic
 
-/- [loops::list_nth_mut_loop_pair_merge] -/
+/- [loops::list_nth_mut_loop_pair_merge]: backward function 0 -/
 def list_nth_mut_loop_pair_merge_back
   (T : Type) (ls0 : List T) (ls1 : List T) (i : U32) (ret0 : (T × T)) :
   Result ((List T) × (List T))
   :=
   list_nth_mut_loop_pair_merge_loop_back T ls0 ls1 i ret0
 
-/- [loops::list_nth_shared_loop_pair_merge] -/
-divergent def list_nth_shared_loop_pair_merge_loop_fwd
+/- [loops::list_nth_shared_loop_pair_merge]: loop 0: forward function -/
+divergent def list_nth_shared_loop_pair_merge_loop
   (T : Type) (ls0 : List T) (ls1 : List T) (i : U32) : Result (T × T) :=
   match ls0 with
   | List.Cons x0 tl0 =>
@@ -417,17 +413,17 @@ divergent def list_nth_shared_loop_pair_merge_loop_fwd
       else
         do
           let i0 ← i - (U32.ofInt 1 (by intlit))
-          list_nth_shared_loop_pair_merge_loop_fwd T tl0 tl1 i0
+          list_nth_shared_loop_pair_merge_loop T tl0 tl1 i0
     | List.Nil => Result.fail Error.panic
   | List.Nil => Result.fail Error.panic
 
-/- [loops::list_nth_shared_loop_pair_merge] -/
-def list_nth_shared_loop_pair_merge_fwd
+/- [loops::list_nth_shared_loop_pair_merge]: forward function -/
+def list_nth_shared_loop_pair_merge
   (T : Type) (ls0 : List T) (ls1 : List T) (i : U32) : Result (T × T) :=
-  list_nth_shared_loop_pair_merge_loop_fwd T ls0 ls1 i
+  list_nth_shared_loop_pair_merge_loop T ls0 ls1 i
 
-/- [loops::list_nth_mut_shared_loop_pair] -/
-divergent def list_nth_mut_shared_loop_pair_loop_fwd
+/- [loops::list_nth_mut_shared_loop_pair]: loop 0: forward function -/
+divergent def list_nth_mut_shared_loop_pair_loop
   (T : Type) (ls0 : List T) (ls1 : List T) (i : U32) : Result (T × T) :=
   match ls0 with
   | List.Cons x0 tl0 =>
@@ -438,16 +434,16 @@ divergent def list_nth_mut_shared_loop_pair_loop_fwd
       else
         do
           let i0 ← i - (U32.ofInt 1 (by intlit))
-          list_nth_mut_shared_loop_pair_loop_fwd T tl0 tl1 i0
+          list_nth_mut_shared_loop_pair_loop T tl0 tl1 i0
     | List.Nil => Result.fail Error.panic
   | List.Nil => Result.fail Error.panic
 
-/- [loops::list_nth_mut_shared_loop_pair] -/
-def list_nth_mut_shared_loop_pair_fwd
+/- [loops::list_nth_mut_shared_loop_pair]: forward function -/
+def list_nth_mut_shared_loop_pair
   (T : Type) (ls0 : List T) (ls1 : List T) (i : U32) : Result (T × T) :=
-  list_nth_mut_shared_loop_pair_loop_fwd T ls0 ls1 i
+  list_nth_mut_shared_loop_pair_loop T ls0 ls1 i
 
-/- [loops::list_nth_mut_shared_loop_pair] -/
+/- [loops::list_nth_mut_shared_loop_pair]: loop 0: backward function 0 -/
 divergent def list_nth_mut_shared_loop_pair_loop_back
   (T : Type) (ls0 : List T) (ls1 : List T) (i : U32) (ret0 : T) :
   Result (List T)
@@ -467,15 +463,15 @@ divergent def list_nth_mut_shared_loop_pair_loop_back
     | List.Nil => Result.fail Error.panic
   | List.Nil => Result.fail Error.panic
 
-/- [loops::list_nth_mut_shared_loop_pair] -/
+/- [loops::list_nth_mut_shared_loop_pair]: backward function 0 -/
 def list_nth_mut_shared_loop_pair_back
   (T : Type) (ls0 : List T) (ls1 : List T) (i : U32) (ret0 : T) :
   Result (List T)
   :=
   list_nth_mut_shared_loop_pair_loop_back T ls0 ls1 i ret0
 
-/- [loops::list_nth_mut_shared_loop_pair_merge] -/
-divergent def list_nth_mut_shared_loop_pair_merge_loop_fwd
+/- [loops::list_nth_mut_shared_loop_pair_merge]: loop 0: forward function -/
+divergent def list_nth_mut_shared_loop_pair_merge_loop
   (T : Type) (ls0 : List T) (ls1 : List T) (i : U32) : Result (T × T) :=
   match ls0 with
   | List.Cons x0 tl0 =>
@@ -486,16 +482,16 @@ divergent def list_nth_mut_shared_loop_pair_merge_loop_fwd
       else
         do
           let i0 ← i - (U32.ofInt 1 (by intlit))
-          list_nth_mut_shared_loop_pair_merge_loop_fwd T tl0 tl1 i0
+          list_nth_mut_shared_loop_pair_merge_loop T tl0 tl1 i0
     | List.Nil => Result.fail Error.panic
   | List.Nil => Result.fail Error.panic
 
-/- [loops::list_nth_mut_shared_loop_pair_merge] -/
-def list_nth_mut_shared_loop_pair_merge_fwd
+/- [loops::list_nth_mut_shared_loop_pair_merge]: forward function -/
+def list_nth_mut_shared_loop_pair_merge
   (T : Type) (ls0 : List T) (ls1 : List T) (i : U32) : Result (T × T) :=
-  list_nth_mut_shared_loop_pair_merge_loop_fwd T ls0 ls1 i
+  list_nth_mut_shared_loop_pair_merge_loop T ls0 ls1 i
 
-/- [loops::list_nth_mut_shared_loop_pair_merge] -/
+/- [loops::list_nth_mut_shared_loop_pair_merge]: loop 0: backward function 0 -/
 divergent def list_nth_mut_shared_loop_pair_merge_loop_back
   (T : Type) (ls0 : List T) (ls1 : List T) (i : U32) (ret0 : T) :
   Result (List T)
@@ -515,15 +511,15 @@ divergent def list_nth_mut_shared_loop_pair_merge_loop_back
     | List.Nil => Result.fail Error.panic
   | List.Nil => Result.fail Error.panic
 
-/- [loops::list_nth_mut_shared_loop_pair_merge] -/
+/- [loops::list_nth_mut_shared_loop_pair_merge]: backward function 0 -/
 def list_nth_mut_shared_loop_pair_merge_back
   (T : Type) (ls0 : List T) (ls1 : List T) (i : U32) (ret0 : T) :
   Result (List T)
   :=
   list_nth_mut_shared_loop_pair_merge_loop_back T ls0 ls1 i ret0
 
-/- [loops::list_nth_shared_mut_loop_pair] -/
-divergent def list_nth_shared_mut_loop_pair_loop_fwd
+/- [loops::list_nth_shared_mut_loop_pair]: loop 0: forward function -/
+divergent def list_nth_shared_mut_loop_pair_loop
   (T : Type) (ls0 : List T) (ls1 : List T) (i : U32) : Result (T × T) :=
   match ls0 with
   | List.Cons x0 tl0 =>
@@ -534,16 +530,16 @@ divergent def list_nth_shared_mut_loop_pair_loop_fwd
       else
         do
           let i0 ← i - (U32.ofInt 1 (by intlit))
-          list_nth_shared_mut_loop_pair_loop_fwd T tl0 tl1 i0
+          list_nth_shared_mut_loop_pair_loop T tl0 tl1 i0
     | List.Nil => Result.fail Error.panic
   | List.Nil => Result.fail Error.panic
 
-/- [loops::list_nth_shared_mut_loop_pair] -/
-def list_nth_shared_mut_loop_pair_fwd
+/- [loops::list_nth_shared_mut_loop_pair]: forward function -/
+def list_nth_shared_mut_loop_pair
   (T : Type) (ls0 : List T) (ls1 : List T) (i : U32) : Result (T × T) :=
-  list_nth_shared_mut_loop_pair_loop_fwd T ls0 ls1 i
+  list_nth_shared_mut_loop_pair_loop T ls0 ls1 i
 
-/- [loops::list_nth_shared_mut_loop_pair] -/
+/- [loops::list_nth_shared_mut_loop_pair]: loop 0: backward function 1 -/
 divergent def list_nth_shared_mut_loop_pair_loop_back
   (T : Type) (ls0 : List T) (ls1 : List T) (i : U32) (ret0 : T) :
   Result (List T)
@@ -563,15 +559,15 @@ divergent def list_nth_shared_mut_loop_pair_loop_back
     | List.Nil => Result.fail Error.panic
   | List.Nil => Result.fail Error.panic
 
-/- [loops::list_nth_shared_mut_loop_pair] -/
+/- [loops::list_nth_shared_mut_loop_pair]: backward function 1 -/
 def list_nth_shared_mut_loop_pair_back
   (T : Type) (ls0 : List T) (ls1 : List T) (i : U32) (ret0 : T) :
   Result (List T)
   :=
   list_nth_shared_mut_loop_pair_loop_back T ls0 ls1 i ret0
 
-/- [loops::list_nth_shared_mut_loop_pair_merge] -/
-divergent def list_nth_shared_mut_loop_pair_merge_loop_fwd
+/- [loops::list_nth_shared_mut_loop_pair_merge]: loop 0: forward function -/
+divergent def list_nth_shared_mut_loop_pair_merge_loop
   (T : Type) (ls0 : List T) (ls1 : List T) (i : U32) : Result (T × T) :=
   match ls0 with
   | List.Cons x0 tl0 =>
@@ -582,16 +578,16 @@ divergent def list_nth_shared_mut_loop_pair_merge_loop_fwd
       else
         do
           let i0 ← i - (U32.ofInt 1 (by intlit))
-          list_nth_shared_mut_loop_pair_merge_loop_fwd T tl0 tl1 i0
+          list_nth_shared_mut_loop_pair_merge_loop T tl0 tl1 i0
     | List.Nil => Result.fail Error.panic
   | List.Nil => Result.fail Error.panic
 
-/- [loops::list_nth_shared_mut_loop_pair_merge] -/
-def list_nth_shared_mut_loop_pair_merge_fwd
+/- [loops::list_nth_shared_mut_loop_pair_merge]: forward function -/
+def list_nth_shared_mut_loop_pair_merge
   (T : Type) (ls0 : List T) (ls1 : List T) (i : U32) : Result (T × T) :=
-  list_nth_shared_mut_loop_pair_merge_loop_fwd T ls0 ls1 i
+  list_nth_shared_mut_loop_pair_merge_loop T ls0 ls1 i
 
-/- [loops::list_nth_shared_mut_loop_pair_merge] -/
+/- [loops::list_nth_shared_mut_loop_pair_merge]: loop 0: backward function 0 -/
 divergent def list_nth_shared_mut_loop_pair_merge_loop_back
   (T : Type) (ls0 : List T) (ls1 : List T) (i : U32) (ret0 : T) :
   Result (List T)
@@ -611,7 +607,7 @@ divergent def list_nth_shared_mut_loop_pair_merge_loop_back
     | List.Nil => Result.fail Error.panic
   | List.Nil => Result.fail Error.panic
 
-/- [loops::list_nth_shared_mut_loop_pair_merge] -/
+/- [loops::list_nth_shared_mut_loop_pair_merge]: backward function 0 -/
 def list_nth_shared_mut_loop_pair_merge_back
   (T : Type) (ls0 : List T) (ls1 : List T) (i : U32) (ret0 : T) :
   Result (List T)
diff --git a/tests/lean/NoNestedBorrows.lean b/tests/lean/NoNestedBorrows.lean
index e4fa7612..dc744a29 100644
--- a/tests/lean/NoNestedBorrows.lean
+++ b/tests/lean/NoNestedBorrows.lean
@@ -35,64 +35,64 @@ inductive Sum (T1 T2 : Type) :=
 | Left : T1 → Sum T1 T2
 | Right : T2 → Sum T1 T2
 
-/- [no_nested_borrows::neg_test] -/
-def neg_test_fwd (x : I32) : Result I32 :=
+/- [no_nested_borrows::neg_test]: forward function -/
+def neg_test (x : I32) : Result I32 :=
   - x
 
-/- [no_nested_borrows::add_test] -/
-def add_test_fwd (x : U32) (y : U32) : Result U32 :=
+/- [no_nested_borrows::add_test]: forward function -/
+def add_test (x : U32) (y : U32) : Result U32 :=
   x + y
 
-/- [no_nested_borrows::subs_test] -/
-def subs_test_fwd (x : U32) (y : U32) : Result U32 :=
+/- [no_nested_borrows::subs_test]: forward function -/
+def subs_test (x : U32) (y : U32) : Result U32 :=
   x - y
 
-/- [no_nested_borrows::div_test] -/
-def div_test_fwd (x : U32) (y : U32) : Result U32 :=
+/- [no_nested_borrows::div_test]: forward function -/
+def div_test (x : U32) (y : U32) : Result U32 :=
   x / y
 
-/- [no_nested_borrows::div_test1] -/
-def div_test1_fwd (x : U32) : Result U32 :=
+/- [no_nested_borrows::div_test1]: forward function -/
+def div_test1 (x : U32) : Result U32 :=
   x / (U32.ofInt 2 (by intlit))
 
-/- [no_nested_borrows::rem_test] -/
-def rem_test_fwd (x : U32) (y : U32) : Result U32 :=
+/- [no_nested_borrows::rem_test]: forward function -/
+def rem_test (x : U32) (y : U32) : Result U32 :=
   x % y
 
-/- [no_nested_borrows::cast_test] -/
-def cast_test_fwd (x : U32) : Result I32 :=
+/- [no_nested_borrows::cast_test]: forward function -/
+def cast_test (x : U32) : Result I32 :=
   Scalar.cast .I32 x
 
-/- [no_nested_borrows::test2] -/
-def test2_fwd : Result Unit :=
+/- [no_nested_borrows::test2]: forward function -/
+def test2 : Result Unit :=
   do
     let _ ← (U32.ofInt 23 (by intlit)) + (U32.ofInt 44 (by intlit))
     Result.ret ()
 
 /- Unit test for [no_nested_borrows::test2] -/
-#assert (test2_fwd == .ret ())
+#assert (test2 == .ret ())
 
-/- [no_nested_borrows::get_max] -/
-def get_max_fwd (x : U32) (y : U32) : Result U32 :=
+/- [no_nested_borrows::get_max]: forward function -/
+def get_max (x : U32) (y : U32) : Result U32 :=
   if x >= y
   then Result.ret x
   else Result.ret y
 
-/- [no_nested_borrows::test3] -/
-def test3_fwd : Result Unit :=
+/- [no_nested_borrows::test3]: forward function -/
+def test3 : Result Unit :=
   do
-    let x ← get_max_fwd (U32.ofInt 4 (by intlit)) (U32.ofInt 3 (by intlit))
-    let y ← get_max_fwd (U32.ofInt 10 (by intlit)) (U32.ofInt 11 (by intlit))
+    let x ← get_max (U32.ofInt 4 (by intlit)) (U32.ofInt 3 (by intlit))
+    let y ← get_max (U32.ofInt 10 (by intlit)) (U32.ofInt 11 (by intlit))
     let z ← x + y
     if not (z = (U32.ofInt 15 (by intlit)))
     then Result.fail Error.panic
     else Result.ret ()
 
 /- Unit test for [no_nested_borrows::test3] -/
-#assert (test3_fwd == .ret ())
+#assert (test3 == .ret ())
 
-/- [no_nested_borrows::test_neg1] -/
-def test_neg1_fwd : Result Unit :=
+/- [no_nested_borrows::test_neg1]: forward function -/
+def test_neg1 : Result Unit :=
   do
     let y ← - (I32.ofInt 3 (by intlit))
     if not (y = (I32.ofInt (-(3:Int)) (by intlit)))
@@ -100,19 +100,19 @@ def test_neg1_fwd : Result Unit :=
     else Result.ret ()
 
 /- Unit test for [no_nested_borrows::test_neg1] -/
-#assert (test_neg1_fwd == .ret ())
+#assert (test_neg1 == .ret ())
 
-/- [no_nested_borrows::refs_test1] -/
-def refs_test1_fwd : Result Unit :=
+/- [no_nested_borrows::refs_test1]: forward function -/
+def refs_test1 : Result Unit :=
   if not ((I32.ofInt 1 (by intlit)) = (I32.ofInt 1 (by intlit)))
   then Result.fail Error.panic
   else Result.ret ()
 
 /- Unit test for [no_nested_borrows::refs_test1] -/
-#assert (refs_test1_fwd == .ret ())
+#assert (refs_test1 == .ret ())
 
-/- [no_nested_borrows::refs_test2] -/
-def refs_test2_fwd : Result Unit :=
+/- [no_nested_borrows::refs_test2]: forward function -/
+def refs_test2 : Result Unit :=
   if not ((I32.ofInt 2 (by intlit)) = (I32.ofInt 2 (by intlit)))
   then Result.fail Error.panic
   else
@@ -127,17 +127,17 @@ def refs_test2_fwd : Result Unit :=
         else Result.ret ()
 
 /- Unit test for [no_nested_borrows::refs_test2] -/
-#assert (refs_test2_fwd == .ret ())
+#assert (refs_test2 == .ret ())
 
-/- [no_nested_borrows::test_list1] -/
-def test_list1_fwd : Result Unit :=
+/- [no_nested_borrows::test_list1]: forward function -/
+def test_list1 : Result Unit :=
   Result.ret ()
 
 /- Unit test for [no_nested_borrows::test_list1] -/
-#assert (test_list1_fwd == .ret ())
+#assert (test_list1 == .ret ())
 
-/- [no_nested_borrows::test_box1] -/
-def test_box1_fwd : Result Unit :=
+/- [no_nested_borrows::test_box1]: forward function -/
+def test_box1 : Result Unit :=
   let b := (I32.ofInt 1 (by intlit))
   let x := b
   if not (x = (I32.ofInt 1 (by intlit)))
@@ -145,90 +145,90 @@ def test_box1_fwd : Result Unit :=
   else Result.ret ()
 
 /- Unit test for [no_nested_borrows::test_box1] -/
-#assert (test_box1_fwd == .ret ())
+#assert (test_box1 == .ret ())
 
-/- [no_nested_borrows::copy_int] -/
-def copy_int_fwd (x : I32) : Result I32 :=
+/- [no_nested_borrows::copy_int]: forward function -/
+def copy_int (x : I32) : Result I32 :=
   Result.ret x
 
-/- [no_nested_borrows::test_unreachable] -/
-def test_unreachable_fwd (b : Bool) : Result Unit :=
+/- [no_nested_borrows::test_unreachable]: forward function -/
+def test_unreachable (b : Bool) : Result Unit :=
   if b
   then Result.fail Error.panic
   else Result.ret ()
 
-/- [no_nested_borrows::test_panic] -/
-def test_panic_fwd (b : Bool) : Result Unit :=
+/- [no_nested_borrows::test_panic]: forward function -/
+def test_panic (b : Bool) : Result Unit :=
   if b
   then Result.fail Error.panic
   else Result.ret ()
 
-/- [no_nested_borrows::test_copy_int] -/
-def test_copy_int_fwd : Result Unit :=
+/- [no_nested_borrows::test_copy_int]: forward function -/
+def test_copy_int : Result Unit :=
   do
-    let y ← copy_int_fwd (I32.ofInt 0 (by intlit))
+    let y ← copy_int (I32.ofInt 0 (by intlit))
     if not ((I32.ofInt 0 (by intlit)) = y)
     then Result.fail Error.panic
     else Result.ret ()
 
 /- Unit test for [no_nested_borrows::test_copy_int] -/
-#assert (test_copy_int_fwd == .ret ())
+#assert (test_copy_int == .ret ())
 
-/- [no_nested_borrows::is_cons] -/
-def is_cons_fwd (T : Type) (l : List T) : Result Bool :=
+/- [no_nested_borrows::is_cons]: forward function -/
+def is_cons (T : Type) (l : List T) : Result Bool :=
   match l with
   | List.Cons t l0 => Result.ret true
   | List.Nil => Result.ret false
 
-/- [no_nested_borrows::test_is_cons] -/
-def test_is_cons_fwd : Result Unit :=
+/- [no_nested_borrows::test_is_cons]: forward function -/
+def test_is_cons : Result Unit :=
   do
     let l := List.Nil
-    let b ← is_cons_fwd I32 (List.Cons (I32.ofInt 0 (by intlit)) l)
+    let b ← is_cons I32 (List.Cons (I32.ofInt 0 (by intlit)) l)
     if not b
     then Result.fail Error.panic
     else Result.ret ()
 
 /- Unit test for [no_nested_borrows::test_is_cons] -/
-#assert (test_is_cons_fwd == .ret ())
+#assert (test_is_cons == .ret ())
 
-/- [no_nested_borrows::split_list] -/
-def split_list_fwd (T : Type) (l : List T) : Result (T × (List T)) :=
+/- [no_nested_borrows::split_list]: forward function -/
+def split_list (T : Type) (l : List T) : Result (T × (List T)) :=
   match l with
   | List.Cons hd tl => Result.ret (hd, tl)
   | List.Nil => Result.fail Error.panic
 
-/- [no_nested_borrows::test_split_list] -/
-def test_split_list_fwd : Result Unit :=
+/- [no_nested_borrows::test_split_list]: forward function -/
+def test_split_list : Result Unit :=
   do
     let l := List.Nil
-    let p ← split_list_fwd I32 (List.Cons (I32.ofInt 0 (by intlit)) l)
+    let p ← split_list I32 (List.Cons (I32.ofInt 0 (by intlit)) l)
     let (hd, _) := p
     if not (hd = (I32.ofInt 0 (by intlit)))
     then Result.fail Error.panic
     else Result.ret ()
 
 /- Unit test for [no_nested_borrows::test_split_list] -/
-#assert (test_split_list_fwd == .ret ())
+#assert (test_split_list == .ret ())
 
-/- [no_nested_borrows::choose] -/
-def choose_fwd (T : Type) (b : Bool) (x : T) (y : T) : Result T :=
+/- [no_nested_borrows::choose]: forward function -/
+def choose (T : Type) (b : Bool) (x : T) (y : T) : Result T :=
   if b
   then Result.ret x
   else Result.ret y
 
-/- [no_nested_borrows::choose] -/
+/- [no_nested_borrows::choose]: backward function 0 -/
 def choose_back
   (T : Type) (b : Bool) (x : T) (y : T) (ret0 : T) : Result (T × T) :=
   if b
   then Result.ret (ret0, y)
   else Result.ret (x, ret0)
 
-/- [no_nested_borrows::choose_test] -/
-def choose_test_fwd : Result Unit :=
+/- [no_nested_borrows::choose_test]: forward function -/
+def choose_test : Result Unit :=
   do
     let z ←
-      choose_fwd I32 true (I32.ofInt 0 (by intlit)) (I32.ofInt 0 (by intlit))
+      choose I32 true (I32.ofInt 0 (by intlit)) (I32.ofInt 0 (by intlit))
     let z0 ← z + (I32.ofInt 1 (by intlit))
     if not (z0 = (I32.ofInt 1 (by intlit)))
     then Result.fail Error.panic
@@ -245,10 +245,10 @@ def choose_test_fwd : Result Unit :=
           else Result.ret ()
 
 /- Unit test for [no_nested_borrows::choose_test] -/
-#assert (choose_test_fwd == .ret ())
+#assert (choose_test == .ret ())
 
-/- [no_nested_borrows::test_char] -/
-def test_char_fwd : Result Char :=
+/- [no_nested_borrows::test_char]: forward function -/
+def test_char : Result Char :=
   Result.ret 'a'
 
 mutual
@@ -265,40 +265,38 @@ inductive Tree (T : Type) :=
 
 end
 
-/- [no_nested_borrows::list_length] -/
-divergent def list_length_fwd (T : Type) (l : List T) : Result U32 :=
+/- [no_nested_borrows::list_length]: forward function -/
+divergent def list_length (T : Type) (l : List T) : Result U32 :=
   match l with
   | List.Cons t l1 =>
     do
-      let i ← list_length_fwd T l1
+      let i ← list_length T l1
       (U32.ofInt 1 (by intlit)) + i
   | List.Nil => Result.ret (U32.ofInt 0 (by intlit))
 
-/- [no_nested_borrows::list_nth_shared] -/
-divergent def list_nth_shared_fwd
-  (T : Type) (l : List T) (i : U32) : Result T :=
+/- [no_nested_borrows::list_nth_shared]: forward function -/
+divergent def list_nth_shared (T : Type) (l : List T) (i : U32) : Result T :=
   match l with
   | List.Cons x tl =>
     if i = (U32.ofInt 0 (by intlit))
     then Result.ret x
-    else
-      do
-        let i0 ← i - (U32.ofInt 1 (by intlit))
-        list_nth_shared_fwd T tl i0
+    else do
+           let i0 ← i - (U32.ofInt 1 (by intlit))
+           list_nth_shared T tl i0
   | List.Nil => Result.fail Error.panic
 
-/- [no_nested_borrows::list_nth_mut] -/
-divergent def list_nth_mut_fwd (T : Type) (l : List T) (i : U32) : Result T :=
+/- [no_nested_borrows::list_nth_mut]: forward function -/
+divergent def list_nth_mut (T : Type) (l : List T) (i : U32) : Result T :=
   match l with
   | List.Cons x tl =>
     if i = (U32.ofInt 0 (by intlit))
     then Result.ret x
     else do
            let i0 ← i - (U32.ofInt 1 (by intlit))
-           list_nth_mut_fwd T tl i0
+           list_nth_mut T tl i0
   | List.Nil => Result.fail Error.panic
 
-/- [no_nested_borrows::list_nth_mut] -/
+/- [no_nested_borrows::list_nth_mut]: backward function 0 -/
 divergent def list_nth_mut_back
   (T : Type) (l : List T) (i : U32) (ret0 : T) : Result (List T) :=
   match l with
@@ -312,46 +310,47 @@ divergent def list_nth_mut_back
         Result.ret (List.Cons x tl0)
   | List.Nil => Result.fail Error.panic
 
-/- [no_nested_borrows::list_rev_aux] -/
-divergent def list_rev_aux_fwd
+/- [no_nested_borrows::list_rev_aux]: forward function -/
+divergent def list_rev_aux
   (T : Type) (li : List T) (lo : List T) : Result (List T) :=
   match li with
-  | List.Cons hd tl => list_rev_aux_fwd T tl (List.Cons hd lo)
+  | List.Cons hd tl => list_rev_aux T tl (List.Cons hd lo)
   | List.Nil => Result.ret lo
 
-/- [no_nested_borrows::list_rev] -/
-def list_rev_fwd_back (T : Type) (l : List T) : Result (List T) :=
-  let li := mem.replace_fwd (List T) l List.Nil
-  list_rev_aux_fwd T li List.Nil
+/- [no_nested_borrows::list_rev]: merged forward/backward function
+   (there is a single backward function, and the forward function returns ()) -/
+def list_rev (T : Type) (l : List T) : Result (List T) :=
+  let li := mem.replace (List T) l List.Nil
+  list_rev_aux T li List.Nil
 
-/- [no_nested_borrows::test_list_functions] -/
-def test_list_functions_fwd : Result Unit :=
+/- [no_nested_borrows::test_list_functions]: forward function -/
+def test_list_functions : Result Unit :=
   do
     let l := List.Nil
     let l0 := List.Cons (I32.ofInt 2 (by intlit)) l
     let l1 := List.Cons (I32.ofInt 1 (by intlit)) l0
-    let i ← list_length_fwd I32 (List.Cons (I32.ofInt 0 (by intlit)) l1)
+    let i ← list_length I32 (List.Cons (I32.ofInt 0 (by intlit)) l1)
     if not (i = (U32.ofInt 3 (by intlit)))
     then Result.fail Error.panic
     else
       do
         let i0 ←
-          list_nth_shared_fwd I32 (List.Cons (I32.ofInt 0 (by intlit)) l1)
+          list_nth_shared I32 (List.Cons (I32.ofInt 0 (by intlit)) l1)
             (U32.ofInt 0 (by intlit))
         if not (i0 = (I32.ofInt 0 (by intlit)))
         then Result.fail Error.panic
         else
           do
             let i1 ←
-              list_nth_shared_fwd I32 (List.Cons (I32.ofInt 0 (by intlit)) l1)
+              list_nth_shared I32 (List.Cons (I32.ofInt 0 (by intlit)) l1)
                 (U32.ofInt 1 (by intlit))
             if not (i1 = (I32.ofInt 1 (by intlit)))
             then Result.fail Error.panic
             else
               do
                 let i2 ←
-                  list_nth_shared_fwd I32 (List.Cons (I32.ofInt 0 (by intlit))
-                    l1) (U32.ofInt 2 (by intlit))
+                  list_nth_shared I32 (List.Cons (I32.ofInt 0 (by intlit)) l1)
+                    (U32.ofInt 2 (by intlit))
                 if not (i2 = (I32.ofInt 2 (by intlit)))
                 then Result.fail Error.panic
                 else
@@ -360,74 +359,72 @@ def test_list_functions_fwd : Result Unit :=
                       list_nth_mut_back I32 (List.Cons
                         (I32.ofInt 0 (by intlit)) l1) (U32.ofInt 1 (by intlit))
                         (I32.ofInt 3 (by intlit))
-                    let i3 ←
-                      list_nth_shared_fwd I32 ls (U32.ofInt 0 (by intlit))
+                    let i3 ← list_nth_shared I32 ls (U32.ofInt 0 (by intlit))
                     if not (i3 = (I32.ofInt 0 (by intlit)))
                     then Result.fail Error.panic
                     else
                       do
                         let i4 ←
-                          list_nth_shared_fwd I32 ls (U32.ofInt 1 (by intlit))
+                          list_nth_shared I32 ls (U32.ofInt 1 (by intlit))
                         if not (i4 = (I32.ofInt 3 (by intlit)))
                         then Result.fail Error.panic
                         else
                           do
                             let i5 ←
-                              list_nth_shared_fwd I32 ls
-                                (U32.ofInt 2 (by intlit))
+                              list_nth_shared I32 ls (U32.ofInt 2 (by intlit))
                             if not (i5 = (I32.ofInt 2 (by intlit)))
                             then Result.fail Error.panic
                             else Result.ret ()
 
 /- Unit test for [no_nested_borrows::test_list_functions] -/
-#assert (test_list_functions_fwd == .ret ())
+#assert (test_list_functions == .ret ())
 
-/- [no_nested_borrows::id_mut_pair1] -/
-def id_mut_pair1_fwd (T1 T2 : Type) (x : T1) (y : T2) : Result (T1 × T2) :=
+/- [no_nested_borrows::id_mut_pair1]: forward function -/
+def id_mut_pair1 (T1 T2 : Type) (x : T1) (y : T2) : Result (T1 × T2) :=
   Result.ret (x, y)
 
-/- [no_nested_borrows::id_mut_pair1] -/
+/- [no_nested_borrows::id_mut_pair1]: backward function 0 -/
 def id_mut_pair1_back
   (T1 T2 : Type) (x : T1) (y : T2) (ret0 : (T1 × T2)) : Result (T1 × T2) :=
   let (t, t0) := ret0
   Result.ret (t, t0)
 
-/- [no_nested_borrows::id_mut_pair2] -/
-def id_mut_pair2_fwd (T1 T2 : Type) (p : (T1 × T2)) : Result (T1 × T2) :=
+/- [no_nested_borrows::id_mut_pair2]: forward function -/
+def id_mut_pair2 (T1 T2 : Type) (p : (T1 × T2)) : Result (T1 × T2) :=
   let (t, t0) := p
   Result.ret (t, t0)
 
-/- [no_nested_borrows::id_mut_pair2] -/
+/- [no_nested_borrows::id_mut_pair2]: backward function 0 -/
 def id_mut_pair2_back
   (T1 T2 : Type) (p : (T1 × T2)) (ret0 : (T1 × T2)) : Result (T1 × T2) :=
   let (t, t0) := ret0
   Result.ret (t, t0)
 
-/- [no_nested_borrows::id_mut_pair3] -/
-def id_mut_pair3_fwd (T1 T2 : Type) (x : T1) (y : T2) : Result (T1 × T2) :=
+/- [no_nested_borrows::id_mut_pair3]: forward function -/
+def id_mut_pair3 (T1 T2 : Type) (x : T1) (y : T2) : Result (T1 × T2) :=
   Result.ret (x, y)
 
-/- [no_nested_borrows::id_mut_pair3] -/
+/- [no_nested_borrows::id_mut_pair3]: backward function 0 -/
 def id_mut_pair3_back'a
   (T1 T2 : Type) (x : T1) (y : T2) (ret0 : T1) : Result T1 :=
   Result.ret ret0
 
-/- [no_nested_borrows::id_mut_pair3] -/
+/- [no_nested_borrows::id_mut_pair3]: backward function 1 -/
 def id_mut_pair3_back'b
   (T1 T2 : Type) (x : T1) (y : T2) (ret0 : T2) : Result T2 :=
   Result.ret ret0
 
-/- [no_nested_borrows::id_mut_pair4] -/
-def id_mut_pair4_fwd (T1 T2 : Type) (p : (T1 × T2)) : Result (T1 × T2) :=
+/- [no_nested_borrows::id_mut_pair4]: forward function -/
+def id_mut_pair4 (T1 T2 : Type) (p : (T1 × T2)) : Result (T1 × T2) :=
   let (t, t0) := p
   Result.ret (t, t0)
 
-/- [no_nested_borrows::id_mut_pair4] -/
+/- [no_nested_borrows::id_mut_pair4]: backward function 0 -/
 def id_mut_pair4_back'a
   (T1 T2 : Type) (p : (T1 × T2)) (ret0 : T1) : Result T1 :=
   Result.ret ret0
 
-/- [no_nested_borrows::id_mut_pair4] -/
+/- [no_nested_borrows::id_mut_pair4]: backward function 1 -/
 def id_mut_pair4_back'b
   (T1 T2 : Type) (p : (T1 × T2)) (ret0 : T2) : Result T2 :=
   Result.ret ret0
@@ -436,24 +433,24 @@ def id_mut_pair4_back'b
 structure StructWithTuple (T1 T2 : Type) where
   struct_with_tuple_p : (T1 × T2)
 
-/- [no_nested_borrows::new_tuple1] -/
-def new_tuple1_fwd : Result (StructWithTuple U32 U32) :=
+/- [no_nested_borrows::new_tuple1]: forward function -/
+def new_tuple1 : Result (StructWithTuple U32 U32) :=
   Result.ret
   {
     struct_with_tuple_p :=
       ((U32.ofInt 1 (by intlit)), (U32.ofInt 2 (by intlit)))
   }
 
-/- [no_nested_borrows::new_tuple2] -/
-def new_tuple2_fwd : Result (StructWithTuple I16 I16) :=
+/- [no_nested_borrows::new_tuple2]: forward function -/
+def new_tuple2 : Result (StructWithTuple I16 I16) :=
   Result.ret
   {
     struct_with_tuple_p :=
       ((I16.ofInt 1 (by intlit)), (I16.ofInt 2 (by intlit)))
   }
 
-/- [no_nested_borrows::new_tuple3] -/
-def new_tuple3_fwd : Result (StructWithTuple U64 I64) :=
+/- [no_nested_borrows::new_tuple3]: forward function -/
+def new_tuple3 : Result (StructWithTuple U64 I64) :=
   Result.ret
   {
     struct_with_tuple_p :=
@@ -464,8 +461,8 @@ def new_tuple3_fwd : Result (StructWithTuple U64 I64) :=
 structure StructWithPair (T1 T2 : Type) where
   struct_with_pair_p : Pair T1 T2
 
-/- [no_nested_borrows::new_pair1] -/
-def new_pair1_fwd : Result (StructWithPair U32 U32) :=
+/- [no_nested_borrows::new_pair1]: forward function -/
+def new_pair1 : Result (StructWithPair U32 U32) :=
   Result.ret
   {
     struct_with_pair_p :=
@@ -475,68 +472,69 @@ def new_pair1_fwd : Result (StructWithPair U32 U32) :=
       }
   }
 
-/- [no_nested_borrows::test_constants] -/
-def test_constants_fwd : Result Unit :=
+/- [no_nested_borrows::test_constants]: forward function -/
+def test_constants : Result Unit :=
   do
-    let swt ← new_tuple1_fwd
+    let swt ← new_tuple1
     let (i, _) := swt.struct_with_tuple_p
     if not (i = (U32.ofInt 1 (by intlit)))
     then Result.fail Error.panic
     else
       do
-        let swt0 ← new_tuple2_fwd
+        let swt0 ← new_tuple2
         let (i0, _) := swt0.struct_with_tuple_p
         if not (i0 = (I16.ofInt 1 (by intlit)))
         then Result.fail Error.panic
         else
           do
-            let swt1 ← new_tuple3_fwd
+            let swt1 ← new_tuple3
             let (i1, _) := swt1.struct_with_tuple_p
             if not (i1 = (U64.ofInt 1 (by intlit)))
             then Result.fail Error.panic
             else
               do
-                let swp ← new_pair1_fwd
+                let swp ← new_pair1
                 if not (swp.struct_with_pair_p.pair_x =
                   (U32.ofInt 1 (by intlit)))
                 then Result.fail Error.panic
                 else Result.ret ()
 
 /- Unit test for [no_nested_borrows::test_constants] -/
-#assert (test_constants_fwd == .ret ())
+#assert (test_constants == .ret ())
 
-/- [no_nested_borrows::test_weird_borrows1] -/
-def test_weird_borrows1_fwd : Result Unit :=
+/- [no_nested_borrows::test_weird_borrows1]: forward function -/
+def test_weird_borrows1 : Result Unit :=
   Result.ret ()
 
 /- Unit test for [no_nested_borrows::test_weird_borrows1] -/
-#assert (test_weird_borrows1_fwd == .ret ())
+#assert (test_weird_borrows1 == .ret ())
 
-/- [no_nested_borrows::test_mem_replace] -/
-def test_mem_replace_fwd_back (px : U32) : Result U32 :=
-  let y := mem.replace_fwd U32 px (U32.ofInt 1 (by intlit))
+/- [no_nested_borrows::test_mem_replace]: merged forward/backward function
+   (there is a single backward function, and the forward function returns ()) -/
+def test_mem_replace (px : U32) : Result U32 :=
+  let y := mem.replace U32 px (U32.ofInt 1 (by intlit))
   if not (y = (U32.ofInt 0 (by intlit)))
   then Result.fail Error.panic
   else Result.ret (U32.ofInt 2 (by intlit))
 
-/- [no_nested_borrows::test_shared_borrow_bool1] -/
-def test_shared_borrow_bool1_fwd (b : Bool) : Result U32 :=
+/- [no_nested_borrows::test_shared_borrow_bool1]: forward function -/
+def test_shared_borrow_bool1 (b : Bool) : Result U32 :=
   if b
   then Result.ret (U32.ofInt 0 (by intlit))
   else Result.ret (U32.ofInt 1 (by intlit))
 
-/- [no_nested_borrows::test_shared_borrow_bool2] -/
-def test_shared_borrow_bool2_fwd : Result U32 :=
+/- [no_nested_borrows::test_shared_borrow_bool2]: forward function -/
+def test_shared_borrow_bool2 : Result U32 :=
   Result.ret (U32.ofInt 0 (by intlit))
 
-/- [no_nested_borrows::test_shared_borrow_enum1] -/
-def test_shared_borrow_enum1_fwd (l : List U32) : Result U32 :=
+/- [no_nested_borrows::test_shared_borrow_enum1]: forward function -/
+def test_shared_borrow_enum1 (l : List U32) : Result U32 :=
   match l with
   | List.Cons i l0 => Result.ret (U32.ofInt 1 (by intlit))
   | List.Nil => Result.ret (U32.ofInt 0 (by intlit))
 
-/- [no_nested_borrows::test_shared_borrow_enum2] -/
-def test_shared_borrow_enum2_fwd : Result U32 :=
+/- [no_nested_borrows::test_shared_borrow_enum2]: forward function -/
+def test_shared_borrow_enum2 : Result U32 :=
   Result.ret (U32.ofInt 0 (by intlit))
 
 end no_nested_borrows
diff --git a/tests/lean/Paper.lean b/tests/lean/Paper.lean
index 9f63b460..ade65656 100644
--- a/tests/lean/Paper.lean
+++ b/tests/lean/Paper.lean
@@ -4,39 +4,40 @@ import Base
 open Primitives
 namespace paper
 
-/- [paper::ref_incr] -/
-def ref_incr_fwd_back (x : I32) : Result I32 :=
+/- [paper::ref_incr]: merged forward/backward function
+   (there is a single backward function, and the forward function returns ()) -/
+def ref_incr (x : I32) : Result I32 :=
   x + (I32.ofInt 1 (by intlit))
 
-/- [paper::test_incr] -/
-def test_incr_fwd : Result Unit :=
+/- [paper::test_incr]: forward function -/
+def test_incr : Result Unit :=
   do
-    let x ← ref_incr_fwd_back (I32.ofInt 0 (by intlit))
+    let x ← ref_incr (I32.ofInt 0 (by intlit))
     if not (x = (I32.ofInt 1 (by intlit)))
     then Result.fail Error.panic
     else Result.ret ()
 
 /- Unit test for [paper::test_incr] -/
-#assert (test_incr_fwd == .ret ())
+#assert (test_incr == .ret ())
 
-/- [paper::choose] -/
-def choose_fwd (T : Type) (b : Bool) (x : T) (y : T) : Result T :=
+/- [paper::choose]: forward function -/
+def choose (T : Type) (b : Bool) (x : T) (y : T) : Result T :=
   if b
   then Result.ret x
   else Result.ret y
 
-/- [paper::choose] -/
+/- [paper::choose]: backward function 0 -/
 def choose_back
   (T : Type) (b : Bool) (x : T) (y : T) (ret0 : T) : Result (T × T) :=
   if b
   then Result.ret (ret0, y)
   else Result.ret (x, ret0)
 
-/- [paper::test_choose] -/
-def test_choose_fwd : Result Unit :=
+/- [paper::test_choose]: forward function -/
+def test_choose : Result Unit :=
   do
     let z ←
-      choose_fwd I32 true (I32.ofInt 0 (by intlit)) (I32.ofInt 0 (by intlit))
+      choose I32 true (I32.ofInt 0 (by intlit)) (I32.ofInt 0 (by intlit))
     let z0 ← z + (I32.ofInt 1 (by intlit))
     if not (z0 = (I32.ofInt 1 (by intlit)))
     then Result.fail Error.panic
@@ -53,25 +54,25 @@ def test_choose_fwd : Result Unit :=
           else Result.ret ()
 
 /- Unit test for [paper::test_choose] -/
-#assert (test_choose_fwd == .ret ())
+#assert (test_choose == .ret ())
 
 /- [paper::List] -/
 inductive List (T : Type) :=
 | Cons : T → List T → List T
 | Nil : List T
 
-/- [paper::list_nth_mut] -/
-divergent def list_nth_mut_fwd (T : Type) (l : List T) (i : U32) : Result T :=
+/- [paper::list_nth_mut]: forward function -/
+divergent def list_nth_mut (T : Type) (l : List T) (i : U32) : Result T :=
   match l with
   | List.Cons x tl =>
     if i = (U32.ofInt 0 (by intlit))
     then Result.ret x
     else do
            let i0 ← i - (U32.ofInt 1 (by intlit))
-           list_nth_mut_fwd T tl i0
+           list_nth_mut T tl i0
   | List.Nil => Result.fail Error.panic
 
-/- [paper::list_nth_mut] -/
+/- [paper::list_nth_mut]: backward function 0 -/
 divergent def list_nth_mut_back
   (T : Type) (l : List T) (i : U32) (ret0 : T) : Result (List T) :=
   match l with
@@ -85,40 +86,40 @@ divergent def list_nth_mut_back
         Result.ret (List.Cons x tl0)
   | List.Nil => Result.fail Error.panic
 
-/- [paper::sum] -/
-divergent def sum_fwd (l : List I32) : Result I32 :=
+/- [paper::sum]: forward function -/
+divergent def sum (l : List I32) : Result I32 :=
   match l with
   | List.Cons x tl => do
-                        let i ← sum_fwd tl
+                        let i ← sum tl
                         x + i
   | List.Nil => Result.ret (I32.ofInt 0 (by intlit))
 
-/- [paper::test_nth] -/
-def test_nth_fwd : Result Unit :=
+/- [paper::test_nth]: forward function -/
+def test_nth : Result Unit :=
   do
     let l := List.Nil
     let l0 := List.Cons (I32.ofInt 3 (by intlit)) l
     let l1 := List.Cons (I32.ofInt 2 (by intlit)) l0
     let x ←
-      list_nth_mut_fwd I32 (List.Cons (I32.ofInt 1 (by intlit)) l1)
+      list_nth_mut I32 (List.Cons (I32.ofInt 1 (by intlit)) l1)
         (U32.ofInt 2 (by intlit))
     let x0 ← x + (I32.ofInt 1 (by intlit))
     let l2 ←
       list_nth_mut_back I32 (List.Cons (I32.ofInt 1 (by intlit)) l1)
         (U32.ofInt 2 (by intlit)) x0
-    let i ← sum_fwd l2
+    let i ← sum l2
     if not (i = (I32.ofInt 7 (by intlit)))
     then Result.fail Error.panic
     else Result.ret ()
 
 /- Unit test for [paper::test_nth] -/
-#assert (test_nth_fwd == .ret ())
+#assert (test_nth == .ret ())
 
-/- [paper::call_choose] -/
-def call_choose_fwd (p : (U32 × U32)) : Result U32 :=
+/- [paper::call_choose]: forward function -/
+def call_choose (p : (U32 × U32)) : Result U32 :=
   do
     let (px, py) := p
-    let pz ← choose_fwd U32 true px py
+    let pz ← choose U32 true px py
     let pz0 ← pz + (U32.ofInt 1 (by intlit))
     let (px0, _) ← choose_back U32 true px py pz0
     Result.ret px0
diff --git a/tests/lean/PoloniusList.lean b/tests/lean/PoloniusList.lean
index 1d7ec99b..1453c275 100644
--- a/tests/lean/PoloniusList.lean
+++ b/tests/lean/PoloniusList.lean
@@ -9,17 +9,16 @@ inductive List (T : Type) :=
 | Cons : T → List T → List T
 | Nil : List T
 
-/- [polonius_list::get_list_at_x] -/
-divergent def get_list_at_x_fwd
-  (ls : List U32) (x : U32) : Result (List U32) :=
+/- [polonius_list::get_list_at_x]: forward function -/
+divergent def get_list_at_x (ls : List U32) (x : U32) : Result (List U32) :=
   match ls with
   | List.Cons hd tl =>
     if hd = x
     then Result.ret (List.Cons hd tl)
-    else get_list_at_x_fwd tl x
+    else get_list_at_x tl x
   | List.Nil => Result.ret List.Nil
 
-/- [polonius_list::get_list_at_x] -/
+/- [polonius_list::get_list_at_x]: backward function 0 -/
 divergent def get_list_at_x_back
   (ls : List U32) (x : U32) (ret0 : List U32) : Result (List U32) :=
   match ls with