Merge pull request #31 from AeneasVerif/son_lean_backend

Improve the Lean backend

1 files changed, 611 insertions, 0 deletions

diff --git a/tests/lean/Loops/Funs.lean b/tests/lean/Loops/Funs.lean
new file mode 100644
index 00000000..f7e6603d
--- /dev/null
+++ b/tests/lean/Loops/Funs.lean
@@ -0,0 +1,611 @@
+-- THIS FILE WAS AUTOMATICALLY GENERATED BY AENEAS
+-- [loops]: function definitions
+import Base
+import Loops.Types
+open Primitives
+namespace loops
+
+/- [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)
+         sum_loop max i0 s0
+  else s * (U32.ofInt 2)
+
+/- [loops::sum]: forward function -/
+def sum (max : U32) : Result U32 :=
+  sum_loop max (U32.ofInt 0) (U32.ofInt 0)
+
+/- [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)
+      sum_with_mut_borrows_loop max mi0 ms0
+  else ms * (U32.ofInt 2)
+
+/- [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) (U32.ofInt 0)
+
+/- [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)
+      let s0 ← s + i0
+      sum_with_shared_borrows_loop max i0 s0
+  else s * (U32.ofInt 2)
+
+/- [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) (U32.ofInt 0)
+
+/- [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)
+      let v0 ← Vec.index_mut_back U32 v i (U32.ofInt 0)
+      clear_loop v0 i1
+  else Result.ret v
+
+/- [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)
+
+/- [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 x tl
+  | List.Nil => Result.ret false
+
+/- [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]: 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 =>
+    if i = (U32.ofInt 0)
+    then Result.ret x
+    else do
+           let i0 ← i - (U32.ofInt 1)
+           list_nth_mut_loop_loop T tl i0
+  | List.Nil => Result.fail Error.panic
+
+/- [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]: 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
+  | List.Cons x tl =>
+    if i = (U32.ofInt 0)
+    then Result.ret (List.Cons ret0 tl)
+    else
+      do
+        let i0 ← i - (U32.ofInt 1)
+        let tl0 ← list_nth_mut_loop_loop_back T tl i0 ret0
+        Result.ret (List.Cons x tl0)
+  | List.Nil => Result.fail Error.panic
+
+/- [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]: 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 =>
+    if i = (U32.ofInt 0)
+    then Result.ret x
+    else do
+           let i0 ← i - (U32.ofInt 1)
+           list_nth_shared_loop_loop T tl i0
+  | List.Nil => Result.fail Error.panic
+
+/- [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]: 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 x tl
+  | List.Nil => Result.fail Error.panic
+
+/- [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)
+    get_elem_mut_loop x l
+
+/- [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
+  | List.Cons y tl =>
+    if y = x
+    then Result.ret (List.Cons ret0 tl)
+    else
+      do
+        let tl0 ← get_elem_mut_loop_back x tl ret0
+        Result.ret (List.Cons y tl0)
+  | List.Nil => Result.fail Error.panic
+
+/- [loops::get_elem_mut]: backward function 0 -/
+def get_elem_mut_back
+  (slots : Vec (List Usize)) (x : Usize) (ret0 : Usize) :
+  Result (Vec (List Usize))
+  :=
+  do
+    let l ← Vec.index_mut (List Usize) slots (Usize.ofInt 0)
+    let l0 ← get_elem_mut_loop_back x l ret0
+    Vec.index_mut_back (List Usize) slots (Usize.ofInt 0) l0
+
+/- [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 x tl
+  | List.Nil => Result.fail Error.panic
+
+/- [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)
+    get_elem_shared_loop x l
+
+/- [loops::id_mut]: forward function -/
+def id_mut (T : Type) (ls : List T) : Result (List T) :=
+  Result.ret ls
+
+/- [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]: forward function -/
+def id_shared (T : Type) (ls : List T) : Result (List T) :=
+  Result.ret ls
+
+/- [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 =>
+    if i = (U32.ofInt 0)
+    then Result.ret x
+    else do
+           let i0 ← i - (U32.ofInt 1)
+           list_nth_mut_loop_with_id_loop T i0 tl
+  | List.Nil => Result.fail Error.panic
+
+/- [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 T ls
+    list_nth_mut_loop_with_id_loop T i ls0
+
+/- [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
+  | List.Cons x tl =>
+    if i = (U32.ofInt 0)
+    then Result.ret (List.Cons ret0 tl)
+    else
+      do
+        let i0 ← i - (U32.ofInt 1)
+        let tl0 ← list_nth_mut_loop_with_id_loop_back T i0 tl ret0
+        Result.ret (List.Cons x tl0)
+  | List.Nil => Result.fail Error.panic
+
+/- [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 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]: 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 =>
+    if i = (U32.ofInt 0)
+    then Result.ret x
+    else
+      do
+        let i0 ← i - (U32.ofInt 1)
+        list_nth_shared_loop_with_id_loop T i0 tl
+  | List.Nil => Result.fail Error.panic
+
+/- [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 T ls
+    list_nth_shared_loop_with_id_loop T i ls0
+
+/- [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 =>
+    match ls1 with
+    | List.Cons x1 tl1 =>
+      if i = (U32.ofInt 0)
+      then Result.ret (x0, x1)
+      else
+        do
+          let i0 ← i - (U32.ofInt 1)
+          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]: 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 T ls0 ls1 i
+
+/- [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)
+  :=
+  match ls0 with
+  | List.Cons x0 tl0 =>
+    match ls1 with
+    | List.Cons x1 tl1 =>
+      if i = (U32.ofInt 0)
+      then Result.ret (List.Cons ret0 tl0)
+      else
+        do
+          let i0 ← i - (U32.ofInt 1)
+          let tl00 ← list_nth_mut_loop_pair_loop_back'a T tl0 tl1 i0 ret0
+          Result.ret (List.Cons x0 tl00)
+    | List.Nil => Result.fail Error.panic
+  | List.Nil => Result.fail Error.panic
+
+/- [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]: 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)
+  :=
+  match ls0 with
+  | List.Cons x0 tl0 =>
+    match ls1 with
+    | List.Cons x1 tl1 =>
+      if i = (U32.ofInt 0)
+      then Result.ret (List.Cons ret0 tl1)
+      else
+        do
+          let i0 ← i - (U32.ofInt 1)
+          let tl10 ← list_nth_mut_loop_pair_loop_back'b T tl0 tl1 i0 ret0
+          Result.ret (List.Cons x1 tl10)
+    | List.Nil => Result.fail Error.panic
+  | List.Nil => Result.fail Error.panic
+
+/- [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]: 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 =>
+    match ls1 with
+    | List.Cons x1 tl1 =>
+      if i = (U32.ofInt 0)
+      then Result.ret (x0, x1)
+      else
+        do
+          let i0 ← i - (U32.ofInt 1)
+          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]: 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 T ls0 ls1 i
+
+/- [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 =>
+    match ls1 with
+    | List.Cons x1 tl1 =>
+      if i = (U32.ofInt 0)
+      then Result.ret (x0, x1)
+      else
+        do
+          let i0 ← i - (U32.ofInt 1)
+          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]: 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 T ls0 ls1 i
+
+/- [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))
+  :=
+  match ls0 with
+  | List.Cons x0 tl0 =>
+    match ls1 with
+    | List.Cons x1 tl1 =>
+      if i = (U32.ofInt 0)
+      then let (t, t0) := ret0
+           Result.ret (List.Cons t tl0, List.Cons t0 tl1)
+      else
+        do
+          let i0 ← i - (U32.ofInt 1)
+          let (tl00, tl10) ←
+            list_nth_mut_loop_pair_merge_loop_back T tl0 tl1 i0 ret0
+          Result.ret (List.Cons x0 tl00, List.Cons x1 tl10)
+    | List.Nil => Result.fail Error.panic
+  | List.Nil => Result.fail Error.panic
+
+/- [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]: 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 =>
+    match ls1 with
+    | List.Cons x1 tl1 =>
+      if i = (U32.ofInt 0)
+      then Result.ret (x0, x1)
+      else
+        do
+          let i0 ← i - (U32.ofInt 1)
+          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]: 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 T ls0 ls1 i
+
+/- [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 =>
+    match ls1 with
+    | List.Cons x1 tl1 =>
+      if i = (U32.ofInt 0)
+      then Result.ret (x0, x1)
+      else
+        do
+          let i0 ← i - (U32.ofInt 1)
+          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]: 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 T ls0 ls1 i
+
+/- [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)
+  :=
+  match ls0 with
+  | List.Cons x0 tl0 =>
+    match ls1 with
+    | List.Cons x1 tl1 =>
+      if i = (U32.ofInt 0)
+      then Result.ret (List.Cons ret0 tl0)
+      else
+        do
+          let i0 ← i - (U32.ofInt 1)
+          let tl00 ←
+            list_nth_mut_shared_loop_pair_loop_back T tl0 tl1 i0 ret0
+          Result.ret (List.Cons x0 tl00)
+    | List.Nil => Result.fail Error.panic
+  | List.Nil => Result.fail Error.panic
+
+/- [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]: 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 =>
+    match ls1 with
+    | List.Cons x1 tl1 =>
+      if i = (U32.ofInt 0)
+      then Result.ret (x0, x1)
+      else
+        do
+          let i0 ← i - (U32.ofInt 1)
+          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]: 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 T ls0 ls1 i
+
+/- [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)
+  :=
+  match ls0 with
+  | List.Cons x0 tl0 =>
+    match ls1 with
+    | List.Cons x1 tl1 =>
+      if i = (U32.ofInt 0)
+      then Result.ret (List.Cons ret0 tl0)
+      else
+        do
+          let i0 ← i - (U32.ofInt 1)
+          let tl00 ←
+            list_nth_mut_shared_loop_pair_merge_loop_back T tl0 tl1 i0 ret0
+          Result.ret (List.Cons x0 tl00)
+    | List.Nil => Result.fail Error.panic
+  | List.Nil => Result.fail Error.panic
+
+/- [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]: 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 =>
+    match ls1 with
+    | List.Cons x1 tl1 =>
+      if i = (U32.ofInt 0)
+      then Result.ret (x0, x1)
+      else
+        do
+          let i0 ← i - (U32.ofInt 1)
+          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]: 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 T ls0 ls1 i
+
+/- [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)
+  :=
+  match ls0 with
+  | List.Cons x0 tl0 =>
+    match ls1 with
+    | List.Cons x1 tl1 =>
+      if i = (U32.ofInt 0)
+      then Result.ret (List.Cons ret0 tl1)
+      else
+        do
+          let i0 ← i - (U32.ofInt 1)
+          let tl10 ←
+            list_nth_shared_mut_loop_pair_loop_back T tl0 tl1 i0 ret0
+          Result.ret (List.Cons x1 tl10)
+    | List.Nil => Result.fail Error.panic
+  | List.Nil => Result.fail Error.panic
+
+/- [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]: 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 =>
+    match ls1 with
+    | List.Cons x1 tl1 =>
+      if i = (U32.ofInt 0)
+      then Result.ret (x0, x1)
+      else
+        do
+          let i0 ← i - (U32.ofInt 1)
+          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]: 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 T ls0 ls1 i
+
+/- [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)
+  :=
+  match ls0 with
+  | List.Cons x0 tl0 =>
+    match ls1 with
+    | List.Cons x1 tl1 =>
+      if i = (U32.ofInt 0)
+      then Result.ret (List.Cons ret0 tl1)
+      else
+        do
+          let i0 ← i - (U32.ofInt 1)
+          let tl10 ←
+            list_nth_shared_mut_loop_pair_merge_loop_back T tl0 tl1 i0 ret0
+          Result.ret (List.Cons x1 tl10)
+    | List.Nil => Result.fail Error.panic
+  | List.Nil => Result.fail Error.panic
+
+/- [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)
+  :=
+  list_nth_shared_mut_loop_pair_merge_loop_back T ls0 ls1 i ret0
+
+end loops