(** THIS FILE WAS AUTOMATICALLY GENERATED BY AENEAS *)
(** [demo] *)
module Demo
open Primitives

#set-options "--z3rlimit 50 --fuel 1 --ifuel 1"

(** [demo::choose]: forward function
    Source: 'src/demo.rs', lines 5:0-5:70 *)
let choose (t : Type0) (b : bool) (x : t) (y : t) : result t =
  if b then Return x else Return y

(** [demo::choose]: backward function 0
    Source: 'src/demo.rs', lines 5:0-5:70 *)
let choose_back
  (t : Type0) (b : bool) (x : t) (y : t) (ret : t) : result (t & t) =
  if b then Return (ret, y) else Return (x, ret)

(** [demo::mul2_add1]: forward function
    Source: 'src/demo.rs', lines 13:0-13:31 *)
let mul2_add1 (x : u32) : result u32 =
  let* i = u32_add x x in u32_add i 1

(** [demo::use_mul2_add1]: forward function
    Source: 'src/demo.rs', lines 17:0-17:43 *)
let use_mul2_add1 (x : u32) (y : u32) : result u32 =
  let* i = mul2_add1 x in u32_add i y

(** [demo::incr]: merged forward/backward function
    (there is a single backward function, and the forward function returns ())
    Source: 'src/demo.rs', lines 21:0-21:31 *)
let incr (x : u32) : result u32 =
  u32_add x 1

(** [demo::CList]
    Source: 'src/demo.rs', lines 27:0-27:17 *)
type cList_t (t : Type0) =
| CList_CCons : t -> cList_t t -> cList_t t
| CList_CNil : cList_t t

(** [demo::list_nth]: forward function
    Source: 'src/demo.rs', lines 32:0-32:56 *)
let rec list_nth (t : Type0) (n : nat) (l : cList_t t) (i : u32) : result t =
  if is_zero n
  then Fail OutOfFuel
  else
    let n1 = decrease n in
    begin match l with
    | CList_CCons x tl ->
      if i = 0 then Return x else let* i1 = u32_sub i 1 in list_nth t n1 tl i1
    | CList_CNil -> Fail Failure
    end

(** [demo::list_nth_mut]: forward function
    Source: 'src/demo.rs', lines 47:0-47:68 *)
let rec list_nth_mut
  (t : Type0) (n : nat) (l : cList_t t) (i : u32) : result t =
  if is_zero n
  then Fail OutOfFuel
  else
    let n1 = decrease n in
    begin match l with
    | CList_CCons x tl ->
      if i = 0
      then Return x
      else let* i1 = u32_sub i 1 in list_nth_mut t n1 tl i1
    | CList_CNil -> Fail Failure
    end

(** [demo::list_nth_mut]: backward function 0
    Source: 'src/demo.rs', lines 47:0-47:68 *)
let rec list_nth_mut_back
  (t : Type0) (n : nat) (l : cList_t t) (i : u32) (ret : t) :
  result (cList_t t)
  =
  if is_zero n
  then Fail OutOfFuel
  else
    let n1 = decrease n in
    begin match l with
    | CList_CCons x tl ->
      if i = 0
      then Return (CList_CCons ret tl)
      else
        let* i1 = u32_sub i 1 in
        let* tl1 = list_nth_mut_back t n1 tl i1 ret in
        Return (CList_CCons x tl1)
    | CList_CNil -> Fail Failure
    end

(** [demo::list_nth_mut1]: loop 0: forward function
    Source: 'src/demo.rs', lines 62:0-71:1 *)
let rec list_nth_mut1_loop
  (t : Type0) (n : nat) (l : cList_t t) (i : u32) : result t =
  if is_zero n
  then Fail OutOfFuel
  else
    let n1 = decrease n in
    begin match l with
    | CList_CCons x tl ->
      if i = 0
      then Return x
      else let* i1 = u32_sub i 1 in list_nth_mut1_loop t n1 tl i1
    | CList_CNil -> Fail Failure
    end

(** [demo::list_nth_mut1]: forward function
    Source: 'src/demo.rs', lines 62:0-62:77 *)
let list_nth_mut1 (t : Type0) (n : nat) (l : cList_t t) (i : u32) : result t =
  list_nth_mut1_loop t n l i

(** [demo::list_nth_mut1]: loop 0: backward function 0
    Source: 'src/demo.rs', lines 62:0-71:1 *)
let rec list_nth_mut1_loop_back
  (t : Type0) (n : nat) (l : cList_t t) (i : u32) (ret : t) :
  result (cList_t t)
  =
  if is_zero n
  then Fail OutOfFuel
  else
    let n1 = decrease n in
    begin match l with
    | CList_CCons x tl ->
      if i = 0
      then Return (CList_CCons ret tl)
      else
        let* i1 = u32_sub i 1 in
        let* tl1 = list_nth_mut1_loop_back t n1 tl i1 ret in
        Return (CList_CCons x tl1)
    | CList_CNil -> Fail Failure
    end

(** [demo::list_nth_mut1]: backward function 0
    Source: 'src/demo.rs', lines 62:0-62:77 *)
let list_nth_mut1_back
  (t : Type0) (n : nat) (l : cList_t t) (i : u32) (ret : t) :
  result (cList_t t)
  =
  list_nth_mut1_loop_back t n l i ret

(** [demo::i32_id]: forward function
    Source: 'src/demo.rs', lines 73:0-73:28 *)
let rec i32_id (n : nat) (i : i32) : result i32 =
  if is_zero n
  then Fail OutOfFuel
  else
    let n1 = decrease n in
    if i = 0
    then Return 0
    else let* i1 = i32_sub i 1 in let* i2 = i32_id n1 i1 in i32_add i2 1

(** Trait declaration: [demo::Counter]
    Source: 'src/demo.rs', lines 83:0-83:17 *)
noeq type counter_t (self : Type0) = {
  incr : self -> result usize;
  incr_back : self -> result self;
}

(** [demo::{usize}::incr]: forward function
    Source: 'src/demo.rs', lines 88:4-88:31 *)
let usize_incr (self : usize) : result usize =
  let* _ = usize_add self 1 in Return self

(** [demo::{usize}::incr]: backward function 0
    Source: 'src/demo.rs', lines 88:4-88:31 *)
let usize_incr_back (self : usize) : result usize =
  usize_add self 1

(** Trait implementation: [demo::{usize}]
    Source: 'src/demo.rs', lines 87:0-87:22 *)
let demo_CounterUsizeInst : counter_t usize = {
  incr = usize_incr;
  incr_back = usize_incr_back;
}

(** [demo::use_counter]: forward function
    Source: 'src/demo.rs', lines 95:0-95:59 *)
let use_counter
  (t : Type0) (counterTInst : counter_t t) (cnt : t) : result usize =
  counterTInst.incr cnt

(** [demo::use_counter]: backward function 0
    Source: 'src/demo.rs', lines 95:0-95:59 *)
let use_counter_back
  (t : Type0) (counterTInst : counter_t t) (cnt : t) : result t =
  counterTInst.incr_back cnt