(** THIS FILE WAS AUTOMATICALLY GENERATED BY AENEAS *)
(** [loops]: function definitions *)
module Loops.Funs
open Primitives
include Loops.Types
include Loops.Clauses

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

(** [loops::sum] *)
let rec sum_loop_fwd
  (max : u32) (i : u32) (s : u32) :
  Tot (result u32) (decreases (sum_decreases max i s))
  =
  if i < max
  then
    begin match u32_add s i with
    | Fail e -> Fail e
    | Return s0 ->
      begin match u32_add i 1 with
      | Fail e -> Fail e
      | Return i0 -> sum_loop_fwd max i0 s0
      end
    end
  else u32_mul s 2

(** [loops::sum] *)
let sum_fwd (max : u32) : result u32 = sum_loop_fwd max 0 0

(** [loops::list_nth_mut_loop] *)
let rec list_nth_mut_loop_loop_fwd
  (t : Type0) (ls : list_t t) (i : u32) :
  Tot (result t) (decreases (list_nth_mut_loop_decreases t ls i))
  =
  begin match ls with
  | ListCons x tl ->
    if i = 0
    then Return x
    else
      begin match u32_sub i 1 with
      | Fail e -> Fail e
      | Return i0 -> list_nth_mut_loop_loop_fwd t tl i0
      end
  | ListNil -> Fail Failure
  end

(** [loops::list_nth_mut_loop] *)
let list_nth_mut_loop_fwd (t : Type0) (ls : list_t t) (i : u32) : result t =
  list_nth_mut_loop_loop_fwd t ls i

(** [loops::list_nth_mut_loop] *)
let rec list_nth_mut_loop_loop_back
  (t : Type0) (ls : list_t t) (i : u32) (ret : t) :
  Tot (result (list_t t)) (decreases (list_nth_mut_loop_decreases t ls i))
  =
  begin match ls with
  | ListCons x tl ->
    if i = 0
    then Return (ListCons ret tl)
    else
      begin match u32_sub i 1 with
      | Fail e -> Fail e
      | Return i0 ->
        begin match list_nth_mut_loop_loop_back t tl i0 ret with
        | Fail e -> Fail e
        | Return l -> Return (ListCons x l)
        end
      end
  | ListNil -> Fail Failure
  end

(** [loops::list_nth_mut_loop] *)
let list_nth_mut_loop_back
  (t : Type0) (ls : list_t t) (i : u32) (ret : t) : result (list_t t) =
  list_nth_mut_loop_loop_back t ls i ret