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| -rw-r--r-- | tests/fstar/misc/Loops.fst | 784 |
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diff --git a/tests/fstar/misc/Loops.fst b/tests/fstar/misc/Loops.fst new file mode 100644 index 00000000..823acdd4 --- /dev/null +++ b/tests/fstar/misc/Loops.fst @@ -0,0 +1,784 @@ +(** THIS FILE WAS AUTOMATICALLY GENERATED BY AENEAS *) +(** [loops] *) +module Loops +open Primitives + +#set-options "--z3rlimit 50 --fuel 1 --ifuel 1" + +(** [loops::sum]: decreases clause *) +unfold let sum_loop_decreases (max : u32) (i : u32) (s : u32) : nat = admit () + +(** [loops::sum]: loop 0: forward function *) +let rec sum_loop + (max : u32) (i : u32) (s : u32) : + Tot (result u32) (decreases (sum_loop_decreases max i s)) + = + if i < max + then let* s0 = u32_add s i in let* i0 = u32_add i 1 in sum_loop max i0 s0 + else u32_mul s 2 + +(** [loops::sum]: forward function *) +let sum (max : u32) : result u32 = + sum_loop max 0 0 + +(** [loops::sum_with_mut_borrows]: decreases clause *) +unfold +let sum_with_mut_borrows_loop_decreases (max : u32) (mi : u32) (ms : u32) : nat + = + admit () + +(** [loops::sum_with_mut_borrows]: loop 0: forward function *) +let rec sum_with_mut_borrows_loop + (max : u32) (mi : u32) (ms : u32) : + Tot (result u32) (decreases (sum_with_mut_borrows_loop_decreases max mi ms)) + = + if mi < max + then + let* ms0 = u32_add ms mi in + let* mi0 = u32_add mi 1 in + sum_with_mut_borrows_loop max mi0 ms0 + else u32_mul ms 2 + +(** [loops::sum_with_mut_borrows]: forward function *) +let sum_with_mut_borrows (max : u32) : result u32 = + sum_with_mut_borrows_loop max 0 0 + +(** [loops::sum_with_shared_borrows]: decreases clause *) +unfold +let sum_with_shared_borrows_loop_decreases (max : u32) (i : u32) (s : u32) : + nat = + admit () + +(** [loops::sum_with_shared_borrows]: loop 0: forward function *) +let rec sum_with_shared_borrows_loop + (max : u32) (i : u32) (s : u32) : + Tot (result u32) (decreases (sum_with_shared_borrows_loop_decreases max i s)) + = + if i < max + then + let* i0 = u32_add i 1 in + let* s0 = u32_add s i0 in + sum_with_shared_borrows_loop max i0 s0 + else u32_mul s 2 + +(** [loops::sum_with_shared_borrows]: forward function *) +let sum_with_shared_borrows (max : u32) : result u32 = + sum_with_shared_borrows_loop max 0 0 + +(** [loops::clear]: decreases clause *) +unfold +let clear_loop_decreases (v : alloc_vec_Vec u32) (i : usize) : nat = admit () + +(** [loops::clear]: loop 0: merged forward/backward function + (there is a single backward function, and the forward function returns ()) *) +let rec clear_loop + (v : alloc_vec_Vec u32) (i : usize) : + Tot (result (alloc_vec_Vec u32)) (decreases (clear_loop_decreases v i)) + = + let i0 = alloc_vec_Vec_len u32 v in + if i < i0 + then + let* i1 = usize_add i 1 in + let* v0 = + alloc_vec_Vec_index_mut_back u32 usize + (core_slice_index_usize_coresliceindexSliceIndexInst u32) v i 0 in + clear_loop v0 i1 + else Return v + +(** [loops::clear]: merged forward/backward function + (there is a single backward function, and the forward function returns ()) *) +let clear (v : alloc_vec_Vec u32) : result (alloc_vec_Vec u32) = + clear_loop v 0 + +(** [loops::List] *) +type list_t (t : Type0) = +| List_Cons : t -> list_t t -> list_t t +| List_Nil : list_t t + +(** [loops::list_mem]: decreases clause *) +unfold let list_mem_loop_decreases (x : u32) (ls : list_t u32) : nat = admit () + +(** [loops::list_mem]: loop 0: forward function *) +let rec list_mem_loop + (x : u32) (ls : list_t u32) : + Tot (result bool) (decreases (list_mem_loop_decreases x ls)) + = + begin match ls with + | List_Cons y tl -> if y = x then Return true else list_mem_loop x tl + | List_Nil -> Return false + end + +(** [loops::list_mem]: forward function *) +let list_mem (x : u32) (ls : list_t u32) : result bool = + list_mem_loop x ls + +(** [loops::list_nth_mut_loop]: decreases clause *) +unfold +let list_nth_mut_loop_loop_decreases (t : Type0) (ls : list_t t) (i : u32) : + nat = + admit () + +(** [loops::list_nth_mut_loop]: loop 0: forward function *) +let rec list_nth_mut_loop_loop + (t : Type0) (ls : list_t t) (i : u32) : + Tot (result t) (decreases (list_nth_mut_loop_loop_decreases t ls i)) + = + begin match ls with + | List_Cons x tl -> + if i = 0 + then Return x + else let* i0 = u32_sub i 1 in list_nth_mut_loop_loop t tl i0 + | List_Nil -> Fail Failure + end + +(** [loops::list_nth_mut_loop]: forward function *) +let list_nth_mut_loop (t : Type0) (ls : list_t t) (i : u32) : result t = + list_nth_mut_loop_loop t ls i + +(** [loops::list_nth_mut_loop]: loop 0: backward function 0 *) +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_loop_decreases t ls i)) + = + begin match ls with + | List_Cons x tl -> + if i = 0 + then Return (List_Cons ret tl) + else + let* i0 = u32_sub i 1 in + let* tl0 = list_nth_mut_loop_loop_back t tl i0 ret in + Return (List_Cons x tl0) + | List_Nil -> Fail Failure + end + +(** [loops::list_nth_mut_loop]: backward function 0 *) +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 + +(** [loops::list_nth_shared_loop]: decreases clause *) +unfold +let list_nth_shared_loop_loop_decreases (t : Type0) (ls : list_t t) (i : u32) : + nat = + admit () + +(** [loops::list_nth_shared_loop]: loop 0: forward function *) +let rec list_nth_shared_loop_loop + (t : Type0) (ls : list_t t) (i : u32) : + Tot (result t) (decreases (list_nth_shared_loop_loop_decreases t ls i)) + = + begin match ls with + | List_Cons x tl -> + if i = 0 + then Return x + else let* i0 = u32_sub i 1 in list_nth_shared_loop_loop t tl i0 + | List_Nil -> Fail Failure + end + +(** [loops::list_nth_shared_loop]: forward function *) +let list_nth_shared_loop (t : Type0) (ls : list_t t) (i : u32) : result t = + list_nth_shared_loop_loop t ls i + +(** [loops::get_elem_mut]: decreases clause *) +unfold +let get_elem_mut_loop_decreases (x : usize) (ls : list_t usize) : nat = + admit () + +(** [loops::get_elem_mut]: loop 0: forward function *) +let rec get_elem_mut_loop + (x : usize) (ls : list_t usize) : + Tot (result usize) (decreases (get_elem_mut_loop_decreases x ls)) + = + begin match ls with + | List_Cons y tl -> if y = x then Return y else get_elem_mut_loop x tl + | List_Nil -> Fail Failure + end + +(** [loops::get_elem_mut]: forward function *) +let get_elem_mut + (slots : alloc_vec_Vec (list_t usize)) (x : usize) : result usize = + let* l = + alloc_vec_Vec_index_mut (list_t usize) usize + (core_slice_index_usize_coresliceindexSliceIndexInst (list_t usize)) + slots 0 in + get_elem_mut_loop x l + +(** [loops::get_elem_mut]: loop 0: backward function 0 *) +let rec get_elem_mut_loop_back + (x : usize) (ls : list_t usize) (ret : usize) : + Tot (result (list_t usize)) (decreases (get_elem_mut_loop_decreases x ls)) + = + begin match ls with + | List_Cons y tl -> + if y = x + then Return (List_Cons ret tl) + else let* tl0 = get_elem_mut_loop_back x tl ret in Return (List_Cons y tl0) + | List_Nil -> Fail Failure + end + +(** [loops::get_elem_mut]: backward function 0 *) +let get_elem_mut_back + (slots : alloc_vec_Vec (list_t usize)) (x : usize) (ret : usize) : + result (alloc_vec_Vec (list_t usize)) + = + let* l = + alloc_vec_Vec_index_mut (list_t usize) usize + (core_slice_index_usize_coresliceindexSliceIndexInst (list_t usize)) + slots 0 in + let* l0 = get_elem_mut_loop_back x l ret in + alloc_vec_Vec_index_mut_back (list_t usize) usize + (core_slice_index_usize_coresliceindexSliceIndexInst (list_t usize)) slots + 0 l0 + +(** [loops::get_elem_shared]: decreases clause *) +unfold +let get_elem_shared_loop_decreases (x : usize) (ls : list_t usize) : nat = + admit () + +(** [loops::get_elem_shared]: loop 0: forward function *) +let rec get_elem_shared_loop + (x : usize) (ls : list_t usize) : + Tot (result usize) (decreases (get_elem_shared_loop_decreases x ls)) + = + begin match ls with + | List_Cons y tl -> if y = x then Return y else get_elem_shared_loop x tl + | List_Nil -> Fail Failure + end + +(** [loops::get_elem_shared]: forward function *) +let get_elem_shared + (slots : alloc_vec_Vec (list_t usize)) (x : usize) : result usize = + let* l = + alloc_vec_Vec_index (list_t usize) usize + (core_slice_index_usize_coresliceindexSliceIndexInst (list_t usize)) + slots 0 in + get_elem_shared_loop x l + +(** [loops::id_mut]: forward function *) +let id_mut (t : Type0) (ls : list_t t) : result (list_t t) = + Return ls + +(** [loops::id_mut]: backward function 0 *) +let id_mut_back + (t : Type0) (ls : list_t t) (ret : list_t t) : result (list_t t) = + Return ret + +(** [loops::id_shared]: forward function *) +let id_shared (t : Type0) (ls : list_t t) : result (list_t t) = + Return ls + +(** [loops::list_nth_mut_loop_with_id]: decreases clause *) +unfold +let list_nth_mut_loop_with_id_loop_decreases (t : Type0) (i : u32) + (ls : list_t t) : nat = + admit () + +(** [loops::list_nth_mut_loop_with_id]: loop 0: forward function *) +let rec list_nth_mut_loop_with_id_loop + (t : Type0) (i : u32) (ls : list_t t) : + Tot (result t) (decreases (list_nth_mut_loop_with_id_loop_decreases t i ls)) + = + begin match ls with + | List_Cons x tl -> + if i = 0 + then Return x + else let* i0 = u32_sub i 1 in list_nth_mut_loop_with_id_loop t i0 tl + | List_Nil -> Fail Failure + end + +(** [loops::list_nth_mut_loop_with_id]: forward function *) +let list_nth_mut_loop_with_id + (t : Type0) (ls : list_t t) (i : u32) : result t = + let* ls0 = id_mut t ls in list_nth_mut_loop_with_id_loop t i ls0 + +(** [loops::list_nth_mut_loop_with_id]: loop 0: backward function 0 *) +let rec list_nth_mut_loop_with_id_loop_back + (t : Type0) (i : u32) (ls : list_t t) (ret : t) : + Tot (result (list_t t)) + (decreases (list_nth_mut_loop_with_id_loop_decreases t i ls)) + = + begin match ls with + | List_Cons x tl -> + if i = 0 + then Return (List_Cons ret tl) + else + let* i0 = u32_sub i 1 in + let* tl0 = list_nth_mut_loop_with_id_loop_back t i0 tl ret in + Return (List_Cons x tl0) + | List_Nil -> Fail Failure + end + +(** [loops::list_nth_mut_loop_with_id]: backward function 0 *) +let list_nth_mut_loop_with_id_back + (t : Type0) (ls : list_t t) (i : u32) (ret : t) : result (list_t t) = + let* ls0 = id_mut t ls in + let* l = list_nth_mut_loop_with_id_loop_back t i ls0 ret in + id_mut_back t ls l + +(** [loops::list_nth_shared_loop_with_id]: decreases clause *) +unfold +let list_nth_shared_loop_with_id_loop_decreases (t : Type0) (i : u32) + (ls : list_t t) : nat = + admit () + +(** [loops::list_nth_shared_loop_with_id]: loop 0: forward function *) +let rec list_nth_shared_loop_with_id_loop + (t : Type0) (i : u32) (ls : list_t t) : + Tot (result t) + (decreases (list_nth_shared_loop_with_id_loop_decreases t i ls)) + = + begin match ls with + | List_Cons x tl -> + if i = 0 + then Return x + else let* i0 = u32_sub i 1 in list_nth_shared_loop_with_id_loop t i0 tl + | List_Nil -> Fail Failure + end + +(** [loops::list_nth_shared_loop_with_id]: forward function *) +let list_nth_shared_loop_with_id + (t : Type0) (ls : list_t t) (i : u32) : result t = + let* ls0 = id_shared t ls in list_nth_shared_loop_with_id_loop t i ls0 + +(** [loops::list_nth_mut_loop_pair]: decreases clause *) +unfold +let list_nth_mut_loop_pair_loop_decreases (t : Type0) (ls0 : list_t t) + (ls1 : list_t t) (i : u32) : nat = + admit () + +(** [loops::list_nth_mut_loop_pair]: loop 0: forward function *) +let rec list_nth_mut_loop_pair_loop + (t : Type0) (ls0 : list_t t) (ls1 : list_t t) (i : u32) : + Tot (result (t & t)) + (decreases (list_nth_mut_loop_pair_loop_decreases t ls0 ls1 i)) + = + begin match ls0 with + | List_Cons x0 tl0 -> + begin match ls1 with + | List_Cons x1 tl1 -> + if i = 0 + then Return (x0, x1) + else let* i0 = u32_sub i 1 in list_nth_mut_loop_pair_loop t tl0 tl1 i0 + | List_Nil -> Fail Failure + end + | List_Nil -> Fail Failure + end + +(** [loops::list_nth_mut_loop_pair]: forward function *) +let list_nth_mut_loop_pair + (t : Type0) (ls0 : list_t t) (ls1 : list_t 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 *) +let rec list_nth_mut_loop_pair_loop_back'a + (t : Type0) (ls0 : list_t t) (ls1 : list_t t) (i : u32) (ret : t) : + Tot (result (list_t t)) + (decreases (list_nth_mut_loop_pair_loop_decreases t ls0 ls1 i)) + = + begin match ls0 with + | List_Cons x0 tl0 -> + begin match ls1 with + | List_Cons x1 tl1 -> + if i = 0 + then Return (List_Cons ret tl0) + else + let* i0 = u32_sub i 1 in + let* tl00 = list_nth_mut_loop_pair_loop_back'a t tl0 tl1 i0 ret in + Return (List_Cons x0 tl00) + | List_Nil -> Fail Failure + end + | List_Nil -> Fail Failure + end + +(** [loops::list_nth_mut_loop_pair]: backward function 0 *) +let list_nth_mut_loop_pair_back'a + (t : Type0) (ls0 : list_t t) (ls1 : list_t t) (i : u32) (ret : t) : + result (list_t t) + = + list_nth_mut_loop_pair_loop_back'a t ls0 ls1 i ret + +(** [loops::list_nth_mut_loop_pair]: loop 0: backward function 1 *) +let rec list_nth_mut_loop_pair_loop_back'b + (t : Type0) (ls0 : list_t t) (ls1 : list_t t) (i : u32) (ret : t) : + Tot (result (list_t t)) + (decreases (list_nth_mut_loop_pair_loop_decreases t ls0 ls1 i)) + = + begin match ls0 with + | List_Cons x0 tl0 -> + begin match ls1 with + | List_Cons x1 tl1 -> + if i = 0 + then Return (List_Cons ret tl1) + else + let* i0 = u32_sub i 1 in + let* tl10 = list_nth_mut_loop_pair_loop_back'b t tl0 tl1 i0 ret in + Return (List_Cons x1 tl10) + | List_Nil -> Fail Failure + end + | List_Nil -> Fail Failure + end + +(** [loops::list_nth_mut_loop_pair]: backward function 1 *) +let list_nth_mut_loop_pair_back'b + (t : Type0) (ls0 : list_t t) (ls1 : list_t t) (i : u32) (ret : t) : + result (list_t t) + = + list_nth_mut_loop_pair_loop_back'b t ls0 ls1 i ret + +(** [loops::list_nth_shared_loop_pair]: decreases clause *) +unfold +let list_nth_shared_loop_pair_loop_decreases (t : Type0) (ls0 : list_t t) + (ls1 : list_t t) (i : u32) : nat = + admit () + +(** [loops::list_nth_shared_loop_pair]: loop 0: forward function *) +let rec list_nth_shared_loop_pair_loop + (t : Type0) (ls0 : list_t t) (ls1 : list_t t) (i : u32) : + Tot (result (t & t)) + (decreases (list_nth_shared_loop_pair_loop_decreases t ls0 ls1 i)) + = + begin match ls0 with + | List_Cons x0 tl0 -> + begin match ls1 with + | List_Cons x1 tl1 -> + if i = 0 + then Return (x0, x1) + else let* i0 = u32_sub i 1 in list_nth_shared_loop_pair_loop t tl0 tl1 i0 + | List_Nil -> Fail Failure + end + | List_Nil -> Fail Failure + end + +(** [loops::list_nth_shared_loop_pair]: forward function *) +let list_nth_shared_loop_pair + (t : Type0) (ls0 : list_t t) (ls1 : list_t t) (i : u32) : result (t & t) = + list_nth_shared_loop_pair_loop t ls0 ls1 i + +(** [loops::list_nth_mut_loop_pair_merge]: decreases clause *) +unfold +let list_nth_mut_loop_pair_merge_loop_decreases (t : Type0) (ls0 : list_t t) + (ls1 : list_t t) (i : u32) : nat = + admit () + +(** [loops::list_nth_mut_loop_pair_merge]: loop 0: forward function *) +let rec list_nth_mut_loop_pair_merge_loop + (t : Type0) (ls0 : list_t t) (ls1 : list_t t) (i : u32) : + Tot (result (t & t)) + (decreases (list_nth_mut_loop_pair_merge_loop_decreases t ls0 ls1 i)) + = + begin match ls0 with + | List_Cons x0 tl0 -> + begin match ls1 with + | List_Cons x1 tl1 -> + if i = 0 + then Return (x0, x1) + else + let* i0 = u32_sub i 1 in list_nth_mut_loop_pair_merge_loop t tl0 tl1 i0 + | List_Nil -> Fail Failure + end + | List_Nil -> Fail Failure + end + +(** [loops::list_nth_mut_loop_pair_merge]: forward function *) +let list_nth_mut_loop_pair_merge + (t : Type0) (ls0 : list_t t) (ls1 : list_t 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 *) +let rec list_nth_mut_loop_pair_merge_loop_back + (t : Type0) (ls0 : list_t t) (ls1 : list_t t) (i : u32) (ret : (t & t)) : + Tot (result ((list_t t) & (list_t t))) + (decreases (list_nth_mut_loop_pair_merge_loop_decreases t ls0 ls1 i)) + = + begin match ls0 with + | List_Cons x0 tl0 -> + begin match ls1 with + | List_Cons x1 tl1 -> + if i = 0 + then let (x, x2) = ret in Return (List_Cons x tl0, List_Cons x2 tl1) + else + let* i0 = u32_sub i 1 in + let* (tl00, tl10) = + list_nth_mut_loop_pair_merge_loop_back t tl0 tl1 i0 ret in + Return (List_Cons x0 tl00, List_Cons x1 tl10) + | List_Nil -> Fail Failure + end + | List_Nil -> Fail Failure + end + +(** [loops::list_nth_mut_loop_pair_merge]: backward function 0 *) +let list_nth_mut_loop_pair_merge_back + (t : Type0) (ls0 : list_t t) (ls1 : list_t t) (i : u32) (ret : (t & t)) : + result ((list_t t) & (list_t t)) + = + list_nth_mut_loop_pair_merge_loop_back t ls0 ls1 i ret + +(** [loops::list_nth_shared_loop_pair_merge]: decreases clause *) +unfold +let list_nth_shared_loop_pair_merge_loop_decreases (t : Type0) (ls0 : list_t t) + (ls1 : list_t t) (i : u32) : nat = + admit () + +(** [loops::list_nth_shared_loop_pair_merge]: loop 0: forward function *) +let rec list_nth_shared_loop_pair_merge_loop + (t : Type0) (ls0 : list_t t) (ls1 : list_t t) (i : u32) : + Tot (result (t & t)) + (decreases (list_nth_shared_loop_pair_merge_loop_decreases t ls0 ls1 i)) + = + begin match ls0 with + | List_Cons x0 tl0 -> + begin match ls1 with + | List_Cons x1 tl1 -> + if i = 0 + then Return (x0, x1) + else + let* i0 = u32_sub i 1 in + list_nth_shared_loop_pair_merge_loop t tl0 tl1 i0 + | List_Nil -> Fail Failure + end + | List_Nil -> Fail Failure + end + +(** [loops::list_nth_shared_loop_pair_merge]: forward function *) +let list_nth_shared_loop_pair_merge + (t : Type0) (ls0 : list_t t) (ls1 : list_t t) (i : u32) : result (t & t) = + list_nth_shared_loop_pair_merge_loop t ls0 ls1 i + +(** [loops::list_nth_mut_shared_loop_pair]: decreases clause *) +unfold +let list_nth_mut_shared_loop_pair_loop_decreases (t : Type0) (ls0 : list_t t) + (ls1 : list_t t) (i : u32) : nat = + admit () + +(** [loops::list_nth_mut_shared_loop_pair]: loop 0: forward function *) +let rec list_nth_mut_shared_loop_pair_loop + (t : Type0) (ls0 : list_t t) (ls1 : list_t t) (i : u32) : + Tot (result (t & t)) + (decreases (list_nth_mut_shared_loop_pair_loop_decreases t ls0 ls1 i)) + = + begin match ls0 with + | List_Cons x0 tl0 -> + begin match ls1 with + | List_Cons x1 tl1 -> + if i = 0 + then Return (x0, x1) + else + let* i0 = u32_sub i 1 in + list_nth_mut_shared_loop_pair_loop t tl0 tl1 i0 + | List_Nil -> Fail Failure + end + | List_Nil -> Fail Failure + end + +(** [loops::list_nth_mut_shared_loop_pair]: forward function *) +let list_nth_mut_shared_loop_pair + (t : Type0) (ls0 : list_t t) (ls1 : list_t 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 *) +let rec list_nth_mut_shared_loop_pair_loop_back + (t : Type0) (ls0 : list_t t) (ls1 : list_t t) (i : u32) (ret : t) : + Tot (result (list_t t)) + (decreases (list_nth_mut_shared_loop_pair_loop_decreases t ls0 ls1 i)) + = + begin match ls0 with + | List_Cons x0 tl0 -> + begin match ls1 with + | List_Cons x1 tl1 -> + if i = 0 + then Return (List_Cons ret tl0) + else + let* i0 = u32_sub i 1 in + let* tl00 = list_nth_mut_shared_loop_pair_loop_back t tl0 tl1 i0 ret in + Return (List_Cons x0 tl00) + | List_Nil -> Fail Failure + end + | List_Nil -> Fail Failure + end + +(** [loops::list_nth_mut_shared_loop_pair]: backward function 0 *) +let list_nth_mut_shared_loop_pair_back + (t : Type0) (ls0 : list_t t) (ls1 : list_t t) (i : u32) (ret : t) : + result (list_t t) + = + list_nth_mut_shared_loop_pair_loop_back t ls0 ls1 i ret + +(** [loops::list_nth_mut_shared_loop_pair_merge]: decreases clause *) +unfold +let list_nth_mut_shared_loop_pair_merge_loop_decreases (t : Type0) + (ls0 : list_t t) (ls1 : list_t t) (i : u32) : nat = + admit () + +(** [loops::list_nth_mut_shared_loop_pair_merge]: loop 0: forward function *) +let rec list_nth_mut_shared_loop_pair_merge_loop + (t : Type0) (ls0 : list_t t) (ls1 : list_t t) (i : u32) : + Tot (result (t & t)) + (decreases (list_nth_mut_shared_loop_pair_merge_loop_decreases t ls0 ls1 i)) + = + begin match ls0 with + | List_Cons x0 tl0 -> + begin match ls1 with + | List_Cons x1 tl1 -> + if i = 0 + then Return (x0, x1) + else + let* i0 = u32_sub i 1 in + list_nth_mut_shared_loop_pair_merge_loop t tl0 tl1 i0 + | List_Nil -> Fail Failure + end + | List_Nil -> Fail Failure + end + +(** [loops::list_nth_mut_shared_loop_pair_merge]: forward function *) +let list_nth_mut_shared_loop_pair_merge + (t : Type0) (ls0 : list_t t) (ls1 : list_t 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 *) +let rec list_nth_mut_shared_loop_pair_merge_loop_back + (t : Type0) (ls0 : list_t t) (ls1 : list_t t) (i : u32) (ret : t) : + Tot (result (list_t t)) + (decreases (list_nth_mut_shared_loop_pair_merge_loop_decreases t ls0 ls1 i)) + = + begin match ls0 with + | List_Cons x0 tl0 -> + begin match ls1 with + | List_Cons x1 tl1 -> + if i = 0 + then Return (List_Cons ret tl0) + else + let* i0 = u32_sub i 1 in + let* tl00 = + list_nth_mut_shared_loop_pair_merge_loop_back t tl0 tl1 i0 ret in + Return (List_Cons x0 tl00) + | List_Nil -> Fail Failure + end + | List_Nil -> Fail Failure + end + +(** [loops::list_nth_mut_shared_loop_pair_merge]: backward function 0 *) +let list_nth_mut_shared_loop_pair_merge_back + (t : Type0) (ls0 : list_t t) (ls1 : list_t t) (i : u32) (ret : t) : + result (list_t t) + = + list_nth_mut_shared_loop_pair_merge_loop_back t ls0 ls1 i ret + +(** [loops::list_nth_shared_mut_loop_pair]: decreases clause *) +unfold +let list_nth_shared_mut_loop_pair_loop_decreases (t : Type0) (ls0 : list_t t) + (ls1 : list_t t) (i : u32) : nat = + admit () + +(** [loops::list_nth_shared_mut_loop_pair]: loop 0: forward function *) +let rec list_nth_shared_mut_loop_pair_loop + (t : Type0) (ls0 : list_t t) (ls1 : list_t t) (i : u32) : + Tot (result (t & t)) + (decreases (list_nth_shared_mut_loop_pair_loop_decreases t ls0 ls1 i)) + = + begin match ls0 with + | List_Cons x0 tl0 -> + begin match ls1 with + | List_Cons x1 tl1 -> + if i = 0 + then Return (x0, x1) + else + let* i0 = u32_sub i 1 in + list_nth_shared_mut_loop_pair_loop t tl0 tl1 i0 + | List_Nil -> Fail Failure + end + | List_Nil -> Fail Failure + end + +(** [loops::list_nth_shared_mut_loop_pair]: forward function *) +let list_nth_shared_mut_loop_pair + (t : Type0) (ls0 : list_t t) (ls1 : list_t 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 *) +let rec list_nth_shared_mut_loop_pair_loop_back + (t : Type0) (ls0 : list_t t) (ls1 : list_t t) (i : u32) (ret : t) : + Tot (result (list_t t)) + (decreases (list_nth_shared_mut_loop_pair_loop_decreases t ls0 ls1 i)) + = + begin match ls0 with + | List_Cons x0 tl0 -> + begin match ls1 with + | List_Cons x1 tl1 -> + if i = 0 + then Return (List_Cons ret tl1) + else + let* i0 = u32_sub i 1 in + let* tl10 = list_nth_shared_mut_loop_pair_loop_back t tl0 tl1 i0 ret in + Return (List_Cons x1 tl10) + | List_Nil -> Fail Failure + end + | List_Nil -> Fail Failure + end + +(** [loops::list_nth_shared_mut_loop_pair]: backward function 1 *) +let list_nth_shared_mut_loop_pair_back + (t : Type0) (ls0 : list_t t) (ls1 : list_t t) (i : u32) (ret : t) : + result (list_t t) + = + list_nth_shared_mut_loop_pair_loop_back t ls0 ls1 i ret + +(** [loops::list_nth_shared_mut_loop_pair_merge]: decreases clause *) +unfold +let list_nth_shared_mut_loop_pair_merge_loop_decreases (t : Type0) + (ls0 : list_t t) (ls1 : list_t t) (i : u32) : nat = + admit () + +(** [loops::list_nth_shared_mut_loop_pair_merge]: loop 0: forward function *) +let rec list_nth_shared_mut_loop_pair_merge_loop + (t : Type0) (ls0 : list_t t) (ls1 : list_t t) (i : u32) : + Tot (result (t & t)) + (decreases (list_nth_shared_mut_loop_pair_merge_loop_decreases t ls0 ls1 i)) + = + begin match ls0 with + | List_Cons x0 tl0 -> + begin match ls1 with + | List_Cons x1 tl1 -> + if i = 0 + then Return (x0, x1) + else + let* i0 = u32_sub i 1 in + list_nth_shared_mut_loop_pair_merge_loop t tl0 tl1 i0 + | List_Nil -> Fail Failure + end + | List_Nil -> Fail Failure + end + +(** [loops::list_nth_shared_mut_loop_pair_merge]: forward function *) +let list_nth_shared_mut_loop_pair_merge + (t : Type0) (ls0 : list_t t) (ls1 : list_t 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 *) +let rec list_nth_shared_mut_loop_pair_merge_loop_back + (t : Type0) (ls0 : list_t t) (ls1 : list_t t) (i : u32) (ret : t) : + Tot (result (list_t t)) + (decreases (list_nth_shared_mut_loop_pair_merge_loop_decreases t ls0 ls1 i)) + = + begin match ls0 with + | List_Cons x0 tl0 -> + begin match ls1 with + | List_Cons x1 tl1 -> + if i = 0 + then Return (List_Cons ret tl1) + else + let* i0 = u32_sub i 1 in + let* tl10 = + list_nth_shared_mut_loop_pair_merge_loop_back t tl0 tl1 i0 ret in + Return (List_Cons x1 tl10) + | List_Nil -> Fail Failure + end + | List_Nil -> Fail Failure + end + +(** [loops::list_nth_shared_mut_loop_pair_merge]: backward function 0 *) +let list_nth_shared_mut_loop_pair_merge_back + (t : Type0) (ls0 : list_t t) (ls1 : list_t t) (i : u32) (ret : t) : + result (list_t t) + = + list_nth_shared_mut_loop_pair_merge_loop_back t ls0 ls1 i ret + |