diff options
Diffstat (limited to 'tests/hol4/misc-loops/loops_FunsTheory.sig')
| -rw-r--r-- | tests/hol4/misc-loops/loops_FunsTheory.sig | 731 |
1 files changed, 0 insertions, 731 deletions
diff --git a/tests/hol4/misc-loops/loops_FunsTheory.sig b/tests/hol4/misc-loops/loops_FunsTheory.sig deleted file mode 100644 index 63fe56c9..00000000 --- a/tests/hol4/misc-loops/loops_FunsTheory.sig +++ /dev/null @@ -1,731 +0,0 @@ -signature loops_FunsTheory = -sig - type thm = Thm.thm - - (* Definitions *) - val clear_fwd_back_def : thm - val clear_loop_fwd_back_def : thm - val get_elem_mut_back_def : thm - val get_elem_mut_fwd_def : thm - val get_elem_mut_loop_back_def : thm - val get_elem_mut_loop_fwd_def : thm - val get_elem_shared_fwd_def : thm - val get_elem_shared_loop_fwd_def : thm - val id_mut_back_def : thm - val id_mut_fwd_def : thm - val id_shared_fwd_def : thm - val list_mem_fwd_def : thm - val list_mem_loop_fwd_def : thm - val list_nth_mut_loop_back_def : thm - val list_nth_mut_loop_fwd_def : thm - val list_nth_mut_loop_loop_back_def : thm - val list_nth_mut_loop_loop_fwd_def : thm - val list_nth_mut_loop_pair_back'a_def : thm - val list_nth_mut_loop_pair_back'b_def : thm - val list_nth_mut_loop_pair_fwd_def : thm - val list_nth_mut_loop_pair_loop_back'a_def : thm - val list_nth_mut_loop_pair_loop_back'b_def : thm - val list_nth_mut_loop_pair_loop_fwd_def : thm - val list_nth_mut_loop_pair_merge_back_def : thm - val list_nth_mut_loop_pair_merge_fwd_def : thm - val list_nth_mut_loop_pair_merge_loop_back_def : thm - val list_nth_mut_loop_pair_merge_loop_fwd_def : thm - val list_nth_mut_loop_with_id_back_def : thm - val list_nth_mut_loop_with_id_fwd_def : thm - val list_nth_mut_loop_with_id_loop_back_def : thm - val list_nth_mut_loop_with_id_loop_fwd_def : thm - val list_nth_mut_shared_loop_pair_back_def : thm - val list_nth_mut_shared_loop_pair_fwd_def : thm - val list_nth_mut_shared_loop_pair_loop_back_def : thm - val list_nth_mut_shared_loop_pair_loop_fwd_def : thm - val list_nth_mut_shared_loop_pair_merge_back_def : thm - val list_nth_mut_shared_loop_pair_merge_fwd_def : thm - val list_nth_mut_shared_loop_pair_merge_loop_back_def : thm - val list_nth_mut_shared_loop_pair_merge_loop_fwd_def : thm - val list_nth_shared_loop_fwd_def : thm - val list_nth_shared_loop_loop_fwd_def : thm - val list_nth_shared_loop_pair_fwd_def : thm - val list_nth_shared_loop_pair_loop_fwd_def : thm - val list_nth_shared_loop_pair_merge_fwd_def : thm - val list_nth_shared_loop_pair_merge_loop_fwd_def : thm - val list_nth_shared_loop_with_id_fwd_def : thm - val list_nth_shared_loop_with_id_loop_fwd_def : thm - val list_nth_shared_mut_loop_pair_back_def : thm - val list_nth_shared_mut_loop_pair_fwd_def : thm - val list_nth_shared_mut_loop_pair_loop_back_def : thm - val list_nth_shared_mut_loop_pair_loop_fwd_def : thm - val list_nth_shared_mut_loop_pair_merge_back_def : thm - val list_nth_shared_mut_loop_pair_merge_fwd_def : thm - val list_nth_shared_mut_loop_pair_merge_loop_back_def : thm - val list_nth_shared_mut_loop_pair_merge_loop_fwd_def : thm - val sum_fwd_def : thm - val sum_loop_fwd_def : thm - val sum_with_mut_borrows_fwd_def : thm - val sum_with_mut_borrows_loop_fwd_def : thm - val sum_with_shared_borrows_fwd_def : thm - val sum_with_shared_borrows_loop_fwd_def : thm - - val loops_Funs_grammars : type_grammar.grammar * term_grammar.grammar -(* - [loops_Types] Parent theory of "loops_Funs" - - [clear_fwd_back_def] Definition - - ⊢ ∀v. clear_fwd_back v = clear_loop_fwd_back v (int_to_usize 0) - - [clear_loop_fwd_back_def] Definition - - ⊢ ∀v i. - clear_loop_fwd_back v i = - (let - i0 = vec_len v - in - if usize_lt i i0 then - do - i1 <- usize_add i (int_to_usize 1); - v0 <- vec_index_mut_back v i (int_to_u32 0); - clear_loop_fwd_back v0 i1 - od - else Return v) - - [get_elem_mut_back_def] Definition - - ⊢ ∀slots x ret. - get_elem_mut_back slots x ret = - do - l <- vec_index_mut_fwd slots (int_to_usize 0); - l0 <- get_elem_mut_loop_back x l ret; - vec_index_mut_back slots (int_to_usize 0) l0 - od - - [get_elem_mut_fwd_def] Definition - - ⊢ ∀slots x. - get_elem_mut_fwd slots x = - do - l <- vec_index_mut_fwd slots (int_to_usize 0); - get_elem_mut_loop_fwd x l - od - - [get_elem_mut_loop_back_def] Definition - - ⊢ ∀x ls ret. - get_elem_mut_loop_back x ls ret = - case ls of - ListCons y tl => - if y = x then Return (ListCons ret tl) - else - do - tl0 <- get_elem_mut_loop_back x tl ret; - Return (ListCons y tl0) - od - | ListNil => Fail Failure - - [get_elem_mut_loop_fwd_def] Definition - - ⊢ ∀x ls. - get_elem_mut_loop_fwd x ls = - case ls of - ListCons y tl => - if y = x then Return y else get_elem_mut_loop_fwd x tl - | ListNil => Fail Failure - - [get_elem_shared_fwd_def] Definition - - ⊢ ∀slots x. - get_elem_shared_fwd slots x = - do - l <- vec_index_fwd slots (int_to_usize 0); - get_elem_shared_loop_fwd x l - od - - [get_elem_shared_loop_fwd_def] Definition - - ⊢ ∀x ls. - get_elem_shared_loop_fwd x ls = - case ls of - ListCons y tl => - if y = x then Return y else get_elem_shared_loop_fwd x tl - | ListNil => Fail Failure - - [id_mut_back_def] Definition - - ⊢ ∀ls ret. id_mut_back ls ret = Return ret - - [id_mut_fwd_def] Definition - - ⊢ ∀ls. id_mut_fwd ls = Return ls - - [id_shared_fwd_def] Definition - - ⊢ ∀ls. id_shared_fwd ls = Return ls - - [list_mem_fwd_def] Definition - - ⊢ ∀x ls. list_mem_fwd x ls = list_mem_loop_fwd x ls - - [list_mem_loop_fwd_def] Definition - - ⊢ ∀x ls. - list_mem_loop_fwd x ls = - case ls of - ListCons y tl => - if y = x then Return T else list_mem_loop_fwd x tl - | ListNil => Return F - - [list_nth_mut_loop_back_def] Definition - - ⊢ ∀ls i ret. - list_nth_mut_loop_back ls i ret = - list_nth_mut_loop_loop_back ls i ret - - [list_nth_mut_loop_fwd_def] Definition - - ⊢ ∀ls i. list_nth_mut_loop_fwd ls i = list_nth_mut_loop_loop_fwd ls i - - [list_nth_mut_loop_loop_back_def] Definition - - ⊢ ∀ls i ret. - list_nth_mut_loop_loop_back ls i ret = - case ls of - ListCons x tl => - if i = int_to_u32 0 then Return (ListCons ret tl) - else - do - i0 <- u32_sub i (int_to_u32 1); - tl0 <- list_nth_mut_loop_loop_back tl i0 ret; - Return (ListCons x tl0) - od - | ListNil => Fail Failure - - [list_nth_mut_loop_loop_fwd_def] Definition - - ⊢ ∀ls i. - list_nth_mut_loop_loop_fwd ls i = - case ls of - ListCons x tl => - if i = int_to_u32 0 then Return x - else - do - i0 <- u32_sub i (int_to_u32 1); - list_nth_mut_loop_loop_fwd tl i0 - od - | ListNil => Fail Failure - - [list_nth_mut_loop_pair_back'a_def] Definition - - ⊢ ∀ls0 ls1 i ret. - list_nth_mut_loop_pair_back'a ls0 ls1 i ret = - list_nth_mut_loop_pair_loop_back'a ls0 ls1 i ret - - [list_nth_mut_loop_pair_back'b_def] Definition - - ⊢ ∀ls0 ls1 i ret. - list_nth_mut_loop_pair_back'b ls0 ls1 i ret = - list_nth_mut_loop_pair_loop_back'b ls0 ls1 i ret - - [list_nth_mut_loop_pair_fwd_def] Definition - - ⊢ ∀ls0 ls1 i. - list_nth_mut_loop_pair_fwd ls0 ls1 i = - list_nth_mut_loop_pair_loop_fwd ls0 ls1 i - - [list_nth_mut_loop_pair_loop_back'a_def] Definition - - ⊢ ∀ls0 ls1 i ret. - list_nth_mut_loop_pair_loop_back'a ls0 ls1 i ret = - case ls0 of - ListCons x0 tl0 => - (case ls1 of - ListCons x1 tl1 => - if i = int_to_u32 0 then Return (ListCons ret tl0) - else - do - i0 <- u32_sub i (int_to_u32 1); - tl00 <- - list_nth_mut_loop_pair_loop_back'a tl0 tl1 i0 ret; - Return (ListCons x0 tl00) - od - | ListNil => Fail Failure) - | ListNil => Fail Failure - - [list_nth_mut_loop_pair_loop_back'b_def] Definition - - ⊢ ∀ls0 ls1 i ret. - list_nth_mut_loop_pair_loop_back'b ls0 ls1 i ret = - case ls0 of - ListCons x0 tl0 => - (case ls1 of - ListCons x1 tl1 => - if i = int_to_u32 0 then Return (ListCons ret tl1) - else - do - i0 <- u32_sub i (int_to_u32 1); - tl10 <- - list_nth_mut_loop_pair_loop_back'b tl0 tl1 i0 ret; - Return (ListCons x1 tl10) - od - | ListNil => Fail Failure) - | ListNil => Fail Failure - - [list_nth_mut_loop_pair_loop_fwd_def] Definition - - ⊢ ∀ls0 ls1 i. - list_nth_mut_loop_pair_loop_fwd ls0 ls1 i = - case ls0 of - ListCons x0 tl0 => - (case ls1 of - ListCons x1 tl1 => - if i = int_to_u32 0 then Return (x0,x1) - else - do - i0 <- u32_sub i (int_to_u32 1); - list_nth_mut_loop_pair_loop_fwd tl0 tl1 i0 - od - | ListNil => Fail Failure) - | ListNil => Fail Failure - - [list_nth_mut_loop_pair_merge_back_def] Definition - - ⊢ ∀ls0 ls1 i ret. - list_nth_mut_loop_pair_merge_back ls0 ls1 i ret = - list_nth_mut_loop_pair_merge_loop_back ls0 ls1 i ret - - [list_nth_mut_loop_pair_merge_fwd_def] Definition - - ⊢ ∀ls0 ls1 i. - list_nth_mut_loop_pair_merge_fwd ls0 ls1 i = - list_nth_mut_loop_pair_merge_loop_fwd ls0 ls1 i - - [list_nth_mut_loop_pair_merge_loop_back_def] Definition - - ⊢ ∀ls0 ls1 i ret. - list_nth_mut_loop_pair_merge_loop_back ls0 ls1 i ret = - case ls0 of - ListCons x0 tl0 => - (case ls1 of - ListCons x1 tl1 => - if i = int_to_u32 0 then - (let - (t,t0) = ret - in - Return (ListCons t tl0,ListCons t0 tl1)) - else - do - i0 <- u32_sub i (int_to_u32 1); - (tl00,tl10) <- - list_nth_mut_loop_pair_merge_loop_back tl0 tl1 i0 - ret; - Return (ListCons x0 tl00,ListCons x1 tl10) - od - | ListNil => Fail Failure) - | ListNil => Fail Failure - - [list_nth_mut_loop_pair_merge_loop_fwd_def] Definition - - ⊢ ∀ls0 ls1 i. - list_nth_mut_loop_pair_merge_loop_fwd ls0 ls1 i = - case ls0 of - ListCons x0 tl0 => - (case ls1 of - ListCons x1 tl1 => - if i = int_to_u32 0 then Return (x0,x1) - else - do - i0 <- u32_sub i (int_to_u32 1); - list_nth_mut_loop_pair_merge_loop_fwd tl0 tl1 i0 - od - | ListNil => Fail Failure) - | ListNil => Fail Failure - - [list_nth_mut_loop_with_id_back_def] Definition - - ⊢ ∀ls i ret. - list_nth_mut_loop_with_id_back ls i ret = - do - ls0 <- id_mut_fwd ls; - l <- list_nth_mut_loop_with_id_loop_back i ls0 ret; - id_mut_back ls l - od - - [list_nth_mut_loop_with_id_fwd_def] Definition - - ⊢ ∀ls i. - list_nth_mut_loop_with_id_fwd ls i = - do - ls0 <- id_mut_fwd ls; - list_nth_mut_loop_with_id_loop_fwd i ls0 - od - - [list_nth_mut_loop_with_id_loop_back_def] Definition - - ⊢ ∀i ls ret. - list_nth_mut_loop_with_id_loop_back i ls ret = - case ls of - ListCons x tl => - if i = int_to_u32 0 then Return (ListCons ret tl) - else - do - i0 <- u32_sub i (int_to_u32 1); - tl0 <- list_nth_mut_loop_with_id_loop_back i0 tl ret; - Return (ListCons x tl0) - od - | ListNil => Fail Failure - - [list_nth_mut_loop_with_id_loop_fwd_def] Definition - - ⊢ ∀i ls. - list_nth_mut_loop_with_id_loop_fwd i ls = - case ls of - ListCons x tl => - if i = int_to_u32 0 then Return x - else - do - i0 <- u32_sub i (int_to_u32 1); - list_nth_mut_loop_with_id_loop_fwd i0 tl - od - | ListNil => Fail Failure - - [list_nth_mut_shared_loop_pair_back_def] Definition - - ⊢ ∀ls0 ls1 i ret. - list_nth_mut_shared_loop_pair_back ls0 ls1 i ret = - list_nth_mut_shared_loop_pair_loop_back ls0 ls1 i ret - - [list_nth_mut_shared_loop_pair_fwd_def] Definition - - ⊢ ∀ls0 ls1 i. - list_nth_mut_shared_loop_pair_fwd ls0 ls1 i = - list_nth_mut_shared_loop_pair_loop_fwd ls0 ls1 i - - [list_nth_mut_shared_loop_pair_loop_back_def] Definition - - ⊢ ∀ls0 ls1 i ret. - list_nth_mut_shared_loop_pair_loop_back ls0 ls1 i ret = - case ls0 of - ListCons x0 tl0 => - (case ls1 of - ListCons x1 tl1 => - if i = int_to_u32 0 then Return (ListCons ret tl0) - else - do - i0 <- u32_sub i (int_to_u32 1); - tl00 <- - list_nth_mut_shared_loop_pair_loop_back tl0 tl1 i0 - ret; - Return (ListCons x0 tl00) - od - | ListNil => Fail Failure) - | ListNil => Fail Failure - - [list_nth_mut_shared_loop_pair_loop_fwd_def] Definition - - ⊢ ∀ls0 ls1 i. - list_nth_mut_shared_loop_pair_loop_fwd ls0 ls1 i = - case ls0 of - ListCons x0 tl0 => - (case ls1 of - ListCons x1 tl1 => - if i = int_to_u32 0 then Return (x0,x1) - else - do - i0 <- u32_sub i (int_to_u32 1); - list_nth_mut_shared_loop_pair_loop_fwd tl0 tl1 i0 - od - | ListNil => Fail Failure) - | ListNil => Fail Failure - - [list_nth_mut_shared_loop_pair_merge_back_def] Definition - - ⊢ ∀ls0 ls1 i ret. - list_nth_mut_shared_loop_pair_merge_back ls0 ls1 i ret = - list_nth_mut_shared_loop_pair_merge_loop_back ls0 ls1 i ret - - [list_nth_mut_shared_loop_pair_merge_fwd_def] Definition - - ⊢ ∀ls0 ls1 i. - list_nth_mut_shared_loop_pair_merge_fwd ls0 ls1 i = - list_nth_mut_shared_loop_pair_merge_loop_fwd ls0 ls1 i - - [list_nth_mut_shared_loop_pair_merge_loop_back_def] Definition - - ⊢ ∀ls0 ls1 i ret. - list_nth_mut_shared_loop_pair_merge_loop_back ls0 ls1 i ret = - case ls0 of - ListCons x0 tl0 => - (case ls1 of - ListCons x1 tl1 => - if i = int_to_u32 0 then Return (ListCons ret tl0) - else - do - i0 <- u32_sub i (int_to_u32 1); - tl00 <- - list_nth_mut_shared_loop_pair_merge_loop_back tl0 - tl1 i0 ret; - Return (ListCons x0 tl00) - od - | ListNil => Fail Failure) - | ListNil => Fail Failure - - [list_nth_mut_shared_loop_pair_merge_loop_fwd_def] Definition - - ⊢ ∀ls0 ls1 i. - list_nth_mut_shared_loop_pair_merge_loop_fwd ls0 ls1 i = - case ls0 of - ListCons x0 tl0 => - (case ls1 of - ListCons x1 tl1 => - if i = int_to_u32 0 then Return (x0,x1) - else - do - i0 <- u32_sub i (int_to_u32 1); - list_nth_mut_shared_loop_pair_merge_loop_fwd tl0 tl1 - i0 - od - | ListNil => Fail Failure) - | ListNil => Fail Failure - - [list_nth_shared_loop_fwd_def] Definition - - ⊢ ∀ls i. - list_nth_shared_loop_fwd ls i = - list_nth_shared_loop_loop_fwd ls i - - [list_nth_shared_loop_loop_fwd_def] Definition - - ⊢ ∀ls i. - list_nth_shared_loop_loop_fwd ls i = - case ls of - ListCons x tl => - if i = int_to_u32 0 then Return x - else - do - i0 <- u32_sub i (int_to_u32 1); - list_nth_shared_loop_loop_fwd tl i0 - od - | ListNil => Fail Failure - - [list_nth_shared_loop_pair_fwd_def] Definition - - ⊢ ∀ls0 ls1 i. - list_nth_shared_loop_pair_fwd ls0 ls1 i = - list_nth_shared_loop_pair_loop_fwd ls0 ls1 i - - [list_nth_shared_loop_pair_loop_fwd_def] Definition - - ⊢ ∀ls0 ls1 i. - list_nth_shared_loop_pair_loop_fwd ls0 ls1 i = - case ls0 of - ListCons x0 tl0 => - (case ls1 of - ListCons x1 tl1 => - if i = int_to_u32 0 then Return (x0,x1) - else - do - i0 <- u32_sub i (int_to_u32 1); - list_nth_shared_loop_pair_loop_fwd tl0 tl1 i0 - od - | ListNil => Fail Failure) - | ListNil => Fail Failure - - [list_nth_shared_loop_pair_merge_fwd_def] Definition - - ⊢ ∀ls0 ls1 i. - list_nth_shared_loop_pair_merge_fwd ls0 ls1 i = - list_nth_shared_loop_pair_merge_loop_fwd ls0 ls1 i - - [list_nth_shared_loop_pair_merge_loop_fwd_def] Definition - - ⊢ ∀ls0 ls1 i. - list_nth_shared_loop_pair_merge_loop_fwd ls0 ls1 i = - case ls0 of - ListCons x0 tl0 => - (case ls1 of - ListCons x1 tl1 => - if i = int_to_u32 0 then Return (x0,x1) - else - do - i0 <- u32_sub i (int_to_u32 1); - list_nth_shared_loop_pair_merge_loop_fwd tl0 tl1 i0 - od - | ListNil => Fail Failure) - | ListNil => Fail Failure - - [list_nth_shared_loop_with_id_fwd_def] Definition - - ⊢ ∀ls i. - list_nth_shared_loop_with_id_fwd ls i = - do - ls0 <- id_shared_fwd ls; - list_nth_shared_loop_with_id_loop_fwd i ls0 - od - - [list_nth_shared_loop_with_id_loop_fwd_def] Definition - - ⊢ ∀i ls. - list_nth_shared_loop_with_id_loop_fwd i ls = - case ls of - ListCons x tl => - if i = int_to_u32 0 then Return x - else - do - i0 <- u32_sub i (int_to_u32 1); - list_nth_shared_loop_with_id_loop_fwd i0 tl - od - | ListNil => Fail Failure - - [list_nth_shared_mut_loop_pair_back_def] Definition - - ⊢ ∀ls0 ls1 i ret. - list_nth_shared_mut_loop_pair_back ls0 ls1 i ret = - list_nth_shared_mut_loop_pair_loop_back ls0 ls1 i ret - - [list_nth_shared_mut_loop_pair_fwd_def] Definition - - ⊢ ∀ls0 ls1 i. - list_nth_shared_mut_loop_pair_fwd ls0 ls1 i = - list_nth_shared_mut_loop_pair_loop_fwd ls0 ls1 i - - [list_nth_shared_mut_loop_pair_loop_back_def] Definition - - ⊢ ∀ls0 ls1 i ret. - list_nth_shared_mut_loop_pair_loop_back ls0 ls1 i ret = - case ls0 of - ListCons x0 tl0 => - (case ls1 of - ListCons x1 tl1 => - if i = int_to_u32 0 then Return (ListCons ret tl1) - else - do - i0 <- u32_sub i (int_to_u32 1); - tl10 <- - list_nth_shared_mut_loop_pair_loop_back tl0 tl1 i0 - ret; - Return (ListCons x1 tl10) - od - | ListNil => Fail Failure) - | ListNil => Fail Failure - - [list_nth_shared_mut_loop_pair_loop_fwd_def] Definition - - ⊢ ∀ls0 ls1 i. - list_nth_shared_mut_loop_pair_loop_fwd ls0 ls1 i = - case ls0 of - ListCons x0 tl0 => - (case ls1 of - ListCons x1 tl1 => - if i = int_to_u32 0 then Return (x0,x1) - else - do - i0 <- u32_sub i (int_to_u32 1); - list_nth_shared_mut_loop_pair_loop_fwd tl0 tl1 i0 - od - | ListNil => Fail Failure) - | ListNil => Fail Failure - - [list_nth_shared_mut_loop_pair_merge_back_def] Definition - - ⊢ ∀ls0 ls1 i ret. - list_nth_shared_mut_loop_pair_merge_back ls0 ls1 i ret = - list_nth_shared_mut_loop_pair_merge_loop_back ls0 ls1 i ret - - [list_nth_shared_mut_loop_pair_merge_fwd_def] Definition - - ⊢ ∀ls0 ls1 i. - list_nth_shared_mut_loop_pair_merge_fwd ls0 ls1 i = - list_nth_shared_mut_loop_pair_merge_loop_fwd ls0 ls1 i - - [list_nth_shared_mut_loop_pair_merge_loop_back_def] Definition - - ⊢ ∀ls0 ls1 i ret. - list_nth_shared_mut_loop_pair_merge_loop_back ls0 ls1 i ret = - case ls0 of - ListCons x0 tl0 => - (case ls1 of - ListCons x1 tl1 => - if i = int_to_u32 0 then Return (ListCons ret tl1) - else - do - i0 <- u32_sub i (int_to_u32 1); - tl10 <- - list_nth_shared_mut_loop_pair_merge_loop_back tl0 - tl1 i0 ret; - Return (ListCons x1 tl10) - od - | ListNil => Fail Failure) - | ListNil => Fail Failure - - [list_nth_shared_mut_loop_pair_merge_loop_fwd_def] Definition - - ⊢ ∀ls0 ls1 i. - list_nth_shared_mut_loop_pair_merge_loop_fwd ls0 ls1 i = - case ls0 of - ListCons x0 tl0 => - (case ls1 of - ListCons x1 tl1 => - if i = int_to_u32 0 then Return (x0,x1) - else - do - i0 <- u32_sub i (int_to_u32 1); - list_nth_shared_mut_loop_pair_merge_loop_fwd tl0 tl1 - i0 - od - | ListNil => Fail Failure) - | ListNil => Fail Failure - - [sum_fwd_def] Definition - - ⊢ ∀max. sum_fwd max = sum_loop_fwd max (int_to_u32 0) (int_to_u32 0) - - [sum_loop_fwd_def] Definition - - ⊢ ∀max i s. - sum_loop_fwd max i s = - if u32_lt i max then - do - s0 <- u32_add s i; - i0 <- u32_add i (int_to_u32 1); - sum_loop_fwd max i0 s0 - od - else u32_mul s (int_to_u32 2) - - [sum_with_mut_borrows_fwd_def] Definition - - ⊢ ∀max. - sum_with_mut_borrows_fwd max = - sum_with_mut_borrows_loop_fwd max (int_to_u32 0) (int_to_u32 0) - - [sum_with_mut_borrows_loop_fwd_def] Definition - - ⊢ ∀max mi ms. - sum_with_mut_borrows_loop_fwd max mi ms = - if u32_lt mi max then - do - ms0 <- u32_add ms mi; - mi0 <- u32_add mi (int_to_u32 1); - sum_with_mut_borrows_loop_fwd max mi0 ms0 - od - else u32_mul ms (int_to_u32 2) - - [sum_with_shared_borrows_fwd_def] Definition - - ⊢ ∀max. - sum_with_shared_borrows_fwd max = - sum_with_shared_borrows_loop_fwd max (int_to_u32 0) - (int_to_u32 0) - - [sum_with_shared_borrows_loop_fwd_def] Definition - - ⊢ ∀max i s. - sum_with_shared_borrows_loop_fwd max i s = - if u32_lt i max then - do - i0 <- u32_add i (int_to_u32 1); - s0 <- u32_add s i0; - sum_with_shared_borrows_loop_fwd max i0 s0 - od - else u32_mul s (int_to_u32 2) - - -*) -end |