| Require Import Coq.ZArith.ZArith. |
| Require Import Coq.Bool.Bool. |
| Require Import Coq.Strings.String. |
| Require Import Coq.Strings.Ascii. |
| Require Import Coq.Lists.List. |
| Require Import Coq.Classes.RelationClasses. |
| Require Import Coq.Classes.Morphisms. |
| Require Import Coq.micromega.Psatz. |
| Require Import Coq.Sorting.Permutation. |
| From AUXLib Require Import int_auto Axioms Feq Idents ListLib VMap. |
| Require Import SetsClass.SetsClass. Import SetsNotation. |
| From SimpleC.SL Require Import Mem SeparationLogic. |
| Require Import Logic.LogicGenerator.demo932.Interface. |
| Local Open Scope Z_scope. |
| Local Open Scope sets. |
| Local Open Scope string_scope. |
| Local Open Scope list. |
| Import naive_C_Rules. |
| Require Import PVbench.Data_structures.stack.rocq.spec_lib. |
| Local Open Scope sac. |
|
|
| (*----- Function push -----*) |
|
|
| Definition push_entail_wit_1 := |
| ( |
| forall (n_pre: Z) (stack_pre: Z) (before: sll) (PreH1 : (n_pre < stack_capacity)) , |
| (store_stack stack_pre before n_pre ) |
| ** (IntArray.undef_seg stack_pre n_pre (n_pre + 1 ) ) |
| |-- |
| EX (concrete: (@list Z)) , |
| “ (0 <= n_pre) ” |
| && “ (n_pre < stack_capacity) ” |
| && “ (StackConcreteView before concrete n_pre ) ” |
| && (IntArray.full stack_pre n_pre concrete ) |
| ** (IntArray.undef_seg stack_pre n_pre (n_pre + 1 ) ) |
| ) \/ |
| ( |
| forall (n_pre: Z) (stack_pre: Z) (before: sll) (PreH1 : (n_pre < stack_capacity)) , |
| (store_stack stack_pre before n_pre ) |
| |-- |
| EX (concrete: (@list Z)) , |
| “ (0 <= n_pre) ” |
| && “ (n_pre < stack_capacity) ” |
| && “ (StackConcreteView before concrete n_pre ) ” |
| && (IntArray.full stack_pre n_pre concrete ) |
| ). |
|
|
| Definition push_entail_wit_2 := |
| ( |
| forall (x_pre: Z) (n_pre: Z) (stack_pre: Z) (before: sll) (concrete: (@list Z)) (PreH1 : (0 <= n_pre)) (PreH2 : (n_pre < stack_capacity)) (PreH3 : (StackConcreteView before concrete n_pre )) , |
| (IntArray.full stack_pre (n_pre + 1 ) (app (concrete) ((cons (x_pre) ((@nil Z))))) ) |
| |-- |
| “ (0 <= n_pre) ” |
| && “ (n_pre < stack_capacity) ” |
| && (store_stack stack_pre (sll_cons (x_pre) (before)) (n_pre + 1 ) ) |
| ) \/ |
| ( |
| forall (x_pre: Z) (n_pre: Z) (stack_pre: Z) (before: sll) (concrete: (@list Z)) (PreH1 : (0 <= n_pre)) (PreH2 : (n_pre < stack_capacity)) (PreH3 : (StackConcreteView before concrete n_pre )) , |
| (IntArray.full stack_pre (n_pre + 1 ) (app (concrete) ((cons (x_pre) ((@nil Z))))) ) |
| |-- |
| (store_stack stack_pre (sll_cons (x_pre) (before)) (n_pre + 1 ) ) |
| ). |
|
|
| Definition push_entail_wit_2_split_goal_spatial := |
| forall (x_pre: Z) (n_pre: Z) (stack_pre: Z) (before: sll) (concrete: (@list Z)) (PreH1 : (0 <= n_pre)) (PreH2 : (n_pre < stack_capacity)) (PreH3 : (StackConcreteView before concrete n_pre )) , |
| (IntArray.full stack_pre (n_pre + 1 ) (app (concrete) ((cons (x_pre) ((@nil Z))))) ) |
| |-- |
| (store_stack stack_pre (sll_cons (x_pre) (before)) (n_pre + 1 ) ) |
| . |
|
|
| Definition push_return_wit_1 := |
| forall (x_pre: Z) (n_pre: Z) (stack_pre: Z) (before: sll) (PreH1 : (0 <= n_pre)) (PreH2 : (n_pre < stack_capacity)) , |
| (store_stack stack_pre (sll_cons (x_pre) (before)) (n_pre + 1 ) ) |
| |-- |
| (store_stack stack_pre (sll_cons (x_pre) (before)) (n_pre + 1 ) ) |
| . |
|
|
| Definition push_partial_solve_wit_1 := |
| forall (n_pre: Z) (stack_pre: Z) (before: sll) (concrete: (@list Z)) (PreH1 : (0 <= n_pre)) (PreH2 : (n_pre < stack_capacity)) (PreH3 : (StackConcreteView before concrete n_pre )) , |
| (IntArray.full stack_pre n_pre concrete ) |
| ** (IntArray.undef_seg stack_pre n_pre (n_pre + 1 ) ) |
| |-- |
| “ (0 <= n_pre) ” |
| && “ (n_pre < stack_capacity) ” |
| && “ (StackConcreteView before concrete n_pre ) ” |
| && (((stack_pre + (n_pre * sizeof(INT)))) # Int |->_) |
| ** (IntArray.full stack_pre n_pre concrete ) |
| . |
|
|
| (*----- Function pop -----*) |
|
|
| Definition pop_safety_wit_1 := |
| forall (n_pre: Z) (stack_pre: Z) (rest: sll) (top: Z) (concrete: (@list Z)) (PreH1 : (1 <= n_pre)) (PreH2 : (n_pre <= stack_capacity)) (PreH3 : (StackConcreteView (sll_cons (top) (rest)) concrete n_pre )) , |
| ((( &( "ret" ) )) # Int |->_) |
| ** ((( &( "stack" ) )) # Ptr |-> stack_pre) |
| ** ((( &( "n" ) )) # Int |-> n_pre) |
| ** (IntArray.full stack_pre n_pre concrete ) |
| |-- |
| “ ((n_pre - 1 ) <= INT_MAX) ” |
| && “ ((INT_MIN) <= (n_pre - 1 )) ” |
| . |
|
|
| Definition pop_safety_wit_2 := |
| forall (n_pre: Z) (stack_pre: Z) (rest: sll) (top: Z) (concrete: (@list Z)) (PreH1 : (1 <= n_pre)) (PreH2 : (n_pre <= stack_capacity)) (PreH3 : (StackConcreteView (sll_cons (top) (rest)) concrete n_pre )) , |
| ((( &( "ret" ) )) # Int |->_) |
| ** ((( &( "stack" ) )) # Ptr |-> stack_pre) |
| ** ((( &( "n" ) )) # Int |-> n_pre) |
| ** (IntArray.full stack_pre n_pre concrete ) |
| |-- |
| “ (1 <= INT_MAX) ” |
| && “ ((INT_MIN) <= 1) ” |
| . |
|
|
| Definition pop_entail_wit_1 := |
| ( |
| forall (n_pre: Z) (stack_pre: Z) (rest: sll) (top: Z) (PreH1 : (1 <= n_pre)) , |
| (store_stack stack_pre (sll_cons (top) (rest)) n_pre ) |
| |-- |
| EX (concrete: (@list Z)) , |
| “ (1 <= n_pre) ” |
| && “ (n_pre <= stack_capacity) ” |
| && “ (StackConcreteView (sll_cons (top) (rest)) concrete n_pre ) ” |
| && (IntArray.full stack_pre n_pre concrete ) |
| ) \/ |
| ( |
| forall (n_pre: Z) (stack_pre: Z) (rest: sll) (top: Z) (PreH1 : (1 <= n_pre)) , |
| (store_stack stack_pre (sll_cons (top) (rest)) n_pre ) |
| |-- |
| EX (concrete: (@list Z)) , |
| “ (1 <= n_pre) ” |
| && “ (n_pre <= stack_capacity) ” |
| && “ (StackConcreteView (sll_cons (top) (rest)) concrete n_pre ) ” |
| && (IntArray.full stack_pre n_pre concrete ) |
| ). |
|
|
| Definition pop_entail_wit_2 := |
| ( |
| forall (n_pre: Z) (stack_pre: Z) (rest: sll) (top: Z) (concrete: (@list Z)) (PreH1 : (1 <= n_pre)) (PreH2 : (n_pre <= stack_capacity)) (PreH3 : (StackConcreteView (sll_cons (top) (rest)) concrete n_pre )) , |
| (IntArray.full stack_pre n_pre concrete ) |
| ** ((( &( "ret" ) )) # Int |-> (Znth (n_pre - 1 ) concrete 0)) |
| |-- |
| “ (1 <= n_pre) ” |
| && “ (n_pre <= stack_capacity) ” |
| && ((( &( "ret" ) )) # Int |-> top) |
| ** (store_stack stack_pre rest (n_pre - 1 ) ) |
| ** (IntArray.undef_seg stack_pre (n_pre - 1 ) n_pre ) |
| ) \/ |
| ( |
| forall (n_pre: Z) (stack_pre: Z) (rest: sll) (top: Z) (concrete: (@list Z)) (PreH1 : (1 <= n_pre)) (PreH2 : (n_pre <= stack_capacity)) (PreH3 : (StackConcreteView (sll_cons (top) (rest)) concrete n_pre )) , |
| (IntArray.full stack_pre n_pre concrete ) |
| |-- |
| “ ((Znth (n_pre - 1 ) concrete 0) = top) ” |
| && (store_stack stack_pre rest (n_pre - 1 ) ) |
| ** (IntArray.undef_seg stack_pre (n_pre - 1 ) n_pre ) |
| ). |
|
|
| Definition pop_entail_wit_2_split_goal_1 := |
| forall (n_pre: Z) (stack_pre: Z) (rest: sll) (top: Z) (concrete: (@list Z)) (PreH1 : (1 <= n_pre)) (PreH2 : (n_pre <= stack_capacity)) (PreH3 : (StackConcreteView (sll_cons (top) (rest)) concrete n_pre )) , |
| (IntArray.full stack_pre n_pre concrete ) |
| |-- |
| “ ((Znth (n_pre - 1 ) concrete 0) = top) ” |
| . |
|
|
| Definition pop_entail_wit_2_split_goal_spatial := |
| forall (n_pre: Z) (stack_pre: Z) (rest: sll) (top: Z) (concrete: (@list Z)) (PreH1 : (1 <= n_pre)) (PreH2 : (n_pre <= stack_capacity)) (PreH3 : (StackConcreteView (sll_cons (top) (rest)) concrete n_pre )) , |
| (IntArray.full stack_pre n_pre concrete ) |
| |-- |
| (store_stack stack_pre rest (n_pre - 1 ) ) |
| ** (IntArray.undef_seg stack_pre (n_pre - 1 ) n_pre ) |
| . |
|
|
| Definition pop_return_wit_1 := |
| forall (n_pre: Z) (stack_pre: Z) (rest: sll) (top: Z) (PreH1 : (1 <= n_pre)) (PreH2 : (n_pre <= stack_capacity)) , |
| (store_stack stack_pre rest (n_pre - 1 ) ) |
| ** (IntArray.undef_seg stack_pre (n_pre - 1 ) n_pre ) |
| |-- |
| “ (top = top) ” |
| && (store_stack stack_pre rest (n_pre - 1 ) ) |
| ** (IntArray.undef_seg stack_pre (n_pre - 1 ) n_pre ) |
| . |
|
|
| Definition pop_partial_solve_wit_1 := |
| forall (n_pre: Z) (stack_pre: Z) (rest: sll) (top: Z) (concrete: (@list Z)) (PreH1 : (1 <= n_pre)) (PreH2 : (n_pre <= stack_capacity)) (PreH3 : (StackConcreteView (sll_cons (top) (rest)) concrete n_pre )) , |
| (IntArray.full stack_pre n_pre concrete ) |
| |-- |
| “ (1 <= n_pre) ” |
| && “ (n_pre <= stack_capacity) ” |
| && “ (StackConcreteView (sll_cons (top) (rest)) concrete n_pre ) ” |
| && (((stack_pre + ((n_pre - 1 ) * sizeof(INT)))) # Int |-> (Znth (n_pre - 1 ) concrete 0)) |
| ** (IntArray.missing_i stack_pre (n_pre - 1 ) 0 n_pre concrete ) |
| . |
|
|
| (*----- Function build -----*) |
|
|
| Definition build_safety_wit_1 := |
| forall (n_pre: Z) (stack_pre: Z) (input: (@list Z)) (PreH1 : (0 <= n_pre)) (PreH2 : (n_pre <= stack_capacity)) (PreH3 : ((Zlength (input)) = n_pre)) , |
| ((( &( "i" ) )) # Int |->_) |
| ** ((( &( "stack" ) )) # Ptr |-> stack_pre) |
| ** ((( &( "n" ) )) # Int |-> n_pre) |
| ** (IntArray.full stack_pre n_pre input ) |
| |-- |
| “ (1 <= INT_MAX) ” |
| && “ ((INT_MIN) <= 1) ” |
| . |
|
|
| Definition build_safety_wit_2 := |
| forall (n_pre: Z) (stack_pre: Z) (input: (@list Z)) (i: Z) (PreH1 : (i < n_pre)) (PreH2 : (n_pre = 0)) (PreH3 : (i = 1)) (PreH4 : ((Zlength (input)) = n_pre)) , |
| ((( &( "stack" ) )) # Ptr |-> stack_pre) |
| ** ((( &( "n" ) )) # Int |-> n_pre) |
| ** ((( &( "i" ) )) # Int |-> i) |
| ** (IntArray.full stack_pre n_pre input ) |
| |-- |
| “ False ” |
| . |
|
|
| Definition build_safety_wit_3 := |
| forall (n_pre: Z) (stack_pre: Z) (input: (@list Z)) (next: sll) (i: Z) (x: Z) (PreH1 : (1 <= n_pre)) (PreH2 : (n_pre <= stack_capacity)) (PreH3 : (1 <= i)) (PreH4 : (i < n_pre)) (PreH5 : (x = (Znth i input 0))) (PreH6 : ((Zlength (input)) = n_pre)) (PreH7 : (BuildStackPrefix next input (i + 1 ) )) , |
| ((( &( "stack" ) )) # Ptr |-> stack_pre) |
| ** ((( &( "n" ) )) # Int |-> n_pre) |
| ** ((( &( "i" ) )) # Int |-> i) |
| ** (store_stack stack_pre next (i + 1 ) ) |
| ** (IntArray.seg stack_pre (i + 1 ) n_pre (sublist ((i + 1 )) (n_pre) (input)) ) |
| |-- |
| “ ((i + 1 ) <= INT_MAX) ” |
| && “ ((INT_MIN) <= (i + 1 )) ” |
| . |
|
|
| Definition build_entail_wit_1 := |
| forall (n_pre: Z) (stack_pre: Z) (input: (@list Z)) (PreH1 : (0 <= n_pre)) (PreH2 : (n_pre <= stack_capacity)) (PreH3 : ((Zlength (input)) = n_pre)) , |
| (IntArray.full stack_pre n_pre input ) |
| |-- |
| (“ (n_pre = 0) ” |
| && “ (1 = 1) ” |
| && “ ((Zlength (input)) = n_pre) ” |
| && (IntArray.full stack_pre n_pre input )) |
| || |
| (EX (prefix: sll) , |
| “ (1 <= n_pre) ” |
| && “ (n_pre <= stack_capacity) ” |
| && “ (1 <= 1) ” |
| && “ (1 <= n_pre) ” |
| && “ ((Zlength (input)) = n_pre) ” |
| && “ (BuildStackPrefix prefix input 1 ) ” |
| && (store_stack stack_pre prefix 1 ) |
| ** (IntArray.seg stack_pre 1 n_pre (sublist (1) (n_pre) (input)) )) |
| . |
|
|
| Definition build_entail_wit_2 := |
| ( |
| forall (n_pre: Z) (stack_pre: Z) (input: (@list Z)) (prefix_2: sll) (i: Z) (PreH1 : (i < n_pre)) (PreH2 : (1 <= n_pre)) (PreH3 : (n_pre <= stack_capacity)) (PreH4 : (1 <= i)) (PreH5 : (i <= n_pre)) (PreH6 : ((Zlength (input)) = n_pre)) (PreH7 : (BuildStackPrefix prefix_2 input i )) , |
| (IntArray.seg stack_pre i n_pre (sublist (i) (n_pre) (input)) ) |
| ** (store_stack stack_pre prefix_2 i ) |
| |-- |
| EX (prefix: sll) , |
| “ (1 <= n_pre) ” |
| && “ (n_pre <= stack_capacity) ” |
| && “ (1 <= i) ” |
| && “ (i < n_pre) ” |
| && “ ((Znth (i - i ) (sublist (i) (n_pre) (input)) 0) = (Znth i input 0)) ” |
| && “ ((Zlength (input)) = n_pre) ” |
| && “ (BuildStackPrefix prefix input i ) ” |
| && (store_stack stack_pre prefix i ) |
| ** (IntArray.undef_seg stack_pre i (i + 1 ) ) |
| ** (IntArray.seg stack_pre (i + 1 ) n_pre (sublist ((i + 1 )) (n_pre) (input)) ) |
| ) \/ |
| ( |
| forall (n_pre: Z) (stack_pre: Z) (input: (@list Z)) (prefix_2: sll) (i: Z) (PreH1 : (i < n_pre)) (PreH2 : (1 <= n_pre)) (PreH3 : (n_pre <= stack_capacity)) (PreH4 : (1 <= i)) (PreH5 : (i <= n_pre)) (PreH6 : ((Zlength (input)) = n_pre)) (PreH7 : (BuildStackPrefix prefix_2 input i )) , |
| (IntArray.seg stack_pre i n_pre (sublist (i) (n_pre) (input)) ) |
| ** (store_stack stack_pre prefix_2 i ) |
| |-- |
| EX (prefix: sll) , |
| “ (1 <= n_pre) ” |
| && “ (n_pre <= stack_capacity) ” |
| && “ (1 <= i) ” |
| && “ (i < n_pre) ” |
| && “ ((Znth (i - i ) (sublist (i) (n_pre) (input)) 0) = (Znth i input 0)) ” |
| && “ ((Zlength (input)) = n_pre) ” |
| && “ (BuildStackPrefix prefix input i ) ” |
| && (store_stack stack_pre prefix i ) |
| ** (IntArray.undef_seg stack_pre i (i + 1 ) ) |
| ** (IntArray.seg stack_pre (i + 1 ) n_pre (sublist ((i + 1 )) (n_pre) (input)) ) |
| ). |
|
|
| Definition build_entail_wit_3 := |
| ( |
| forall (n_pre: Z) (stack_pre: Z) (input: (@list Z)) (prefix: sll) (i: Z) (x: Z) (PreH1 : (1 <= n_pre)) (PreH2 : (n_pre <= stack_capacity)) (PreH3 : (1 <= i)) (PreH4 : (i < n_pre)) (PreH5 : (x = (Znth i input 0))) (PreH6 : ((Zlength (input)) = n_pre)) (PreH7 : (BuildStackPrefix prefix input i )) , |
| (store_stack stack_pre (sll_cons (x) (prefix)) (i + 1 ) ) |
| ** (IntArray.seg stack_pre (i + 1 ) n_pre (sublist ((i + 1 )) (n_pre) (input)) ) |
| |-- |
| EX (next: sll) , |
| “ (1 <= n_pre) ” |
| && “ (n_pre <= stack_capacity) ” |
| && “ (1 <= i) ” |
| && “ (i < n_pre) ” |
| && “ (x = (Znth i input 0)) ” |
| && “ ((Zlength (input)) = n_pre) ” |
| && “ (BuildStackPrefix next input (i + 1 ) ) ” |
| && (store_stack stack_pre next (i + 1 ) ) |
| ** (IntArray.seg stack_pre (i + 1 ) n_pre (sublist ((i + 1 )) (n_pre) (input)) ) |
| ) \/ |
| ( |
| forall (n_pre: Z) (input: (@list Z)) (prefix: sll) (i: Z) (x: Z) (PreH1 : (1 <= n_pre)) (PreH2 : (n_pre <= stack_capacity)) (PreH3 : (1 <= i)) (PreH4 : (i < n_pre)) (PreH5 : (x = (Znth i input 0))) (PreH6 : ((Zlength (input)) = n_pre)) (PreH7 : (BuildStackPrefix prefix input i )) , |
| TT && emp |
| |-- |
| “ (BuildStackPrefix (sll_cons (x) (prefix)) input (i + 1 ) ) ” |
| && emp |
| ). |
|
|
| Definition build_entail_wit_3_split_goal_1 := |
| forall (n_pre: Z) (input: (@list Z)) (prefix: sll) (i: Z) (x: Z) (PreH1 : (1 <= n_pre)) (PreH2 : (n_pre <= stack_capacity)) (PreH3 : (1 <= i)) (PreH4 : (i < n_pre)) (PreH5 : (x = (Znth i input 0))) (PreH6 : ((Zlength (input)) = n_pre)) (PreH7 : (BuildStackPrefix prefix input i )) , |
| (BuildStackPrefix (sll_cons (x) (prefix)) input (i + 1 ) ) |
| . |
|
|
| Definition build_entail_wit_4 := |
| forall (n_pre: Z) (stack_pre: Z) (input: (@list Z)) (next: sll) (i: Z) (x: Z) (PreH1 : (1 <= n_pre)) (PreH2 : (n_pre <= stack_capacity)) (PreH3 : (1 <= i)) (PreH4 : (i < n_pre)) (PreH5 : (x = (Znth i input 0))) (PreH6 : ((Zlength (input)) = n_pre)) (PreH7 : (BuildStackPrefix next input (i + 1 ) )) , |
| (store_stack stack_pre next (i + 1 ) ) |
| ** (IntArray.seg stack_pre (i + 1 ) n_pre (sublist ((i + 1 )) (n_pre) (input)) ) |
| |-- |
| EX (prefix: sll) , |
| “ (1 <= n_pre) ” |
| && “ (n_pre <= stack_capacity) ” |
| && “ (1 <= (i + 1 )) ” |
| && “ ((i + 1 ) <= n_pre) ” |
| && “ ((Zlength (input)) = n_pre) ” |
| && “ (BuildStackPrefix prefix input (i + 1 ) ) ” |
| && (store_stack stack_pre prefix (i + 1 ) ) |
| ** (IntArray.seg stack_pre (i + 1 ) n_pre (sublist ((i + 1 )) (n_pre) (input)) ) |
| . |
|
|
| Definition build_entail_wit_5_1 := |
| ( |
| forall (n_pre: Z) (stack_pre: Z) (input: (@list Z)) (i: Z) (PreH1 : (i >= n_pre)) (PreH2 : (n_pre = 0)) (PreH3 : (i = 1)) (PreH4 : ((Zlength (input)) = n_pre)) , |
| (IntArray.full stack_pre n_pre input ) |
| |-- |
| “ (0 <= n_pre) ” |
| && “ (n_pre <= stack_capacity) ” |
| && “ ((Zlength (input)) = n_pre) ” |
| && (store_stack stack_pre (sll_from_array (input)) n_pre ) |
| ) \/ |
| ( |
| forall (n_pre: Z) (stack_pre: Z) (input: (@list Z)) (i: Z) (PreH1 : (i >= n_pre)) (PreH2 : (n_pre = 0)) (PreH3 : (i = 1)) (PreH4 : ((Zlength (input)) = n_pre)) , |
| (IntArray.full stack_pre n_pre input ) |
| |-- |
| “ (0 <= stack_capacity) ” |
| && (store_stack stack_pre (sll_from_array (input)) n_pre ) |
| ). |
|
|
| Definition build_entail_wit_5_1_split_goal_1 := |
| forall (n_pre: Z) (stack_pre: Z) (input: (@list Z)) (i: Z) (PreH1 : (i >= n_pre)) (PreH2 : (n_pre = 0)) (PreH3 : (i = 1)) (PreH4 : ((Zlength (input)) = n_pre)) , |
| (IntArray.full stack_pre n_pre input ) |
| |-- |
| “ (0 <= stack_capacity) ” |
| . |
|
|
| Definition build_entail_wit_5_1_split_goal_spatial := |
| forall (n_pre: Z) (stack_pre: Z) (input: (@list Z)) (i: Z) (PreH1 : (i >= n_pre)) (PreH2 : (n_pre = 0)) (PreH3 : (i = 1)) (PreH4 : ((Zlength (input)) = n_pre)) , |
| (IntArray.full stack_pre n_pre input ) |
| |-- |
| (store_stack stack_pre (sll_from_array (input)) n_pre ) |
| . |
|
|
| Definition build_entail_wit_5_2 := |
| ( |
| forall (n_pre: Z) (stack_pre: Z) (input: (@list Z)) (prefix: sll) (i: Z) (PreH1 : (i >= n_pre)) (PreH2 : (1 <= n_pre)) (PreH3 : (n_pre <= stack_capacity)) (PreH4 : (1 <= i)) (PreH5 : (i <= n_pre)) (PreH6 : ((Zlength (input)) = n_pre)) (PreH7 : (BuildStackPrefix prefix input i )) , |
| (store_stack stack_pre prefix i ) |
| ** (IntArray.seg stack_pre i n_pre (sublist (i) (n_pre) (input)) ) |
| |-- |
| “ (0 <= n_pre) ” |
| && “ (n_pre <= stack_capacity) ” |
| && “ ((Zlength (input)) = n_pre) ” |
| && (store_stack stack_pre (sll_from_array (input)) n_pre ) |
| ) \/ |
| ( |
| forall (n_pre: Z) (stack_pre: Z) (input: (@list Z)) (prefix: sll) (i: Z) (PreH1 : (i >= n_pre)) (PreH2 : (1 <= n_pre)) (PreH3 : (n_pre <= stack_capacity)) (PreH4 : (1 <= i)) (PreH5 : (i <= n_pre)) (PreH6 : ((Zlength (input)) = n_pre)) (PreH7 : (BuildStackPrefix prefix input i )) , |
| (store_stack stack_pre prefix i ) |
| ** (IntArray.seg stack_pre i n_pre (sublist (i) (n_pre) (input)) ) |
| |-- |
| (store_stack stack_pre (sll_from_array (input)) n_pre ) |
| ). |
|
|
| Definition build_entail_wit_5_2_split_goal_spatial := |
| forall (n_pre: Z) (stack_pre: Z) (input: (@list Z)) (prefix: sll) (i: Z) (PreH1 : (i >= n_pre)) (PreH2 : (1 <= n_pre)) (PreH3 : (n_pre <= stack_capacity)) (PreH4 : (1 <= i)) (PreH5 : (i <= n_pre)) (PreH6 : ((Zlength (input)) = n_pre)) (PreH7 : (BuildStackPrefix prefix input i )) , |
| (store_stack stack_pre prefix i ) |
| ** (IntArray.seg stack_pre i n_pre (sublist (i) (n_pre) (input)) ) |
| |-- |
| (store_stack stack_pre (sll_from_array (input)) n_pre ) |
| . |
|
|
| Definition build_return_wit_1 := |
| forall (n_pre: Z) (stack_pre: Z) (input: (@list Z)) (PreH1 : (0 <= n_pre)) (PreH2 : (n_pre <= stack_capacity)) (PreH3 : ((Zlength (input)) = n_pre)) , |
| (store_stack stack_pre (sll_from_array (input)) n_pre ) |
| |-- |
| (store_stack stack_pre (sll_from_array (input)) n_pre ) |
| . |
|
|
| Definition build_partial_solve_wit_1 := |
| forall (n_pre: Z) (stack_pre: Z) (input: (@list Z)) (prefix: sll) (i: Z) (PreH1 : (i < n_pre)) (PreH2 : (1 <= n_pre)) (PreH3 : (n_pre <= stack_capacity)) (PreH4 : (1 <= i)) (PreH5 : (i <= n_pre)) (PreH6 : ((Zlength (input)) = n_pre)) (PreH7 : (BuildStackPrefix prefix input i )) , |
| (store_stack stack_pre prefix i ) |
| ** (IntArray.seg stack_pre i n_pre (sublist (i) (n_pre) (input)) ) |
| |-- |
| “ (i < n_pre) ” |
| && “ (1 <= n_pre) ” |
| && “ (n_pre <= stack_capacity) ” |
| && “ (1 <= i) ” |
| && “ (i <= n_pre) ” |
| && “ ((Zlength (input)) = n_pre) ” |
| && “ (BuildStackPrefix prefix input i ) ” |
| && (((stack_pre + (i * sizeof(INT)))) # Int |-> (Znth (i - i ) (sublist (i) (n_pre) (input)) 0)) |
| ** (IntArray.missing_i stack_pre i i n_pre (sublist (i) (n_pre) (input)) ) |
| ** (store_stack stack_pre prefix i ) |
| . |
|
|
| Definition build_partial_solve_wit_2_pure := |
| forall (n_pre: Z) (stack_pre: Z) (input: (@list Z)) (prefix: sll) (i: Z) (x: Z) (PreH1 : (1 <= n_pre)) (PreH2 : (n_pre <= stack_capacity)) (PreH3 : (1 <= i)) (PreH4 : (i < n_pre)) (PreH5 : (x = (Znth i input 0))) (PreH6 : ((Zlength (input)) = n_pre)) (PreH7 : (BuildStackPrefix prefix input i )) , |
| ((( &( "stack" ) )) # Ptr |-> stack_pre) |
| ** ((( &( "n" ) )) # Int |-> n_pre) |
| ** ((( &( "i" ) )) # Int |-> i) |
| ** ((( &( "x" ) )) # Int |-> x) |
| ** (store_stack stack_pre prefix i ) |
| ** (IntArray.undef_seg stack_pre i (i + 1 ) ) |
| ** (IntArray.seg stack_pre (i + 1 ) n_pre (sublist ((i + 1 )) (n_pre) (input)) ) |
| |-- |
| “ (i < stack_capacity) ” |
| . |
|
|
| Definition build_partial_solve_wit_2_aux := |
| forall (n_pre: Z) (stack_pre: Z) (input: (@list Z)) (prefix: sll) (i: Z) (x: Z) (PreH1 : (1 <= n_pre)) (PreH2 : (n_pre <= stack_capacity)) (PreH3 : (1 <= i)) (PreH4 : (i < n_pre)) (PreH5 : (x = (Znth i input 0))) (PreH6 : ((Zlength (input)) = n_pre)) (PreH7 : (BuildStackPrefix prefix input i )) , |
| (store_stack stack_pre prefix i ) |
| ** (IntArray.undef_seg stack_pre i (i + 1 ) ) |
| ** (IntArray.seg stack_pre (i + 1 ) n_pre (sublist ((i + 1 )) (n_pre) (input)) ) |
| |-- |
| “ (i < stack_capacity) ” |
| && “ (1 <= n_pre) ” |
| && “ (n_pre <= stack_capacity) ” |
| && “ (1 <= i) ” |
| && “ (i < n_pre) ” |
| && “ (x = (Znth i input 0)) ” |
| && “ ((Zlength (input)) = n_pre) ” |
| && “ (BuildStackPrefix prefix input i ) ” |
| && (store_stack stack_pre prefix i ) |
| ** (IntArray.undef_seg stack_pre i (i + 1 ) ) |
| ** (IntArray.seg stack_pre (i + 1 ) n_pre (sublist ((i + 1 )) (n_pre) (input)) ) |
| . |
|
|
| Definition build_partial_solve_wit_2 := build_partial_solve_wit_2_pure -> build_partial_solve_wit_2_aux. |
|
|
| Module Type VC_Correct. |
|
|
|
|
| Axiom proof_of_push_entail_wit_1 : push_entail_wit_1. |
| Axiom proof_of_push_entail_wit_2 : push_entail_wit_2. |
| Axiom proof_of_push_return_wit_1 : push_return_wit_1. |
| Axiom proof_of_push_partial_solve_wit_1 : push_partial_solve_wit_1. |
| Axiom proof_of_pop_safety_wit_1 : pop_safety_wit_1. |
| Axiom proof_of_pop_safety_wit_2 : pop_safety_wit_2. |
| Axiom proof_of_pop_entail_wit_1 : pop_entail_wit_1. |
| Axiom proof_of_pop_entail_wit_2 : pop_entail_wit_2. |
| Axiom proof_of_pop_return_wit_1 : pop_return_wit_1. |
| Axiom proof_of_pop_partial_solve_wit_1 : pop_partial_solve_wit_1. |
| Axiom proof_of_build_safety_wit_1 : build_safety_wit_1. |
| Axiom proof_of_build_safety_wit_2 : build_safety_wit_2. |
| Axiom proof_of_build_safety_wit_3 : build_safety_wit_3. |
| Axiom proof_of_build_entail_wit_1 : build_entail_wit_1. |
| Axiom proof_of_build_entail_wit_2 : build_entail_wit_2. |
| Axiom proof_of_build_entail_wit_3 : build_entail_wit_3. |
| Axiom proof_of_build_entail_wit_4 : build_entail_wit_4. |
| Axiom proof_of_build_entail_wit_5_1 : build_entail_wit_5_1. |
| Axiom proof_of_build_entail_wit_5_2 : build_entail_wit_5_2. |
| Axiom proof_of_build_return_wit_1 : build_return_wit_1. |
| Axiom proof_of_build_partial_solve_wit_1 : build_partial_solve_wit_1. |
| Axiom proof_of_build_partial_solve_wit_2_pure : build_partial_solve_wit_2_pure. |
| Axiom proof_of_build_partial_solve_wit_2 : build_partial_solve_wit_2. |
|
|
| End VC_Correct. |
|
|
