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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.
From PVbench.Data_structures.stack.rocq.groundtruth Require Import stack_goal.
From PVbench.Data_structures.stack.rocq.groundtruth Require Import stack_proof_auto.
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.groundtruth.proof_lib.
Local Open Scope sac.
Lemma proof_of_push_entail_wit_1 : push_entail_wit_1.
Proof.
LLM_pre_process ltac:(lia || int_auto).
unfold store_stack.
Intros concrete.
Exists concrete.
unfold StackConcreteView.
split_pure_spatial.
- cancel (IntArray.full stack_pre n_pre concrete).
cancel (IntArray.undef_seg stack_pre n_pre (n_pre + 1)).
- split_pures.
+ dump_pre_spatial.
unfold stack_representation in H.
lia.
+ dump_pre_spatial.
lia.
+ dump_pre_spatial.
exact H.
Qed.
Lemma proof_of_push_entail_wit_2_split_goal_spatial : push_entail_wit_2_split_goal_spatial.
Proof.
LLM_pre_process ltac:(lia || int_auto).
unfold store_stack.
Exists (concrete ++ (x_pre :: nil)).
split_pure_spatial.
- cancel (IntArray.full stack_pre (n_pre + 1)
(concrete ++ (x_pre :: nil))).
- dump_pre_spatial.
unfold StackConcreteView in *.
eapply stack_representation_push__push_state; eauto.
Qed.
Lemma proof_of_push_entail_wit_2 : push_entail_wit_2.
Proof.
aggressive_pre_process.
- Goal_apply proof_of_push_entail_wit_2_split_goal_spatial.
Qed.
Lemma proof_of_pop_entail_wit_1 : pop_entail_wit_1.
Proof.
LLM_pre_process ltac:(lia || int_auto).
unfold store_stack.
Intros concrete.
match goal with
| Hrepresentation : stack_representation _ concrete n_pre |- _ =>
pose proof Hrepresentation as Hrepresentation_parts;
destruct Hrepresentation_parts as [_ [Hcapacity _]]
end.
Exists concrete.
unfold StackConcreteView.
split_pure_spatial.
- cancel (IntArray.full stack_pre n_pre concrete).
- split_pures; dump_pre_spatial; try assumption.
Qed.
Lemma proof_of_pop_entail_wit_2_split_goal_1 : pop_entail_wit_2_split_goal_1.
Proof.
LLM_pre_process ltac:(lia || int_auto).
unfold StackConcreteView in PreH3.
pose proof
(stack_representation_pop__pop_state
top rest concrete n_pre PreH1 PreH3)
as [_ [_ [_ Htop]]].
dump_pre_spatial.
exact Htop.
Qed.
Lemma proof_of_pop_entail_wit_2_split_goal_spatial : pop_entail_wit_2_split_goal_spatial.
Proof.
LLM_pre_process ltac:(lia || int_auto).
unfold StackConcreteView in PreH3.
pose proof
(stack_representation_pop__pop_state
top rest concrete n_pre PreH1 PreH3)
as [Hconcrete [Hprefix_length [Hrest_representation _]]].
assert (Hprefix : sublist 0 (n_pre - 1) concrete = rev rest).
{
rewrite Hconcrete.
rewrite <- Hprefix_length.
apply sublist_app_exact1.
}
unfold store_stack.
Exists (rev rest).
sep_apply_l_atomic
(IntArray.full_split_to_seg
stack_pre (n_pre - 1) n_pre concrete ltac:(lia)).
rewrite Hprefix.
sep_apply_l_atomic
(IntArray.seg_to_full
stack_pre 0 (n_pre - 1) (rev rest)).
sep_apply_l_atomic
(IntArray.seg_to_undef_seg
stack_pre (n_pre - 1) n_pre
(sublist (n_pre - 1) n_pre concrete)).
replace (stack_pre + 0 * sizeof(INT)) with stack_pre by lia.
replace (n_pre - 1 - 0) with (n_pre - 1) by lia.
split_pure_spatial.
- repeat cancel.
- dump_pre_spatial.
exact Hrest_representation.
Qed.
Lemma proof_of_pop_entail_wit_2 : pop_entail_wit_2.
Proof.
aggressive_pre_process.
- Goal_apply proof_of_pop_entail_wit_2_split_goal_spatial.
- Goal_apply proof_of_pop_entail_wit_2_split_goal_1.
Qed.
Lemma proof_of_build_entail_wit_1 : build_entail_wit_1.
Proof.
LLM_pre_process ltac:(lia || int_auto).
destruct (Z.eq_dec n_pre 0) as [Hzero | Hpositive].
- subst n_pre.
Left.
split_pure_spatial;
[ repeat cancel
| split_pures; dump_pre_spatial; try lia; try int_auto;
try assumption; try reflexivity ].
- Right.
assert (Hone : 1 <= n_pre) by lia.
pose proof
(stack_representation_prefix__build_loop
input 1 ltac:(lia) ltac:(lia))
as Hrepresentation.
sep_apply
(IntArray.full_split_to_seg
stack_pre 1 n_pre input);
try lia.
unfold store_stack.
Exists (sll_from_array (sublist 0 1 input)).
Exists (sublist 0 1 input).
sep_apply
(IntArray.seg_to_full
stack_pre 0 1 (sublist 0 1 input)).
split_pure_spatial;
[ repeat cancel
| split_pures; dump_pre_spatial; try lia; try int_auto;
try assumption; try reflexivity ].
replace (stack_pre + 0 * sizeof(INT)) with stack_pre by lia.
replace (1 - 0) with 1 by lia.
cancel.
Qed.
Lemma proof_of_build_entail_wit_2 : build_entail_wit_2.
Proof.
LLM_pre_process ltac:(lia || int_auto).
Exists prefix_2.
sep_apply
(IntArray.seg_split_to_seg
stack_pre i (i + 1) n_pre (sublist i n_pre input));
try lia.
sep_apply
(IntArray.seg_to_undef_seg
stack_pre i (i + 1)
(sublist 0 (i + 1 - i) (sublist i n_pre input))).
replace
(sublist (i + 1 - i) (n_pre - i) (sublist i n_pre input))
with (sublist (i + 1) n_pre input).
2: {
rewrite Zsublist_Zsublist by lia.
f_equal; lia.
}
split_pure_spatial.
- repeat cancel.
- split_pures; dump_pre_spatial; try lia; try int_auto;
try assumption; try reflexivity.
all: try (rewrite Znth_sublist by lia; f_equal; lia).
Qed.
Lemma proof_of_build_entail_wit_3_split_goal_1 : build_entail_wit_3_split_goal_1.
Proof.
LLM_pre_process ltac:(lia || int_auto).
eapply build_stack_prefix_succ__build_loop; eauto; lia.
Qed.
Lemma proof_of_build_entail_wit_3 : build_entail_wit_3.
Proof.
aggressive_pre_process.
Goal_apply proof_of_build_entail_wit_3_split_goal_1.
Qed.
Lemma proof_of_build_entail_wit_5_1_split_goal_1 : build_entail_wit_5_1_split_goal_1.
Proof.
LLM_pre_process ltac:(lia || int_auto).
unfold stack_capacity.
dump_pre_spatial.
lia.
Qed.
Lemma proof_of_build_entail_wit_5_1_split_goal_spatial : build_entail_wit_5_1_split_goal_spatial.
Proof.
LLM_pre_process ltac:(lia || int_auto).
subst n_pre.
apply Zlength_nil_inv in PreH4.
subst input.
unfold store_stack.
Exists (@nil Z).
split_pure_spatial.
- cancel (IntArray.full stack_pre 0 (@nil Z)).
- dump_pre_spatial.
unfold stack_representation, sll_from_array, stack_capacity.
simpl.
repeat split; lia.
Qed.
Lemma proof_of_build_entail_wit_5_1 : build_entail_wit_5_1.
Proof.
aggressive_pre_process.
- Goal_apply proof_of_build_entail_wit_5_1_split_goal_spatial.
- Goal_apply proof_of_build_entail_wit_5_1_split_goal_1.
Qed.
Lemma proof_of_build_entail_wit_5_2_split_goal_spatial : build_entail_wit_5_2_split_goal_spatial.
Proof.
LLM_pre_process ltac:(lia || int_auto).
pose proof
(build_stack_prefix_complete__build_completion
prefix input i n_pre PreH1 PreH5 PreH6 PreH7)
as [Hi Hprefix].
subst i.
subst prefix.
rewrite Zsublist_nil by lia.
rewrite IntArray.seg_empty.
Intros_p Hempty.
cancel (store_stack stack_pre (sll_from_array input) n_pre).
Qed.
Lemma proof_of_build_entail_wit_5_2 : build_entail_wit_5_2.
Proof.
aggressive_pre_process.
- Goal_apply proof_of_build_entail_wit_5_2_split_goal_spatial.
Qed.
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