forked from afp-mirror/Core_DOM
Added a few new lemmas.
This commit is contained in:
Michael Herzberg
parent
874251f8c1
commit
d90812beed
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@ -2358,6 +2358,15 @@ proof -
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using assms(1) get_child_nodes_ptr_in_heap by blast
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qed
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lemma remove_child_child_in_heap:
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assumes "h \<turnstile> remove_child ptr' child \<rightarrow>\<^sub>h h'"
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shows "child |\<in>| node_ptr_kinds h"
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using assms
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apply(auto simp add: remove_child_def elim!: bind_returns_heap_E bind_returns_heap_E2[rotated, OF get_child_nodes_pure, rotated] split: if_splits)
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by (meson is_OK_returns_result_I local.get_owner_document_ptr_in_heap node_ptr_kinds_commutes)
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lemma remove_child_in_disconnected_nodes:
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(* assumes "known_ptrs h" *)
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assumes "h \<turnstile> remove_child ptr child \<rightarrow>\<^sub>h h'"
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@ -2490,6 +2499,7 @@ locale l_remove_child = l_type_wf + l_known_ptrs + l_remove_child_defs + l_get_o
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\<Longrightarrow> h' \<turnstile> get_disconnected_nodes owner_document \<rightarrow>\<^sub>r disc_nodes
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\<Longrightarrow> child \<in> set disc_nodes"
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assumes remove_child_ptr_in_heap: "h \<turnstile> ok (remove_child ptr child) \<Longrightarrow> ptr |\<in>| object_ptr_kinds h"
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assumes remove_child_child_in_heap: "h \<turnstile> remove_child ptr' child \<rightarrow>\<^sub>h h' \<Longrightarrow> child |\<in>| node_ptr_kinds h"
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assumes remove_child_children_subset:
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"known_ptrs h \<Longrightarrow> type_wf h \<Longrightarrow> h \<turnstile> remove_child parent child \<rightarrow>\<^sub>h h'
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\<Longrightarrow> h \<turnstile> get_child_nodes ptr \<rightarrow>\<^sub>r children
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@ -2535,6 +2545,7 @@ lemma remove_child_is_l_remove_child [instances]:
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using remove_child_types_preserved apply(blast)
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using remove_child_in_disconnected_nodes apply(blast)
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using remove_child_ptr_in_heap apply(blast)
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using remove_child_child_in_heap apply(blast)
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using remove_child_children_subset apply(blast)
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done
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@ -3012,6 +3023,13 @@ proof -
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unfolding insert_before_def by auto
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qed
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lemma insert_before_ptr_in_heap:
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assumes "h \<turnstile> ok (insert_before ptr node reference_child)"
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shows "ptr |\<in>| object_ptr_kinds h"
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using assms
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apply(auto simp add: insert_before_def elim!: bind_is_OK_E)
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by (metis (mono_tags, lifting) ensure_pre_insertion_validity_pure is_OK_returns_result_I local.get_owner_document_ptr_in_heap next_sibling_pure pure_returns_heap_eq return_returns_heap)
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lemma insert_before_child_in_heap:
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assumes "h \<turnstile> ok (insert_before ptr node reference_child)"
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shows "node |\<in>| node_ptr_kinds h"
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@ -3166,10 +3184,21 @@ global_interpretation l_create_element\<^sub>C\<^sub>o\<^sub>r\<^sub>e\<^sub>_\<
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.
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locale l_create_element\<^sub>C\<^sub>o\<^sub>r\<^sub>e\<^sub>_\<^sub>D\<^sub>O\<^sub>M =
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l_create_element\<^sub>C\<^sub>o\<^sub>r\<^sub>e\<^sub>_\<^sub>D\<^sub>O\<^sub>M_defs +
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l_get_disconnected_nodes +
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l_set_tag_type +
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l_create_element_defs +
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l_create_element\<^sub>C\<^sub>o\<^sub>r\<^sub>e\<^sub>_\<^sub>D\<^sub>O\<^sub>M_defs get_disconnected_nodes get_disconnected_nodes_locs set_disconnected_nodes set_disconnected_nodes_locs set_tag_type set_tag_type_locs +
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l_get_disconnected_nodes type_wf get_disconnected_nodes get_disconnected_nodes_locs +
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l_set_tag_type type_wf set_tag_type set_tag_type_locs +
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l_create_element_defs create_element +
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l_known_ptr known_ptr
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for get_disconnected_nodes :: "(_) document_ptr \<Rightarrow> ((_) heap, exception, (_) node_ptr list) prog"
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and get_disconnected_nodes_locs :: "(_) document_ptr \<Rightarrow> ((_) heap \<Rightarrow> (_) heap \<Rightarrow> bool) set"
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and set_disconnected_nodes :: "(_) document_ptr \<Rightarrow> (_) node_ptr list \<Rightarrow> ((_) heap, exception, unit) prog"
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and set_disconnected_nodes_locs :: "(_) document_ptr \<Rightarrow> ((_) heap, exception, unit) prog set"
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and set_tag_type :: "(_) element_ptr \<Rightarrow> char list \<Rightarrow> ((_) heap, exception, unit) prog"
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and set_tag_type_locs :: "(_) element_ptr \<Rightarrow> ((_) heap, exception, unit) prog set"
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and type_wf :: "(_) heap \<Rightarrow> bool"
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and create_element :: "(_) document_ptr \<Rightarrow> char list \<Rightarrow> ((_) heap, exception, (_) element_ptr) prog"
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and known_ptr :: "(_) object_ptr \<Rightarrow> bool" +
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assumes known_ptr_impl: "known_ptr = a_known_ptr"
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assumes create_element_impl: "create_element = a_create_element"
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begin
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lemmas create_element_def = a_create_element_def[folded create_element_impl]
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@ -3205,12 +3234,25 @@ proof -
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ultimately show ?thesis
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by (auto simp add: document_ptr_kinds_def)
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qed
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lemma create_element_known_ptr:
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assumes "h \<turnstile> create_element document_ptr tag \<rightarrow>\<^sub>r new_element_ptr"
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shows "known_ptr (cast new_element_ptr)"
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proof -
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have "is_element_ptr new_element_ptr"
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using assms
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apply(auto simp add: create_element_def elim!: bind_returns_result_E)
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using new_element_is_element_ptr
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by blast
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then show ?thesis
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by(auto simp add: known_ptr_impl DocumentClass.known_ptr_defs CharacterDataClass.known_ptr_defs ElementClass.known_ptr_defs)
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qed
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end
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locale l_create_element = l_create_element_defs
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interpretation
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i_create_element?: l_create_element\<^sub>C\<^sub>o\<^sub>r\<^sub>e\<^sub>_\<^sub>D\<^sub>O\<^sub>M get_disconnected_nodes get_disconnected_nodes_locs set_disconnected_nodes set_disconnected_nodes_locs set_tag_type set_tag_type_locs type_wf create_element
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i_create_element?: l_create_element\<^sub>C\<^sub>o\<^sub>r\<^sub>e\<^sub>_\<^sub>D\<^sub>O\<^sub>M get_disconnected_nodes get_disconnected_nodes_locs set_disconnected_nodes set_disconnected_nodes_locs set_tag_type set_tag_type_locs type_wf create_element known_ptr
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by(auto simp add: l_create_element\<^sub>C\<^sub>o\<^sub>r\<^sub>e\<^sub>_\<^sub>D\<^sub>O\<^sub>M_def l_create_element\<^sub>C\<^sub>o\<^sub>r\<^sub>e\<^sub>_\<^sub>D\<^sub>O\<^sub>M_axioms_def create_element_def instances)
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declare l_create_element\<^sub>C\<^sub>o\<^sub>r\<^sub>e\<^sub>_\<^sub>D\<^sub>O\<^sub>M_axioms[instances]
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@ -2623,8 +2623,7 @@ proof -
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by (metis (no_types, hide_lams))
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moreover have "node_ptr |\<in>| node_ptr_kinds h"
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using assms(2) get_parent_ptr_in_heap by blast
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thm heap_is_wellformed_children_disc_nodes_different
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ultimately
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ultimately
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have 0: "\<exists>document_ptr\<in>set |h \<turnstile> document_ptr_kinds_M|\<^sub>r. node_ptr \<in> set |h \<turnstile> get_disconnected_nodes document_ptr|\<^sub>r"
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by (metis DocumentMonad.ptr_kinds_ptr_kinds_M assms(1) finite_set_in heap_is_wellformed_children_disc_nodes)
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then obtain document_ptr where
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@ -2785,6 +2784,7 @@ next
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by (meson bind_pure_I bind_returns_result_E2 filter_M_holds_for_result is_OK_returns_result_I local.get_disconnected_nodes_ptr_in_heap local.get_disconnected_nodes_pure return_pure)
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qed
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qed
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end
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locale l_get_owner_document_wf = l_heap_is_wellformed_defs + l_type_wf + l_known_ptrs
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@ -2829,8 +2829,86 @@ lemma get_owner_document_wf_is_l_get_owner_document_wf [instances]:
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done
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subsection \<open>Preserving heap-wellformedness\<close>
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subsubsection \<open>get\_root\_node\<close>
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locale l_get_owner_document_wf_get_root_node_wf\<^sub>C\<^sub>o\<^sub>r\<^sub>e\<^sub>_\<^sub>D\<^sub>O\<^sub>M =
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l_get_root_node\<^sub>C\<^sub>o\<^sub>r\<^sub>e\<^sub>_\<^sub>D\<^sub>O\<^sub>M +
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l_get_root_node_wf +
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l_get_owner_document\<^sub>C\<^sub>o\<^sub>r\<^sub>e\<^sub>_\<^sub>D\<^sub>O\<^sub>M +
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l_get_owner_document_wf
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begin
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lemma get_root_node_document:
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assumes "heap_is_wellformed h" and "type_wf h" and "known_ptrs h"
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assumes "h \<turnstile> get_root_node ptr \<rightarrow>\<^sub>r root"
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assumes "is_document_ptr_kind root"
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shows "h \<turnstile> get_owner_document ptr \<rightarrow>\<^sub>r the (cast root)"
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proof -
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have "ptr |\<in>| object_ptr_kinds h"
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using assms(4)
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by (meson is_OK_returns_result_I local.get_root_node_ptr_in_heap)
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then have "known_ptr ptr"
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using assms(3) local.known_ptrs_known_ptr by blast
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{
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assume "is_document_ptr_kind ptr"
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then have "ptr = root"
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using assms(4)
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by(auto simp add: get_root_node_def get_ancestors_def elim!: bind_returns_result_E2 split: option.splits)
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then have ?thesis
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using \<open>is_document_ptr_kind ptr\<close> \<open>known_ptr ptr\<close> \<open>ptr |\<in>| object_ptr_kinds h\<close>
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apply(auto simp add: known_ptr_impl get_owner_document_def a_get_owner_document_tups_def)
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apply(split invoke_splits, (rule conjI | rule impI)+)+
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apply(drule(1) known_ptr_not_document_ptr[folded known_ptr_impl])
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apply(drule(1) known_ptr_not_character_data_ptr)
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apply(drule(1) known_ptr_not_element_ptr)
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apply(simp add: NodeClass.known_ptr_defs)
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by(auto simp add: a_get_owner_document\<^sub>d\<^sub>o\<^sub>c\<^sub>u\<^sub>m\<^sub>e\<^sub>n\<^sub>t\<^sub>_\<^sub>p\<^sub>t\<^sub>r_def intro!: bind_pure_returns_result_I split: option.splits)
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}
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moreover
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{
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assume "is_node_ptr_kind ptr"
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then have ?thesis
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using \<open>known_ptr ptr\<close> \<open>ptr |\<in>| object_ptr_kinds h\<close>
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apply(auto simp add: known_ptr_impl get_owner_document_def a_get_owner_document_tups_def)
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apply(split invoke_splits, (rule conjI | rule impI)+)+
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apply(drule(1) known_ptr_not_document_ptr[folded known_ptr_impl])
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apply(drule(1) known_ptr_not_character_data_ptr)
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apply(drule(1) known_ptr_not_element_ptr)
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apply(simp add: NodeClass.known_ptr_defs)
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apply(auto split: option.splits)[1]
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using \<open>h \<turnstile> get_root_node ptr \<rightarrow>\<^sub>r root\<close> assms(5)
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by(auto simp add: a_get_owner_document\<^sub>n\<^sub>o\<^sub>d\<^sub>e\<^sub>_\<^sub>p\<^sub>t\<^sub>r_def is_document_ptr_kind_def intro!: bind_pure_returns_result_I split: option.splits)[2]
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}
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ultimately
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show ?thesis
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using \<open>known_ptr ptr\<close>
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by(auto simp add: known_ptr_impl DocumentClass.known_ptr_defs CharacterDataClass.known_ptr_defs ElementClass.known_ptr_defs NodeClass.known_ptr_defs split: option.splits)
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qed
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lemma get_root_node_same_owner_document:
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assumes "heap_is_wellformed h" and "type_wf h" and "known_ptrs h"
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assumes "h \<turnstile> get_root_node ptr \<rightarrow>\<^sub>r root"
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shows "h \<turnstile> get_owner_document ptr \<rightarrow>\<^sub>r owner_document \<longleftrightarrow> h \<turnstile> get_owner_document root \<rightarrow>\<^sub>r owner_document"
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sorry
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end
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interpretation get_owner_document_wf_get_root_node_wf?: l_get_owner_document_wf_get_root_node_wf\<^sub>C\<^sub>o\<^sub>r\<^sub>e\<^sub>_\<^sub>D\<^sub>O\<^sub>M type_wf known_ptr known_ptrs get_parent get_parent_locs get_child_nodes get_child_nodes_locs get_ancestors get_ancestors_locs get_root_node get_root_node_locs heap_is_wellformed parent_child_rel get_disconnected_nodes get_disconnected_nodes_locs get_owner_document
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by(auto simp add: l_get_owner_document_wf_get_root_node_wf\<^sub>C\<^sub>o\<^sub>r\<^sub>e\<^sub>_\<^sub>D\<^sub>O\<^sub>M_def instances)
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declare l_get_owner_document_wf_get_root_node_wf\<^sub>C\<^sub>o\<^sub>r\<^sub>e\<^sub>_\<^sub>D\<^sub>O\<^sub>M_axioms [instances]
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locale l_get_owner_document_wf_get_root_node_wf = l_heap_is_wellformed_defs + l_type_wf + l_known_ptrs + l_get_root_node_defs + l_get_owner_document_defs +
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assumes get_root_node_document: "heap_is_wellformed h \<Longrightarrow> type_wf h \<Longrightarrow> known_ptrs h \<Longrightarrow> h \<turnstile> get_root_node ptr \<rightarrow>\<^sub>r root \<Longrightarrow> is_document_ptr_kind root \<Longrightarrow> h \<turnstile> get_owner_document ptr \<rightarrow>\<^sub>r the (cast root)"
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assumes get_root_node_same_owner_document: "heap_is_wellformed h \<Longrightarrow> type_wf h \<Longrightarrow> known_ptrs h \<Longrightarrow> h \<turnstile> get_root_node ptr \<rightarrow>\<^sub>r root \<Longrightarrow> h \<turnstile> get_owner_document ptr \<rightarrow>\<^sub>r owner_document \<longleftrightarrow> h \<turnstile> get_owner_document root \<rightarrow>\<^sub>r owner_document"
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lemma get_owner_document_wf_get_root_node_wf_is_l_get_owner_document_wf_get_root_node_wf [instances]:
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"l_get_owner_document_wf_get_root_node_wf heap_is_wellformed type_wf known_ptr known_ptrs get_root_node get_owner_document"
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apply(auto simp add: l_get_owner_document_wf_get_root_node_wf_def l_get_owner_document_wf_get_root_node_wf_axioms_def instances)
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using get_root_node_document apply blast
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using get_root_node_same_owner_document apply (blast, blast)
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done
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subsection \<open>Preserving heap-wellformedness\<close>
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subsection \<open>set\_attribute\<close>
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@ -5356,7 +5434,7 @@ locale l_create_element_wf\<^sub>C\<^sub>o\<^sub>r\<^sub>e\<^sub>_\<^sub>D\<^sub
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l_set_tag_type_get_disconnected_nodes type_wf set_tag_type set_tag_type_locs
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get_disconnected_nodes get_disconnected_nodes_locs +
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l_create_element\<^sub>C\<^sub>o\<^sub>r\<^sub>e\<^sub>_\<^sub>D\<^sub>O\<^sub>M get_disconnected_nodes get_disconnected_nodes_locs set_disconnected_nodes
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set_disconnected_nodes_locs set_tag_type set_tag_type_locs type_wf create_element +
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set_disconnected_nodes_locs set_tag_type set_tag_type_locs type_wf create_element known_ptr +
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l_new_element_get_child_nodes type_wf known_ptr get_child_nodes get_child_nodes_locs +
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l_set_tag_type_get_child_nodes type_wf set_tag_type set_tag_type_locs known_ptr
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get_child_nodes get_child_nodes_locs +
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@ -5387,7 +5465,7 @@ lemma create_element_preserves_wellformedness:
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and "h \<turnstile> create_element document_ptr tag \<rightarrow>\<^sub>h h'"
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and "type_wf h"
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and "known_ptrs h"
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shows "heap_is_wellformed h'"
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shows "heap_is_wellformed h'" and "type_wf h'" and "known_ptrs h'"
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proof -
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obtain new_element_ptr h2 h3 disc_nodes_h3 where
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new_element_ptr: "h \<turnstile> new_element \<rightarrow>\<^sub>r new_element_ptr" and
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@ -5399,6 +5477,11 @@ proof -
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by(auto simp add: create_element_def
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elim!: bind_returns_heap_E
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bind_returns_heap_E2[rotated, OF get_disconnected_nodes_pure, rotated] )
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then have "h \<turnstile> create_element document_ptr tag \<rightarrow>\<^sub>r new_element_ptr"
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apply(auto simp add: create_element_def intro!: bind_returns_result_I)
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apply (metis is_OK_returns_heap_I is_OK_returns_result_E old.unit.exhaust)
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apply (metis is_OK_returns_heap_E is_OK_returns_result_I local.get_disconnected_nodes_pure pure_returns_heap_eq)
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by (metis is_OK_returns_heap_I is_OK_returns_result_E old.unit.exhaust)
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have "new_element_ptr \<notin> set |h \<turnstile> element_ptr_kinds_M|\<^sub>r"
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using new_element_ptr ElementMonad.ptr_kinds_ptr_kinds_M h2
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@ -5444,6 +5527,19 @@ proof -
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using object_ptr_kinds_eq_h3
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by(auto simp add: node_ptr_kinds_def)
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have "known_ptr (cast new_element_ptr)"
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using \<open>h \<turnstile> create_element document_ptr tag \<rightarrow>\<^sub>r new_element_ptr\<close> local.create_element_known_ptr by blast
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then
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have "known_ptrs h2"
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using known_ptrs_new_ptr object_ptr_kinds_eq_h \<open>known_ptrs h\<close> h2
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by blast
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then
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have "known_ptrs h3"
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using known_ptrs_preserved object_ptr_kinds_eq_h2 by blast
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then
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show "known_ptrs h'"
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using known_ptrs_preserved object_ptr_kinds_eq_h3 by blast
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have "document_ptr |\<in>| document_ptr_kinds h"
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using disc_nodes_h3 document_ptr_kinds_eq_h object_ptr_kinds_eq_h2
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@ -5496,7 +5592,7 @@ proof -
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using writes_small_big[where P="\<lambda>h h'. type_wf h \<longrightarrow> type_wf h'", OF set_tag_type_writes h3]
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using set_tag_type_types_preserved
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by(auto simp add: reflp_def transp_def)
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then have "type_wf h'"
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then show "type_wf h'"
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using writes_small_big[where P="\<lambda>h h'. type_wf h \<longrightarrow> type_wf h'", OF set_disconnected_nodes_writes h']
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using set_disconnected_nodes_types_preserved
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by(auto simp add: reflp_def transp_def)
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@ -336,12 +336,14 @@ lemma known_ptrs_preserved:
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lemma known_ptrs_subset:
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"object_ptr_kinds h' |\<subseteq>| object_ptr_kinds h \<Longrightarrow> a_known_ptrs h \<Longrightarrow> a_known_ptrs h'"
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by(auto simp add: a_known_ptrs_def)
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lemma known_ptrs_new_ptr: "object_ptr_kinds h' = object_ptr_kinds h |\<union>| {|new_ptr|} \<Longrightarrow> known_ptr new_ptr \<Longrightarrow> a_known_ptrs h \<Longrightarrow> a_known_ptrs h'"
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by(simp add: a_known_ptrs_def)
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end
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global_interpretation l_known_ptrs\<^sub>C\<^sub>h\<^sub>a\<^sub>r\<^sub>a\<^sub>c\<^sub>t\<^sub>e\<^sub>r\<^sub>D\<^sub>a\<^sub>t\<^sub>a known_ptr defines known_ptrs = a_known_ptrs .
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lemmas known_ptrs_defs = a_known_ptrs_def
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lemma known_ptrs_is_l_known_ptrs: "l_known_ptrs known_ptr known_ptrs"
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using known_ptrs_known_ptr known_ptrs_preserved l_known_ptrs_def known_ptrs_subset
|
||||
using known_ptrs_known_ptr known_ptrs_preserved known_ptrs_subset known_ptrs_new_ptr l_known_ptrs_def
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by blast
|
||||
|
||||
end
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|
|
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|
@ -326,11 +326,14 @@ lemma known_ptrs_preserved:
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lemma known_ptrs_subset:
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"object_ptr_kinds h' |\<subseteq>| object_ptr_kinds h \<Longrightarrow> a_known_ptrs h \<Longrightarrow> a_known_ptrs h'"
|
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by(auto simp add: a_known_ptrs_def)
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lemma known_ptrs_new_ptr: "object_ptr_kinds h' = object_ptr_kinds h |\<union>| {|new_ptr|} \<Longrightarrow> known_ptr new_ptr \<Longrightarrow> a_known_ptrs h \<Longrightarrow> a_known_ptrs h'"
|
||||
by(simp add: a_known_ptrs_def)
|
||||
end
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global_interpretation l_known_ptrs\<^sub>D\<^sub>o\<^sub>c\<^sub>u\<^sub>m\<^sub>e\<^sub>n\<^sub>t known_ptr defines known_ptrs = a_known_ptrs .
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lemmas known_ptrs_defs = a_known_ptrs_def
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|
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lemma known_ptrs_is_l_known_ptrs [instances]: "l_known_ptrs known_ptr known_ptrs"
|
||||
using known_ptrs_known_ptr known_ptrs_preserved l_known_ptrs_def known_ptrs_subset by blast
|
||||
using known_ptrs_known_ptr known_ptrs_preserved l_known_ptrs_def known_ptrs_subset known_ptrs_new_ptr
|
||||
by blast
|
||||
|
||||
end
|
||||
|
|
|
|||
|
|
@ -273,7 +273,6 @@ lemma new\<^sub>E\<^sub>l\<^sub>e\<^sub>m\<^sub>e\<^sub>n\<^sub>t_get\<^sub>E\<^
|
|||
using assms
|
||||
by(auto simp add: new\<^sub>E\<^sub>l\<^sub>e\<^sub>m\<^sub>e\<^sub>n\<^sub>t_def Let_def)
|
||||
|
||||
|
||||
locale l_known_ptr\<^sub>E\<^sub>l\<^sub>e\<^sub>m\<^sub>e\<^sub>n\<^sub>t
|
||||
begin
|
||||
definition a_known_ptr :: "(_) object_ptr \<Rightarrow> bool"
|
||||
|
|
@ -301,11 +300,13 @@ lemma known_ptrs_preserved: "object_ptr_kinds h = object_ptr_kinds h' \<Longrigh
|
|||
by(auto simp add: a_known_ptrs_def)
|
||||
lemma known_ptrs_subset: "object_ptr_kinds h' |\<subseteq>| object_ptr_kinds h \<Longrightarrow> a_known_ptrs h \<Longrightarrow> a_known_ptrs h'"
|
||||
by(auto simp add: a_known_ptrs_def)
|
||||
lemma known_ptrs_new_ptr: "object_ptr_kinds h' = object_ptr_kinds h |\<union>| {|new_ptr|} \<Longrightarrow> known_ptr new_ptr \<Longrightarrow> a_known_ptrs h \<Longrightarrow> a_known_ptrs h'"
|
||||
by(simp add: a_known_ptrs_def)
|
||||
end
|
||||
global_interpretation l_known_ptrs\<^sub>E\<^sub>l\<^sub>e\<^sub>m\<^sub>e\<^sub>n\<^sub>t known_ptr defines known_ptrs = a_known_ptrs .
|
||||
lemmas known_ptrs_defs = a_known_ptrs_def
|
||||
|
||||
lemma known_ptrs_is_l_known_ptrs: "l_known_ptrs known_ptr known_ptrs"
|
||||
using known_ptrs_known_ptr known_ptrs_preserved l_known_ptrs_def known_ptrs_subset by blast
|
||||
using known_ptrs_known_ptr known_ptrs_preserved known_ptrs_subset known_ptrs_new_ptr l_known_ptrs_def by blast
|
||||
|
||||
end
|
||||
|
|
|
|||
|
|
@ -186,12 +186,15 @@ lemma known_ptrs_preserved: "object_ptr_kinds h = object_ptr_kinds h' \<Longrigh
|
|||
by(auto simp add: a_known_ptrs_def)
|
||||
lemma known_ptrs_subset: "object_ptr_kinds h' |\<subseteq>| object_ptr_kinds h \<Longrightarrow> a_known_ptrs h \<Longrightarrow> a_known_ptrs h'"
|
||||
by(auto simp add: a_known_ptrs_def)
|
||||
lemma known_ptrs_new_ptr: "object_ptr_kinds h' = object_ptr_kinds h |\<union>| {|new_ptr|} \<Longrightarrow> known_ptr new_ptr \<Longrightarrow> a_known_ptrs h \<Longrightarrow> a_known_ptrs h'"
|
||||
by(simp add: a_known_ptrs_def)
|
||||
end
|
||||
global_interpretation l_known_ptrs\<^sub>N\<^sub>o\<^sub>d\<^sub>e known_ptr defines known_ptrs = a_known_ptrs .
|
||||
lemmas known_ptrs_defs = a_known_ptrs_def
|
||||
|
||||
lemma known_ptrs_is_l_known_ptrs: "l_known_ptrs known_ptr known_ptrs"
|
||||
using known_ptrs_known_ptr known_ptrs_preserved l_known_ptrs_def known_ptrs_subset by blast
|
||||
using known_ptrs_known_ptr known_ptrs_preserved l_known_ptrs_def known_ptrs_subset known_ptrs_new_ptr
|
||||
by blast
|
||||
|
||||
lemma get_node_ptr_simp1 [simp]: "get\<^sub>N\<^sub>o\<^sub>d\<^sub>e node_ptr (put\<^sub>N\<^sub>o\<^sub>d\<^sub>e node_ptr node h) = Some node"
|
||||
by(auto simp add: get\<^sub>N\<^sub>o\<^sub>d\<^sub>e_def put\<^sub>N\<^sub>o\<^sub>d\<^sub>e_def)
|
||||
|
|
|
|||
|
|
@ -128,6 +128,7 @@ locale l_known_ptrs = l_known_ptr known_ptr for known_ptr :: "(_) object_ptr \<R
|
|||
assumes known_ptrs_known_ptr: "known_ptrs h \<Longrightarrow> ptr |\<in>| object_ptr_kinds h \<Longrightarrow> known_ptr ptr"
|
||||
assumes known_ptrs_preserved: "object_ptr_kinds h = object_ptr_kinds h' \<Longrightarrow> known_ptrs h = known_ptrs h'"
|
||||
assumes known_ptrs_subset: "object_ptr_kinds h' |\<subseteq>| object_ptr_kinds h \<Longrightarrow> known_ptrs h \<Longrightarrow> known_ptrs h'"
|
||||
assumes known_ptrs_new_ptr: "object_ptr_kinds h' = object_ptr_kinds h |\<union>| {|new_ptr|} \<Longrightarrow> known_ptr new_ptr \<Longrightarrow> known_ptrs h \<Longrightarrow> known_ptrs h'"
|
||||
|
||||
locale l_known_ptrs\<^sub>O\<^sub>b\<^sub>j\<^sub>e\<^sub>c\<^sub>t = l_known_ptr known_ptr for known_ptr :: "(_) object_ptr \<Rightarrow> bool"
|
||||
begin
|
||||
|
|
@ -143,12 +144,15 @@ lemma known_ptrs_preserved: "object_ptr_kinds h = object_ptr_kinds h' \<Longrigh
|
|||
by(auto simp add: a_known_ptrs_def)
|
||||
lemma known_ptrs_subset: "object_ptr_kinds h' |\<subseteq>| object_ptr_kinds h \<Longrightarrow> a_known_ptrs h \<Longrightarrow> a_known_ptrs h'"
|
||||
by(auto simp add: a_known_ptrs_def)
|
||||
lemma known_ptrs_new_ptr: "object_ptr_kinds h' = object_ptr_kinds h |\<union>| {|new_ptr|} \<Longrightarrow> known_ptr new_ptr \<Longrightarrow> a_known_ptrs h \<Longrightarrow> a_known_ptrs h'"
|
||||
by(simp add: a_known_ptrs_def)
|
||||
end
|
||||
global_interpretation l_known_ptrs\<^sub>O\<^sub>b\<^sub>j\<^sub>e\<^sub>c\<^sub>t known_ptr defines known_ptrs = a_known_ptrs .
|
||||
lemmas known_ptrs_defs = a_known_ptrs_def
|
||||
|
||||
lemma known_ptrs_is_l_known_ptrs: "l_known_ptrs known_ptr known_ptrs"
|
||||
using known_ptrs_known_ptr known_ptrs_preserved l_known_ptrs_def known_ptrs_subset by blast
|
||||
using known_ptrs_known_ptr known_ptrs_preserved l_known_ptrs_def known_ptrs_subset known_ptrs_new_ptr
|
||||
by blast
|
||||
|
||||
|
||||
lemma get_object_ptr_simp1 [simp]: "get\<^sub>O\<^sub>b\<^sub>j\<^sub>e\<^sub>c\<^sub>t object_ptr (put\<^sub>O\<^sub>b\<^sub>j\<^sub>e\<^sub>c\<^sub>t object_ptr object h) = Some object"
|
||||
|
|
|
|||
Reference in New Issue