Merge branch 'main' into afp_resubmission
This commit is contained in:
Nicolas Méric
commit
20e90f688f
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@ -590,15 +590,15 @@ text \<open>underlying idea: a monitor class automatically receives a
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doc_class article =
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style_id :: string <= "''LNCS''"
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version :: "(int \<times> int \<times> int)" <= "(0,0,0)"
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accepts "(title ~~
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\<lbrakk>subtitle\<rbrakk> ~~
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\<lbrace>author\<rbrace>\<^sup>+ ~~
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abstract ~~
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\<lbrace>introduction\<rbrace>\<^sup>+ ~~
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\<lbrace>background\<rbrace>\<^sup>* ~~
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\<lbrace>technical || example \<rbrace>\<^sup>+ ~~
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\<lbrace>conclusion\<rbrace>\<^sup>+ ~~
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bibliography ~~
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accepts "(title ~~
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\<lbrakk>subtitle\<rbrakk> ~~
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\<lbrace>author\<rbrace>\<^sup>+ ~~
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abstract ~~
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\<lbrace>introduction\<rbrace>\<^sup>+ ~~
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\<lbrace>background\<rbrace>\<^sup>* ~~
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\<lbrace>technical || example || float \<rbrace>\<^sup>+ ~~
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\<lbrace>conclusion\<rbrace>\<^sup>+ ~~
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bibliography ~~
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\<lbrace>annex\<rbrace>\<^sup>* )"
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@ -662,6 +662,7 @@ let val cidS = ["scholarly_paper.introduction","scholarly_paper.technical",
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in DOF_core.add_ml_invariant binding (DOF_core.make_ml_invariant (body, cid_long)) thy end)
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\<close>
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term\<open>float\<close>
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section\<open>Miscelleous\<close>
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subsection\<open>Common Abbreviations\<close>
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@ -76,7 +76,7 @@ doc_class report =
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\<lbrakk>table_of_contents\<rbrakk> ~~
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\<lbrace>introduction\<rbrace>\<^sup>+ ~~
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\<lbrace>background\<rbrace>\<^sup>* ~~
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\<lbrace>technical || example \<rbrace>\<^sup>+ ~~
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\<lbrace>technical || example || float \<rbrace>\<^sup>+ ~~
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\<lbrace>conclusion\<rbrace>\<^sup>+ ~~
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bibliography ~~
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\<lbrakk>index\<rbrakk> ~~ \<lbrace>annex\<rbrace>\<^sup>* )"
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@ -95,36 +95,189 @@ notation Plus (infixr "||" 55)
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notation Times (infixr "~~" 60)
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notation Atom ("\<lfloor>_\<rfloor>" 65)
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lemma regexp_sub : "a \<le> b \<Longrightarrow> L\<^sub>s\<^sub>u\<^sub>b (\<lfloor>a\<rfloor>) \<subseteq> L\<^sub>s\<^sub>u\<^sub>b (\<lfloor>b\<rfloor>)"
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using dual_order.trans by auto
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lemma regexp_seq_mono:
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"Lang(a) \<subseteq> Lang (a') \<Longrightarrow> Lang(b) \<subseteq> Lang (b') \<Longrightarrow> Lang(a ~~ b) \<subseteq> Lang(a' ~~ b')" by auto
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lemma regexp_seq_mono':
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"L\<^sub>s\<^sub>u\<^sub>b(a) \<subseteq> L\<^sub>s\<^sub>u\<^sub>b (a') \<Longrightarrow> L\<^sub>s\<^sub>u\<^sub>b(b) \<subseteq> L\<^sub>s\<^sub>u\<^sub>b (b') \<Longrightarrow> L\<^sub>s\<^sub>u\<^sub>b(a ~~ b) \<subseteq> L\<^sub>s\<^sub>u\<^sub>b(a' ~~ b')" by auto
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lemma regexp_alt_mono :"Lang(a) \<subseteq> Lang (a') \<Longrightarrow> Lang(a || b) \<subseteq> Lang(a' || b)" by auto
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lemma regexp_alt_mono' :"L\<^sub>s\<^sub>u\<^sub>b(a) \<subseteq> L\<^sub>s\<^sub>u\<^sub>b (a') \<Longrightarrow> L\<^sub>s\<^sub>u\<^sub>b(a || b) \<subseteq> L\<^sub>s\<^sub>u\<^sub>b(a' || b)" by auto
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lemma regexp_alt_commute : "Lang(a || b) = Lang(b || a)" by auto
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lemma regexp_alt_commute' : "L\<^sub>s\<^sub>u\<^sub>b(a || b) = L\<^sub>s\<^sub>u\<^sub>b(b || a)" by auto
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lemma regexp_unit_right : "Lang (a) = Lang (a ~~ One) " by simp
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lemma regexp_unit_right' : "L\<^sub>s\<^sub>u\<^sub>b (a) = L\<^sub>s\<^sub>u\<^sub>b (a ~~ One) " by simp
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lemma regexp_unit_left : "Lang (a) = Lang (One ~~ a) " by simp
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lemma regexp_unit_left' : "L\<^sub>s\<^sub>u\<^sub>b (a) = L\<^sub>s\<^sub>u\<^sub>b (One ~~ a) " by simp
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lemma opt_star_incl :"Lang (opt a) \<subseteq> Lang (Star a)" by (simp add: opt_def subset_iff)
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lemma opt_star_incl':"L\<^sub>s\<^sub>u\<^sub>b (opt a) \<subseteq> L\<^sub>s\<^sub>u\<^sub>b (Star a)" by (simp add: opt_def subset_iff)
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lemma rep1_star_incl:"Lang (rep1 a) \<subseteq> Lang (Star a)"
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unfolding rep1_def by(subst L_Star, subst L_Conc)(force)
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lemma rep1_star_incl':"L\<^sub>s\<^sub>u\<^sub>b (rep1 a) \<subseteq> L\<^sub>s\<^sub>u\<^sub>b (Star a)"
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unfolding rep1_def by(subst L\<^sub>s\<^sub>u\<^sub>b_Star, subst L\<^sub>s\<^sub>u\<^sub>b_Conc)(force)
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lemma cancel_rep1 : "Lang (a) \<subseteq> Lang (rep1 a)"
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unfolding rep1_def by auto
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lemma cancel_rep1' : "L\<^sub>s\<^sub>u\<^sub>b (a) \<subseteq> L\<^sub>s\<^sub>u\<^sub>b (rep1 a)"
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unfolding rep1_def by auto
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lemma seq_cancel_opt : "Lang (a) \<subseteq> Lang (c) \<Longrightarrow> Lang (a) \<subseteq> Lang (opt b ~~ c)"
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by(subst regexp_unit_left, rule regexp_seq_mono)(simp_all add: opt_def)
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lemma seq_cancel_opt' : "L\<^sub>s\<^sub>u\<^sub>b (a) \<subseteq> L\<^sub>s\<^sub>u\<^sub>b (c) \<Longrightarrow> L\<^sub>s\<^sub>u\<^sub>b (a) \<subseteq> L\<^sub>s\<^sub>u\<^sub>b (opt b ~~ c)"
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by(subst regexp_unit_left', rule regexp_seq_mono')(simp_all add: opt_def)
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lemma seq_cancel_Star : "Lang (a) \<subseteq> Lang (c) \<Longrightarrow> Lang (a) \<subseteq> Lang (Star b ~~ c)"
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by auto
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lemma seq_cancel_Star' : "L\<^sub>s\<^sub>u\<^sub>b (a) \<subseteq> L\<^sub>s\<^sub>u\<^sub>b (c) \<Longrightarrow> L\<^sub>s\<^sub>u\<^sub>b (a) \<subseteq> L\<^sub>s\<^sub>u\<^sub>b (Star b ~~ c)"
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by auto
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lemma mono_Star : "Lang (a) \<subseteq> Lang (b) \<Longrightarrow> Lang (Star a) \<subseteq> Lang (Star b)"
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by(auto)(metis in_star_iff_concat order.trans)
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lemma mono_Star' : "L\<^sub>s\<^sub>u\<^sub>b (a) \<subseteq> L\<^sub>s\<^sub>u\<^sub>b (b) \<Longrightarrow> L\<^sub>s\<^sub>u\<^sub>b (Star a) \<subseteq> L\<^sub>s\<^sub>u\<^sub>b (Star b)"
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by(auto)(metis in_star_iff_concat order.trans)
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lemma mono_rep1_star:"Lang (a) \<subseteq> Lang (b) \<Longrightarrow> Lang (rep1 a) \<subseteq> Lang (Star b)"
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using mono_Star rep1_star_incl by blast
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lemma mono_rep1_star':"L\<^sub>s\<^sub>u\<^sub>b (a) \<subseteq> L\<^sub>s\<^sub>u\<^sub>b (b) \<Longrightarrow> L\<^sub>s\<^sub>u\<^sub>b (rep1 a) \<subseteq> L\<^sub>s\<^sub>u\<^sub>b (Star b)"
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using mono_Star' rep1_star_incl' by blast
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text\<open>Not a terribly deep theorem, but an interesting property of consistency between
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ontologies - so, a lemma that shouldn't break if the involved ontologies were changed:
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the structural language of articles should be included in the structural language of
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reports, that is to say, reports should just have a richer structure than ordinary papers. \<close>
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ontologies - so, a lemma that shouldn't break if the involved ontologies were changed.
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It reads as follows:
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"The structural language of articles should be included in the structural language of
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reports, that is to say, reports should just have a richer structure than ordinary papers." \<close>
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theorem articles_sub_reports: \<open>(Lang article_monitor) \<subseteq> Lang report_monitor\<close>
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unfolding article_monitor_def report_monitor_def
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apply(rule regexp_seq_mono[OF subset_refl] | rule seq_cancel_opt | rule subset_refl)+
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done
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text\<open>The proof proceeds by blindly applying the monotonicity rules
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on the language of regular expressions.\<close>
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print_doc_classes
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text\<open>All Class-Id's --- should be generated.\<close>
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lemmas class_ids =
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SML_def code_def annex_def title_def figure_def chapter_def article_def theorem_def
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paragraph_def tech_code_def assumption_def definition_def hypothesis_def eng_example_def
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text_element_def math_content_def tech_example_def subsubsection_def tech_definition_def
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engineering_content_def data_def float_def axiom_def LATEX_def author_def listing_def example_def
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abstract_def assertion_def technical_def background_def evaluation_def math_proof_def
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math_formal_def bibliography_def math_example_def text_section_def conclusion_stmt_def
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math_explanation_def ISAR_def frame_def lemma_def index_def report_def section_def premise_def
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subtitle_def corollary_def subsection_def conclusion_def experiment_def consequence_def
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proposition_def introduction_def related_work_def front_matter_def math_motivation_def
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table_of_contents_def
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term\<open>{
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SML,code, annex, title ,figure,chapter, article , theorem ,paragraph,tech_code,
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assumption, definition , hypothesis ,eng_example ,text_element,math_content,tech_example,
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subsubsection,tech_definition,engineering_content,data,float,axiom,LATEX,author,listing,
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example,abstract,assertion,technical,background,evaluation,math_proof,math_formal,
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bibliography,math_example,text_section,conclusion_stmt,math_explanation,ISAR,frame,
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lemma,index,report,section,premise,subtitle,corollary,subsection,conclusion,experiment,
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consequence,proposition,introduction,related_work,front_matter,math_motivation,table_of_contents}
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\<close>
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definition allClasses
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where \<open>allClasses \<equiv> {SML, code, annex, title,figure,chapter, article, theorem, paragraph,
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tech_code, assumption, definition, hypothesis, eng_example, text_element,
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math_content,tech_example, subsubsection,tech_definition,
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engineering_content,data,float,axiom,LATEX,author,listing, example,abstract,
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assertion,technical,background,evaluation,math_proof,math_formal,bibliography,
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math_example,text_section,conclusion_stmt,math_explanation,ISAR,frame,
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lemma,index,report,section,premise,subtitle,corollary,subsection,conclusion,
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experiment, consequence,proposition,introduction,related_work,front_matter,
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math_motivation,table_of_contents}
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\<close>
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text\<open>A rudimentary fragment of the class hierarchy re-modeled on classid's :\<close>
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definition doc_class_rel
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where \<open>doc_class_rel \<equiv> {(proposition,math_content),
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(listing,float),
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(figure,float)} \<close>
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instantiation "doc_class" :: ord
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begin
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definition
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le_class_def: "x \<le> y \<longleftrightarrow> (x,y) \<in> doc_class_rel\<^sup>*"
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definition
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less_class_def: "(x::doc_class) < y \<longleftrightarrow> (x \<le> y \<and> \<not> y \<le> x)"
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instance ..
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end
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lemma drc_acyclic : "acyclic doc_class_rel"
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proof -
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let ?measure = " (\<lambda>x.3::int)(float := 0, math_content := 0,
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listing := 1, figure := 1,
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proposition := 1)"
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show ?thesis
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unfolding doc_class_rel_def
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apply(rule_tac f = "?measure" in acyclicI_order)
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by auto
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qed
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instantiation "doc_class" :: order
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begin
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instance
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proof
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fix x::"doc_class"
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show \<open>x \<le> x\<close>
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unfolding le_class_def by simp
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next
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fix x y z:: "doc_class"
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show \<open>x \<le> y \<Longrightarrow> y \<le> z \<Longrightarrow> x \<le> z\<close>
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unfolding le_class_def
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by force
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next
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fix x y::"doc_class"
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have * : "antisym (doc_class_rel\<^sup>*)"
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by (simp add: acyclic_impl_antisym_rtrancl drc_acyclic)
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show \<open>x \<le> y \<Longrightarrow> y \<le> x \<Longrightarrow> x = y\<close>
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apply(insert antisymD[OF *])
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unfolding le_class_def
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by auto
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next
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fix x y::"doc_class"
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show \<open>(x < y) = (x \<le> y \<and> \<not> y \<le> x)\<close>
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by(simp add: less_class_def )
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qed
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end
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theorem articles_Lsub_reports: \<open>(L\<^sub>s\<^sub>u\<^sub>b article_monitor) \<subseteq> L\<^sub>s\<^sub>u\<^sub>b report_monitor\<close>
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unfolding article_monitor_def report_monitor_def
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by (meson order_refl regexp_seq_mono' seq_cancel_opt')
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end
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