src/Pure/Pure.thy

merged

(*  Title:      Pure/Pure.thy
    Author:     Makarius

Final stage of bootstrapping Pure, based on implicit background theory.
*)

theory Pure
  keywords
    "!!" "!" "+" "--" ":" ";" "<" "<=" "=" "=>" "?" "[" "\<equiv>"
    "\<leftharpoondown>" "\<rightharpoonup>" "\<rightleftharpoons>"
    "\<subseteq>" "]" "assumes" "attach" "binder" "constrains"
    "defines" "fixes" "for" "identifier" "if" "in" "includes" "infix"
    "infixl" "infixr" "is" "notes" "obtains" "open" "output"
    "overloaded" "pervasive" "premises" "private" "qualified" "shows"
    "structure" "unchecked" "where" "when" "|"
  and "text" "txt" :: document_body
  and "text_raw" :: document_raw
  and "default_sort" :: thy_decl == ""
  and "typedecl" "type_synonym" "nonterminal" "judgment"
    "consts" "syntax" "no_syntax" "translations" "no_translations" "defs"
    "definition" "abbreviation" "type_notation" "no_type_notation" "notation"
    "no_notation" "axiomatization" "theorems" "lemmas" "declare"
    "hide_class" "hide_type" "hide_const" "hide_fact" :: thy_decl
  and "SML_file" "SML_file_debug" "SML_file_no_debug" :: thy_load % "ML"
  and "SML_import" "SML_export" :: thy_decl % "ML"
  and "ML" :: thy_decl % "ML"
  and "ML_prf" :: prf_decl % "proof"  (* FIXME % "ML" ?? *)
  and "ML_val" "ML_command" :: diag % "ML"
  and "simproc_setup" :: thy_decl % "ML" == ""
  and "setup" "local_setup" "attribute_setup" "method_setup"
    "declaration" "syntax_declaration"
    "parse_ast_translation" "parse_translation" "print_translation"
    "typed_print_translation" "print_ast_translation" "oracle" :: thy_decl % "ML"
  and "bundle" :: thy_decl
  and "include" "including" :: prf_decl
  and "print_bundles" :: diag
  and "context" "locale" "experiment" :: thy_decl_block
  and "sublocale" "interpretation" :: thy_goal
  and "interpret" :: prf_goal % "proof"
  and "class" :: thy_decl_block
  and "subclass" :: thy_goal
  and "instantiation" :: thy_decl_block
  and "instance" :: thy_goal
  and "overloading" :: thy_decl_block
  and "code_datatype" :: thy_decl
  and "theorem" "lemma" "corollary" :: thy_goal
  and "schematic_theorem" "schematic_lemma" "schematic_corollary" :: thy_goal
  and "notepad" :: thy_decl_block
  and "have" :: prf_goal % "proof"
  and "hence" :: prf_goal % "proof" == "then have"
  and "show" :: prf_asm_goal % "proof"
  and "thus" :: prf_asm_goal % "proof" == "then show"
  and "then" "from" "with" :: prf_chain % "proof"
  and "note" :: prf_decl % "proof"
  and "supply" :: prf_script % "proof"
  and "using" "unfolding" :: prf_decl % "proof"
  and "fix" "assume" "presume" "def" :: prf_asm % "proof"
  and "consider" :: prf_goal % "proof"
  and "obtain" :: prf_asm_goal % "proof"
  and "guess" :: prf_script_asm_goal % "proof"
  and "let" "write" :: prf_decl % "proof"
  and "case" :: prf_asm % "proof"
  and "{" :: prf_open % "proof"
  and "}" :: prf_close % "proof"
  and "next" :: next_block % "proof"
  and "qed" :: qed_block % "proof"
  and "by" ".." "." "sorry" :: "qed" % "proof"
  and "done" :: "qed_script" % "proof"
  and "oops" :: qed_global % "proof"
  and "defer" "prefer" "apply" :: prf_script % "proof"
  and "apply_end" :: prf_script % "proof" == ""
  and "subgoal" :: prf_script_goal % "proof"
  and "proof" :: prf_block % "proof"
  and "also" "moreover" :: prf_decl % "proof"
  and "finally" "ultimately" :: prf_chain % "proof"
  and "back" :: prf_script % "proof"
  and "help" "print_commands" "print_options" "print_context" "print_theory"
    "print_definitions" "print_syntax" "print_abbrevs" "print_defn_rules"
    "print_theorems" "print_locales" "print_classes" "print_locale"
    "print_interps" "print_dependencies" "print_attributes"
    "print_simpset" "print_rules" "print_trans_rules" "print_methods"
    "print_antiquotations" "print_ML_antiquotations" "thy_deps"
    "locale_deps" "class_deps" "thm_deps" "print_term_bindings"
    "print_facts" "print_cases" "print_statement" "thm" "prf" "full_prf"
    "prop" "term" "typ" "print_codesetup" "unused_thms" :: diag
  and "display_drafts" "print_state" :: diag
  and "welcome" :: diag
  and "end" :: thy_end % "theory"
  and "realizers" :: thy_decl == ""
  and "realizability" :: thy_decl == ""
  and "extract_type" "extract" :: thy_decl
  and "find_theorems" "find_consts" :: diag
  and "named_theorems" :: thy_decl
begin

ML_file "ML/ml_antiquotations.ML"
ML_file "ML/ml_thms.ML"
ML_file "Tools/print_operation.ML"
ML_file "Isar/isar_syn.ML"
ML_file "Isar/calculation.ML"
ML_file "Tools/bibtex.ML"
ML_file "Tools/rail.ML"
ML_file "Tools/rule_insts.ML"
ML_file "Tools/thm_deps.ML"
ML_file "Tools/thy_deps.ML"
ML_file "Tools/class_deps.ML"
ML_file "Tools/find_theorems.ML"
ML_file "Tools/find_consts.ML"
ML_file "Tools/simplifier_trace.ML"
ML_file "Tools/debugger.ML"
ML_file "Tools/named_theorems.ML"


section \<open>Basic attributes\<close>

attribute_setup tagged =
  \<open>Scan.lift (Args.name -- Args.name) >> Thm.tag\<close>
  "tagged theorem"

attribute_setup untagged =
  \<open>Scan.lift Args.name >> Thm.untag\<close>
  "untagged theorem"

attribute_setup kind =
  \<open>Scan.lift Args.name >> Thm.kind\<close>
  "theorem kind"

attribute_setup THEN =
  \<open>Scan.lift (Scan.optional (Args.bracks Parse.nat) 1) -- Attrib.thm
    >> (fn (i, B) => Thm.rule_attribute (fn _ => fn A => A RSN (i, B)))\<close>
  "resolution with rule"

attribute_setup OF =
  \<open>Attrib.thms >> (fn Bs => Thm.rule_attribute (fn _ => fn A => A OF Bs))\<close>
  "rule resolved with facts"

attribute_setup rename_abs =
  \<open>Scan.lift (Scan.repeat (Args.maybe Args.name)) >> (fn vs =>
    Thm.rule_attribute (K (Drule.rename_bvars' vs)))\<close>
  "rename bound variables in abstractions"

attribute_setup unfolded =
  \<open>Attrib.thms >> (fn ths =>
    Thm.rule_attribute (fn context => Local_Defs.unfold (Context.proof_of context) ths))\<close>
  "unfolded definitions"

attribute_setup folded =
  \<open>Attrib.thms >> (fn ths =>
    Thm.rule_attribute (fn context => Local_Defs.fold (Context.proof_of context) ths))\<close>
  "folded definitions"

attribute_setup consumes =
  \<open>Scan.lift (Scan.optional Parse.int 1) >> Rule_Cases.consumes\<close>
  "number of consumed facts"

attribute_setup constraints =
  \<open>Scan.lift Parse.nat >> Rule_Cases.constraints\<close>
  "number of equality constraints"

attribute_setup case_names =
  \<open>Scan.lift (Scan.repeat1 (Args.name --
    Scan.optional (@{keyword "["} |-- Scan.repeat1 (Args.maybe Args.name) --| @{keyword "]"}) []))
    >> (fn cs =>
      Rule_Cases.cases_hyp_names
        (map #1 cs)
        (map (map (the_default Rule_Cases.case_hypsN) o #2) cs))\<close>
  "named rule cases"

attribute_setup case_conclusion =
  \<open>Scan.lift (Args.name -- Scan.repeat Args.name) >> Rule_Cases.case_conclusion\<close>
  "named conclusion of rule cases"

attribute_setup params =
  \<open>Scan.lift (Parse.and_list1 (Scan.repeat Args.name)) >> Rule_Cases.params\<close>
  "named rule parameters"

attribute_setup rule_format =
  \<open>Scan.lift (Args.mode "no_asm")
    >> (fn true => Object_Logic.rule_format_no_asm | false => Object_Logic.rule_format)\<close>
  "result put into canonical rule format"

attribute_setup elim_format =
  \<open>Scan.succeed (Thm.rule_attribute (K Tactic.make_elim))\<close>
  "destruct rule turned into elimination rule format"

attribute_setup no_vars =
  \<open>Scan.succeed (Thm.rule_attribute (fn context => fn th =>
    let
      val ctxt = Variable.set_body false (Context.proof_of context);
      val ((_, [th']), _) = Variable.import true [th] ctxt;
    in th' end))\<close>
  "imported schematic variables"

attribute_setup atomize =
  \<open>Scan.succeed Object_Logic.declare_atomize\<close>
  "declaration of atomize rule"

attribute_setup rulify =
  \<open>Scan.succeed Object_Logic.declare_rulify\<close>
  "declaration of rulify rule"

attribute_setup rotated =
  \<open>Scan.lift (Scan.optional Parse.int 1
    >> (fn n => Thm.rule_attribute (fn _ => rotate_prems n)))\<close>
  "rotated theorem premises"

attribute_setup defn =
  \<open>Attrib.add_del Local_Defs.defn_add Local_Defs.defn_del\<close>
  "declaration of definitional transformations"

attribute_setup abs_def =
  \<open>Scan.succeed (Thm.rule_attribute (fn context =>
    Local_Defs.meta_rewrite_rule (Context.proof_of context) #> Drule.abs_def))\<close>
  "abstract over free variables of definitional theorem"


section \<open>Further content for the Pure theory\<close>

subsection \<open>Meta-level connectives in assumptions\<close>

lemma meta_mp:
  assumes "PROP P \<Longrightarrow> PROP Q" and "PROP P"
  shows "PROP Q"
    by (rule \<open>PROP P \<Longrightarrow> PROP Q\<close> [OF \<open>PROP P\<close>])

lemmas meta_impE = meta_mp [elim_format]

lemma meta_spec:
  assumes "\<And>x. PROP P x"
  shows "PROP P x"
    by (rule \<open>\<And>x. PROP P x\<close>)

lemmas meta_allE = meta_spec [elim_format]

lemma swap_params:
  "(\<And>x y. PROP P x y) \<equiv> (\<And>y x. PROP P x y)" ..


subsection \<open>Meta-level conjunction\<close>

lemma all_conjunction:
  "(\<And>x. PROP A x &&& PROP B x) \<equiv> ((\<And>x. PROP A x) &&& (\<And>x. PROP B x))"
proof
  assume conj: "\<And>x. PROP A x &&& PROP B x"
  show "(\<And>x. PROP A x) &&& (\<And>x. PROP B x)"
  proof -
    fix x
    from conj show "PROP A x" by (rule conjunctionD1)
    from conj show "PROP B x" by (rule conjunctionD2)
  qed
next
  assume conj: "(\<And>x. PROP A x) &&& (\<And>x. PROP B x)"
  fix x
  show "PROP A x &&& PROP B x"
  proof -
    show "PROP A x" by (rule conj [THEN conjunctionD1, rule_format])
    show "PROP B x" by (rule conj [THEN conjunctionD2, rule_format])
  qed
qed

lemma imp_conjunction:
  "(PROP A \<Longrightarrow> PROP B &&& PROP C) \<equiv> ((PROP A \<Longrightarrow> PROP B) &&& (PROP A \<Longrightarrow> PROP C))"
proof
  assume conj: "PROP A \<Longrightarrow> PROP B &&& PROP C"
  show "(PROP A \<Longrightarrow> PROP B) &&& (PROP A \<Longrightarrow> PROP C)"
  proof -
    assume "PROP A"
    from conj [OF \<open>PROP A\<close>] show "PROP B" by (rule conjunctionD1)
    from conj [OF \<open>PROP A\<close>] show "PROP C" by (rule conjunctionD2)
  qed
next
  assume conj: "(PROP A \<Longrightarrow> PROP B) &&& (PROP A \<Longrightarrow> PROP C)"
  assume "PROP A"
  show "PROP B &&& PROP C"
  proof -
    from \<open>PROP A\<close> show "PROP B" by (rule conj [THEN conjunctionD1])
    from \<open>PROP A\<close> show "PROP C" by (rule conj [THEN conjunctionD2])
  qed
qed

lemma conjunction_imp:
  "(PROP A &&& PROP B \<Longrightarrow> PROP C) \<equiv> (PROP A \<Longrightarrow> PROP B \<Longrightarrow> PROP C)"
proof
  assume r: "PROP A &&& PROP B \<Longrightarrow> PROP C"
  assume ab: "PROP A" "PROP B"
  show "PROP C"
  proof (rule r)
    from ab show "PROP A &&& PROP B" .
  qed
next
  assume r: "PROP A \<Longrightarrow> PROP B \<Longrightarrow> PROP C"
  assume conj: "PROP A &&& PROP B"
  show "PROP C"
  proof (rule r)
    from conj show "PROP A" by (rule conjunctionD1)
    from conj show "PROP B" by (rule conjunctionD2)
  qed
qed

end