src/Pure/Pure.thy
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(*  Title:      Pure/Pure.thy
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    Author:     Makarius
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Final stage of bootstrapping Pure, based on implicit background theory.
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*)
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theory Pure
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  keywords
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    "!!" "!" "%" "(" ")" "+" "," "--" ":" "::" ";" "<" "<=" "=" "=="
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    "=>" "?" "[" "\<equiv>" "\<leftharpoondown>" "\<rightharpoonup>"
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    "\<rightleftharpoons>" "\<subseteq>" "]" "and" "assumes"
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    "attach" "begin" "binder" "constrains" "defines" "fixes" "for"
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    "identifier" "if" "imports" "in" "includes" "infix" "infixl"
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    "infixr" "is" "keywords" "notes" "obtains" "open" "output"
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    "overloaded" "pervasive" "shows" "structure" "unchecked" "where" "|"
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  and "theory" :: thy_begin % "theory"
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  and "header" :: diag
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  and "chapter" :: thy_heading1
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  and "section" :: thy_heading2
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  and "subsection" :: thy_heading3
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  and "subsubsection" :: thy_heading4
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  and "text" "text_raw" :: thy_decl
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  and "sect" :: prf_heading2 % "proof"
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  and "subsect" :: prf_heading3 % "proof"
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  and "subsubsect" :: prf_heading4 % "proof"
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  and "txt" "txt_raw" :: prf_decl % "proof"
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  and "default_sort" :: thy_decl == ""
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  and "typedecl" "type_synonym" "nonterminal" "judgment"
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    "consts" "syntax" "no_syntax" "translations" "no_translations" "defs"
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    "definition" "abbreviation" "type_notation" "no_type_notation" "notation"
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    "no_notation" "axiomatization" "theorems" "lemmas" "declare"
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    "hide_class" "hide_type" "hide_const" "hide_fact" :: thy_decl
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  and "SML_file" "ML_file" :: thy_load % "ML"
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  and "SML_import" "SML_export" :: thy_decl % "ML"
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  and "ML" :: thy_decl % "ML"
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  and "ML_prf" :: prf_decl % "proof"  (* FIXME % "ML" ?? *)
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  and "ML_val" "ML_command" :: diag % "ML"
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  and "simproc_setup" :: thy_decl % "ML" == ""
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  and "setup" "local_setup" "attribute_setup" "method_setup"
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    "declaration" "syntax_declaration"
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    "parse_ast_translation" "parse_translation" "print_translation"
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    "typed_print_translation" "print_ast_translation" "oracle" :: thy_decl % "ML"
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  and "bundle" :: thy_decl
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  and "include" "including" :: prf_decl
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  and "print_bundles" :: diag
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  and "context" "locale" :: thy_decl_block
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  and "sublocale" "interpretation" :: thy_goal
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  and "interpret" :: prf_goal % "proof"
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  and "class" :: thy_decl_block
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  and "subclass" :: thy_goal
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  and "instantiation" :: thy_decl_block
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  and "instance" :: thy_goal
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  and "overloading" :: thy_decl_block
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  and "code_datatype" :: thy_decl
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  and "theorem" "lemma" "corollary" :: thy_goal
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  and "schematic_theorem" "schematic_lemma" "schematic_corollary" :: thy_goal
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  and "notepad" :: thy_decl_block
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  and "have" :: prf_goal % "proof"
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  and "hence" :: prf_goal % "proof" == "then have"
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  and "show" :: prf_asm_goal % "proof"
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  and "thus" :: prf_asm_goal % "proof" == "then show"
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  and "then" "from" "with" :: prf_chain % "proof"
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  and "note" "using" "unfolding" :: prf_decl % "proof"
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  and "fix" "assume" "presume" "def" :: prf_asm % "proof"
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  and "obtain" :: prf_asm_goal % "proof"
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  and "guess" :: prf_asm_goal_script % "proof"
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  and "let" "write" :: prf_decl % "proof"
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  and "case" :: prf_asm % "proof"
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  and "{" :: prf_open % "proof"
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  and "}" :: prf_close % "proof"
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  and "next" :: prf_block % "proof"
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  and "qed" :: qed_block % "proof"
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  and "by" ".." "." "sorry" :: "qed" % "proof"
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  and "done" :: "qed_script" % "proof"
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  and "oops" :: qed_global % "proof"
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  and "defer" "prefer" "apply" :: prf_script % "proof"
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  and "apply_end" :: prf_script % "proof" == ""
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  and "proof" :: prf_block % "proof"
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  and "also" "moreover" :: prf_decl % "proof"
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  and "finally" "ultimately" :: prf_chain % "proof"
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  and "back" :: prf_script % "proof"
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  and "help" "print_commands" "print_options" "print_context"
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    "print_theory" "print_syntax" "print_abbrevs" "print_defn_rules"
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    "print_theorems" "print_locales" "print_classes" "print_locale"
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    "print_interps" "print_dependencies" "print_attributes"
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    "print_simpset" "print_rules" "print_trans_rules" "print_methods"
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    "print_antiquotations" "print_ML_antiquotations" "thy_deps"
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    "locale_deps" "class_deps" "thm_deps" "print_term_bindings"
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    "print_facts" "print_cases" "print_statement" "thm" "prf" "full_prf"
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    "prop" "term" "typ" "print_codesetup" "unused_thms" :: diag
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  and "display_drafts" "print_state" :: diag
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  and "welcome" :: diag
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  and "end" :: thy_end % "theory"
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  and "realizers" :: thy_decl == ""
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  and "realizability" :: thy_decl == ""
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  and "extract_type" "extract" :: thy_decl
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  and "find_theorems" "find_consts" :: diag
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  and "named_theorems" :: thy_decl
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begin
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ML_file "ML/ml_antiquotations.ML"
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ML_file "ML/ml_thms.ML"
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ML_file "Tools/print_operation.ML"
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ML_file "Isar/isar_syn.ML"
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ML_file "Isar/calculation.ML"
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ML_file "Tools/bibtex.ML"
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ML_file "Tools/rail.ML"
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ML_file "Tools/rule_insts.ML"
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ML_file "Tools/thm_deps.ML"
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ML_file "Tools/class_deps.ML"
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ML_file "Tools/find_theorems.ML"
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ML_file "Tools/find_consts.ML"
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ML_file "Tools/simplifier_trace.ML"
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ML_file "Tools/named_theorems.ML"
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section \<open>Basic attributes\<close>
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attribute_setup tagged =
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  \<open>Scan.lift (Args.name -- Args.name) >> Thm.tag\<close>
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  "tagged theorem"
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attribute_setup untagged =
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  \<open>Scan.lift Args.name >> Thm.untag\<close>
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  "untagged theorem"
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attribute_setup kind =
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  \<open>Scan.lift Args.name >> Thm.kind\<close>
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  "theorem kind"
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attribute_setup THEN =
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  \<open>Scan.lift (Scan.optional (Args.bracks Parse.nat) 1) -- Attrib.thm
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    >> (fn (i, B) => Thm.rule_attribute (fn _ => fn A => A RSN (i, B)))\<close>
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  "resolution with rule"
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attribute_setup OF =
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  \<open>Attrib.thms >> (fn Bs => Thm.rule_attribute (fn _ => fn A => A OF Bs))\<close>
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  "rule resolved with facts"
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attribute_setup rename_abs =
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  \<open>Scan.lift (Scan.repeat (Args.maybe Args.name)) >> (fn vs =>
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    Thm.rule_attribute (K (Drule.rename_bvars' vs)))\<close>
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  "rename bound variables in abstractions"
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attribute_setup unfolded =
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  \<open>Attrib.thms >> (fn ths =>
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    Thm.rule_attribute (fn context => Local_Defs.unfold (Context.proof_of context) ths))\<close>
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  "unfolded definitions"
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attribute_setup folded =
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  \<open>Attrib.thms >> (fn ths =>
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    Thm.rule_attribute (fn context => Local_Defs.fold (Context.proof_of context) ths))\<close>
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  "folded definitions"
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attribute_setup consumes =
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  \<open>Scan.lift (Scan.optional Parse.int 1) >> Rule_Cases.consumes\<close>
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  "number of consumed facts"
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attribute_setup constraints =
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  \<open>Scan.lift Parse.nat >> Rule_Cases.constraints\<close>
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  "number of equality constraints"
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attribute_setup case_names =
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  \<open>Scan.lift (Scan.repeat1 (Args.name --
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    Scan.optional (@{keyword "["} |-- Scan.repeat1 (Args.maybe Args.name) --| @{keyword "]"}) []))
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    >> (fn cs =>
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      Rule_Cases.cases_hyp_names
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        (map #1 cs)
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        (map (map (the_default Rule_Cases.case_hypsN) o #2) cs))\<close>
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  "named rule cases"
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   171
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attribute_setup case_conclusion =
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  \<open>Scan.lift (Args.name -- Scan.repeat Args.name) >> Rule_Cases.case_conclusion\<close>
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  "named conclusion of rule cases"
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   175
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attribute_setup params =
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  \<open>Scan.lift (Parse.and_list1 (Scan.repeat Args.name)) >> Rule_Cases.params\<close>
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  "named rule parameters"
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   179
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attribute_setup rule_format =
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   181
  \<open>Scan.lift (Args.mode "no_asm")
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    >> (fn true => Object_Logic.rule_format_no_asm | false => Object_Logic.rule_format)\<close>
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  "result put into canonical rule format"
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   184
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   185
attribute_setup elim_format =
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   186
  \<open>Scan.succeed (Thm.rule_attribute (K Tactic.make_elim))\<close>
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   187
  "destruct rule turned into elimination rule format"
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   188
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   189
attribute_setup no_vars =
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   190
  \<open>Scan.succeed (Thm.rule_attribute (fn context => fn th =>
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   191
    let
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      val ctxt = Variable.set_body false (Context.proof_of context);
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   193
      val ((_, [th']), _) = Variable.import true [th] ctxt;
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   194
    in th' end))\<close>
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   195
  "imported schematic variables"
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   196
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   197
attribute_setup eta_long =
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   198
  \<open>Scan.succeed (Thm.rule_attribute (fn _ => Conv.fconv_rule Drule.eta_long_conversion))\<close>
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   199
  "put theorem into eta long beta normal form"
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   200
7eb0c04e4c40 define basic attributes in user-space Pure.thy -- which provides better hyperlinks and may serve as example;
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   201
attribute_setup atomize =
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   202
  \<open>Scan.succeed Object_Logic.declare_atomize\<close>
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   203
  "declaration of atomize rule"
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   204
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   205
attribute_setup rulify =
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   206
  \<open>Scan.succeed Object_Logic.declare_rulify\<close>
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   207
  "declaration of rulify rule"
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   208
7eb0c04e4c40 define basic attributes in user-space Pure.thy -- which provides better hyperlinks and may serve as example;
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   209
attribute_setup rotated =
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   210
  \<open>Scan.lift (Scan.optional Parse.int 1
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   211
    >> (fn n => Thm.rule_attribute (fn _ => rotate_prems n)))\<close>
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   212
  "rotated theorem premises"
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   213
7eb0c04e4c40 define basic attributes in user-space Pure.thy -- which provides better hyperlinks and may serve as example;
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   214
attribute_setup defn =
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   215
  \<open>Attrib.add_del Local_Defs.defn_add Local_Defs.defn_del\<close>
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   216
  "declaration of definitional transformations"
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   217
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   218
attribute_setup abs_def =
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   219
  \<open>Scan.succeed (Thm.rule_attribute (fn context =>
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   220
    Local_Defs.meta_rewrite_rule (Context.proof_of context) #> Drule.abs_def))\<close>
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   221
  "abstract over free variables of definitional theorem"
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   222
7eb0c04e4c40 define basic attributes in user-space Pure.thy -- which provides better hyperlinks and may serve as example;
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   223
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   224
section \<open>Further content for the Pure theory\<close>
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   225
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   226
subsection \<open>Meta-level connectives in assumptions\<close>
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42c75e0c9140 The Pure theory.
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   227
42c75e0c9140 The Pure theory.
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   228
lemma meta_mp:
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   229
  assumes "PROP P \<Longrightarrow> PROP Q" and "PROP P"
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42c75e0c9140 The Pure theory.
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   230
  shows "PROP Q"
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   231
    by (rule \<open>PROP P \<Longrightarrow> PROP Q\<close> [OF \<open>PROP P\<close>])
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42c75e0c9140 The Pure theory.
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   232
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cec811764a38 added meta_impE
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   233
lemmas meta_impE = meta_mp [elim_format]
cec811764a38 added meta_impE
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   234
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42c75e0c9140 The Pure theory.
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   235
lemma meta_spec:
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   236
  assumes "\<And>x. PROP P x"
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   237
  shows "PROP P x"
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   238
    by (rule \<open>\<And>x. PROP P x\<close>)
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42c75e0c9140 The Pure theory.
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   239
42c75e0c9140 The Pure theory.
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   240
lemmas meta_allE = meta_spec [elim_format]
42c75e0c9140 The Pure theory.
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   241
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   242
lemma swap_params:
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   243
  "(\<And>x y. PROP P x y) \<equiv> (\<And>y x. PROP P x y)" ..
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dbc458262f4c added swap_params;
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   244
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   245
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   246
subsection \<open>Meta-level conjunction\<close>
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   247
389a6f9c31f4 added locale meta_conjunction_syntax and various conjunction rules;
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   248
lemma all_conjunction:
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   249
  "(\<And>x. PROP A x &&& PROP B x) \<equiv> ((\<And>x. PROP A x) &&& (\<And>x. PROP B x))"
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   250
proof
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   251
  assume conj: "\<And>x. PROP A x &&& PROP B x"
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   252
  show "(\<And>x. PROP A x) &&& (\<And>x. PROP B x)"
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   253
  proof -
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   254
    fix x
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   255
    from conj show "PROP A x" by (rule conjunctionD1)
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   256
    from conj show "PROP B x" by (rule conjunctionD2)
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   257
  qed
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   258
next
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   259
  assume conj: "(\<And>x. PROP A x) &&& (\<And>x. PROP B x)"
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   260
  fix x
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5e009a80fe6d Pure syntax: more coherent treatment of aprop, permanent TERM and &&&;
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   261
  show "PROP A x &&& PROP B x"
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d7fd5415a781 simplified Pure conjunction;
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   262
  proof -
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ed3a58a9eae1 converted to regular application syntax;
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   263
    show "PROP A x" by (rule conj [THEN conjunctionD1, rule_format])
ed3a58a9eae1 converted to regular application syntax;
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   264
    show "PROP B x" by (rule conj [THEN conjunctionD2, rule_format])
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   265
  qed
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   266
qed
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   267
19121
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   268
lemma imp_conjunction:
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   269
  "(PROP A \<Longrightarrow> PROP B &&& PROP C) \<equiv> ((PROP A \<Longrightarrow> PROP B) &&& (PROP A \<Longrightarrow> PROP C))"
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3a1e4ee72075 tuned proofs;
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   270
proof
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   271
  assume conj: "PROP A \<Longrightarrow> PROP B &&& PROP C"
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   272
  show "(PROP A \<Longrightarrow> PROP B) &&& (PROP A \<Longrightarrow> PROP C)"
19121
d7fd5415a781 simplified Pure conjunction;
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   273
  proof -
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   274
    assume "PROP A"
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   275
    from conj [OF \<open>PROP A\<close>] show "PROP B" by (rule conjunctionD1)
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   276
    from conj [OF \<open>PROP A\<close>] show "PROP C" by (rule conjunctionD2)
18466
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  qed
389a6f9c31f4 added locale meta_conjunction_syntax and various conjunction rules;
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diff changeset
   278
next
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   279
  assume conj: "(PROP A \<Longrightarrow> PROP B) &&& (PROP A \<Longrightarrow> PROP C)"
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   280
  assume "PROP A"
28856
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   281
  show "PROP B &&& PROP C"
19121
d7fd5415a781 simplified Pure conjunction;
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   282
  proof -
58611
d49f3181030e more cartouches;
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   283
    from \<open>PROP A\<close> show "PROP B" by (rule conj [THEN conjunctionD1])
d49f3181030e more cartouches;
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   284
    from \<open>PROP A\<close> show "PROP C" by (rule conj [THEN conjunctionD2])
18466
389a6f9c31f4 added locale meta_conjunction_syntax and various conjunction rules;
wenzelm
parents: 18019
diff changeset
   285
  qed
389a6f9c31f4 added locale meta_conjunction_syntax and various conjunction rules;
wenzelm
parents: 18019
diff changeset
   286
qed
389a6f9c31f4 added locale meta_conjunction_syntax and various conjunction rules;
wenzelm
parents: 18019
diff changeset
   287
389a6f9c31f4 added locale meta_conjunction_syntax and various conjunction rules;
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   288
lemma conjunction_imp:
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   289
  "(PROP A &&& PROP B \<Longrightarrow> PROP C) \<equiv> (PROP A \<Longrightarrow> PROP B \<Longrightarrow> PROP C)"
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diff changeset
   290
proof
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   291
  assume r: "PROP A &&& PROP B \<Longrightarrow> PROP C"
22933
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   292
  assume ab: "PROP A" "PROP B"
338c7890c96f tuned proofs;
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   293
  show "PROP C"
338c7890c96f tuned proofs;
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   294
  proof (rule r)
28856
5e009a80fe6d Pure syntax: more coherent treatment of aprop, permanent TERM and &&&;
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   295
    from ab show "PROP A &&& PROP B" .
22933
338c7890c96f tuned proofs;
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parents: 21627
diff changeset
   296
  qed
18466
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wenzelm
parents: 18019
diff changeset
   297
next
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diff changeset
   298
  assume r: "PROP A \<Longrightarrow> PROP B \<Longrightarrow> PROP C"
28856
5e009a80fe6d Pure syntax: more coherent treatment of aprop, permanent TERM and &&&;
wenzelm
parents: 28699
diff changeset
   299
  assume conj: "PROP A &&& PROP B"
18466
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parents: 18019
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   300
  show "PROP C"
389a6f9c31f4 added locale meta_conjunction_syntax and various conjunction rules;
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   301
  proof (rule r)
19121
d7fd5415a781 simplified Pure conjunction;
wenzelm
parents: 19048
diff changeset
   302
    from conj show "PROP A" by (rule conjunctionD1)
d7fd5415a781 simplified Pure conjunction;
wenzelm
parents: 19048
diff changeset
   303
    from conj show "PROP B" by (rule conjunctionD2)
18466
389a6f9c31f4 added locale meta_conjunction_syntax and various conjunction rules;
wenzelm
parents: 18019
diff changeset
   304
  qed
389a6f9c31f4 added locale meta_conjunction_syntax and various conjunction rules;
wenzelm
parents: 18019
diff changeset
   305
qed
389a6f9c31f4 added locale meta_conjunction_syntax and various conjunction rules;
wenzelm
parents: 18019
diff changeset
   306
48638
22d65e375c01 more standard bootstrapping of Pure.thy;
wenzelm
parents: 29606
diff changeset
   307
end
22d65e375c01 more standard bootstrapping of Pure.thy;
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parents: 29606
diff changeset
   308