src/Pure/Pure.thy
author wenzelm
Fri Jan 17 20:31:39 2014 +0100 (2014-01-17)
changeset 55030 9a9049d12e21
parent 54730 de2d99b459b3
child 55140 7eb0c04e4c40
permissions -rw-r--r--
prefer user-space tool within Pure.thy;
wenzelm@48929
     1
(*  Title:      Pure/Pure.thy
wenzelm@48929
     2
    Author:     Makarius
wenzelm@48929
     3
wenzelm@48929
     4
Final stage of bootstrapping Pure, based on implicit background theory.
wenzelm@48929
     5
*)
wenzelm@48929
     6
wenzelm@48638
     7
theory Pure
wenzelm@48641
     8
  keywords
wenzelm@48641
     9
    "!!" "!" "%" "(" ")" "+" "," "--" ":" "::" ";" "<" "<=" "=" "=="
wenzelm@48641
    10
    "=>" "?" "[" "\<equiv>" "\<leftharpoondown>" "\<rightharpoonup>"
wenzelm@52143
    11
    "\<rightleftharpoons>" "\<subseteq>" "]" "and" "assumes"
wenzelm@48641
    12
    "attach" "begin" "binder" "constrains" "defines" "fixes" "for"
wenzelm@48641
    13
    "identifier" "if" "imports" "in" "includes" "infix" "infixl"
wenzelm@48641
    14
    "infixr" "is" "keywords" "notes" "obtains" "open" "output"
wenzelm@51293
    15
    "overloaded" "pervasive" "shows" "structure" "unchecked" "where" "|"
wenzelm@52449
    16
  and "theory" :: thy_begin % "theory"
wenzelm@52449
    17
  and "ML_file" :: thy_load % "ML"
wenzelm@48641
    18
  and "header" :: diag
wenzelm@48641
    19
  and "chapter" :: thy_heading1
wenzelm@48641
    20
  and "section" :: thy_heading2
wenzelm@48641
    21
  and "subsection" :: thy_heading3
wenzelm@48641
    22
  and "subsubsection" :: thy_heading4
wenzelm@48641
    23
  and "text" "text_raw" :: thy_decl
wenzelm@48641
    24
  and "sect" :: prf_heading2 % "proof"
wenzelm@48641
    25
  and "subsect" :: prf_heading3 % "proof"
wenzelm@48641
    26
  and "subsubsect" :: prf_heading4 % "proof"
wenzelm@48641
    27
  and "txt" "txt_raw" :: prf_decl % "proof"
wenzelm@48641
    28
  and "classes" "classrel" "default_sort" "typedecl" "type_synonym"
wenzelm@48641
    29
    "nonterminal" "arities" "judgment" "consts" "syntax" "no_syntax"
wenzelm@51313
    30
    "translations" "no_translations" "defs" "definition"
wenzelm@48641
    31
    "abbreviation" "type_notation" "no_type_notation" "notation"
wenzelm@48641
    32
    "no_notation" "axiomatization" "theorems" "lemmas" "declare"
wenzelm@48641
    33
    "hide_class" "hide_type" "hide_const" "hide_fact" :: thy_decl
wenzelm@51295
    34
  and "ML" :: thy_decl % "ML"
wenzelm@48641
    35
  and "ML_prf" :: prf_decl % "proof"  (* FIXME % "ML" ?? *)
wenzelm@48641
    36
  and "ML_val" "ML_command" :: diag % "ML"
wenzelm@48641
    37
  and "setup" "local_setup" "attribute_setup" "method_setup"
wenzelm@48641
    38
    "declaration" "syntax_declaration" "simproc_setup"
wenzelm@48641
    39
    "parse_ast_translation" "parse_translation" "print_translation"
wenzelm@48641
    40
    "typed_print_translation" "print_ast_translation" "oracle" :: thy_decl % "ML"
wenzelm@48641
    41
  and "bundle" :: thy_decl
wenzelm@48641
    42
  and "include" "including" :: prf_decl
wenzelm@48641
    43
  and "print_bundles" :: diag
wenzelm@48641
    44
  and "context" "locale" :: thy_decl
wenzelm@51224
    45
  and "sublocale" "interpretation" :: thy_goal
wenzelm@51224
    46
  and "interpret" :: prf_goal % "proof"
wenzelm@48641
    47
  and "class" :: thy_decl
wenzelm@48641
    48
  and "subclass" :: thy_goal
wenzelm@48641
    49
  and "instantiation" :: thy_decl
wenzelm@48641
    50
  and "instance" :: thy_goal
wenzelm@48641
    51
  and "overloading" :: thy_decl
wenzelm@48641
    52
  and "code_datatype" :: thy_decl
wenzelm@48641
    53
  and "theorem" "lemma" "corollary" :: thy_goal
wenzelm@51274
    54
  and "schematic_theorem" "schematic_lemma" "schematic_corollary" :: thy_goal
wenzelm@48641
    55
  and "notepad" :: thy_decl
wenzelm@50128
    56
  and "have" :: prf_goal % "proof"
wenzelm@50128
    57
  and "hence" :: prf_goal % "proof" == "then have"
wenzelm@50128
    58
  and "show" :: prf_asm_goal % "proof"
wenzelm@50128
    59
  and "thus" :: prf_asm_goal % "proof" == "then show"
wenzelm@48641
    60
  and "then" "from" "with" :: prf_chain % "proof"
wenzelm@48641
    61
  and "note" "using" "unfolding" :: prf_decl % "proof"
wenzelm@48641
    62
  and "fix" "assume" "presume" "def" :: prf_asm % "proof"
wenzelm@53371
    63
  and "obtain" :: prf_asm_goal % "proof"
wenzelm@53371
    64
  and "guess" :: prf_asm_goal_script % "proof"
wenzelm@48641
    65
  and "let" "write" :: prf_decl % "proof"
wenzelm@48641
    66
  and "case" :: prf_asm % "proof"
wenzelm@48641
    67
  and "{" :: prf_open % "proof"
wenzelm@48641
    68
  and "}" :: prf_close % "proof"
wenzelm@48641
    69
  and "next" :: prf_block % "proof"
wenzelm@48641
    70
  and "qed" :: qed_block % "proof"
wenzelm@53571
    71
  and "by" ".." "." "sorry" :: "qed" % "proof"
wenzelm@53571
    72
  and "done" :: "qed_script" % "proof"
wenzelm@48641
    73
  and "oops" :: qed_global % "proof"
wenzelm@50128
    74
  and "defer" "prefer" "apply" :: prf_script % "proof"
wenzelm@50128
    75
  and "apply_end" :: prf_script % "proof" == ""
wenzelm@48641
    76
  and "proof" :: prf_block % "proof"
wenzelm@48641
    77
  and "also" "moreover" :: prf_decl % "proof"
wenzelm@48641
    78
  and "finally" "ultimately" :: prf_chain % "proof"
wenzelm@48641
    79
  and "back" :: prf_script % "proof"
wenzelm@48641
    80
  and "Isabelle.command" :: control
wenzelm@52060
    81
  and "help" "print_commands" "print_options"
wenzelm@51585
    82
    "print_context" "print_theory" "print_syntax" "print_abbrevs" "print_defn_rules"
wenzelm@48641
    83
    "print_theorems" "print_locales" "print_classes" "print_locale"
wenzelm@48641
    84
    "print_interps" "print_dependencies" "print_attributes"
wenzelm@48641
    85
    "print_simpset" "print_rules" "print_trans_rules" "print_methods"
wenzelm@49569
    86
    "print_antiquotations" "thy_deps" "locale_deps" "class_deps" "thm_deps"
wenzelm@48641
    87
    "print_binds" "print_facts" "print_cases" "print_statement" "thm"
wenzelm@48641
    88
    "prf" "full_prf" "prop" "term" "typ" "print_codesetup" "unused_thms"
wenzelm@48641
    89
    :: diag
wenzelm@48641
    90
  and "cd" :: control
wenzelm@48641
    91
  and "pwd" :: diag
wenzelm@48641
    92
  and "use_thy" "remove_thy" "kill_thy" :: control
wenzelm@52549
    93
  and "display_drafts" "print_state" "pr" :: diag
wenzelm@52438
    94
  and "pretty_setmargin" "disable_pr" "enable_pr" "commit" "quit" "exit" :: control
wenzelm@48646
    95
  and "welcome" :: diag
wenzelm@48646
    96
  and "init_toplevel" "linear_undo" "undo" "undos_proof" "cannot_undo" "kill" :: control
wenzelm@48641
    97
  and "end" :: thy_end % "theory"
wenzelm@48646
    98
  and "realizers" "realizability" "extract_type" "extract" :: thy_decl
wenzelm@48646
    99
  and "find_theorems" "find_consts" :: diag
wenzelm@52437
   100
  and "ProofGeneral.process_pgip" "ProofGeneral.pr" "ProofGeneral.undo"
wenzelm@52437
   101
    "ProofGeneral.restart" "ProofGeneral.kill_proof" "ProofGeneral.inform_file_processed"
wenzelm@52437
   102
    "ProofGeneral.inform_file_retracted" :: control
wenzelm@48638
   103
begin
wenzelm@15803
   104
wenzelm@48891
   105
ML_file "Isar/isar_syn.ML"
wenzelm@55030
   106
ML_file "Tools/rail.ML"
wenzelm@53707
   107
ML_file "Tools/rule_insts.ML";
wenzelm@48891
   108
ML_file "Tools/find_theorems.ML"
wenzelm@48891
   109
ML_file "Tools/find_consts.ML"
wenzelm@52009
   110
ML_file "Tools/proof_general_pure.ML"
wenzelm@54730
   111
ML_file "Tools/simplifier_trace.ML"
wenzelm@48891
   112
wenzelm@48891
   113
wenzelm@26435
   114
section {* Further content for the Pure theory *}
wenzelm@20627
   115
wenzelm@18466
   116
subsection {* Meta-level connectives in assumptions *}
wenzelm@15803
   117
wenzelm@15803
   118
lemma meta_mp:
wenzelm@18019
   119
  assumes "PROP P ==> PROP Q" and "PROP P"
wenzelm@15803
   120
  shows "PROP Q"
wenzelm@18019
   121
    by (rule `PROP P ==> PROP Q` [OF `PROP P`])
wenzelm@15803
   122
nipkow@23432
   123
lemmas meta_impE = meta_mp [elim_format]
nipkow@23432
   124
wenzelm@15803
   125
lemma meta_spec:
wenzelm@26958
   126
  assumes "!!x. PROP P x"
wenzelm@26958
   127
  shows "PROP P x"
wenzelm@26958
   128
    by (rule `!!x. PROP P x`)
wenzelm@15803
   129
wenzelm@15803
   130
lemmas meta_allE = meta_spec [elim_format]
wenzelm@15803
   131
wenzelm@26570
   132
lemma swap_params:
wenzelm@26958
   133
  "(!!x y. PROP P x y) == (!!y x. PROP P x y)" ..
wenzelm@26570
   134
wenzelm@18466
   135
wenzelm@18466
   136
subsection {* Meta-level conjunction *}
wenzelm@18466
   137
wenzelm@18466
   138
lemma all_conjunction:
wenzelm@28856
   139
  "(!!x. PROP A x &&& PROP B x) == ((!!x. PROP A x) &&& (!!x. PROP B x))"
wenzelm@18466
   140
proof
wenzelm@28856
   141
  assume conj: "!!x. PROP A x &&& PROP B x"
wenzelm@28856
   142
  show "(!!x. PROP A x) &&& (!!x. PROP B x)"
wenzelm@19121
   143
  proof -
wenzelm@18466
   144
    fix x
wenzelm@26958
   145
    from conj show "PROP A x" by (rule conjunctionD1)
wenzelm@26958
   146
    from conj show "PROP B x" by (rule conjunctionD2)
wenzelm@18466
   147
  qed
wenzelm@18466
   148
next
wenzelm@28856
   149
  assume conj: "(!!x. PROP A x) &&& (!!x. PROP B x)"
wenzelm@18466
   150
  fix x
wenzelm@28856
   151
  show "PROP A x &&& PROP B x"
wenzelm@19121
   152
  proof -
wenzelm@26958
   153
    show "PROP A x" by (rule conj [THEN conjunctionD1, rule_format])
wenzelm@26958
   154
    show "PROP B x" by (rule conj [THEN conjunctionD2, rule_format])
wenzelm@18466
   155
  qed
wenzelm@18466
   156
qed
wenzelm@18466
   157
wenzelm@19121
   158
lemma imp_conjunction:
nipkow@50603
   159
  "(PROP A ==> PROP B &&& PROP C) == ((PROP A ==> PROP B) &&& (PROP A ==> PROP C))"
wenzelm@18836
   160
proof
wenzelm@28856
   161
  assume conj: "PROP A ==> PROP B &&& PROP C"
wenzelm@28856
   162
  show "(PROP A ==> PROP B) &&& (PROP A ==> PROP C)"
wenzelm@19121
   163
  proof -
wenzelm@18466
   164
    assume "PROP A"
wenzelm@19121
   165
    from conj [OF `PROP A`] show "PROP B" by (rule conjunctionD1)
wenzelm@19121
   166
    from conj [OF `PROP A`] show "PROP C" by (rule conjunctionD2)
wenzelm@18466
   167
  qed
wenzelm@18466
   168
next
wenzelm@28856
   169
  assume conj: "(PROP A ==> PROP B) &&& (PROP A ==> PROP C)"
wenzelm@18466
   170
  assume "PROP A"
wenzelm@28856
   171
  show "PROP B &&& PROP C"
wenzelm@19121
   172
  proof -
wenzelm@19121
   173
    from `PROP A` show "PROP B" by (rule conj [THEN conjunctionD1])
wenzelm@19121
   174
    from `PROP A` show "PROP C" by (rule conj [THEN conjunctionD2])
wenzelm@18466
   175
  qed
wenzelm@18466
   176
qed
wenzelm@18466
   177
wenzelm@18466
   178
lemma conjunction_imp:
wenzelm@28856
   179
  "(PROP A &&& PROP B ==> PROP C) == (PROP A ==> PROP B ==> PROP C)"
wenzelm@18466
   180
proof
wenzelm@28856
   181
  assume r: "PROP A &&& PROP B ==> PROP C"
wenzelm@22933
   182
  assume ab: "PROP A" "PROP B"
wenzelm@22933
   183
  show "PROP C"
wenzelm@22933
   184
  proof (rule r)
wenzelm@28856
   185
    from ab show "PROP A &&& PROP B" .
wenzelm@22933
   186
  qed
wenzelm@18466
   187
next
wenzelm@18466
   188
  assume r: "PROP A ==> PROP B ==> PROP C"
wenzelm@28856
   189
  assume conj: "PROP A &&& PROP B"
wenzelm@18466
   190
  show "PROP C"
wenzelm@18466
   191
  proof (rule r)
wenzelm@19121
   192
    from conj show "PROP A" by (rule conjunctionD1)
wenzelm@19121
   193
    from conj show "PROP B" by (rule conjunctionD2)
wenzelm@18466
   194
  qed
wenzelm@18466
   195
qed
wenzelm@18466
   196
wenzelm@48638
   197
end
wenzelm@48638
   198