src/Pure/conjunction.ML
author wenzelm
Thu Jun 09 20:22:22 2011 +0200 (2011-06-09)
changeset 43329 84472e198515
parent 35985 0bbf0d2348f9
child 46497 89ccf66aa73d
permissions -rw-r--r--
tuned signature: Name.invent and Name.invent_names;
wenzelm@19416
     1
(*  Title:      Pure/conjunction.ML
wenzelm@19416
     2
    Author:     Makarius
wenzelm@19416
     3
wenzelm@19416
     4
Meta-level conjunction.
wenzelm@19416
     5
*)
wenzelm@19416
     6
wenzelm@19416
     7
signature CONJUNCTION =
wenzelm@19416
     8
sig
wenzelm@19416
     9
  val conjunction: cterm
wenzelm@19416
    10
  val mk_conjunction: cterm * cterm -> cterm
wenzelm@23422
    11
  val mk_conjunction_balanced: cterm list -> cterm
wenzelm@19416
    12
  val dest_conjunction: cterm -> cterm * cterm
wenzelm@30823
    13
  val dest_conjunctions: cterm -> cterm list
wenzelm@19416
    14
  val cong: thm -> thm -> thm
wenzelm@23422
    15
  val convs: (cterm -> thm) -> cterm -> thm
wenzelm@19416
    16
  val conjunctionD1: thm
wenzelm@19416
    17
  val conjunctionD2: thm
wenzelm@19416
    18
  val conjunctionI: thm
wenzelm@19416
    19
  val intr: thm -> thm -> thm
wenzelm@23422
    20
  val intr_balanced: thm list -> thm
wenzelm@19416
    21
  val elim: thm -> thm * thm
wenzelm@23422
    22
  val elim_balanced: int -> thm -> thm list
wenzelm@23422
    23
  val curry_balanced: int -> thm -> thm
wenzelm@23422
    24
  val uncurry_balanced: int -> thm -> thm
wenzelm@19416
    25
end;
wenzelm@19416
    26
wenzelm@19416
    27
structure Conjunction: CONJUNCTION =
wenzelm@19416
    28
struct
wenzelm@19416
    29
wenzelm@19416
    30
(** abstract syntax **)
wenzelm@19416
    31
wenzelm@26485
    32
fun certify t = Thm.cterm_of (Context.the_theory (Context.the_thread_data ())) t;
wenzelm@33384
    33
val read_prop = certify o Simple_Syntax.read_prop;
wenzelm@19416
    34
wenzelm@26485
    35
val true_prop = certify Logic.true_prop;
wenzelm@26485
    36
val conjunction = certify Logic.conjunction;
wenzelm@23422
    37
wenzelm@19416
    38
fun mk_conjunction (A, B) = Thm.capply (Thm.capply conjunction A) B;
wenzelm@19416
    39
wenzelm@23422
    40
fun mk_conjunction_balanced [] = true_prop
wenzelm@32765
    41
  | mk_conjunction_balanced ts = Balanced_Tree.make mk_conjunction ts;
wenzelm@23422
    42
wenzelm@19416
    43
fun dest_conjunction ct =
wenzelm@19416
    44
  (case Thm.term_of ct of
wenzelm@26424
    45
    (Const ("Pure.conjunction", _) $ _ $ _) => Thm.dest_binop ct
wenzelm@23422
    46
  | _ => raise TERM ("dest_conjunction", [Thm.term_of ct]));
wenzelm@19416
    47
wenzelm@30823
    48
fun dest_conjunctions ct =
wenzelm@30823
    49
  (case try dest_conjunction ct of
wenzelm@30823
    50
    NONE => [ct]
wenzelm@30823
    51
  | SOME (A, B) => dest_conjunctions A @ dest_conjunctions B);
wenzelm@30823
    52
wenzelm@19416
    53
wenzelm@19416
    54
wenzelm@19416
    55
(** derived rules **)
wenzelm@19416
    56
wenzelm@19416
    57
(* conversion *)
wenzelm@19416
    58
wenzelm@19416
    59
val cong = Thm.combination o Thm.combination (Thm.reflexive conjunction);
wenzelm@19416
    60
wenzelm@23422
    61
fun convs cv ct =
wenzelm@23422
    62
  (case try dest_conjunction ct of
wenzelm@23422
    63
    NONE => cv ct
wenzelm@23422
    64
  | SOME (A, B) => cong (convs cv A) (convs cv B));
wenzelm@19416
    65
wenzelm@19416
    66
wenzelm@19416
    67
(* intro/elim *)
wenzelm@19416
    68
wenzelm@19416
    69
local
wenzelm@19416
    70
wenzelm@24241
    71
val A = read_prop "A" and vA = read_prop "?A";
wenzelm@24241
    72
val B = read_prop "B" and vB = read_prop "?B";
wenzelm@24241
    73
val C = read_prop "C";
wenzelm@24241
    74
val ABC = read_prop "A ==> B ==> C";
wenzelm@28856
    75
val A_B = read_prop "A &&& B";
wenzelm@19416
    76
wenzelm@26424
    77
val conjunction_def =
wenzelm@35845
    78
  Thm.unvarify_global
wenzelm@35845
    79
    (Thm.axiom (Context.the_theory (Context.the_thread_data ())) "Pure.conjunction_def");
wenzelm@19416
    80
wenzelm@19416
    81
fun conjunctionD which =
wenzelm@19416
    82
  Drule.implies_intr_list [A, B] (Thm.assume (which (A, B))) COMP
wenzelm@26653
    83
  Thm.forall_elim_vars 0 (Thm.equal_elim conjunction_def (Thm.assume A_B));
wenzelm@19416
    84
wenzelm@19416
    85
in
wenzelm@19416
    86
wenzelm@33277
    87
val conjunctionD1 = Drule.store_standard_thm (Binding.name "conjunctionD1") (conjunctionD #1);
wenzelm@33277
    88
val conjunctionD2 = Drule.store_standard_thm (Binding.name "conjunctionD2") (conjunctionD #2);
wenzelm@19416
    89
wenzelm@33277
    90
val conjunctionI =
wenzelm@33277
    91
  Drule.store_standard_thm (Binding.name "conjunctionI")
wenzelm@33277
    92
    (Drule.implies_intr_list [A, B]
wenzelm@33277
    93
      (Thm.equal_elim
wenzelm@33277
    94
        (Thm.symmetric conjunction_def)
wenzelm@33277
    95
        (Thm.forall_intr C (Thm.implies_intr ABC
wenzelm@33277
    96
          (Drule.implies_elim_list (Thm.assume ABC) [Thm.assume A, Thm.assume B])))));
wenzelm@19416
    97
wenzelm@23422
    98
wenzelm@20508
    99
fun intr tha thb =
wenzelm@20508
   100
  Thm.implies_elim
wenzelm@20508
   101
    (Thm.implies_elim
wenzelm@20508
   102
      (Thm.instantiate ([], [(vA, Thm.cprop_of tha), (vB, Thm.cprop_of thb)]) conjunctionI)
wenzelm@20508
   103
    tha)
wenzelm@20508
   104
  thb;
wenzelm@19416
   105
wenzelm@19416
   106
fun elim th =
wenzelm@20508
   107
  let
wenzelm@20508
   108
    val (A, B) = dest_conjunction (Thm.cprop_of th)
wenzelm@20508
   109
      handle TERM (msg, _) => raise THM (msg, 0, [th]);
wenzelm@20508
   110
    val inst = Thm.instantiate ([], [(vA, A), (vB, B)]);
wenzelm@20508
   111
  in
wenzelm@20508
   112
   (Thm.implies_elim (inst conjunctionD1) th,
wenzelm@20508
   113
    Thm.implies_elim (inst conjunctionD2) th)
wenzelm@20508
   114
  end;
wenzelm@19416
   115
wenzelm@23422
   116
end;
wenzelm@23422
   117
wenzelm@23422
   118
wenzelm@23535
   119
(* balanced conjuncts *)
wenzelm@23422
   120
wenzelm@23422
   121
fun intr_balanced [] = asm_rl
wenzelm@32765
   122
  | intr_balanced ths = Balanced_Tree.make (uncurry intr) ths;
wenzelm@23422
   123
wenzelm@23422
   124
fun elim_balanced 0 _ = []
wenzelm@32765
   125
  | elim_balanced n th = Balanced_Tree.dest elim n th;
wenzelm@19416
   126
wenzelm@19416
   127
wenzelm@19416
   128
(* currying *)
wenzelm@19416
   129
wenzelm@19416
   130
local
wenzelm@19416
   131
wenzelm@26424
   132
fun conjs thy n =
wenzelm@43329
   133
  let val As = map (fn A => Thm.cterm_of thy (Free (A, propT))) (Name.invent Name.context "A" n)
wenzelm@23422
   134
  in (As, mk_conjunction_balanced As) end;
wenzelm@19416
   135
wenzelm@24241
   136
val B = read_prop "B";
wenzelm@19416
   137
wenzelm@19416
   138
fun comp_rule th rule =
wenzelm@20260
   139
  Thm.adjust_maxidx_thm ~1 (th COMP
wenzelm@35985
   140
    (rule |> Thm.forall_intr_frees |> Thm.forall_elim_vars (Thm.maxidx_of th + 1)));
wenzelm@19416
   141
wenzelm@19416
   142
in
wenzelm@19416
   143
wenzelm@19416
   144
(*
wenzelm@28856
   145
  A1 &&& ... &&& An ==> B
wenzelm@19416
   146
  -----------------------
wenzelm@19416
   147
  A1 ==> ... ==> An ==> B
wenzelm@19416
   148
*)
wenzelm@23422
   149
fun curry_balanced n th =
wenzelm@23422
   150
  if n < 2 then th
wenzelm@23422
   151
  else
wenzelm@23422
   152
    let
wenzelm@26424
   153
      val thy = Thm.theory_of_thm th;
wenzelm@26424
   154
      val (As, C) = conjs thy n;
wenzelm@23422
   155
      val D = Drule.mk_implies (C, B);
wenzelm@23422
   156
    in
wenzelm@23422
   157
      comp_rule th
wenzelm@23422
   158
        (Thm.implies_elim (Thm.assume D) (intr_balanced (map Thm.assume As))
wenzelm@23422
   159
          |> Drule.implies_intr_list (D :: As))
wenzelm@23422
   160
    end;
wenzelm@19416
   161
wenzelm@19416
   162
(*
wenzelm@19416
   163
  A1 ==> ... ==> An ==> B
wenzelm@19416
   164
  -----------------------
wenzelm@28856
   165
  A1 &&& ... &&& An ==> B
wenzelm@19416
   166
*)
wenzelm@23422
   167
fun uncurry_balanced n th =
wenzelm@23422
   168
  if n < 2 then th
wenzelm@23422
   169
  else
wenzelm@23422
   170
    let
wenzelm@26424
   171
      val thy = Thm.theory_of_thm th;
wenzelm@26424
   172
      val (As, C) = conjs thy n;
wenzelm@23422
   173
      val D = Drule.list_implies (As, B);
wenzelm@23422
   174
    in
wenzelm@23422
   175
      comp_rule th
wenzelm@23422
   176
        (Drule.implies_elim_list (Thm.assume D) (elim_balanced n (Thm.assume C))
wenzelm@23422
   177
          |> Drule.implies_intr_list [D, C])
wenzelm@23422
   178
    end;
wenzelm@19416
   179
wenzelm@19416
   180
end;
wenzelm@19416
   181
wenzelm@19416
   182
end;