src/Pure/thm.ML
author wenzelm
Thu Mar 12 11:10:02 2009 +0100 (2009-03-12)
changeset 30466 5f31e24937c5
parent 30342 d32daa6aba3c
child 30554 73f8bd5f0af8
permissions -rw-r--r--
renamed NameSpace.bind to NameSpace.define;
wenzelm@250
     1
(*  Title:      Pure/thm.ML
wenzelm@250
     2
    Author:     Lawrence C Paulson, Cambridge University Computer Laboratory
wenzelm@29269
     3
    Author:     Makarius
lcp@229
     4
wenzelm@16425
     5
The very core of Isabelle's Meta Logic: certified types and terms,
wenzelm@28321
     6
derivations, theorems, framework rules (including lifting and
wenzelm@28321
     7
resolution), oracles.
clasohm@0
     8
*)
clasohm@0
     9
wenzelm@6089
    10
signature BASIC_THM =
paulson@1503
    11
  sig
wenzelm@1160
    12
  (*certified types*)
wenzelm@387
    13
  type ctyp
wenzelm@16656
    14
  val rep_ctyp: ctyp ->
wenzelm@26631
    15
   {thy_ref: theory_ref,
wenzelm@16656
    16
    T: typ,
wenzelm@20512
    17
    maxidx: int,
wenzelm@28354
    18
    sorts: sort OrdList.T}
wenzelm@16425
    19
  val theory_of_ctyp: ctyp -> theory
wenzelm@16425
    20
  val typ_of: ctyp -> typ
wenzelm@16425
    21
  val ctyp_of: theory -> typ -> ctyp
wenzelm@1160
    22
wenzelm@1160
    23
  (*certified terms*)
wenzelm@1160
    24
  type cterm
wenzelm@22584
    25
  exception CTERM of string * cterm list
wenzelm@16601
    26
  val rep_cterm: cterm ->
wenzelm@26631
    27
   {thy_ref: theory_ref,
wenzelm@16656
    28
    t: term,
wenzelm@16656
    29
    T: typ,
wenzelm@16656
    30
    maxidx: int,
wenzelm@28354
    31
    sorts: sort OrdList.T}
wenzelm@28354
    32
  val crep_cterm: cterm ->
wenzelm@28354
    33
    {thy_ref: theory_ref, t: term, T: ctyp, maxidx: int, sorts: sort OrdList.T}
wenzelm@16425
    34
  val theory_of_cterm: cterm -> theory
wenzelm@16425
    35
  val term_of: cterm -> term
wenzelm@16425
    36
  val cterm_of: theory -> term -> cterm
wenzelm@16425
    37
  val ctyp_of_term: cterm -> ctyp
wenzelm@1160
    38
wenzelm@28321
    39
  (*theorems*)
wenzelm@1160
    40
  type thm
wenzelm@23601
    41
  type conv = cterm -> thm
wenzelm@23601
    42
  type attribute = Context.generic * thm -> Context.generic * thm
wenzelm@16425
    43
  val rep_thm: thm ->
wenzelm@26631
    44
   {thy_ref: theory_ref,
wenzelm@28017
    45
    tags: Properties.T,
wenzelm@16425
    46
    maxidx: int,
wenzelm@28354
    47
    shyps: sort OrdList.T,
wenzelm@28354
    48
    hyps: term OrdList.T,
wenzelm@16425
    49
    tpairs: (term * term) list,
wenzelm@16425
    50
    prop: term}
wenzelm@16425
    51
  val crep_thm: thm ->
wenzelm@26631
    52
   {thy_ref: theory_ref,
wenzelm@28017
    53
    tags: Properties.T,
wenzelm@16425
    54
    maxidx: int,
wenzelm@28354
    55
    shyps: sort OrdList.T,
wenzelm@28354
    56
    hyps: cterm OrdList.T,
wenzelm@16425
    57
    tpairs: (cterm * cterm) list,
wenzelm@16425
    58
    prop: cterm}
wenzelm@6089
    59
  exception THM of string * int * thm list
wenzelm@16425
    60
  val theory_of_thm: thm -> theory
wenzelm@16425
    61
  val prop_of: thm -> term
wenzelm@16425
    62
  val tpairs_of: thm -> (term * term) list
wenzelm@16656
    63
  val concl_of: thm -> term
wenzelm@16425
    64
  val prems_of: thm -> term list
wenzelm@16425
    65
  val nprems_of: thm -> int
wenzelm@16425
    66
  val cprop_of: thm -> cterm
wenzelm@18145
    67
  val cprem_of: thm -> int -> cterm
wenzelm@16656
    68
  val transfer: theory -> thm -> thm
wenzelm@16945
    69
  val weaken: cterm -> thm -> thm
wenzelm@28624
    70
  val weaken_sorts: sort list -> cterm -> cterm
wenzelm@16425
    71
  val extra_shyps: thm -> sort list
wenzelm@16425
    72
  val strip_shyps: thm -> thm
wenzelm@1160
    73
wenzelm@1160
    74
  (*meta rules*)
wenzelm@16425
    75
  val assume: cterm -> thm
wenzelm@16425
    76
  val implies_intr: cterm -> thm -> thm
wenzelm@16425
    77
  val implies_elim: thm -> thm -> thm
wenzelm@16425
    78
  val forall_intr: cterm -> thm -> thm
wenzelm@16425
    79
  val forall_elim: cterm -> thm -> thm
wenzelm@16425
    80
  val reflexive: cterm -> thm
wenzelm@16425
    81
  val symmetric: thm -> thm
wenzelm@16425
    82
  val transitive: thm -> thm -> thm
wenzelm@23601
    83
  val beta_conversion: bool -> conv
wenzelm@23601
    84
  val eta_conversion: conv
wenzelm@23601
    85
  val eta_long_conversion: conv
wenzelm@16425
    86
  val abstract_rule: string -> cterm -> thm -> thm
wenzelm@16425
    87
  val combination: thm -> thm -> thm
wenzelm@16425
    88
  val equal_intr: thm -> thm -> thm
wenzelm@16425
    89
  val equal_elim: thm -> thm -> thm
wenzelm@16425
    90
  val flexflex_rule: thm -> thm Seq.seq
wenzelm@19910
    91
  val generalize: string list * string list -> int -> thm -> thm
wenzelm@16425
    92
  val instantiate: (ctyp * ctyp) list * (cterm * cterm) list -> thm -> thm
wenzelm@22584
    93
  val instantiate_cterm: (ctyp * ctyp) list * (cterm * cterm) list -> cterm -> cterm
wenzelm@16425
    94
  val trivial: cterm -> thm
wenzelm@16425
    95
  val class_triv: theory -> class -> thm
wenzelm@19505
    96
  val unconstrainT: ctyp -> thm -> thm
wenzelm@16425
    97
  val dest_state: thm * int -> (term * term) list * term list * term * term
wenzelm@18035
    98
  val lift_rule: cterm -> thm -> thm
wenzelm@16425
    99
  val incr_indexes: int -> thm -> thm
wenzelm@16425
   100
  val assumption: int -> thm -> thm Seq.seq
wenzelm@16425
   101
  val eq_assumption: int -> thm -> thm
wenzelm@16425
   102
  val rotate_rule: int -> int -> thm -> thm
wenzelm@16425
   103
  val permute_prems: int -> int -> thm -> thm
wenzelm@1160
   104
  val rename_params_rule: string list * int -> thm -> thm
wenzelm@18501
   105
  val compose_no_flatten: bool -> thm * int -> int -> thm -> thm Seq.seq
wenzelm@16425
   106
  val bicompose: bool -> bool * thm * int -> int -> thm -> thm Seq.seq
wenzelm@16425
   107
  val biresolution: bool -> (bool * thm) list -> int -> thm -> thm Seq.seq
wenzelm@250
   108
end;
clasohm@0
   109
wenzelm@6089
   110
signature THM =
wenzelm@6089
   111
sig
wenzelm@6089
   112
  include BASIC_THM
wenzelm@16425
   113
  val dest_ctyp: ctyp -> ctyp list
wenzelm@16425
   114
  val dest_comb: cterm -> cterm * cterm
wenzelm@22909
   115
  val dest_fun: cterm -> cterm
wenzelm@20580
   116
  val dest_arg: cterm -> cterm
wenzelm@22909
   117
  val dest_fun2: cterm -> cterm
wenzelm@22909
   118
  val dest_arg1: cterm -> cterm
wenzelm@16425
   119
  val dest_abs: string option -> cterm -> cterm * cterm
wenzelm@20261
   120
  val adjust_maxidx_cterm: int -> cterm -> cterm
wenzelm@16425
   121
  val capply: cterm -> cterm -> cterm
wenzelm@16425
   122
  val cabs: cterm -> cterm -> cterm
wenzelm@16425
   123
  val major_prem_of: thm -> term
wenzelm@16425
   124
  val no_prems: thm -> bool
wenzelm@16945
   125
  val terms_of_tpairs: (term * term) list -> term list
wenzelm@19881
   126
  val maxidx_of: thm -> int
wenzelm@19910
   127
  val maxidx_thm: thm -> int -> int
wenzelm@19881
   128
  val hyps_of: thm -> term list
wenzelm@16945
   129
  val full_prop_of: thm -> term
wenzelm@28675
   130
  val axiom: theory -> string -> thm
wenzelm@28675
   131
  val axioms_of: theory -> (string * thm) list
wenzelm@21646
   132
  val get_name: thm -> string
wenzelm@21646
   133
  val put_name: string -> thm -> thm
wenzelm@28017
   134
  val get_tags: thm -> Properties.T
wenzelm@28017
   135
  val map_tags: (Properties.T -> Properties.T) -> thm -> thm
berghofe@23781
   136
  val norm_proof: thm -> thm
wenzelm@20261
   137
  val adjust_maxidx_thm: int -> thm -> thm
wenzelm@16425
   138
  val rename_boundvars: term -> term -> thm -> thm
wenzelm@22909
   139
  val match: cterm * cterm -> (ctyp * ctyp) list * (cterm * cterm) list
wenzelm@22909
   140
  val first_order_match: cterm * cterm -> (ctyp * ctyp) list * (cterm * cterm) list
wenzelm@22909
   141
  val incr_indexes_cterm: int -> cterm -> cterm
wenzelm@20002
   142
  val varifyT: thm -> thm
wenzelm@20002
   143
  val varifyT': (string * sort) list -> thm -> ((string * sort) * indexname) list * thm
wenzelm@19881
   144
  val freezeT: thm -> thm
wenzelm@28978
   145
  val future: thm future -> cterm -> thm
wenzelm@29432
   146
  val pending_groups: thm -> Task_Queue.group list -> Task_Queue.group list
wenzelm@28814
   147
  val proof_body_of: thm -> proof_body
wenzelm@28814
   148
  val proof_of: thm -> proof
wenzelm@29003
   149
  val join_proof: thm -> unit
wenzelm@28330
   150
  val extern_oracles: theory -> xstring list
wenzelm@30288
   151
  val add_oracle: binding * ('a -> cterm) -> theory -> (string * ('a -> thm)) * theory
wenzelm@6089
   152
end;
wenzelm@6089
   153
wenzelm@28356
   154
structure Thm:> THM =
clasohm@0
   155
struct
wenzelm@250
   156
wenzelm@22237
   157
structure Pt = Proofterm;
wenzelm@22237
   158
wenzelm@16656
   159
wenzelm@387
   160
(*** Certified terms and types ***)
wenzelm@387
   161
wenzelm@250
   162
(** certified types **)
wenzelm@250
   163
wenzelm@28356
   164
datatype ctyp = Ctyp of
wenzelm@20512
   165
 {thy_ref: theory_ref,
wenzelm@20512
   166
  T: typ,
wenzelm@20512
   167
  maxidx: int,
wenzelm@28356
   168
  sorts: sort OrdList.T};
wenzelm@250
   169
wenzelm@26631
   170
fun rep_ctyp (Ctyp args) = args;
wenzelm@16656
   171
fun theory_of_ctyp (Ctyp {thy_ref, ...}) = Theory.deref thy_ref;
wenzelm@250
   172
fun typ_of (Ctyp {T, ...}) = T;
wenzelm@250
   173
wenzelm@16656
   174
fun ctyp_of thy raw_T =
wenzelm@24143
   175
  let
wenzelm@24143
   176
    val T = Sign.certify_typ thy raw_T;
wenzelm@24143
   177
    val maxidx = Term.maxidx_of_typ T;
wenzelm@26640
   178
    val sorts = Sorts.insert_typ T [];
wenzelm@24143
   179
  in Ctyp {thy_ref = Theory.check_thy thy, T = T, maxidx = maxidx, sorts = sorts} end;
wenzelm@250
   180
wenzelm@20512
   181
fun dest_ctyp (Ctyp {thy_ref, T = Type (s, Ts), maxidx, sorts}) =
wenzelm@20512
   182
      map (fn T => Ctyp {thy_ref = thy_ref, T = T, maxidx = maxidx, sorts = sorts}) Ts
wenzelm@16679
   183
  | dest_ctyp cT = raise TYPE ("dest_ctyp", [typ_of cT], []);
berghofe@15087
   184
lcp@229
   185
lcp@229
   186
wenzelm@250
   187
(** certified terms **)
lcp@229
   188
wenzelm@16601
   189
(*certified terms with checked typ, maxidx, and sorts*)
wenzelm@28356
   190
datatype cterm = Cterm of
wenzelm@16601
   191
 {thy_ref: theory_ref,
wenzelm@16601
   192
  t: term,
wenzelm@16601
   193
  T: typ,
wenzelm@16601
   194
  maxidx: int,
wenzelm@28356
   195
  sorts: sort OrdList.T};
wenzelm@16425
   196
wenzelm@22584
   197
exception CTERM of string * cterm list;
wenzelm@16679
   198
wenzelm@26631
   199
fun rep_cterm (Cterm args) = args;
lcp@229
   200
wenzelm@16601
   201
fun crep_cterm (Cterm {thy_ref, t, T, maxidx, sorts}) =
wenzelm@26631
   202
  {thy_ref = thy_ref, t = t, maxidx = maxidx, sorts = sorts,
wenzelm@26631
   203
    T = Ctyp {thy_ref = thy_ref, T = T, maxidx = maxidx, sorts = sorts}};
wenzelm@3967
   204
wenzelm@16425
   205
fun theory_of_cterm (Cterm {thy_ref, ...}) = Theory.deref thy_ref;
wenzelm@250
   206
fun term_of (Cterm {t, ...}) = t;
lcp@229
   207
wenzelm@20512
   208
fun ctyp_of_term (Cterm {thy_ref, T, maxidx, sorts, ...}) =
wenzelm@20512
   209
  Ctyp {thy_ref = thy_ref, T = T, maxidx = maxidx, sorts = sorts};
paulson@2671
   210
wenzelm@16425
   211
fun cterm_of thy tm =
wenzelm@16601
   212
  let
wenzelm@18969
   213
    val (t, T, maxidx) = Sign.certify_term thy tm;
wenzelm@26640
   214
    val sorts = Sorts.insert_term t [];
wenzelm@24143
   215
  in Cterm {thy_ref = Theory.check_thy thy, t = t, T = T, maxidx = maxidx, sorts = sorts} end;
lcp@229
   216
wenzelm@20057
   217
fun merge_thys0 (Cterm {thy_ref = r1, t = t1, ...}) (Cterm {thy_ref = r2, t = t2, ...}) =
wenzelm@23601
   218
  Theory.merge_refs (r1, r2);
wenzelm@16656
   219
wenzelm@20580
   220
wenzelm@22909
   221
(* destructors *)
wenzelm@22909
   222
wenzelm@22909
   223
fun dest_comb (ct as Cterm {t = c $ a, T, thy_ref, maxidx, sorts}) =
wenzelm@22909
   224
      let val A = Term.argument_type_of c 0 in
wenzelm@22909
   225
        (Cterm {t = c, T = A --> T, thy_ref = thy_ref, maxidx = maxidx, sorts = sorts},
wenzelm@22909
   226
         Cterm {t = a, T = A, thy_ref = thy_ref, maxidx = maxidx, sorts = sorts})
clasohm@1493
   227
      end
wenzelm@22584
   228
  | dest_comb ct = raise CTERM ("dest_comb", [ct]);
clasohm@1493
   229
wenzelm@22909
   230
fun dest_fun (ct as Cterm {t = c $ _, T, thy_ref, maxidx, sorts}) =
wenzelm@22909
   231
      let val A = Term.argument_type_of c 0
wenzelm@22909
   232
      in Cterm {t = c, T = A --> T, thy_ref = thy_ref, maxidx = maxidx, sorts = sorts} end
wenzelm@22909
   233
  | dest_fun ct = raise CTERM ("dest_fun", [ct]);
wenzelm@22909
   234
wenzelm@22909
   235
fun dest_arg (ct as Cterm {t = c $ a, T = _, thy_ref, maxidx, sorts}) =
wenzelm@22909
   236
      let val A = Term.argument_type_of c 0
wenzelm@22909
   237
      in Cterm {t = a, T = A, thy_ref = thy_ref, maxidx = maxidx, sorts = sorts} end
wenzelm@22584
   238
  | dest_arg ct = raise CTERM ("dest_arg", [ct]);
wenzelm@20580
   239
wenzelm@22909
   240
wenzelm@22909
   241
fun dest_fun2 (Cterm {t = c $ a $ b, T, thy_ref, maxidx, sorts}) =
wenzelm@22909
   242
      let
wenzelm@22909
   243
        val A = Term.argument_type_of c 0;
wenzelm@22909
   244
        val B = Term.argument_type_of c 1;
wenzelm@22909
   245
      in Cterm {t = c, T = A --> B --> T, thy_ref = thy_ref, maxidx = maxidx, sorts = sorts} end
wenzelm@22909
   246
  | dest_fun2 ct = raise CTERM ("dest_fun2", [ct]);
wenzelm@22909
   247
wenzelm@22909
   248
fun dest_arg1 (Cterm {t = c $ a $ _, T = _, thy_ref, maxidx, sorts}) =
wenzelm@22909
   249
      let val A = Term.argument_type_of c 0
wenzelm@22909
   250
      in Cterm {t = a, T = A, thy_ref = thy_ref, maxidx = maxidx, sorts = sorts} end
wenzelm@22909
   251
  | dest_arg1 ct = raise CTERM ("dest_arg1", [ct]);
wenzelm@20673
   252
wenzelm@22584
   253
fun dest_abs a (ct as
wenzelm@22584
   254
        Cterm {t = Abs (x, T, t), T = Type ("fun", [_, U]), thy_ref, maxidx, sorts}) =
wenzelm@18944
   255
      let val (y', t') = Term.dest_abs (the_default x a, T, t) in
wenzelm@16679
   256
        (Cterm {t = Free (y', T), T = T, thy_ref = thy_ref, maxidx = maxidx, sorts = sorts},
wenzelm@16679
   257
          Cterm {t = t', T = U, thy_ref = thy_ref, maxidx = maxidx, sorts = sorts})
clasohm@1493
   258
      end
wenzelm@22584
   259
  | dest_abs _ ct = raise CTERM ("dest_abs", [ct]);
clasohm@1493
   260
wenzelm@22909
   261
wenzelm@22909
   262
(* constructors *)
wenzelm@22909
   263
wenzelm@16601
   264
fun capply
wenzelm@16656
   265
  (cf as Cterm {t = f, T = Type ("fun", [dty, rty]), maxidx = maxidx1, sorts = sorts1, ...})
wenzelm@16656
   266
  (cx as Cterm {t = x, T, maxidx = maxidx2, sorts = sorts2, ...}) =
wenzelm@16601
   267
    if T = dty then
wenzelm@16656
   268
      Cterm {thy_ref = merge_thys0 cf cx,
wenzelm@16656
   269
        t = f $ x,
wenzelm@16656
   270
        T = rty,
wenzelm@16656
   271
        maxidx = Int.max (maxidx1, maxidx2),
wenzelm@16601
   272
        sorts = Sorts.union sorts1 sorts2}
wenzelm@22584
   273
      else raise CTERM ("capply: types don't agree", [cf, cx])
wenzelm@22584
   274
  | capply cf cx = raise CTERM ("capply: first arg is not a function", [cf, cx]);
wenzelm@250
   275
wenzelm@16601
   276
fun cabs
wenzelm@16656
   277
  (ct1 as Cterm {t = t1, T = T1, maxidx = maxidx1, sorts = sorts1, ...})
wenzelm@16656
   278
  (ct2 as Cterm {t = t2, T = T2, maxidx = maxidx2, sorts = sorts2, ...}) =
wenzelm@21975
   279
    let val t = Term.lambda t1 t2 in
wenzelm@16656
   280
      Cterm {thy_ref = merge_thys0 ct1 ct2,
wenzelm@16656
   281
        t = t, T = T1 --> T2,
wenzelm@16656
   282
        maxidx = Int.max (maxidx1, maxidx2),
wenzelm@16656
   283
        sorts = Sorts.union sorts1 sorts2}
wenzelm@16601
   284
    end;
lcp@229
   285
wenzelm@20580
   286
wenzelm@22909
   287
(* indexes *)
wenzelm@22909
   288
wenzelm@20580
   289
fun adjust_maxidx_cterm i (ct as Cterm {thy_ref, t, T, maxidx, sorts}) =
wenzelm@20580
   290
  if maxidx = i then ct
wenzelm@20580
   291
  else if maxidx < i then
wenzelm@20580
   292
    Cterm {maxidx = i, thy_ref = thy_ref, t = t, T = T, sorts = sorts}
wenzelm@20580
   293
  else
wenzelm@20580
   294
    Cterm {maxidx = Int.max (maxidx_of_term t, i), thy_ref = thy_ref, t = t, T = T, sorts = sorts};
wenzelm@20580
   295
wenzelm@22909
   296
fun incr_indexes_cterm i (ct as Cterm {thy_ref, t, T, maxidx, sorts}) =
wenzelm@22909
   297
  if i < 0 then raise CTERM ("negative increment", [ct])
wenzelm@22909
   298
  else if i = 0 then ct
wenzelm@22909
   299
  else Cterm {thy_ref = thy_ref, t = Logic.incr_indexes ([], i) t,
wenzelm@22909
   300
    T = Logic.incr_tvar i T, maxidx = maxidx + i, sorts = sorts};
wenzelm@22909
   301
wenzelm@22909
   302
wenzelm@22909
   303
(* matching *)
wenzelm@22909
   304
wenzelm@22909
   305
local
wenzelm@22909
   306
wenzelm@22909
   307
fun gen_match match
wenzelm@20512
   308
    (ct1 as Cterm {t = t1, sorts = sorts1, ...},
wenzelm@20815
   309
     ct2 as Cterm {t = t2, sorts = sorts2, maxidx = maxidx2, ...}) =
berghofe@10416
   310
  let
wenzelm@24143
   311
    val thy = Theory.deref (merge_thys0 ct1 ct2);
wenzelm@24143
   312
    val (Tinsts, tinsts) = match thy (t1, t2) (Vartab.empty, Vartab.empty);
wenzelm@16601
   313
    val sorts = Sorts.union sorts1 sorts2;
wenzelm@20512
   314
    fun mk_cTinst ((a, i), (S, T)) =
wenzelm@24143
   315
      (Ctyp {T = TVar ((a, i), S), thy_ref = Theory.check_thy thy, maxidx = i, sorts = sorts},
wenzelm@24143
   316
       Ctyp {T = T, thy_ref = Theory.check_thy thy, maxidx = maxidx2, sorts = sorts});
wenzelm@20512
   317
    fun mk_ctinst ((x, i), (T, t)) =
wenzelm@16601
   318
      let val T = Envir.typ_subst_TVars Tinsts T in
wenzelm@24143
   319
        (Cterm {t = Var ((x, i), T), T = T, thy_ref = Theory.check_thy thy,
wenzelm@24143
   320
          maxidx = i, sorts = sorts},
wenzelm@24143
   321
         Cterm {t = t, T = T, thy_ref = Theory.check_thy thy, maxidx = maxidx2, sorts = sorts})
berghofe@10416
   322
      end;
wenzelm@16656
   323
  in (Vartab.fold (cons o mk_cTinst) Tinsts [], Vartab.fold (cons o mk_ctinst) tinsts []) end;
berghofe@10416
   324
wenzelm@22909
   325
in
berghofe@10416
   326
wenzelm@22909
   327
val match = gen_match Pattern.match;
wenzelm@22909
   328
val first_order_match = gen_match Pattern.first_order_match;
wenzelm@22909
   329
wenzelm@22909
   330
end;
berghofe@10416
   331
wenzelm@2509
   332
wenzelm@2509
   333
wenzelm@28321
   334
(*** Derivations and Theorems ***)
lcp@229
   335
wenzelm@28356
   336
datatype thm = Thm of
wenzelm@28378
   337
 deriv *                                        (*derivation*)
wenzelm@28378
   338
 {thy_ref: theory_ref,                          (*dynamic reference to theory*)
wenzelm@28378
   339
  tags: Properties.T,                           (*additional annotations/comments*)
wenzelm@28378
   340
  maxidx: int,                                  (*maximum index of any Var or TVar*)
wenzelm@28378
   341
  shyps: sort OrdList.T,                        (*sort hypotheses*)
wenzelm@28378
   342
  hyps: term OrdList.T,                         (*hypotheses*)
wenzelm@28378
   343
  tpairs: (term * term) list,                   (*flex-flex pairs*)
wenzelm@28378
   344
  prop: term}                                   (*conclusion*)
wenzelm@28624
   345
and deriv = Deriv of
wenzelm@28996
   346
 {max_promise: serial,
wenzelm@28996
   347
  open_promises: (serial * thm future) OrdList.T,
wenzelm@28978
   348
  promises: (serial * thm future) OrdList.T,
wenzelm@28804
   349
  body: Pt.proof_body};
clasohm@0
   350
wenzelm@23601
   351
type conv = cterm -> thm;
wenzelm@23601
   352
wenzelm@22365
   353
(*attributes subsume any kind of rules or context modifiers*)
wenzelm@22365
   354
type attribute = Context.generic * thm -> Context.generic * thm;
wenzelm@22365
   355
wenzelm@16725
   356
(*errors involving theorems*)
wenzelm@16725
   357
exception THM of string * int * thm list;
berghofe@13658
   358
wenzelm@28321
   359
fun rep_thm (Thm (_, args)) = args;
clasohm@0
   360
wenzelm@28321
   361
fun crep_thm (Thm (_, {thy_ref, tags, maxidx, shyps, hyps, tpairs, prop})) =
wenzelm@26631
   362
  let fun cterm max t = Cterm {thy_ref = thy_ref, t = t, T = propT, maxidx = max, sorts = shyps} in
wenzelm@28321
   363
   {thy_ref = thy_ref, tags = tags, maxidx = maxidx, shyps = shyps,
wenzelm@16425
   364
    hyps = map (cterm ~1) hyps,
wenzelm@16425
   365
    tpairs = map (pairself (cterm maxidx)) tpairs,
wenzelm@16425
   366
    prop = cterm maxidx prop}
clasohm@1517
   367
  end;
clasohm@1517
   368
wenzelm@16725
   369
fun terms_of_tpairs tpairs = fold_rev (fn (t, u) => cons t o cons u) tpairs [];
wenzelm@16725
   370
wenzelm@16725
   371
fun eq_tpairs ((t, u), (t', u')) = t aconv t' andalso u aconv u';
wenzelm@18944
   372
fun union_tpairs ts us = Library.merge eq_tpairs (ts, us);
wenzelm@16884
   373
val maxidx_tpairs = fold (fn (t, u) => Term.maxidx_term t #> Term.maxidx_term u);
wenzelm@16725
   374
wenzelm@16725
   375
fun attach_tpairs tpairs prop =
wenzelm@16725
   376
  Logic.list_implies (map Logic.mk_equals tpairs, prop);
wenzelm@16725
   377
wenzelm@28321
   378
fun full_prop_of (Thm (_, {tpairs, prop, ...})) = attach_tpairs tpairs prop;
wenzelm@16945
   379
wenzelm@29269
   380
val union_hyps = OrdList.union TermOrd.fast_term_ord;
wenzelm@29269
   381
val insert_hyps = OrdList.insert TermOrd.fast_term_ord;
wenzelm@29269
   382
val remove_hyps = OrdList.remove TermOrd.fast_term_ord;
wenzelm@22365
   383
wenzelm@16945
   384
wenzelm@24143
   385
(* merge theories of cterms/thms -- trivial absorption only *)
wenzelm@16945
   386
wenzelm@28321
   387
fun merge_thys1 (Cterm {thy_ref = r1, ...}) (th as Thm (_, {thy_ref = r2, ...})) =
wenzelm@23601
   388
  Theory.merge_refs (r1, r2);
wenzelm@16945
   389
wenzelm@28321
   390
fun merge_thys2 (th1 as Thm (_, {thy_ref = r1, ...})) (th2 as Thm (_, {thy_ref = r2, ...})) =
wenzelm@23601
   391
  Theory.merge_refs (r1, r2);
wenzelm@16945
   392
clasohm@0
   393
wenzelm@22365
   394
(* basic components *)
wenzelm@16135
   395
wenzelm@28321
   396
val theory_of_thm = Theory.deref o #thy_ref o rep_thm;
wenzelm@28321
   397
val maxidx_of = #maxidx o rep_thm;
wenzelm@19910
   398
fun maxidx_thm th i = Int.max (maxidx_of th, i);
wenzelm@28321
   399
val hyps_of = #hyps o rep_thm;
wenzelm@28321
   400
val prop_of = #prop o rep_thm;
wenzelm@28321
   401
val tpairs_of = #tpairs o rep_thm;
clasohm@0
   402
wenzelm@16601
   403
val concl_of = Logic.strip_imp_concl o prop_of;
wenzelm@16601
   404
val prems_of = Logic.strip_imp_prems o prop_of;
wenzelm@21576
   405
val nprems_of = Logic.count_prems o prop_of;
wenzelm@19305
   406
fun no_prems th = nprems_of th = 0;
wenzelm@16601
   407
wenzelm@16601
   408
fun major_prem_of th =
wenzelm@16601
   409
  (case prems_of th of
wenzelm@16601
   410
    prem :: _ => Logic.strip_assums_concl prem
wenzelm@16601
   411
  | [] => raise THM ("major_prem_of: rule with no premises", 0, [th]));
wenzelm@16601
   412
wenzelm@16601
   413
(*the statement of any thm is a cterm*)
wenzelm@28321
   414
fun cprop_of (Thm (_, {thy_ref, maxidx, shyps, prop, ...})) =
wenzelm@16601
   415
  Cterm {thy_ref = thy_ref, maxidx = maxidx, T = propT, t = prop, sorts = shyps};
wenzelm@16601
   416
wenzelm@28321
   417
fun cprem_of (th as Thm (_, {thy_ref, maxidx, shyps, prop, ...})) i =
wenzelm@18035
   418
  Cterm {thy_ref = thy_ref, maxidx = maxidx, T = propT, sorts = shyps,
wenzelm@18145
   419
    t = Logic.nth_prem (i, prop) handle TERM _ => raise THM ("cprem_of", i, [th])};
wenzelm@18035
   420
wenzelm@16656
   421
(*explicit transfer to a super theory*)
wenzelm@16425
   422
fun transfer thy' thm =
wenzelm@3895
   423
  let
wenzelm@28321
   424
    val Thm (der, {thy_ref, tags, maxidx, shyps, hyps, tpairs, prop}) = thm;
wenzelm@16425
   425
    val thy = Theory.deref thy_ref;
wenzelm@26665
   426
    val _ = Theory.subthy (thy, thy') orelse raise THM ("transfer: not a super theory", 0, [thm]);
wenzelm@26665
   427
    val is_eq = Theory.eq_thy (thy, thy');
wenzelm@24143
   428
    val _ = Theory.check_thy thy;
wenzelm@3895
   429
  in
wenzelm@24143
   430
    if is_eq then thm
wenzelm@16945
   431
    else
wenzelm@28321
   432
      Thm (der,
wenzelm@28321
   433
       {thy_ref = Theory.check_thy thy',
wenzelm@21646
   434
        tags = tags,
wenzelm@16945
   435
        maxidx = maxidx,
wenzelm@16945
   436
        shyps = shyps,
wenzelm@16945
   437
        hyps = hyps,
wenzelm@16945
   438
        tpairs = tpairs,
wenzelm@28321
   439
        prop = prop})
wenzelm@3895
   440
  end;
wenzelm@387
   441
wenzelm@16945
   442
(*explicit weakening: maps |- B to A |- B*)
wenzelm@16945
   443
fun weaken raw_ct th =
wenzelm@16945
   444
  let
wenzelm@20261
   445
    val ct as Cterm {t = A, T, sorts, maxidx = maxidxA, ...} = adjust_maxidx_cterm ~1 raw_ct;
wenzelm@28321
   446
    val Thm (der, {tags, maxidx, shyps, hyps, tpairs, prop, ...}) = th;
wenzelm@16945
   447
  in
wenzelm@16945
   448
    if T <> propT then
wenzelm@16945
   449
      raise THM ("weaken: assumptions must have type prop", 0, [])
wenzelm@16945
   450
    else if maxidxA <> ~1 then
wenzelm@16945
   451
      raise THM ("weaken: assumptions may not contain schematic variables", maxidxA, [])
wenzelm@16945
   452
    else
wenzelm@28321
   453
      Thm (der,
wenzelm@28321
   454
       {thy_ref = merge_thys1 ct th,
wenzelm@21646
   455
        tags = tags,
wenzelm@16945
   456
        maxidx = maxidx,
wenzelm@16945
   457
        shyps = Sorts.union sorts shyps,
wenzelm@28354
   458
        hyps = insert_hyps A hyps,
wenzelm@16945
   459
        tpairs = tpairs,
wenzelm@28321
   460
        prop = prop})
wenzelm@16945
   461
  end;
wenzelm@16656
   462
wenzelm@28624
   463
fun weaken_sorts raw_sorts ct =
wenzelm@28624
   464
  let
wenzelm@28624
   465
    val Cterm {thy_ref, t, T, maxidx, sorts} = ct;
wenzelm@28624
   466
    val thy = Theory.deref thy_ref;
wenzelm@28624
   467
    val more_sorts = Sorts.make (map (Sign.certify_sort thy) raw_sorts);
wenzelm@28624
   468
    val sorts' = Sorts.union sorts more_sorts;
wenzelm@28624
   469
  in Cterm {thy_ref = Theory.check_thy thy, t = t, T = T, maxidx = maxidx, sorts = sorts'} end;
wenzelm@28624
   470
wenzelm@16656
   471
clasohm@0
   472
wenzelm@1238
   473
(** sort contexts of theorems **)
wenzelm@1238
   474
wenzelm@28321
   475
fun present_sorts (Thm (_, {hyps, tpairs, prop, ...})) =
wenzelm@16656
   476
  fold (fn (t, u) => Sorts.insert_term t o Sorts.insert_term u) tpairs
wenzelm@16656
   477
    (Sorts.insert_terms hyps (Sorts.insert_term prop []));
wenzelm@1238
   478
wenzelm@7642
   479
(*remove extra sorts that are non-empty by virtue of type signature information*)
wenzelm@28321
   480
fun strip_shyps (thm as Thm (_, {shyps = [], ...})) = thm
wenzelm@28321
   481
  | strip_shyps (thm as Thm (der, {thy_ref, tags, maxidx, shyps, hyps, tpairs, prop})) =
wenzelm@7642
   482
      let
wenzelm@16425
   483
        val thy = Theory.deref thy_ref;
wenzelm@26640
   484
        val present = present_sorts thm;
wenzelm@26640
   485
        val extra = Sorts.subtract present shyps;
wenzelm@28624
   486
        val extra' =
wenzelm@28624
   487
          Sorts.subtract (map #2 (Sign.witness_sorts thy present extra)) extra
wenzelm@28624
   488
          |> Sorts.minimal_sorts (Sign.classes_of thy);
wenzelm@28624
   489
        val shyps' = Sorts.union present extra';
wenzelm@7642
   490
      in
wenzelm@28321
   491
        Thm (der, {thy_ref = Theory.check_thy thy, tags = tags, maxidx = maxidx,
wenzelm@28321
   492
          shyps = shyps', hyps = hyps, tpairs = tpairs, prop = prop})
wenzelm@7642
   493
      end;
wenzelm@1238
   494
wenzelm@16656
   495
(*dangling sort constraints of a thm*)
wenzelm@28321
   496
fun extra_shyps (th as Thm (_, {shyps, ...})) = Sorts.subtract (present_sorts th) shyps;
wenzelm@28321
   497
wenzelm@28321
   498
wenzelm@28321
   499
wenzelm@28321
   500
(** derivations **)
wenzelm@28321
   501
wenzelm@28996
   502
fun make_deriv max_promise open_promises promises oracles thms proof =
wenzelm@28996
   503
  Deriv {max_promise = max_promise, open_promises = open_promises, promises = promises,
wenzelm@28804
   504
    body = PBody {oracles = oracles, thms = thms, proof = proof}};
wenzelm@28321
   505
wenzelm@28996
   506
val empty_deriv = make_deriv ~1 [] [] [] [] Pt.MinProof;
wenzelm@28321
   507
wenzelm@28330
   508
wenzelm@28354
   509
(* inference rules *)
wenzelm@28321
   510
wenzelm@28378
   511
fun promise_ord ((i, _), (j, _)) = int_ord (j, i);
wenzelm@28330
   512
wenzelm@28321
   513
fun deriv_rule2 f
wenzelm@28996
   514
    (Deriv {max_promise = max1, open_promises = open_ps1, promises = ps1,
wenzelm@28804
   515
      body = PBody {oracles = oras1, thms = thms1, proof = prf1}})
wenzelm@28996
   516
    (Deriv {max_promise = max2, open_promises = open_ps2, promises = ps2,
wenzelm@28804
   517
      body = PBody {oracles = oras2, thms = thms2, proof = prf2}}) =
wenzelm@28321
   518
  let
wenzelm@28996
   519
    val max = Int.max (max1, max2);
wenzelm@28996
   520
    val open_ps = OrdList.union promise_ord open_ps1 open_ps2;
wenzelm@28330
   521
    val ps = OrdList.union promise_ord ps1 ps2;
wenzelm@28804
   522
    val oras = Pt.merge_oracles oras1 oras2;
wenzelm@28804
   523
    val thms = Pt.merge_thms thms1 thms2;
wenzelm@28321
   524
    val prf =
wenzelm@28321
   525
      (case ! Pt.proofs of
wenzelm@28321
   526
        2 => f prf1 prf2
wenzelm@28804
   527
      | 1 => MinProof
wenzelm@28804
   528
      | 0 => MinProof
wenzelm@28321
   529
      | i => error ("Illegal level of detail for proof objects: " ^ string_of_int i));
wenzelm@28996
   530
  in make_deriv max open_ps ps oras thms prf end;
wenzelm@28321
   531
wenzelm@28321
   532
fun deriv_rule1 f = deriv_rule2 (K f) empty_deriv;
wenzelm@28996
   533
fun deriv_rule0 prf = deriv_rule1 I (make_deriv ~1 [] [] [] [] prf);
wenzelm@28321
   534
wenzelm@1238
   535
wenzelm@1238
   536
paulson@1529
   537
(** Axioms **)
wenzelm@387
   538
wenzelm@28675
   539
fun axiom theory name =
wenzelm@387
   540
  let
wenzelm@16425
   541
    fun get_ax thy =
wenzelm@22685
   542
      Symtab.lookup (Theory.axiom_table thy) name
wenzelm@16601
   543
      |> Option.map (fn prop =>
wenzelm@24143
   544
           let
wenzelm@28321
   545
             val der = deriv_rule0 (Pt.axm_proof name prop);
wenzelm@24143
   546
             val maxidx = maxidx_of_term prop;
wenzelm@26640
   547
             val shyps = Sorts.insert_term prop [];
wenzelm@24143
   548
           in
wenzelm@28321
   549
             Thm (der, {thy_ref = Theory.check_thy thy, tags = [],
wenzelm@28321
   550
               maxidx = maxidx, shyps = shyps, hyps = [], tpairs = [], prop = prop})
wenzelm@24143
   551
           end);
wenzelm@387
   552
  in
wenzelm@16425
   553
    (case get_first get_ax (theory :: Theory.ancestors_of theory) of
skalberg@15531
   554
      SOME thm => thm
skalberg@15531
   555
    | NONE => raise THEORY ("No axiom " ^ quote name, [theory]))
wenzelm@387
   556
  end;
wenzelm@387
   557
wenzelm@776
   558
(*return additional axioms of this theory node*)
wenzelm@776
   559
fun axioms_of thy =
wenzelm@28675
   560
  map (fn s => (s, axiom thy s)) (Symtab.keys (Theory.axiom_table thy));
wenzelm@776
   561
wenzelm@6089
   562
wenzelm@28804
   563
(* tags *)
wenzelm@6089
   564
wenzelm@21646
   565
val get_tags = #tags o rep_thm;
wenzelm@6089
   566
wenzelm@28321
   567
fun map_tags f (Thm (der, {thy_ref, tags, maxidx, shyps, hyps, tpairs, prop})) =
wenzelm@28321
   568
  Thm (der, {thy_ref = thy_ref, tags = f tags, maxidx = maxidx,
wenzelm@28321
   569
    shyps = shyps, hyps = hyps, tpairs = tpairs, prop = prop});
clasohm@0
   570
clasohm@0
   571
wenzelm@28321
   572
fun norm_proof (Thm (der, args as {thy_ref, ...})) =
wenzelm@24143
   573
  let
wenzelm@24143
   574
    val thy = Theory.deref thy_ref;
wenzelm@28321
   575
    val der' = deriv_rule1 (Pt.rew_proof thy) der;
wenzelm@28321
   576
    val _ = Theory.check_thy thy;
wenzelm@28321
   577
  in Thm (der', args) end;
berghofe@23781
   578
wenzelm@28321
   579
fun adjust_maxidx_thm i (th as Thm (der, {thy_ref, tags, maxidx, shyps, hyps, tpairs, prop})) =
wenzelm@20261
   580
  if maxidx = i then th
wenzelm@20261
   581
  else if maxidx < i then
wenzelm@28321
   582
    Thm (der, {maxidx = i, thy_ref = thy_ref, tags = tags, shyps = shyps,
wenzelm@28321
   583
      hyps = hyps, tpairs = tpairs, prop = prop})
wenzelm@20261
   584
  else
wenzelm@28321
   585
    Thm (der, {maxidx = Int.max (maxidx_tpairs tpairs (maxidx_of_term prop), i), thy_ref = thy_ref,
wenzelm@28321
   586
      tags = tags, shyps = shyps, hyps = hyps, tpairs = tpairs, prop = prop});
wenzelm@564
   587
wenzelm@387
   588
wenzelm@2509
   589
paulson@1529
   590
(*** Meta rules ***)
clasohm@0
   591
wenzelm@16601
   592
(** primitive rules **)
clasohm@0
   593
wenzelm@16656
   594
(*The assumption rule A |- A*)
wenzelm@16601
   595
fun assume raw_ct =
wenzelm@20261
   596
  let val Cterm {thy_ref, t = prop, T, maxidx, sorts} = adjust_maxidx_cterm ~1 raw_ct in
wenzelm@16601
   597
    if T <> propT then
mengj@19230
   598
      raise THM ("assume: prop", 0, [])
wenzelm@16601
   599
    else if maxidx <> ~1 then
mengj@19230
   600
      raise THM ("assume: variables", maxidx, [])
wenzelm@28321
   601
    else Thm (deriv_rule0 (Pt.Hyp prop),
wenzelm@28321
   602
     {thy_ref = thy_ref,
wenzelm@21646
   603
      tags = [],
wenzelm@16601
   604
      maxidx = ~1,
wenzelm@16601
   605
      shyps = sorts,
wenzelm@16601
   606
      hyps = [prop],
wenzelm@16601
   607
      tpairs = [],
wenzelm@28321
   608
      prop = prop})
clasohm@0
   609
  end;
clasohm@0
   610
wenzelm@1220
   611
(*Implication introduction
wenzelm@3529
   612
    [A]
wenzelm@3529
   613
     :
wenzelm@3529
   614
     B
wenzelm@1220
   615
  -------
wenzelm@1220
   616
  A ==> B
wenzelm@1220
   617
*)
wenzelm@16601
   618
fun implies_intr
wenzelm@16679
   619
    (ct as Cterm {t = A, T, maxidx = maxidxA, sorts, ...})
wenzelm@28321
   620
    (th as Thm (der, {maxidx, hyps, shyps, tpairs, prop, ...})) =
wenzelm@16601
   621
  if T <> propT then
wenzelm@16601
   622
    raise THM ("implies_intr: assumptions must have type prop", 0, [th])
wenzelm@16601
   623
  else
wenzelm@28321
   624
    Thm (deriv_rule1 (Pt.implies_intr_proof A) der,
wenzelm@28321
   625
     {thy_ref = merge_thys1 ct th,
wenzelm@21646
   626
      tags = [],
wenzelm@16601
   627
      maxidx = Int.max (maxidxA, maxidx),
wenzelm@16601
   628
      shyps = Sorts.union sorts shyps,
wenzelm@28354
   629
      hyps = remove_hyps A hyps,
wenzelm@16601
   630
      tpairs = tpairs,
wenzelm@28321
   631
      prop = Logic.mk_implies (A, prop)});
clasohm@0
   632
paulson@1529
   633
wenzelm@1220
   634
(*Implication elimination
wenzelm@1220
   635
  A ==> B    A
wenzelm@1220
   636
  ------------
wenzelm@1220
   637
        B
wenzelm@1220
   638
*)
wenzelm@16601
   639
fun implies_elim thAB thA =
wenzelm@16601
   640
  let
wenzelm@28321
   641
    val Thm (derA, {maxidx = maxA, hyps = hypsA, shyps = shypsA, tpairs = tpairsA,
wenzelm@28321
   642
      prop = propA, ...}) = thA
wenzelm@28321
   643
    and Thm (der, {maxidx, hyps, shyps, tpairs, prop, ...}) = thAB;
wenzelm@16601
   644
    fun err () = raise THM ("implies_elim: major premise", 0, [thAB, thA]);
wenzelm@16601
   645
  in
wenzelm@16601
   646
    case prop of
wenzelm@20512
   647
      Const ("==>", _) $ A $ B =>
wenzelm@20512
   648
        if A aconv propA then
wenzelm@28321
   649
          Thm (deriv_rule2 (curry Pt.%%) der derA,
wenzelm@28321
   650
           {thy_ref = merge_thys2 thAB thA,
wenzelm@21646
   651
            tags = [],
wenzelm@16601
   652
            maxidx = Int.max (maxA, maxidx),
wenzelm@16601
   653
            shyps = Sorts.union shypsA shyps,
wenzelm@16601
   654
            hyps = union_hyps hypsA hyps,
wenzelm@16601
   655
            tpairs = union_tpairs tpairsA tpairs,
wenzelm@28321
   656
            prop = B})
wenzelm@16601
   657
        else err ()
wenzelm@16601
   658
    | _ => err ()
wenzelm@16601
   659
  end;
wenzelm@250
   660
wenzelm@1220
   661
(*Forall introduction.  The Free or Var x must not be free in the hypotheses.
wenzelm@16656
   662
    [x]
wenzelm@16656
   663
     :
wenzelm@16656
   664
     A
wenzelm@16656
   665
  ------
wenzelm@16656
   666
  !!x. A
wenzelm@1220
   667
*)
wenzelm@16601
   668
fun forall_intr
wenzelm@16601
   669
    (ct as Cterm {t = x, T, sorts, ...})
wenzelm@28321
   670
    (th as Thm (der, {maxidx, shyps, hyps, tpairs, prop, ...})) =
wenzelm@16601
   671
  let
wenzelm@16601
   672
    fun result a =
wenzelm@28321
   673
      Thm (deriv_rule1 (Pt.forall_intr_proof x a) der,
wenzelm@28321
   674
       {thy_ref = merge_thys1 ct th,
wenzelm@21646
   675
        tags = [],
wenzelm@16601
   676
        maxidx = maxidx,
wenzelm@16601
   677
        shyps = Sorts.union sorts shyps,
wenzelm@16601
   678
        hyps = hyps,
wenzelm@16601
   679
        tpairs = tpairs,
wenzelm@28321
   680
        prop = Term.all T $ Abs (a, T, abstract_over (x, prop))});
wenzelm@21798
   681
    fun check_occs a x ts =
wenzelm@16847
   682
      if exists (fn t => Logic.occs (x, t)) ts then
wenzelm@21798
   683
        raise THM ("forall_intr: variable " ^ quote a ^ " free in assumptions", 0, [th])
wenzelm@16601
   684
      else ();
wenzelm@16601
   685
  in
wenzelm@16601
   686
    case x of
wenzelm@21798
   687
      Free (a, _) => (check_occs a x hyps; check_occs a x (terms_of_tpairs tpairs); result a)
wenzelm@21798
   688
    | Var ((a, _), _) => (check_occs a x (terms_of_tpairs tpairs); result a)
wenzelm@16601
   689
    | _ => raise THM ("forall_intr: not a variable", 0, [th])
clasohm@0
   690
  end;
clasohm@0
   691
wenzelm@1220
   692
(*Forall elimination
wenzelm@16656
   693
  !!x. A
wenzelm@1220
   694
  ------
wenzelm@1220
   695
  A[t/x]
wenzelm@1220
   696
*)
wenzelm@16601
   697
fun forall_elim
wenzelm@16601
   698
    (ct as Cterm {t, T, maxidx = maxt, sorts, ...})
wenzelm@28321
   699
    (th as Thm (der, {maxidx, shyps, hyps, tpairs, prop, ...})) =
wenzelm@16601
   700
  (case prop of
wenzelm@16601
   701
    Const ("all", Type ("fun", [Type ("fun", [qary, _]), _])) $ A =>
wenzelm@16601
   702
      if T <> qary then
wenzelm@16601
   703
        raise THM ("forall_elim: type mismatch", 0, [th])
wenzelm@16601
   704
      else
wenzelm@28321
   705
        Thm (deriv_rule1 (Pt.% o rpair (SOME t)) der,
wenzelm@28321
   706
         {thy_ref = merge_thys1 ct th,
wenzelm@21646
   707
          tags = [],
wenzelm@16601
   708
          maxidx = Int.max (maxidx, maxt),
wenzelm@16601
   709
          shyps = Sorts.union sorts shyps,
wenzelm@16601
   710
          hyps = hyps,
wenzelm@16601
   711
          tpairs = tpairs,
wenzelm@28321
   712
          prop = Term.betapply (A, t)})
wenzelm@16601
   713
  | _ => raise THM ("forall_elim: not quantified", 0, [th]));
clasohm@0
   714
clasohm@0
   715
wenzelm@1220
   716
(* Equality *)
clasohm@0
   717
wenzelm@16601
   718
(*Reflexivity
wenzelm@16601
   719
  t == t
wenzelm@16601
   720
*)
wenzelm@16601
   721
fun reflexive (ct as Cterm {thy_ref, t, T, maxidx, sorts}) =
wenzelm@28321
   722
  Thm (deriv_rule0 Pt.reflexive,
wenzelm@28321
   723
   {thy_ref = thy_ref,
wenzelm@21646
   724
    tags = [],
wenzelm@16601
   725
    maxidx = maxidx,
wenzelm@16601
   726
    shyps = sorts,
wenzelm@16601
   727
    hyps = [],
wenzelm@16601
   728
    tpairs = [],
wenzelm@28321
   729
    prop = Logic.mk_equals (t, t)});
clasohm@0
   730
wenzelm@16601
   731
(*Symmetry
wenzelm@16601
   732
  t == u
wenzelm@16601
   733
  ------
wenzelm@16601
   734
  u == t
wenzelm@1220
   735
*)
wenzelm@28321
   736
fun symmetric (th as Thm (der, {thy_ref, maxidx, shyps, hyps, tpairs, prop, ...})) =
wenzelm@16601
   737
  (case prop of
wenzelm@16601
   738
    (eq as Const ("==", Type (_, [T, _]))) $ t $ u =>
wenzelm@28321
   739
      Thm (deriv_rule1 Pt.symmetric der,
wenzelm@28321
   740
       {thy_ref = thy_ref,
wenzelm@21646
   741
        tags = [],
wenzelm@16601
   742
        maxidx = maxidx,
wenzelm@16601
   743
        shyps = shyps,
wenzelm@16601
   744
        hyps = hyps,
wenzelm@16601
   745
        tpairs = tpairs,
wenzelm@28321
   746
        prop = eq $ u $ t})
wenzelm@16601
   747
    | _ => raise THM ("symmetric", 0, [th]));
clasohm@0
   748
wenzelm@16601
   749
(*Transitivity
wenzelm@16601
   750
  t1 == u    u == t2
wenzelm@16601
   751
  ------------------
wenzelm@16601
   752
       t1 == t2
wenzelm@1220
   753
*)
clasohm@0
   754
fun transitive th1 th2 =
wenzelm@16601
   755
  let
wenzelm@28321
   756
    val Thm (der1, {maxidx = max1, hyps = hyps1, shyps = shyps1, tpairs = tpairs1,
wenzelm@28321
   757
      prop = prop1, ...}) = th1
wenzelm@28321
   758
    and Thm (der2, {maxidx = max2, hyps = hyps2, shyps = shyps2, tpairs = tpairs2,
wenzelm@28321
   759
      prop = prop2, ...}) = th2;
wenzelm@16601
   760
    fun err msg = raise THM ("transitive: " ^ msg, 0, [th1, th2]);
wenzelm@16601
   761
  in
wenzelm@16601
   762
    case (prop1, prop2) of
wenzelm@16601
   763
      ((eq as Const ("==", Type (_, [T, _]))) $ t1 $ u, Const ("==", _) $ u' $ t2) =>
wenzelm@16601
   764
        if not (u aconv u') then err "middle term"
wenzelm@16601
   765
        else
wenzelm@28321
   766
          Thm (deriv_rule2 (Pt.transitive u T) der1 der2,
wenzelm@28321
   767
           {thy_ref = merge_thys2 th1 th2,
wenzelm@21646
   768
            tags = [],
wenzelm@16601
   769
            maxidx = Int.max (max1, max2),
wenzelm@16601
   770
            shyps = Sorts.union shyps1 shyps2,
wenzelm@16601
   771
            hyps = union_hyps hyps1 hyps2,
wenzelm@16601
   772
            tpairs = union_tpairs tpairs1 tpairs2,
wenzelm@28321
   773
            prop = eq $ t1 $ t2})
wenzelm@16601
   774
     | _ =>  err "premises"
clasohm@0
   775
  end;
clasohm@0
   776
wenzelm@16601
   777
(*Beta-conversion
wenzelm@16656
   778
  (%x. t)(u) == t[u/x]
wenzelm@16601
   779
  fully beta-reduces the term if full = true
berghofe@10416
   780
*)
wenzelm@16601
   781
fun beta_conversion full (Cterm {thy_ref, t, T, maxidx, sorts}) =
wenzelm@16601
   782
  let val t' =
wenzelm@16601
   783
    if full then Envir.beta_norm t
wenzelm@16601
   784
    else
wenzelm@16601
   785
      (case t of Abs (_, _, bodt) $ u => subst_bound (u, bodt)
wenzelm@16601
   786
      | _ => raise THM ("beta_conversion: not a redex", 0, []));
wenzelm@16601
   787
  in
wenzelm@28321
   788
    Thm (deriv_rule0 Pt.reflexive,
wenzelm@28321
   789
     {thy_ref = thy_ref,
wenzelm@21646
   790
      tags = [],
wenzelm@16601
   791
      maxidx = maxidx,
wenzelm@16601
   792
      shyps = sorts,
wenzelm@16601
   793
      hyps = [],
wenzelm@16601
   794
      tpairs = [],
wenzelm@28321
   795
      prop = Logic.mk_equals (t, t')})
berghofe@10416
   796
  end;
berghofe@10416
   797
wenzelm@16601
   798
fun eta_conversion (Cterm {thy_ref, t, T, maxidx, sorts}) =
wenzelm@28321
   799
  Thm (deriv_rule0 Pt.reflexive,
wenzelm@28321
   800
   {thy_ref = thy_ref,
wenzelm@21646
   801
    tags = [],
wenzelm@16601
   802
    maxidx = maxidx,
wenzelm@16601
   803
    shyps = sorts,
wenzelm@16601
   804
    hyps = [],
wenzelm@16601
   805
    tpairs = [],
wenzelm@28321
   806
    prop = Logic.mk_equals (t, Envir.eta_contract t)});
clasohm@0
   807
wenzelm@23493
   808
fun eta_long_conversion (Cterm {thy_ref, t, T, maxidx, sorts}) =
wenzelm@28321
   809
  Thm (deriv_rule0 Pt.reflexive,
wenzelm@28321
   810
   {thy_ref = thy_ref,
wenzelm@23493
   811
    tags = [],
wenzelm@23493
   812
    maxidx = maxidx,
wenzelm@23493
   813
    shyps = sorts,
wenzelm@23493
   814
    hyps = [],
wenzelm@23493
   815
    tpairs = [],
wenzelm@28321
   816
    prop = Logic.mk_equals (t, Pattern.eta_long [] t)});
wenzelm@23493
   817
clasohm@0
   818
(*The abstraction rule.  The Free or Var x must not be free in the hypotheses.
clasohm@0
   819
  The bound variable will be named "a" (since x will be something like x320)
wenzelm@16601
   820
      t == u
wenzelm@16601
   821
  --------------
wenzelm@16601
   822
  %x. t == %x. u
wenzelm@1220
   823
*)
wenzelm@16601
   824
fun abstract_rule a
wenzelm@16601
   825
    (Cterm {t = x, T, sorts, ...})
wenzelm@28321
   826
    (th as Thm (der, {thy_ref, maxidx, hyps, shyps, tpairs, prop, ...})) =
wenzelm@16601
   827
  let
wenzelm@16601
   828
    val (t, u) = Logic.dest_equals prop
wenzelm@16601
   829
      handle TERM _ => raise THM ("abstract_rule: premise not an equality", 0, [th]);
wenzelm@16601
   830
    val result =
wenzelm@28321
   831
      Thm (deriv_rule1 (Pt.abstract_rule x a) der,
wenzelm@28321
   832
       {thy_ref = thy_ref,
wenzelm@21646
   833
        tags = [],
wenzelm@16601
   834
        maxidx = maxidx,
wenzelm@16601
   835
        shyps = Sorts.union sorts shyps,
wenzelm@16601
   836
        hyps = hyps,
wenzelm@16601
   837
        tpairs = tpairs,
wenzelm@16601
   838
        prop = Logic.mk_equals
wenzelm@28321
   839
          (Abs (a, T, abstract_over (x, t)), Abs (a, T, abstract_over (x, u)))});
wenzelm@21798
   840
    fun check_occs a x ts =
wenzelm@16847
   841
      if exists (fn t => Logic.occs (x, t)) ts then
wenzelm@21798
   842
        raise THM ("abstract_rule: variable " ^ quote a ^ " free in assumptions", 0, [th])
wenzelm@16601
   843
      else ();
wenzelm@16601
   844
  in
wenzelm@16601
   845
    case x of
wenzelm@21798
   846
      Free (a, _) => (check_occs a x hyps; check_occs a x (terms_of_tpairs tpairs); result)
wenzelm@21798
   847
    | Var ((a, _), _) => (check_occs a x (terms_of_tpairs tpairs); result)
wenzelm@21798
   848
    | _ => raise THM ("abstract_rule: not a variable", 0, [th])
clasohm@0
   849
  end;
clasohm@0
   850
clasohm@0
   851
(*The combination rule
wenzelm@3529
   852
  f == g  t == u
wenzelm@3529
   853
  --------------
wenzelm@16601
   854
    f t == g u
wenzelm@1220
   855
*)
clasohm@0
   856
fun combination th1 th2 =
wenzelm@16601
   857
  let
wenzelm@28321
   858
    val Thm (der1, {maxidx = max1, shyps = shyps1, hyps = hyps1, tpairs = tpairs1,
wenzelm@28321
   859
      prop = prop1, ...}) = th1
wenzelm@28321
   860
    and Thm (der2, {maxidx = max2, shyps = shyps2, hyps = hyps2, tpairs = tpairs2,
wenzelm@28321
   861
      prop = prop2, ...}) = th2;
wenzelm@16601
   862
    fun chktypes fT tT =
wenzelm@16601
   863
      (case fT of
wenzelm@16601
   864
        Type ("fun", [T1, T2]) =>
wenzelm@16601
   865
          if T1 <> tT then
wenzelm@16601
   866
            raise THM ("combination: types", 0, [th1, th2])
wenzelm@16601
   867
          else ()
wenzelm@16601
   868
      | _ => raise THM ("combination: not function type", 0, [th1, th2]));
wenzelm@16601
   869
  in
wenzelm@16601
   870
    case (prop1, prop2) of
wenzelm@16601
   871
      (Const ("==", Type ("fun", [fT, _])) $ f $ g,
wenzelm@16601
   872
       Const ("==", Type ("fun", [tT, _])) $ t $ u) =>
wenzelm@16601
   873
        (chktypes fT tT;
wenzelm@28321
   874
          Thm (deriv_rule2 (Pt.combination f g t u fT) der1 der2,
wenzelm@28321
   875
           {thy_ref = merge_thys2 th1 th2,
wenzelm@21646
   876
            tags = [],
wenzelm@16601
   877
            maxidx = Int.max (max1, max2),
wenzelm@16601
   878
            shyps = Sorts.union shyps1 shyps2,
wenzelm@16601
   879
            hyps = union_hyps hyps1 hyps2,
wenzelm@16601
   880
            tpairs = union_tpairs tpairs1 tpairs2,
wenzelm@28321
   881
            prop = Logic.mk_equals (f $ t, g $ u)}))
wenzelm@16601
   882
     | _ => raise THM ("combination: premises", 0, [th1, th2])
clasohm@0
   883
  end;
clasohm@0
   884
wenzelm@16601
   885
(*Equality introduction
wenzelm@3529
   886
  A ==> B  B ==> A
wenzelm@3529
   887
  ----------------
wenzelm@3529
   888
       A == B
wenzelm@1220
   889
*)
clasohm@0
   890
fun equal_intr th1 th2 =
wenzelm@16601
   891
  let
wenzelm@28321
   892
    val Thm (der1, {maxidx = max1, shyps = shyps1, hyps = hyps1, tpairs = tpairs1,
wenzelm@28321
   893
      prop = prop1, ...}) = th1
wenzelm@28321
   894
    and Thm (der2, {maxidx = max2, shyps = shyps2, hyps = hyps2, tpairs = tpairs2,
wenzelm@28321
   895
      prop = prop2, ...}) = th2;
wenzelm@16601
   896
    fun err msg = raise THM ("equal_intr: " ^ msg, 0, [th1, th2]);
wenzelm@16601
   897
  in
wenzelm@16601
   898
    case (prop1, prop2) of
wenzelm@16601
   899
      (Const("==>", _) $ A $ B, Const("==>", _) $ B' $ A') =>
wenzelm@16601
   900
        if A aconv A' andalso B aconv B' then
wenzelm@28321
   901
          Thm (deriv_rule2 (Pt.equal_intr A B) der1 der2,
wenzelm@28321
   902
           {thy_ref = merge_thys2 th1 th2,
wenzelm@21646
   903
            tags = [],
wenzelm@16601
   904
            maxidx = Int.max (max1, max2),
wenzelm@16601
   905
            shyps = Sorts.union shyps1 shyps2,
wenzelm@16601
   906
            hyps = union_hyps hyps1 hyps2,
wenzelm@16601
   907
            tpairs = union_tpairs tpairs1 tpairs2,
wenzelm@28321
   908
            prop = Logic.mk_equals (A, B)})
wenzelm@16601
   909
        else err "not equal"
wenzelm@16601
   910
    | _ =>  err "premises"
paulson@1529
   911
  end;
paulson@1529
   912
paulson@1529
   913
(*The equal propositions rule
wenzelm@3529
   914
  A == B  A
paulson@1529
   915
  ---------
paulson@1529
   916
      B
paulson@1529
   917
*)
paulson@1529
   918
fun equal_elim th1 th2 =
wenzelm@16601
   919
  let
wenzelm@28321
   920
    val Thm (der1, {maxidx = max1, shyps = shyps1, hyps = hyps1,
wenzelm@28321
   921
      tpairs = tpairs1, prop = prop1, ...}) = th1
wenzelm@28321
   922
    and Thm (der2, {maxidx = max2, shyps = shyps2, hyps = hyps2,
wenzelm@28321
   923
      tpairs = tpairs2, prop = prop2, ...}) = th2;
wenzelm@16601
   924
    fun err msg = raise THM ("equal_elim: " ^ msg, 0, [th1, th2]);
wenzelm@16601
   925
  in
wenzelm@16601
   926
    case prop1 of
wenzelm@16601
   927
      Const ("==", _) $ A $ B =>
wenzelm@16601
   928
        if prop2 aconv A then
wenzelm@28321
   929
          Thm (deriv_rule2 (Pt.equal_elim A B) der1 der2,
wenzelm@28321
   930
           {thy_ref = merge_thys2 th1 th2,
wenzelm@21646
   931
            tags = [],
wenzelm@16601
   932
            maxidx = Int.max (max1, max2),
wenzelm@16601
   933
            shyps = Sorts.union shyps1 shyps2,
wenzelm@16601
   934
            hyps = union_hyps hyps1 hyps2,
wenzelm@16601
   935
            tpairs = union_tpairs tpairs1 tpairs2,
wenzelm@28321
   936
            prop = B})
wenzelm@16601
   937
        else err "not equal"
paulson@1529
   938
     | _ =>  err"major premise"
paulson@1529
   939
  end;
clasohm@0
   940
wenzelm@1220
   941
wenzelm@1220
   942
clasohm@0
   943
(**** Derived rules ****)
clasohm@0
   944
wenzelm@16601
   945
(*Smash unifies the list of term pairs leaving no flex-flex pairs.
wenzelm@24143
   946
  Instantiates the theorem and deletes trivial tpairs.  Resulting
wenzelm@24143
   947
  sequence may contain multiple elements if the tpairs are not all
wenzelm@24143
   948
  flex-flex.*)
wenzelm@28321
   949
fun flexflex_rule (th as Thm (der, {thy_ref, maxidx, shyps, hyps, tpairs, prop, ...})) =
wenzelm@24143
   950
  let val thy = Theory.deref thy_ref in
wenzelm@24143
   951
    Unify.smash_unifiers thy tpairs (Envir.empty maxidx)
wenzelm@24143
   952
    |> Seq.map (fn env =>
wenzelm@24143
   953
        if Envir.is_empty env then th
wenzelm@24143
   954
        else
wenzelm@24143
   955
          let
wenzelm@24143
   956
            val tpairs' = tpairs |> map (pairself (Envir.norm_term env))
wenzelm@24143
   957
              (*remove trivial tpairs, of the form t==t*)
wenzelm@24143
   958
              |> filter_out (op aconv);
wenzelm@28321
   959
            val der' = deriv_rule1 (Pt.norm_proof' env) der;
wenzelm@24143
   960
            val prop' = Envir.norm_term env prop;
wenzelm@24143
   961
            val maxidx = maxidx_tpairs tpairs' (maxidx_of_term prop');
wenzelm@26640
   962
            val shyps = Envir.insert_sorts env shyps;
wenzelm@24143
   963
          in
wenzelm@28321
   964
            Thm (der', {thy_ref = Theory.check_thy thy, tags = [], maxidx = maxidx,
wenzelm@28321
   965
              shyps = shyps, hyps = hyps, tpairs = tpairs', prop = prop'})
wenzelm@24143
   966
          end)
wenzelm@24143
   967
  end;
wenzelm@16601
   968
clasohm@0
   969
wenzelm@19910
   970
(*Generalization of fixed variables
wenzelm@19910
   971
           A
wenzelm@19910
   972
  --------------------
wenzelm@19910
   973
  A[?'a/'a, ?x/x, ...]
wenzelm@19910
   974
*)
wenzelm@19910
   975
wenzelm@19910
   976
fun generalize ([], []) _ th = th
wenzelm@19910
   977
  | generalize (tfrees, frees) idx th =
wenzelm@19910
   978
      let
wenzelm@28321
   979
        val Thm (der, {thy_ref, maxidx, shyps, hyps, tpairs, prop, ...}) = th;
wenzelm@19910
   980
        val _ = idx <= maxidx andalso raise THM ("generalize: bad index", idx, [th]);
wenzelm@19910
   981
wenzelm@19910
   982
        val bad_type = if null tfrees then K false else
wenzelm@19910
   983
          Term.exists_subtype (fn TFree (a, _) => member (op =) tfrees a | _ => false);
wenzelm@19910
   984
        fun bad_term (Free (x, T)) = bad_type T orelse member (op =) frees x
wenzelm@19910
   985
          | bad_term (Var (_, T)) = bad_type T
wenzelm@19910
   986
          | bad_term (Const (_, T)) = bad_type T
wenzelm@19910
   987
          | bad_term (Abs (_, T, t)) = bad_type T orelse bad_term t
wenzelm@19910
   988
          | bad_term (t $ u) = bad_term t orelse bad_term u
wenzelm@19910
   989
          | bad_term (Bound _) = false;
wenzelm@19910
   990
        val _ = exists bad_term hyps andalso
wenzelm@19910
   991
          raise THM ("generalize: variable free in assumptions", 0, [th]);
wenzelm@19910
   992
wenzelm@20512
   993
        val gen = TermSubst.generalize (tfrees, frees) idx;
wenzelm@19910
   994
        val prop' = gen prop;
wenzelm@19910
   995
        val tpairs' = map (pairself gen) tpairs;
wenzelm@19910
   996
        val maxidx' = maxidx_tpairs tpairs' (maxidx_of_term prop');
wenzelm@19910
   997
      in
wenzelm@28321
   998
        Thm (deriv_rule1 (Pt.generalize (tfrees, frees) idx) der,
wenzelm@28321
   999
         {thy_ref = thy_ref,
wenzelm@21646
  1000
          tags = [],
wenzelm@19910
  1001
          maxidx = maxidx',
wenzelm@19910
  1002
          shyps = shyps,
wenzelm@19910
  1003
          hyps = hyps,
wenzelm@19910
  1004
          tpairs = tpairs',
wenzelm@28321
  1005
          prop = prop'})
wenzelm@19910
  1006
      end;
wenzelm@19910
  1007
wenzelm@19910
  1008
wenzelm@22584
  1009
(*Instantiation of schematic variables
wenzelm@16656
  1010
           A
wenzelm@16656
  1011
  --------------------
wenzelm@16656
  1012
  A[t1/v1, ..., tn/vn]
wenzelm@1220
  1013
*)
clasohm@0
  1014
wenzelm@6928
  1015
local
wenzelm@6928
  1016
wenzelm@26939
  1017
fun pretty_typing thy t T = Pretty.block
wenzelm@26939
  1018
  [Syntax.pretty_term_global thy t, Pretty.str " ::", Pretty.brk 1, Syntax.pretty_typ_global thy T];
berghofe@15797
  1019
wenzelm@16884
  1020
fun add_inst (ct, cu) (thy_ref, sorts) =
wenzelm@6928
  1021
  let
wenzelm@26939
  1022
    val Cterm {t = t, T = T, ...} = ct;
wenzelm@26939
  1023
    val Cterm {t = u, T = U, sorts = sorts_u, maxidx = maxidx_u, ...} = cu;
wenzelm@16884
  1024
    val thy_ref' = Theory.merge_refs (thy_ref, merge_thys0 ct cu);
wenzelm@16884
  1025
    val sorts' = Sorts.union sorts_u sorts;
wenzelm@3967
  1026
  in
wenzelm@16884
  1027
    (case t of Var v =>
wenzelm@20512
  1028
      if T = U then ((v, (u, maxidx_u)), (thy_ref', sorts'))
wenzelm@16884
  1029
      else raise TYPE (Pretty.string_of (Pretty.block
wenzelm@16884
  1030
       [Pretty.str "instantiate: type conflict",
wenzelm@16884
  1031
        Pretty.fbrk, pretty_typing (Theory.deref thy_ref') t T,
wenzelm@16884
  1032
        Pretty.fbrk, pretty_typing (Theory.deref thy_ref') u U]), [T, U], [t, u])
wenzelm@16884
  1033
    | _ => raise TYPE (Pretty.string_of (Pretty.block
wenzelm@16884
  1034
       [Pretty.str "instantiate: not a variable",
wenzelm@26939
  1035
        Pretty.fbrk, Syntax.pretty_term_global (Theory.deref thy_ref') t]), [], [t]))
clasohm@0
  1036
  end;
clasohm@0
  1037
wenzelm@16884
  1038
fun add_instT (cT, cU) (thy_ref, sorts) =
wenzelm@16656
  1039
  let
wenzelm@16884
  1040
    val Ctyp {T, thy_ref = thy_ref1, ...} = cT
wenzelm@20512
  1041
    and Ctyp {T = U, thy_ref = thy_ref2, sorts = sorts_U, maxidx = maxidx_U, ...} = cU;
wenzelm@24143
  1042
    val thy' = Theory.deref (Theory.merge_refs (thy_ref, Theory.merge_refs (thy_ref1, thy_ref2)));
wenzelm@16884
  1043
    val sorts' = Sorts.union sorts_U sorts;
wenzelm@16656
  1044
  in
wenzelm@16884
  1045
    (case T of TVar (v as (_, S)) =>
wenzelm@24143
  1046
      if Sign.of_sort thy' (U, S) then ((v, (U, maxidx_U)), (Theory.check_thy thy', sorts'))
wenzelm@26939
  1047
      else raise TYPE ("Type not of sort " ^ Syntax.string_of_sort_global thy' S, [U], [])
wenzelm@16656
  1048
    | _ => raise TYPE (Pretty.string_of (Pretty.block
berghofe@15797
  1049
        [Pretty.str "instantiate: not a type variable",
wenzelm@26939
  1050
         Pretty.fbrk, Syntax.pretty_typ_global thy' T]), [T], []))
wenzelm@16656
  1051
  end;
clasohm@0
  1052
wenzelm@6928
  1053
in
wenzelm@6928
  1054
wenzelm@16601
  1055
(*Left-to-right replacements: ctpairs = [..., (vi, ti), ...].
clasohm@0
  1056
  Instantiates distinct Vars by terms of same type.
wenzelm@16601
  1057
  Does NOT normalize the resulting theorem!*)
paulson@1529
  1058
fun instantiate ([], []) th = th
wenzelm@16884
  1059
  | instantiate (instT, inst) th =
wenzelm@16656
  1060
      let
wenzelm@28321
  1061
        val Thm (der, {thy_ref, hyps, shyps, tpairs, prop, ...}) = th;
wenzelm@16884
  1062
        val (inst', (instT', (thy_ref', shyps'))) =
wenzelm@16884
  1063
          (thy_ref, shyps) |> fold_map add_inst inst ||> fold_map add_instT instT;
wenzelm@20512
  1064
        val subst = TermSubst.instantiate_maxidx (instT', inst');
wenzelm@20512
  1065
        val (prop', maxidx1) = subst prop ~1;
wenzelm@20512
  1066
        val (tpairs', maxidx') =
wenzelm@20512
  1067
          fold_map (fn (t, u) => fn i => subst t i ||>> subst u) tpairs maxidx1;
wenzelm@16656
  1068
      in
wenzelm@28321
  1069
        Thm (deriv_rule1 (fn d => Pt.instantiate (map (apsnd #1) instT', map (apsnd #1) inst') d) der,
wenzelm@28321
  1070
         {thy_ref = thy_ref',
wenzelm@21646
  1071
          tags = [],
wenzelm@20545
  1072
          maxidx = maxidx',
wenzelm@20545
  1073
          shyps = shyps',
wenzelm@20545
  1074
          hyps = hyps,
wenzelm@20545
  1075
          tpairs = tpairs',
wenzelm@28321
  1076
          prop = prop'})
wenzelm@16656
  1077
      end
wenzelm@16656
  1078
      handle TYPE (msg, _, _) => raise THM (msg, 0, [th]);
wenzelm@6928
  1079
wenzelm@22584
  1080
fun instantiate_cterm ([], []) ct = ct
wenzelm@22584
  1081
  | instantiate_cterm (instT, inst) ct =
wenzelm@22584
  1082
      let
wenzelm@22584
  1083
        val Cterm {thy_ref, t, T, sorts, ...} = ct;
wenzelm@22584
  1084
        val (inst', (instT', (thy_ref', sorts'))) =
wenzelm@22584
  1085
          (thy_ref, sorts) |> fold_map add_inst inst ||> fold_map add_instT instT;
wenzelm@22584
  1086
        val subst = TermSubst.instantiate_maxidx (instT', inst');
wenzelm@22584
  1087
        val substT = TermSubst.instantiateT_maxidx instT';
wenzelm@22584
  1088
        val (t', maxidx1) = subst t ~1;
wenzelm@22584
  1089
        val (T', maxidx') = substT T maxidx1;
wenzelm@22584
  1090
      in Cterm {thy_ref = thy_ref', t = t', T = T', sorts = sorts', maxidx = maxidx'} end
wenzelm@22584
  1091
      handle TYPE (msg, _, _) => raise CTERM (msg, [ct]);
wenzelm@22584
  1092
wenzelm@6928
  1093
end;
wenzelm@6928
  1094
clasohm@0
  1095
wenzelm@16601
  1096
(*The trivial implication A ==> A, justified by assume and forall rules.
wenzelm@16601
  1097
  A can contain Vars, not so for assume!*)
wenzelm@16601
  1098
fun trivial (Cterm {thy_ref, t =A, T, maxidx, sorts}) =
wenzelm@16601
  1099
  if T <> propT then
wenzelm@16601
  1100
    raise THM ("trivial: the term must have type prop", 0, [])
wenzelm@16601
  1101
  else
wenzelm@28321
  1102
    Thm (deriv_rule0 (Pt.AbsP ("H", NONE, Pt.PBound 0)),
wenzelm@28321
  1103
     {thy_ref = thy_ref,
wenzelm@21646
  1104
      tags = [],
wenzelm@16601
  1105
      maxidx = maxidx,
wenzelm@16601
  1106
      shyps = sorts,
wenzelm@16601
  1107
      hyps = [],
wenzelm@16601
  1108
      tpairs = [],
wenzelm@28321
  1109
      prop = Logic.mk_implies (A, A)});
clasohm@0
  1110
paulson@1503
  1111
(*Axiom-scheme reflecting signature contents: "OFCLASS(?'a::c, c_class)" *)
wenzelm@16425
  1112
fun class_triv thy c =
wenzelm@24143
  1113
  let
wenzelm@24143
  1114
    val Cterm {t, maxidx, sorts, ...} =
wenzelm@24848
  1115
      cterm_of thy (Logic.mk_inclass (TVar ((Name.aT, 0), [c]), Sign.certify_class thy c))
wenzelm@24143
  1116
        handle TERM (msg, _) => raise THM ("class_triv: " ^ msg, 0, []);
wenzelm@28321
  1117
    val der = deriv_rule0 (Pt.PAxm ("Pure.class_triv:" ^ c, t, SOME []));
wenzelm@399
  1118
  in
wenzelm@28321
  1119
    Thm (der, {thy_ref = Theory.check_thy thy, tags = [], maxidx = maxidx,
wenzelm@28321
  1120
      shyps = sorts, hyps = [], tpairs = [], prop = t})
wenzelm@399
  1121
  end;
wenzelm@399
  1122
wenzelm@19505
  1123
(*Internalize sort constraints of type variable*)
wenzelm@19505
  1124
fun unconstrainT
wenzelm@19505
  1125
    (Ctyp {thy_ref = thy_ref1, T, ...})
wenzelm@28321
  1126
    (th as Thm (_, {thy_ref = thy_ref2, maxidx, shyps, hyps, tpairs, prop, ...})) =
wenzelm@19505
  1127
  let
wenzelm@19505
  1128
    val ((x, i), S) = Term.dest_TVar T handle TYPE _ =>
wenzelm@19505
  1129
      raise THM ("unconstrainT: not a type variable", 0, [th]);
wenzelm@19505
  1130
    val T' = TVar ((x, i), []);
wenzelm@20548
  1131
    val unconstrain = Term.map_types (Term.map_atyps (fn U => if U = T then T' else U));
wenzelm@19505
  1132
    val constraints = map (curry Logic.mk_inclass T') S;
wenzelm@19505
  1133
  in
wenzelm@28321
  1134
    Thm (deriv_rule0 (Pt.PAxm ("Pure.unconstrainT", prop, SOME [])),
wenzelm@28321
  1135
     {thy_ref = Theory.merge_refs (thy_ref1, thy_ref2),
wenzelm@21646
  1136
      tags = [],
wenzelm@19505
  1137
      maxidx = Int.max (maxidx, i),
wenzelm@19505
  1138
      shyps = Sorts.remove_sort S shyps,
wenzelm@19505
  1139
      hyps = hyps,
wenzelm@19505
  1140
      tpairs = map (pairself unconstrain) tpairs,
wenzelm@28321
  1141
      prop = Logic.list_implies (constraints, unconstrain prop)})
wenzelm@19505
  1142
  end;
wenzelm@399
  1143
wenzelm@6786
  1144
(* Replace all TFrees not fixed or in the hyps by new TVars *)
wenzelm@28321
  1145
fun varifyT' fixed (Thm (der, {thy_ref, maxidx, shyps, hyps, tpairs, prop, ...})) =
wenzelm@12500
  1146
  let
wenzelm@29272
  1147
    val tfrees = fold Term.add_tfrees hyps fixed;
berghofe@13658
  1148
    val prop1 = attach_tpairs tpairs prop;
haftmann@21116
  1149
    val (al, prop2) = Type.varify tfrees prop1;
wenzelm@16601
  1150
    val (ts, prop3) = Logic.strip_prems (length tpairs, [], prop2);
wenzelm@16601
  1151
  in
wenzelm@28321
  1152
    (al, Thm (deriv_rule1 (Pt.varify_proof prop tfrees) der,
wenzelm@28321
  1153
     {thy_ref = thy_ref,
wenzelm@21646
  1154
      tags = [],
wenzelm@16601
  1155
      maxidx = Int.max (0, maxidx),
wenzelm@16601
  1156
      shyps = shyps,
wenzelm@16601
  1157
      hyps = hyps,
wenzelm@16601
  1158
      tpairs = rev (map Logic.dest_equals ts),
wenzelm@28321
  1159
      prop = prop3}))
wenzelm@28321
  1160
  end;
wenzelm@28321
  1161
wenzelm@28321
  1162
val varifyT = #2 o varifyT' [];
wenzelm@28321
  1163
wenzelm@28321
  1164
(* Replace all TVars by new TFrees *)
wenzelm@28321
  1165
fun freezeT (Thm (der, {thy_ref, maxidx, shyps, hyps, tpairs, prop, ...})) =
wenzelm@28321
  1166
  let
wenzelm@28321
  1167
    val prop1 = attach_tpairs tpairs prop;
wenzelm@28321
  1168
    val prop2 = Type.freeze prop1;
wenzelm@28321
  1169
    val (ts, prop3) = Logic.strip_prems (length tpairs, [], prop2);
wenzelm@28321
  1170
  in
wenzelm@28321
  1171
    Thm (deriv_rule1 (Pt.freezeT prop1) der,
wenzelm@28321
  1172
     {thy_ref = thy_ref,
wenzelm@28321
  1173
      tags = [],
wenzelm@28321
  1174
      maxidx = maxidx_of_term prop2,
wenzelm@28321
  1175
      shyps = shyps,
wenzelm@28321
  1176
      hyps = hyps,
wenzelm@28321
  1177
      tpairs = rev (map Logic.dest_equals ts),
wenzelm@18127
  1178
      prop = prop3})
clasohm@0
  1179
  end;
clasohm@0
  1180
clasohm@0
  1181
clasohm@0
  1182
(*** Inference rules for tactics ***)
clasohm@0
  1183
clasohm@0
  1184
(*Destruct proof state into constraints, other goals, goal(i), rest *)
wenzelm@28321
  1185
fun dest_state (state as Thm (_, {prop,tpairs,...}), i) =
berghofe@13658
  1186
  (case  Logic.strip_prems(i, [], prop) of
berghofe@13658
  1187
      (B::rBs, C) => (tpairs, rev rBs, B, C)
berghofe@13658
  1188
    | _ => raise THM("dest_state", i, [state]))
clasohm@0
  1189
  handle TERM _ => raise THM("dest_state", i, [state]);
clasohm@0
  1190
lcp@309
  1191
(*Increment variables and parameters of orule as required for
wenzelm@18035
  1192
  resolution with a goal.*)
wenzelm@18035
  1193
fun lift_rule goal orule =
wenzelm@16601
  1194
  let
wenzelm@18035
  1195
    val Cterm {t = gprop, T, maxidx = gmax, sorts, ...} = goal;
wenzelm@18035
  1196
    val inc = gmax + 1;
wenzelm@18035
  1197
    val lift_abs = Logic.lift_abs inc gprop;
wenzelm@18035
  1198
    val lift_all = Logic.lift_all inc gprop;
wenzelm@28321
  1199
    val Thm (der, {maxidx, shyps, hyps, tpairs, prop, ...}) = orule;
wenzelm@16601
  1200
    val (As, B) = Logic.strip_horn prop;
wenzelm@16601
  1201
  in
wenzelm@18035
  1202
    if T <> propT then raise THM ("lift_rule: the term must have type prop", 0, [])
wenzelm@18035
  1203
    else
wenzelm@28321
  1204
      Thm (deriv_rule1 (Pt.lift_proof gprop inc prop) der,
wenzelm@28321
  1205
       {thy_ref = merge_thys1 goal orule,
wenzelm@21646
  1206
        tags = [],
wenzelm@18035
  1207
        maxidx = maxidx + inc,
wenzelm@18035
  1208
        shyps = Sorts.union shyps sorts,  (*sic!*)
wenzelm@18035
  1209
        hyps = hyps,
wenzelm@18035
  1210
        tpairs = map (pairself lift_abs) tpairs,
wenzelm@28321
  1211
        prop = Logic.list_implies (map lift_all As, lift_all B)})
clasohm@0
  1212
  end;
clasohm@0
  1213
wenzelm@28321
  1214
fun incr_indexes i (thm as Thm (der, {thy_ref, maxidx, shyps, hyps, tpairs, prop, ...})) =
wenzelm@16601
  1215
  if i < 0 then raise THM ("negative increment", 0, [thm])
wenzelm@16601
  1216
  else if i = 0 then thm
wenzelm@16601
  1217
  else
wenzelm@28321
  1218
    Thm (deriv_rule1 (Pt.map_proof_terms (Logic.incr_indexes ([], i)) (Logic.incr_tvar i)) der,
wenzelm@28321
  1219
     {thy_ref = thy_ref,
wenzelm@21646
  1220
      tags = [],
wenzelm@16601
  1221
      maxidx = maxidx + i,
wenzelm@16601
  1222
      shyps = shyps,
wenzelm@16601
  1223
      hyps = hyps,
wenzelm@16601
  1224
      tpairs = map (pairself (Logic.incr_indexes ([], i))) tpairs,
wenzelm@28321
  1225
      prop = Logic.incr_indexes ([], i) prop});
berghofe@10416
  1226
clasohm@0
  1227
(*Solve subgoal Bi of proof state B1...Bn/C by assumption. *)
clasohm@0
  1228
fun assumption i state =
wenzelm@16601
  1229
  let
wenzelm@28321
  1230
    val Thm (der, {thy_ref, maxidx, shyps, hyps, prop, ...}) = state;
wenzelm@16656
  1231
    val thy = Theory.deref thy_ref;
wenzelm@16601
  1232
    val (tpairs, Bs, Bi, C) = dest_state (state, i);
wenzelm@16601
  1233
    fun newth n (env as Envir.Envir {maxidx, ...}, tpairs) =
wenzelm@28321
  1234
      Thm (deriv_rule1
wenzelm@16601
  1235
          ((if Envir.is_empty env then I else (Pt.norm_proof' env)) o
wenzelm@16601
  1236
            Pt.assumption_proof Bs Bi n) der,
wenzelm@28321
  1237
       {tags = [],
wenzelm@16601
  1238
        maxidx = maxidx,
wenzelm@26640
  1239
        shyps = Envir.insert_sorts env shyps,
wenzelm@16601
  1240
        hyps = hyps,
wenzelm@16601
  1241
        tpairs =
wenzelm@16601
  1242
          if Envir.is_empty env then tpairs
wenzelm@16601
  1243
          else map (pairself (Envir.norm_term env)) tpairs,
wenzelm@16601
  1244
        prop =
wenzelm@16601
  1245
          if Envir.is_empty env then (*avoid wasted normalizations*)
wenzelm@16601
  1246
            Logic.list_implies (Bs, C)
wenzelm@16601
  1247
          else (*normalize the new rule fully*)
wenzelm@24143
  1248
            Envir.norm_term env (Logic.list_implies (Bs, C)),
wenzelm@28321
  1249
        thy_ref = Theory.check_thy thy});
wenzelm@16601
  1250
    fun addprfs [] _ = Seq.empty
wenzelm@16601
  1251
      | addprfs ((t, u) :: apairs) n = Seq.make (fn () => Seq.pull
wenzelm@16601
  1252
          (Seq.mapp (newth n)
wenzelm@16656
  1253
            (Unify.unifiers (thy, Envir.empty maxidx, (t, u) :: tpairs))
wenzelm@16601
  1254
            (addprfs apairs (n + 1))))
wenzelm@16601
  1255
  in addprfs (Logic.assum_pairs (~1, Bi)) 1 end;
clasohm@0
  1256
wenzelm@250
  1257
(*Solve subgoal Bi of proof state B1...Bn/C by assumption.
clasohm@0
  1258
  Checks if Bi's conclusion is alpha-convertible to one of its assumptions*)
clasohm@0
  1259
fun eq_assumption i state =
wenzelm@16601
  1260
  let
wenzelm@28321
  1261
    val Thm (der, {thy_ref, maxidx, shyps, hyps, prop, ...}) = state;
wenzelm@16601
  1262
    val (tpairs, Bs, Bi, C) = dest_state (state, i);
wenzelm@16601
  1263
  in
berghofe@26832
  1264
    (case find_index Pattern.aeconv (Logic.assum_pairs (~1, Bi)) of
wenzelm@16601
  1265
      ~1 => raise THM ("eq_assumption", 0, [state])
wenzelm@16601
  1266
    | n =>
wenzelm@28321
  1267
        Thm (deriv_rule1 (Pt.assumption_proof Bs Bi (n + 1)) der,
wenzelm@28321
  1268
         {thy_ref = thy_ref,
wenzelm@21646
  1269
          tags = [],
wenzelm@16601
  1270
          maxidx = maxidx,
wenzelm@16601
  1271
          shyps = shyps,
wenzelm@16601
  1272
          hyps = hyps,
wenzelm@16601
  1273
          tpairs = tpairs,
wenzelm@28321
  1274
          prop = Logic.list_implies (Bs, C)}))
clasohm@0
  1275
  end;
clasohm@0
  1276
clasohm@0
  1277
paulson@2671
  1278
(*For rotate_tac: fast rotation of assumptions of subgoal i*)
paulson@2671
  1279
fun rotate_rule k i state =
wenzelm@16601
  1280
  let
wenzelm@28321
  1281
    val Thm (der, {thy_ref, maxidx, shyps, hyps, prop, ...}) = state;
wenzelm@16601
  1282
    val (tpairs, Bs, Bi, C) = dest_state (state, i);
wenzelm@16601
  1283
    val params = Term.strip_all_vars Bi
wenzelm@16601
  1284
    and rest   = Term.strip_all_body Bi;
wenzelm@16601
  1285
    val asms   = Logic.strip_imp_prems rest
wenzelm@16601
  1286
    and concl  = Logic.strip_imp_concl rest;
wenzelm@16601
  1287
    val n = length asms;
wenzelm@16601
  1288
    val m = if k < 0 then n + k else k;
wenzelm@16601
  1289
    val Bi' =
wenzelm@16601
  1290
      if 0 = m orelse m = n then Bi
wenzelm@16601
  1291
      else if 0 < m andalso m < n then
wenzelm@19012
  1292
        let val (ps, qs) = chop m asms
wenzelm@16601
  1293
        in list_all (params, Logic.list_implies (qs @ ps, concl)) end
wenzelm@16601
  1294
      else raise THM ("rotate_rule", k, [state]);
wenzelm@16601
  1295
  in
wenzelm@28321
  1296
    Thm (deriv_rule1 (Pt.rotate_proof Bs Bi m) der,
wenzelm@28321
  1297
     {thy_ref = thy_ref,
wenzelm@21646
  1298
      tags = [],
wenzelm@16601
  1299
      maxidx = maxidx,
wenzelm@16601
  1300
      shyps = shyps,
wenzelm@16601
  1301
      hyps = hyps,
wenzelm@16601
  1302
      tpairs = tpairs,
wenzelm@28321
  1303
      prop = Logic.list_implies (Bs @ [Bi'], C)})
paulson@2671
  1304
  end;
paulson@2671
  1305
paulson@2671
  1306
paulson@7248
  1307
(*Rotates a rule's premises to the left by k, leaving the first j premises
paulson@7248
  1308
  unchanged.  Does nothing if k=0 or if k equals n-j, where n is the
wenzelm@16656
  1309
  number of premises.  Useful with etac and underlies defer_tac*)
paulson@7248
  1310
fun permute_prems j k rl =
wenzelm@16601
  1311
  let
wenzelm@28321
  1312
    val Thm (der, {thy_ref, maxidx, shyps, hyps, tpairs, prop, ...}) = rl;
wenzelm@16601
  1313
    val prems = Logic.strip_imp_prems prop
wenzelm@16601
  1314
    and concl = Logic.strip_imp_concl prop;
wenzelm@16601
  1315
    val moved_prems = List.drop (prems, j)
wenzelm@16601
  1316
    and fixed_prems = List.take (prems, j)
wenzelm@16601
  1317
      handle Subscript => raise THM ("permute_prems: j", j, [rl]);
wenzelm@16601
  1318
    val n_j = length moved_prems;
wenzelm@16601
  1319
    val m = if k < 0 then n_j + k else k;
wenzelm@16601
  1320
    val prop' =
wenzelm@16601
  1321
      if 0 = m orelse m = n_j then prop
wenzelm@16601
  1322
      else if 0 < m andalso m < n_j then
wenzelm@19012
  1323
        let val (ps, qs) = chop m moved_prems
wenzelm@16601
  1324
        in Logic.list_implies (fixed_prems @ qs @ ps, concl) end
wenzelm@16725
  1325
      else raise THM ("permute_prems: k", k, [rl]);
wenzelm@16601
  1326
  in
wenzelm@28321
  1327
    Thm (deriv_rule1 (Pt.permute_prems_prf prems j m) der,
wenzelm@28321
  1328
     {thy_ref = thy_ref,
wenzelm@21646
  1329
      tags = [],
wenzelm@16601
  1330
      maxidx = maxidx,
wenzelm@16601
  1331
      shyps = shyps,
wenzelm@16601
  1332
      hyps = hyps,
wenzelm@16601
  1333
      tpairs = tpairs,
wenzelm@28321
  1334
      prop = prop'})
paulson@7248
  1335
  end;
paulson@7248
  1336
paulson@7248
  1337
clasohm@0
  1338
(** User renaming of parameters in a subgoal **)
clasohm@0
  1339
clasohm@0
  1340
(*Calls error rather than raising an exception because it is intended
clasohm@0
  1341
  for top-level use -- exception handling would not make sense here.
clasohm@0
  1342
  The names in cs, if distinct, are used for the innermost parameters;
wenzelm@17868
  1343
  preceding parameters may be renamed to make all params distinct.*)
clasohm@0
  1344
fun rename_params_rule (cs, i) state =
wenzelm@16601
  1345
  let
wenzelm@28321
  1346
    val Thm (der, {thy_ref, tags, maxidx, shyps, hyps, ...}) = state;
wenzelm@16601
  1347
    val (tpairs, Bs, Bi, C) = dest_state (state, i);
wenzelm@16601
  1348
    val iparams = map #1 (Logic.strip_params Bi);
wenzelm@16601
  1349
    val short = length iparams - length cs;
wenzelm@16601
  1350
    val newnames =
wenzelm@16601
  1351
      if short < 0 then error "More names than abstractions!"
wenzelm@20071
  1352
      else Name.variant_list cs (Library.take (short, iparams)) @ cs;
wenzelm@20330
  1353
    val freenames = Term.fold_aterms (fn Free (x, _) => insert (op =) x | _ => I) Bi [];
wenzelm@16601
  1354
    val newBi = Logic.list_rename_params (newnames, Bi);
wenzelm@250
  1355
  in
wenzelm@21182
  1356
    (case duplicates (op =) cs of
wenzelm@21182
  1357
      a :: _ => (warning ("Can't rename.  Bound variables not distinct: " ^ a); state)
wenzelm@21182
  1358
    | [] =>
wenzelm@16601
  1359
      (case cs inter_string freenames of
wenzelm@16601
  1360
        a :: _ => (warning ("Can't rename.  Bound/Free variable clash: " ^ a); state)
wenzelm@16601
  1361
      | [] =>
wenzelm@28321
  1362
        Thm (der,
wenzelm@28321
  1363
         {thy_ref = thy_ref,
wenzelm@21646
  1364
          tags = tags,
wenzelm@16601
  1365
          maxidx = maxidx,
wenzelm@16601
  1366
          shyps = shyps,
wenzelm@16601
  1367
          hyps = hyps,
wenzelm@16601
  1368
          tpairs = tpairs,
wenzelm@28321
  1369
          prop = Logic.list_implies (Bs @ [newBi], C)})))
clasohm@0
  1370
  end;
clasohm@0
  1371
wenzelm@12982
  1372
clasohm@0
  1373
(*** Preservation of bound variable names ***)
clasohm@0
  1374
wenzelm@28321
  1375
fun rename_boundvars pat obj (thm as Thm (der, {thy_ref, tags, maxidx, shyps, hyps, tpairs, prop})) =
wenzelm@12982
  1376
  (case Term.rename_abs pat obj prop of
skalberg@15531
  1377
    NONE => thm
wenzelm@28321
  1378
  | SOME prop' => Thm (der,
wenzelm@16425
  1379
      {thy_ref = thy_ref,
wenzelm@21646
  1380
       tags = tags,
wenzelm@12982
  1381
       maxidx = maxidx,
wenzelm@12982
  1382
       hyps = hyps,
wenzelm@12982
  1383
       shyps = shyps,
berghofe@13658
  1384
       tpairs = tpairs,
wenzelm@28321
  1385
       prop = prop'}));
berghofe@10416
  1386
clasohm@0
  1387
wenzelm@16656
  1388
(* strip_apply f (A, B) strips off all assumptions/parameters from A
clasohm@0
  1389
   introduced by lifting over B, and applies f to remaining part of A*)
clasohm@0
  1390
fun strip_apply f =
clasohm@0
  1391
  let fun strip(Const("==>",_)$ A1 $ B1,
wenzelm@27336
  1392
                Const("==>",_)$ _  $ B2) = Logic.mk_implies (A1, strip(B1,B2))
wenzelm@250
  1393
        | strip((c as Const("all",_)) $ Abs(a,T,t1),
wenzelm@250
  1394
                      Const("all",_)  $ Abs(_,_,t2)) = c$Abs(a,T,strip(t1,t2))
wenzelm@250
  1395
        | strip(A,_) = f A
clasohm@0
  1396
  in strip end;
clasohm@0
  1397
clasohm@0
  1398
(*Use the alist to rename all bound variables and some unknowns in a term
clasohm@0
  1399
  dpairs = current disagreement pairs;  tpairs = permanent ones (flexflex);
clasohm@0
  1400
  Preserves unknowns in tpairs and on lhs of dpairs. *)
clasohm@0
  1401
fun rename_bvs([],_,_,_) = I
clasohm@0
  1402
  | rename_bvs(al,dpairs,tpairs,B) =
wenzelm@20330
  1403
      let
wenzelm@20330
  1404
        val add_var = fold_aterms (fn Var ((x, _), _) => insert (op =) x | _ => I);
wenzelm@20330
  1405
        val vids = []
wenzelm@20330
  1406
          |> fold (add_var o fst) dpairs
wenzelm@20330
  1407
          |> fold (add_var o fst) tpairs
wenzelm@20330
  1408
          |> fold (add_var o snd) tpairs;
wenzelm@250
  1409
        (*unknowns appearing elsewhere be preserved!*)
wenzelm@250
  1410
        fun rename(t as Var((x,i),T)) =
wenzelm@20330
  1411
              (case AList.lookup (op =) al x of
wenzelm@20330
  1412
                SOME y =>
wenzelm@20330
  1413
                  if member (op =) vids x orelse member (op =) vids y then t
wenzelm@20330
  1414
                  else Var((y,i),T)
wenzelm@20330
  1415
              | NONE=> t)
clasohm@0
  1416
          | rename(Abs(x,T,t)) =
wenzelm@18944
  1417
              Abs (the_default x (AList.lookup (op =) al x), T, rename t)
clasohm@0
  1418
          | rename(f$t) = rename f $ rename t
clasohm@0
  1419
          | rename(t) = t;
wenzelm@250
  1420
        fun strip_ren Ai = strip_apply rename (Ai,B)
wenzelm@20330
  1421
      in strip_ren end;
clasohm@0
  1422
clasohm@0
  1423
(*Function to rename bounds/unknowns in the argument, lifted over B*)
clasohm@0
  1424
fun rename_bvars(dpairs, tpairs, B) =
wenzelm@23178
  1425
        rename_bvs(List.foldr Term.match_bvars [] dpairs, dpairs, tpairs, B);
clasohm@0
  1426
clasohm@0
  1427
clasohm@0
  1428
(*** RESOLUTION ***)
clasohm@0
  1429
lcp@721
  1430
(** Lifting optimizations **)
lcp@721
  1431
clasohm@0
  1432
(*strip off pairs of assumptions/parameters in parallel -- they are
clasohm@0
  1433
  identical because of lifting*)
wenzelm@250
  1434
fun strip_assums2 (Const("==>", _) $ _ $ B1,
wenzelm@250
  1435
                   Const("==>", _) $ _ $ B2) = strip_assums2 (B1,B2)
clasohm@0
  1436
  | strip_assums2 (Const("all",_)$Abs(a,T,t1),
wenzelm@250
  1437
                   Const("all",_)$Abs(_,_,t2)) =
clasohm@0
  1438
      let val (B1,B2) = strip_assums2 (t1,t2)
clasohm@0
  1439
      in  (Abs(a,T,B1), Abs(a,T,B2))  end
clasohm@0
  1440
  | strip_assums2 BB = BB;
clasohm@0
  1441
clasohm@0
  1442
lcp@721
  1443
(*Faster normalization: skip assumptions that were lifted over*)
lcp@721
  1444
fun norm_term_skip env 0 t = Envir.norm_term env t
lcp@721
  1445
  | norm_term_skip env n (Const("all",_)$Abs(a,T,t)) =
lcp@721
  1446
        let val Envir.Envir{iTs, ...} = env
berghofe@15797
  1447
            val T' = Envir.typ_subst_TVars iTs T
wenzelm@1238
  1448
            (*Must instantiate types of parameters because they are flattened;
lcp@721
  1449
              this could be a NEW parameter*)
wenzelm@27336
  1450
        in Term.all T' $ Abs(a, T', norm_term_skip env n t)  end
lcp@721
  1451
  | norm_term_skip env n (Const("==>", _) $ A $ B) =
wenzelm@27336
  1452
        Logic.mk_implies (A, norm_term_skip env (n-1) B)
lcp@721
  1453
  | norm_term_skip env n t = error"norm_term_skip: too few assumptions??";
lcp@721
  1454
lcp@721
  1455
clasohm@0
  1456
(*Composition of object rule r=(A1...Am/B) with proof state s=(B1...Bn/C)
wenzelm@250
  1457
  Unifies B with Bi, replacing subgoal i    (1 <= i <= n)
clasohm@0
  1458
  If match then forbid instantiations in proof state
clasohm@0
  1459
  If lifted then shorten the dpair using strip_assums2.
clasohm@0
  1460
  If eres_flg then simultaneously proves A1 by assumption.
wenzelm@250
  1461
  nsubgoal is the number of new subgoals (written m above).
clasohm@0
  1462
  Curried so that resolution calls dest_state only once.
clasohm@0
  1463
*)
wenzelm@4270
  1464
local exception COMPOSE
clasohm@0
  1465
in
wenzelm@18486
  1466
fun bicompose_aux flatten match (state, (stpairs, Bs, Bi, C), lifted)
clasohm@0
  1467
                        (eres_flg, orule, nsubgoal) =
wenzelm@28321
  1468
 let val Thm (sder, {maxidx=smax, shyps=sshyps, hyps=shyps, ...}) = state
wenzelm@28321
  1469
     and Thm (rder, {maxidx=rmax, shyps=rshyps, hyps=rhyps,
wenzelm@28321
  1470
             tpairs=rtpairs, prop=rprop,...}) = orule
paulson@1529
  1471
         (*How many hyps to skip over during normalization*)
wenzelm@21576
  1472
     and nlift = Logic.count_prems (strip_all_body Bi) + (if eres_flg then ~1 else 0)
wenzelm@24143
  1473
     val thy = Theory.deref (merge_thys2 state orule);
clasohm@0
  1474
     (** Add new theorem with prop = '[| Bs; As |] ==> C' to thq **)
berghofe@11518
  1475
     fun addth A (As, oldAs, rder', n) ((env as Envir.Envir {maxidx, ...}, tpairs), thq) =
wenzelm@250
  1476
       let val normt = Envir.norm_term env;
wenzelm@250
  1477
           (*perform minimal copying here by examining env*)
berghofe@13658
  1478
           val (ntpairs, normp) =
berghofe@13658
  1479
             if Envir.is_empty env then (tpairs, (Bs @ As, C))
wenzelm@250
  1480
             else
wenzelm@250
  1481
             let val ntps = map (pairself normt) tpairs
wenzelm@19861
  1482
             in if Envir.above env smax then
wenzelm@1238
  1483
                  (*no assignments in state; normalize the rule only*)
wenzelm@1238
  1484
                  if lifted
berghofe@13658
  1485
                  then (ntps, (Bs @ map (norm_term_skip env nlift) As, C))
berghofe@13658
  1486
                  else (ntps, (Bs @ map normt As, C))
paulson@1529
  1487
                else if match then raise COMPOSE
wenzelm@250
  1488
                else (*normalize the new rule fully*)
berghofe@13658
  1489
                  (ntps, (map normt (Bs @ As), normt C))
wenzelm@250
  1490
             end
wenzelm@16601
  1491
           val th =
wenzelm@28321
  1492
             Thm (deriv_rule2
berghofe@11518
  1493
                   ((if Envir.is_empty env then I
wenzelm@19861
  1494
                     else if Envir.above env smax then
berghofe@11518
  1495
                       (fn f => fn der => f (Pt.norm_proof' env der))
berghofe@11518
  1496
                     else
berghofe@11518
  1497
                       curry op oo (Pt.norm_proof' env))
berghofe@23296
  1498
                    (Pt.bicompose_proof flatten Bs oldAs As A n (nlift+1))) rder' sder,
wenzelm@28321
  1499
                {tags = [],
wenzelm@2386
  1500
                 maxidx = maxidx,
wenzelm@26640
  1501
                 shyps = Envir.insert_sorts env (Sorts.union rshyps sshyps),
wenzelm@16601
  1502
                 hyps = union_hyps rhyps shyps,
berghofe@13658
  1503
                 tpairs = ntpairs,
wenzelm@24143
  1504
                 prop = Logic.list_implies normp,
wenzelm@28321
  1505
                 thy_ref = Theory.check_thy thy})
wenzelm@19475
  1506
        in  Seq.cons th thq  end  handle COMPOSE => thq;
berghofe@13658
  1507
     val (rAs,B) = Logic.strip_prems(nsubgoal, [], rprop)
clasohm@0
  1508
       handle TERM _ => raise THM("bicompose: rule", 0, [orule,state]);
clasohm@0
  1509
     (*Modify assumptions, deleting n-th if n>0 for e-resolution*)
clasohm@0
  1510
     fun newAs(As0, n, dpairs, tpairs) =
berghofe@11518
  1511
       let val (As1, rder') =
berghofe@25939
  1512
         if not lifted then (As0, rder)
berghofe@11518
  1513
         else (map (rename_bvars(dpairs,tpairs,B)) As0,
wenzelm@28321
  1514
           deriv_rule1 (Pt.map_proof_terms
berghofe@11518
  1515
             (rename_bvars (dpairs, tpairs, Bound 0)) I) rder);
wenzelm@18486
  1516
       in (map (if flatten then (Logic.flatten_params n) else I) As1, As1, rder', n)
wenzelm@250
  1517
          handle TERM _ =>
wenzelm@250
  1518
          raise THM("bicompose: 1st premise", 0, [orule])
clasohm@0
  1519
       end;
paulson@2147
  1520
     val env = Envir.empty(Int.max(rmax,smax));
clasohm@0
  1521
     val BBi = if lifted then strip_assums2(B,Bi) else (B,Bi);
clasohm@0
  1522
     val dpairs = BBi :: (rtpairs@stpairs);
clasohm@0
  1523
     (*elim-resolution: try each assumption in turn.  Initially n=1*)
berghofe@11518
  1524
     fun tryasms (_, _, _, []) = Seq.empty
berghofe@11518
  1525
       | tryasms (A, As, n, (t,u)::apairs) =
wenzelm@16425
  1526
          (case Seq.pull(Unify.unifiers(thy, env, (t,u)::dpairs))  of
wenzelm@16425
  1527
              NONE                   => tryasms (A, As, n+1, apairs)
wenzelm@16425
  1528
            | cell as SOME((_,tpairs),_) =>
wenzelm@16425
  1529
                Seq.it_right (addth A (newAs(As, n, [BBi,(u,t)], tpairs)))
wenzelm@16425
  1530
                    (Seq.make(fn()=> cell),
wenzelm@16425
  1531
                     Seq.make(fn()=> Seq.pull (tryasms(A, As, n+1, apairs)))))
clasohm@0
  1532
     fun eres [] = raise THM("bicompose: no premises", 0, [orule,state])
skalberg@15531
  1533
       | eres (A1::As) = tryasms(SOME A1, As, 1, Logic.assum_pairs(nlift+1,A1))
clasohm@0
  1534
     (*ordinary resolution*)
skalberg@15531
  1535
     fun res(NONE) = Seq.empty
skalberg@15531
  1536
       | res(cell as SOME((_,tpairs),_)) =
skalberg@15531
  1537
             Seq.it_right (addth NONE (newAs(rev rAs, 0, [BBi], tpairs)))
wenzelm@4270
  1538
                       (Seq.make (fn()=> cell), Seq.empty)
clasohm@0
  1539
 in  if eres_flg then eres(rev rAs)
wenzelm@16425
  1540
     else res(Seq.pull(Unify.unifiers(thy, env, dpairs)))
clasohm@0
  1541
 end;
wenzelm@7528
  1542
end;
clasohm@0
  1543
wenzelm@18501
  1544
fun compose_no_flatten match (orule, nsubgoal) i state =
wenzelm@18501
  1545
  bicompose_aux false match (state, dest_state (state, i), false) (false, orule, nsubgoal);
clasohm@0
  1546
wenzelm@18501
  1547
fun bicompose match arg i state =
wenzelm@18501
  1548
  bicompose_aux true match (state, dest_state (state,i), false) arg;
clasohm@0
  1549
clasohm@0
  1550
(*Quick test whether rule is resolvable with the subgoal with hyps Hs
clasohm@0
  1551
  and conclusion B.  If eres_flg then checks 1st premise of rule also*)
clasohm@0
  1552
fun could_bires (Hs, B, eres_flg, rule) =
wenzelm@29269
  1553
    let fun could_reshyp (A1::_) = exists (fn H => Term.could_unify (A1, H)) Hs
wenzelm@250
  1554
          | could_reshyp [] = false;  (*no premise -- illegal*)
wenzelm@29269
  1555
    in  Term.could_unify(concl_of rule, B) andalso
wenzelm@250
  1556
        (not eres_flg  orelse  could_reshyp (prems_of rule))
clasohm@0
  1557
    end;
clasohm@0
  1558
clasohm@0
  1559
(*Bi-resolution of a state with a list of (flag,rule) pairs.
clasohm@0
  1560
  Puts the rule above:  rule/state.  Renames vars in the rules. *)
wenzelm@250
  1561
fun biresolution match brules i state =
wenzelm@18035
  1562
    let val (stpairs, Bs, Bi, C) = dest_state(state,i);
wenzelm@18145
  1563
        val lift = lift_rule (cprem_of state i);
wenzelm@250
  1564
        val B = Logic.strip_assums_concl Bi;
wenzelm@250
  1565
        val Hs = Logic.strip_assums_hyp Bi;
wenzelm@22573
  1566
        val compose = bicompose_aux true match (state, (stpairs, Bs, Bi, C), true);
wenzelm@4270
  1567
        fun res [] = Seq.empty
wenzelm@250
  1568
          | res ((eres_flg, rule)::brules) =
nipkow@13642
  1569
              if !Pattern.trace_unify_fail orelse
nipkow@13642
  1570
                 could_bires (Hs, B, eres_flg, rule)
wenzelm@4270
  1571
              then Seq.make (*delay processing remainder till needed*)
wenzelm@22573
  1572
                  (fn()=> SOME(compose (eres_flg, lift rule, nprems_of rule),
wenzelm@250
  1573
                               res brules))
wenzelm@250
  1574
              else res brules
wenzelm@4270
  1575
    in  Seq.flat (res brules)  end;
clasohm@0
  1576
clasohm@0
  1577
wenzelm@28321
  1578
wenzelm@28978
  1579
(*** Future theorems -- proofs with promises ***)
wenzelm@28356
  1580
wenzelm@28446
  1581
(* future rule *)
wenzelm@28330
  1582
wenzelm@28446
  1583
fun future_result i orig_thy orig_shyps orig_prop raw_thm =
wenzelm@28378
  1584
  let
wenzelm@28378
  1585
    val _ = Theory.check_thy orig_thy;
wenzelm@28378
  1586
    val thm = strip_shyps (transfer orig_thy raw_thm);
wenzelm@28378
  1587
    val _ = Theory.check_thy orig_thy;
wenzelm@28446
  1588
    fun err msg = raise THM ("future_result: " ^ msg, 0, [thm]);
wenzelm@28378
  1589
wenzelm@28996
  1590
    val Thm (Deriv {max_promise, ...}, {shyps, hyps, tpairs, prop, ...}) = thm;
wenzelm@28378
  1591
    val _ = prop aconv orig_prop orelse err "bad prop";
wenzelm@28378
  1592
    val _ = null tpairs orelse err "bad tpairs";
wenzelm@28378
  1593
    val _ = null hyps orelse err "bad hyps";
wenzelm@28378
  1594
    val _ = Sorts.subset (shyps, orig_shyps) orelse err "bad shyps";
wenzelm@28996
  1595
    val _ = max_promise < i orelse err "bad dependencies";
wenzelm@28378
  1596
  in thm end;
wenzelm@28378
  1597
wenzelm@28978
  1598
fun future future_thm ct =
wenzelm@28321
  1599
  let
wenzelm@28624
  1600
    val Cterm {thy_ref = thy_ref, t = prop, T, maxidx, sorts} = ct;
wenzelm@28321
  1601
    val thy = Context.reject_draft (Theory.deref thy_ref);
wenzelm@28446
  1602
    val _ = T <> propT andalso raise CTERM ("future: prop expected", [ct]);
wenzelm@28378
  1603
wenzelm@28389
  1604
    val i = serial ();
wenzelm@29436
  1605
    val future = future_thm |> Future.map (future_result i thy sorts prop);
wenzelm@28829
  1606
    val promise = (i, future);
wenzelm@28321
  1607
  in
wenzelm@28996
  1608
    Thm (make_deriv i [promise] [promise] [] [] (Pt.promise_proof thy i prop),
wenzelm@28321
  1609
     {thy_ref = thy_ref,
wenzelm@28321
  1610
      tags = [],
wenzelm@28321
  1611
      maxidx = maxidx,
wenzelm@28321
  1612
      shyps = sorts,
wenzelm@28321
  1613
      hyps = [],
wenzelm@28321
  1614
      tpairs = [],
wenzelm@28321
  1615
      prop = prop})
wenzelm@28321
  1616
  end;
wenzelm@28321
  1617
wenzelm@28330
  1618
wenzelm@29432
  1619
(* pending task groups *)
wenzelm@29432
  1620
wenzelm@29432
  1621
fun pending_groups (Thm (Deriv {open_promises, ...}, _)) =
wenzelm@29432
  1622
  fold (insert Task_Queue.eq_group o Future.group_of o #2) open_promises;
wenzelm@29432
  1623
wenzelm@29432
  1624
wenzelm@29432
  1625
(* fulfilled proofs *)
wenzelm@28330
  1626
wenzelm@28816
  1627
fun raw_proof_of (Thm (Deriv {body, ...}, _)) = Proofterm.proof_of body;
wenzelm@28814
  1628
wenzelm@28996
  1629
fun proof_body_of (Thm (Deriv {open_promises, promises, body, ...}, {thy_ref, ...})) =
wenzelm@28330
  1630
  let
wenzelm@28996
  1631
    val _ = Exn.release_all (map (Future.join_result o #2) (rev open_promises));
wenzelm@28847
  1632
    val ps = map (apsnd (raw_proof_of o Future.join)) promises;
wenzelm@28829
  1633
  in Pt.fulfill_proof (Theory.deref thy_ref) ps body end;
wenzelm@28804
  1634
wenzelm@28814
  1635
val proof_of = Proofterm.proof_of o proof_body_of;
wenzelm@29003
  1636
val join_proof = ignore o proof_body_of;
wenzelm@28814
  1637
wenzelm@28804
  1638
wenzelm@28804
  1639
(* closed derivations with official name *)
wenzelm@28804
  1640
wenzelm@28804
  1641
fun get_name thm =
wenzelm@28814
  1642
  Pt.get_name (hyps_of thm) (prop_of thm) (raw_proof_of thm);
wenzelm@28330
  1643
wenzelm@28804
  1644
fun put_name name (thm as Thm (der, args)) =
wenzelm@28804
  1645
  let
wenzelm@28996
  1646
    val Deriv {max_promise, open_promises, promises, body, ...} = der;
wenzelm@28804
  1647
    val {thy_ref, hyps, prop, tpairs, ...} = args;
wenzelm@28996
  1648
    val _ = null tpairs orelse raise THM ("put_name: unsolved flex-flex constraints", 0, [thm]);
wenzelm@28804
  1649
wenzelm@29636
  1650
    val ps = map (apsnd (Future.map proof_of)) promises;
wenzelm@28804
  1651
    val thy = Theory.deref thy_ref;
wenzelm@28804
  1652
    val (pthm, proof) = Pt.thm_proof thy name hyps prop ps body;
wenzelm@28996
  1653
wenzelm@28996
  1654
    val open_promises' = open_promises |> filter (fn (_, p) =>
wenzelm@28996
  1655
      (case Future.peek p of SOME (Exn.Result _) => false | _ => true));
wenzelm@28996
  1656
    val der' = make_deriv max_promise open_promises' [] [] [pthm] proof;
wenzelm@28804
  1657
    val _ = Theory.check_thy thy;
wenzelm@28804
  1658
  in Thm (der', args) end;
wenzelm@28330
  1659
wenzelm@28321
  1660
wenzelm@28321
  1661
wenzelm@2509
  1662
(*** Oracles ***)
wenzelm@2509
  1663
wenzelm@28290
  1664
(* oracle rule *)
wenzelm@28290
  1665
wenzelm@28290
  1666
fun invoke_oracle thy_ref1 name oracle arg =
wenzelm@28624
  1667
  let val Cterm {thy_ref = thy_ref2, t = prop, T, maxidx, sorts} = oracle arg in
wenzelm@28290
  1668
    if T <> propT then
wenzelm@28290
  1669
      raise THM ("Oracle's result must have type prop: " ^ name, 0, [])
wenzelm@28290
  1670
    else
wenzelm@28804
  1671
      let val prf = Pt.oracle_proof name prop in
wenzelm@28996
  1672
        Thm (make_deriv ~1 [] [] (Pt.make_oracles prf) [] prf,
wenzelm@28804
  1673
         {thy_ref = Theory.merge_refs (thy_ref1, thy_ref2),
wenzelm@28804
  1674
          tags = [],
wenzelm@28804
  1675
          maxidx = maxidx,
wenzelm@28804
  1676
          shyps = sorts,
wenzelm@28804
  1677
          hyps = [],
wenzelm@28804
  1678
          tpairs = [],
wenzelm@28804
  1679
          prop = prop})
wenzelm@28804
  1680
      end
wenzelm@3812
  1681
  end;
wenzelm@3812
  1682
wenzelm@28290
  1683
wenzelm@28290
  1684
(* authentic derivation names *)
wenzelm@28290
  1685
wenzelm@28290
  1686
fun err_dup_ora dup = error ("Duplicate oracle: " ^ quote dup);
wenzelm@28290
  1687
wenzelm@28290
  1688
structure Oracles = TheoryDataFun
wenzelm@28290
  1689
(
wenzelm@30288
  1690
  type T = serial NameSpace.table;
wenzelm@28290
  1691
  val empty = NameSpace.empty_table;
wenzelm@28290
  1692
  val copy = I;
wenzelm@28290
  1693
  val extend = I;
wenzelm@29288
  1694
  fun merge _ oracles : T = NameSpace.merge_tables (op =) oracles
wenzelm@28290
  1695
    handle Symtab.DUP dup => err_dup_ora dup;
wenzelm@28290
  1696
);
wenzelm@28290
  1697
wenzelm@28290
  1698
val extern_oracles = map #1 o NameSpace.extern_table o Oracles.get;
wenzelm@28290
  1699
wenzelm@30288
  1700
fun add_oracle (b, oracle) thy =
wenzelm@28290
  1701
  let
wenzelm@28290
  1702
    val naming = Sign.naming_of thy;
wenzelm@30466
  1703
    val (name, tab') = NameSpace.define naming (b, serial ()) (Oracles.get thy)
wenzelm@30288
  1704
      handle Symtab.DUP _ => err_dup_ora (Binding.str_of b);
wenzelm@30288
  1705
    val thy' = Oracles.put tab' thy;
wenzelm@28290
  1706
  in ((name, invoke_oracle (Theory.check_thy thy') name oracle), thy') end;
wenzelm@28290
  1707
clasohm@0
  1708
end;
paulson@1503
  1709
wenzelm@6089
  1710
structure BasicThm: BASIC_THM = Thm;
wenzelm@6089
  1711
open BasicThm;