src/Pure/thm.ML
author wenzelm
Sun Sep 28 12:23:44 2008 +0200 (2008-09-28)
changeset 28389 777bdc429ea3
parent 28381 0b8237df37bd
child 28391 1a4804fc2216
permissions -rw-r--r--
promise_result: enforce strictly sequential dependencies, via serial numbers;
wenzelm@250
     1
(*  Title:      Pure/thm.ML
clasohm@0
     2
    ID:         $Id$
wenzelm@250
     3
    Author:     Lawrence C Paulson, Cambridge University Computer Laboratory
lcp@229
     4
    Copyright   1994  University of Cambridge
lcp@229
     5
wenzelm@16425
     6
The very core of Isabelle's Meta Logic: certified types and terms,
wenzelm@28321
     7
derivations, theorems, framework rules (including lifting and
wenzelm@28321
     8
resolution), oracles.
clasohm@0
     9
*)
clasohm@0
    10
wenzelm@6089
    11
signature BASIC_THM =
paulson@1503
    12
  sig
wenzelm@1160
    13
  (*certified types*)
wenzelm@387
    14
  type ctyp
wenzelm@16656
    15
  val rep_ctyp: ctyp ->
wenzelm@26631
    16
   {thy_ref: theory_ref,
wenzelm@16656
    17
    T: typ,
wenzelm@20512
    18
    maxidx: int,
wenzelm@28354
    19
    sorts: sort OrdList.T}
wenzelm@16425
    20
  val theory_of_ctyp: ctyp -> theory
wenzelm@16425
    21
  val typ_of: ctyp -> typ
wenzelm@16425
    22
  val ctyp_of: theory -> typ -> ctyp
wenzelm@1160
    23
wenzelm@1160
    24
  (*certified terms*)
wenzelm@1160
    25
  type cterm
wenzelm@22584
    26
  exception CTERM of string * cterm list
wenzelm@16601
    27
  val rep_cterm: cterm ->
wenzelm@26631
    28
   {thy_ref: theory_ref,
wenzelm@16656
    29
    t: term,
wenzelm@16656
    30
    T: typ,
wenzelm@16656
    31
    maxidx: int,
wenzelm@28354
    32
    sorts: sort OrdList.T}
wenzelm@28354
    33
  val crep_cterm: cterm ->
wenzelm@28354
    34
    {thy_ref: theory_ref, t: term, T: ctyp, maxidx: int, sorts: sort OrdList.T}
wenzelm@16425
    35
  val theory_of_cterm: cterm -> theory
wenzelm@16425
    36
  val term_of: cterm -> term
wenzelm@16425
    37
  val cterm_of: theory -> term -> cterm
wenzelm@16425
    38
  val ctyp_of_term: cterm -> ctyp
wenzelm@1160
    39
wenzelm@28321
    40
  (*theorems*)
wenzelm@1160
    41
  type thm
wenzelm@23601
    42
  type conv = cterm -> thm
wenzelm@23601
    43
  type attribute = Context.generic * thm -> Context.generic * thm
wenzelm@16425
    44
  val rep_thm: thm ->
wenzelm@26631
    45
   {thy_ref: theory_ref,
wenzelm@28017
    46
    tags: Properties.T,
wenzelm@16425
    47
    maxidx: int,
wenzelm@28354
    48
    shyps: sort OrdList.T,
wenzelm@28354
    49
    hyps: term OrdList.T,
wenzelm@16425
    50
    tpairs: (term * term) list,
wenzelm@16425
    51
    prop: term}
wenzelm@16425
    52
  val crep_thm: thm ->
wenzelm@26631
    53
   {thy_ref: theory_ref,
wenzelm@28017
    54
    tags: Properties.T,
wenzelm@16425
    55
    maxidx: int,
wenzelm@28354
    56
    shyps: sort OrdList.T,
wenzelm@28354
    57
    hyps: cterm OrdList.T,
wenzelm@16425
    58
    tpairs: (cterm * cterm) list,
wenzelm@16425
    59
    prop: cterm}
wenzelm@6089
    60
  exception THM of string * int * thm list
wenzelm@16425
    61
  val theory_of_thm: thm -> theory
wenzelm@16425
    62
  val prop_of: thm -> term
wenzelm@16425
    63
  val tpairs_of: thm -> (term * term) list
wenzelm@16656
    64
  val concl_of: thm -> term
wenzelm@16425
    65
  val prems_of: thm -> term list
wenzelm@16425
    66
  val nprems_of: thm -> int
wenzelm@16425
    67
  val cprop_of: thm -> cterm
wenzelm@18145
    68
  val cprem_of: thm -> int -> cterm
wenzelm@16656
    69
  val transfer: theory -> thm -> thm
wenzelm@16945
    70
  val weaken: cterm -> thm -> thm
wenzelm@16425
    71
  val extra_shyps: thm -> sort list
wenzelm@16425
    72
  val strip_shyps: thm -> thm
wenzelm@16425
    73
  val get_axiom_i: theory -> string -> thm
wenzelm@16425
    74
  val get_axiom: theory -> xstring -> thm
wenzelm@16425
    75
  val def_name: string -> string
wenzelm@20884
    76
  val def_name_optional: string -> string -> string
wenzelm@16425
    77
  val get_def: theory -> xstring -> thm
wenzelm@16425
    78
  val axioms_of: theory -> (string * thm) list
wenzelm@1160
    79
wenzelm@1160
    80
  (*meta rules*)
wenzelm@16425
    81
  val assume: cterm -> thm
wenzelm@16425
    82
  val implies_intr: cterm -> thm -> thm
wenzelm@16425
    83
  val implies_elim: thm -> thm -> thm
wenzelm@16425
    84
  val forall_intr: cterm -> thm -> thm
wenzelm@16425
    85
  val forall_elim: cterm -> thm -> thm
wenzelm@16425
    86
  val reflexive: cterm -> thm
wenzelm@16425
    87
  val symmetric: thm -> thm
wenzelm@16425
    88
  val transitive: thm -> thm -> thm
wenzelm@23601
    89
  val beta_conversion: bool -> conv
wenzelm@23601
    90
  val eta_conversion: conv
wenzelm@23601
    91
  val eta_long_conversion: conv
wenzelm@16425
    92
  val abstract_rule: string -> cterm -> thm -> thm
wenzelm@16425
    93
  val combination: thm -> thm -> thm
wenzelm@16425
    94
  val equal_intr: thm -> thm -> thm
wenzelm@16425
    95
  val equal_elim: thm -> thm -> thm
wenzelm@16425
    96
  val flexflex_rule: thm -> thm Seq.seq
wenzelm@19910
    97
  val generalize: string list * string list -> int -> thm -> thm
wenzelm@16425
    98
  val instantiate: (ctyp * ctyp) list * (cterm * cterm) list -> thm -> thm
wenzelm@22584
    99
  val instantiate_cterm: (ctyp * ctyp) list * (cterm * cterm) list -> cterm -> cterm
wenzelm@16425
   100
  val trivial: cterm -> thm
wenzelm@16425
   101
  val class_triv: theory -> class -> thm
wenzelm@19505
   102
  val unconstrainT: ctyp -> thm -> thm
wenzelm@16425
   103
  val dest_state: thm * int -> (term * term) list * term list * term * term
wenzelm@18035
   104
  val lift_rule: cterm -> thm -> thm
wenzelm@16425
   105
  val incr_indexes: int -> thm -> thm
wenzelm@16425
   106
  val assumption: int -> thm -> thm Seq.seq
wenzelm@16425
   107
  val eq_assumption: int -> thm -> thm
wenzelm@16425
   108
  val rotate_rule: int -> int -> thm -> thm
wenzelm@16425
   109
  val permute_prems: int -> int -> thm -> thm
wenzelm@1160
   110
  val rename_params_rule: string list * int -> thm -> thm
wenzelm@18501
   111
  val compose_no_flatten: bool -> thm * int -> int -> thm -> thm Seq.seq
wenzelm@16425
   112
  val bicompose: bool -> bool * thm * int -> int -> thm -> thm Seq.seq
wenzelm@16425
   113
  val biresolution: bool -> (bool * thm) list -> int -> thm -> thm Seq.seq
wenzelm@250
   114
end;
clasohm@0
   115
wenzelm@6089
   116
signature THM =
wenzelm@6089
   117
sig
wenzelm@6089
   118
  include BASIC_THM
wenzelm@16425
   119
  val dest_ctyp: ctyp -> ctyp list
wenzelm@16425
   120
  val dest_comb: cterm -> cterm * cterm
wenzelm@22909
   121
  val dest_fun: cterm -> cterm
wenzelm@20580
   122
  val dest_arg: cterm -> cterm
wenzelm@22909
   123
  val dest_fun2: cterm -> cterm
wenzelm@22909
   124
  val dest_arg1: cterm -> cterm
wenzelm@16425
   125
  val dest_abs: string option -> cterm -> cterm * cterm
wenzelm@20261
   126
  val adjust_maxidx_cterm: int -> cterm -> cterm
wenzelm@16425
   127
  val capply: cterm -> cterm -> cterm
wenzelm@16425
   128
  val cabs: cterm -> cterm -> cterm
wenzelm@28378
   129
  val rep_deriv: thm ->
wenzelm@28330
   130
   {oracle: bool,
wenzelm@28330
   131
    proof: Proofterm.proof,
wenzelm@28378
   132
    promises: (serial * thm Future.T) OrdList.T}
wenzelm@28330
   133
  val oracle_of: thm -> bool
wenzelm@16425
   134
  val major_prem_of: thm -> term
wenzelm@16425
   135
  val no_prems: thm -> bool
wenzelm@16945
   136
  val terms_of_tpairs: (term * term) list -> term list
wenzelm@19881
   137
  val maxidx_of: thm -> int
wenzelm@19910
   138
  val maxidx_thm: thm -> int -> int
wenzelm@19881
   139
  val hyps_of: thm -> term list
wenzelm@16945
   140
  val full_prop_of: thm -> term
wenzelm@21646
   141
  val get_name: thm -> string
wenzelm@21646
   142
  val put_name: string -> thm -> thm
wenzelm@28017
   143
  val get_tags: thm -> Properties.T
wenzelm@28017
   144
  val map_tags: (Properties.T -> Properties.T) -> thm -> thm
berghofe@23781
   145
  val norm_proof: thm -> thm
wenzelm@20261
   146
  val adjust_maxidx_thm: int -> thm -> thm
wenzelm@16425
   147
  val rename_boundvars: term -> term -> thm -> thm
wenzelm@22909
   148
  val match: cterm * cterm -> (ctyp * ctyp) list * (cterm * cterm) list
wenzelm@22909
   149
  val first_order_match: cterm * cterm -> (ctyp * ctyp) list * (cterm * cterm) list
wenzelm@22909
   150
  val incr_indexes_cterm: int -> cterm -> cterm
wenzelm@20002
   151
  val varifyT: thm -> thm
wenzelm@20002
   152
  val varifyT': (string * sort) list -> thm -> ((string * sort) * indexname) list * thm
wenzelm@19881
   153
  val freezeT: thm -> thm
wenzelm@28364
   154
  val promise: (unit -> thm) -> cterm -> thm
wenzelm@28330
   155
  val proof_of: thm -> Proofterm.proof
wenzelm@28330
   156
  val extern_oracles: theory -> xstring list
wenzelm@28330
   157
  val add_oracle: bstring * ('a -> cterm) -> theory -> (string * ('a -> thm)) * theory
wenzelm@6089
   158
end;
wenzelm@6089
   159
wenzelm@28356
   160
structure Thm:> THM =
clasohm@0
   161
struct
wenzelm@250
   162
wenzelm@22237
   163
structure Pt = Proofterm;
wenzelm@22237
   164
wenzelm@16656
   165
wenzelm@387
   166
(*** Certified terms and types ***)
wenzelm@387
   167
wenzelm@250
   168
(** certified types **)
wenzelm@250
   169
wenzelm@28356
   170
datatype ctyp = Ctyp of
wenzelm@20512
   171
 {thy_ref: theory_ref,
wenzelm@20512
   172
  T: typ,
wenzelm@20512
   173
  maxidx: int,
wenzelm@28356
   174
  sorts: sort OrdList.T};
wenzelm@250
   175
wenzelm@26631
   176
fun rep_ctyp (Ctyp args) = args;
wenzelm@16656
   177
fun theory_of_ctyp (Ctyp {thy_ref, ...}) = Theory.deref thy_ref;
wenzelm@250
   178
fun typ_of (Ctyp {T, ...}) = T;
wenzelm@250
   179
wenzelm@16656
   180
fun ctyp_of thy raw_T =
wenzelm@24143
   181
  let
wenzelm@24143
   182
    val T = Sign.certify_typ thy raw_T;
wenzelm@24143
   183
    val maxidx = Term.maxidx_of_typ T;
wenzelm@26640
   184
    val sorts = Sorts.insert_typ T [];
wenzelm@24143
   185
  in Ctyp {thy_ref = Theory.check_thy thy, T = T, maxidx = maxidx, sorts = sorts} end;
wenzelm@250
   186
wenzelm@20512
   187
fun dest_ctyp (Ctyp {thy_ref, T = Type (s, Ts), maxidx, sorts}) =
wenzelm@20512
   188
      map (fn T => Ctyp {thy_ref = thy_ref, T = T, maxidx = maxidx, sorts = sorts}) Ts
wenzelm@16679
   189
  | dest_ctyp cT = raise TYPE ("dest_ctyp", [typ_of cT], []);
berghofe@15087
   190
lcp@229
   191
lcp@229
   192
wenzelm@250
   193
(** certified terms **)
lcp@229
   194
wenzelm@16601
   195
(*certified terms with checked typ, maxidx, and sorts*)
wenzelm@28356
   196
datatype cterm = Cterm of
wenzelm@16601
   197
 {thy_ref: theory_ref,
wenzelm@16601
   198
  t: term,
wenzelm@16601
   199
  T: typ,
wenzelm@16601
   200
  maxidx: int,
wenzelm@28356
   201
  sorts: sort OrdList.T};
wenzelm@16425
   202
wenzelm@22584
   203
exception CTERM of string * cterm list;
wenzelm@16679
   204
wenzelm@26631
   205
fun rep_cterm (Cterm args) = args;
lcp@229
   206
wenzelm@16601
   207
fun crep_cterm (Cterm {thy_ref, t, T, maxidx, sorts}) =
wenzelm@26631
   208
  {thy_ref = thy_ref, t = t, maxidx = maxidx, sorts = sorts,
wenzelm@26631
   209
    T = Ctyp {thy_ref = thy_ref, T = T, maxidx = maxidx, sorts = sorts}};
wenzelm@3967
   210
wenzelm@16425
   211
fun theory_of_cterm (Cterm {thy_ref, ...}) = Theory.deref thy_ref;
wenzelm@250
   212
fun term_of (Cterm {t, ...}) = t;
lcp@229
   213
wenzelm@20512
   214
fun ctyp_of_term (Cterm {thy_ref, T, maxidx, sorts, ...}) =
wenzelm@20512
   215
  Ctyp {thy_ref = thy_ref, T = T, maxidx = maxidx, sorts = sorts};
paulson@2671
   216
wenzelm@16425
   217
fun cterm_of thy tm =
wenzelm@16601
   218
  let
wenzelm@18969
   219
    val (t, T, maxidx) = Sign.certify_term thy tm;
wenzelm@26640
   220
    val sorts = Sorts.insert_term t [];
wenzelm@24143
   221
  in Cterm {thy_ref = Theory.check_thy thy, t = t, T = T, maxidx = maxidx, sorts = sorts} end;
lcp@229
   222
wenzelm@20057
   223
fun merge_thys0 (Cterm {thy_ref = r1, t = t1, ...}) (Cterm {thy_ref = r2, t = t2, ...}) =
wenzelm@23601
   224
  Theory.merge_refs (r1, r2);
wenzelm@16656
   225
wenzelm@20580
   226
wenzelm@22909
   227
(* destructors *)
wenzelm@22909
   228
wenzelm@22909
   229
fun dest_comb (ct as Cterm {t = c $ a, T, thy_ref, maxidx, sorts}) =
wenzelm@22909
   230
      let val A = Term.argument_type_of c 0 in
wenzelm@22909
   231
        (Cterm {t = c, T = A --> T, thy_ref = thy_ref, maxidx = maxidx, sorts = sorts},
wenzelm@22909
   232
         Cterm {t = a, T = A, thy_ref = thy_ref, maxidx = maxidx, sorts = sorts})
clasohm@1493
   233
      end
wenzelm@22584
   234
  | dest_comb ct = raise CTERM ("dest_comb", [ct]);
clasohm@1493
   235
wenzelm@22909
   236
fun dest_fun (ct as Cterm {t = c $ _, T, thy_ref, maxidx, sorts}) =
wenzelm@22909
   237
      let val A = Term.argument_type_of c 0
wenzelm@22909
   238
      in Cterm {t = c, T = A --> T, thy_ref = thy_ref, maxidx = maxidx, sorts = sorts} end
wenzelm@22909
   239
  | dest_fun ct = raise CTERM ("dest_fun", [ct]);
wenzelm@22909
   240
wenzelm@22909
   241
fun dest_arg (ct as Cterm {t = c $ a, T = _, thy_ref, maxidx, sorts}) =
wenzelm@22909
   242
      let val A = Term.argument_type_of c 0
wenzelm@22909
   243
      in Cterm {t = a, T = A, thy_ref = thy_ref, maxidx = maxidx, sorts = sorts} end
wenzelm@22584
   244
  | dest_arg ct = raise CTERM ("dest_arg", [ct]);
wenzelm@20580
   245
wenzelm@22909
   246
wenzelm@22909
   247
fun dest_fun2 (Cterm {t = c $ a $ b, T, thy_ref, maxidx, sorts}) =
wenzelm@22909
   248
      let
wenzelm@22909
   249
        val A = Term.argument_type_of c 0;
wenzelm@22909
   250
        val B = Term.argument_type_of c 1;
wenzelm@22909
   251
      in Cterm {t = c, T = A --> B --> T, thy_ref = thy_ref, maxidx = maxidx, sorts = sorts} end
wenzelm@22909
   252
  | dest_fun2 ct = raise CTERM ("dest_fun2", [ct]);
wenzelm@22909
   253
wenzelm@22909
   254
fun dest_arg1 (Cterm {t = c $ a $ _, T = _, thy_ref, maxidx, sorts}) =
wenzelm@22909
   255
      let val A = Term.argument_type_of c 0
wenzelm@22909
   256
      in Cterm {t = a, T = A, thy_ref = thy_ref, maxidx = maxidx, sorts = sorts} end
wenzelm@22909
   257
  | dest_arg1 ct = raise CTERM ("dest_arg1", [ct]);
wenzelm@20673
   258
wenzelm@22584
   259
fun dest_abs a (ct as
wenzelm@22584
   260
        Cterm {t = Abs (x, T, t), T = Type ("fun", [_, U]), thy_ref, maxidx, sorts}) =
wenzelm@18944
   261
      let val (y', t') = Term.dest_abs (the_default x a, T, t) in
wenzelm@16679
   262
        (Cterm {t = Free (y', T), T = T, thy_ref = thy_ref, maxidx = maxidx, sorts = sorts},
wenzelm@16679
   263
          Cterm {t = t', T = U, thy_ref = thy_ref, maxidx = maxidx, sorts = sorts})
clasohm@1493
   264
      end
wenzelm@22584
   265
  | dest_abs _ ct = raise CTERM ("dest_abs", [ct]);
clasohm@1493
   266
wenzelm@22909
   267
wenzelm@22909
   268
(* constructors *)
wenzelm@22909
   269
wenzelm@16601
   270
fun capply
wenzelm@16656
   271
  (cf as Cterm {t = f, T = Type ("fun", [dty, rty]), maxidx = maxidx1, sorts = sorts1, ...})
wenzelm@16656
   272
  (cx as Cterm {t = x, T, maxidx = maxidx2, sorts = sorts2, ...}) =
wenzelm@16601
   273
    if T = dty then
wenzelm@16656
   274
      Cterm {thy_ref = merge_thys0 cf cx,
wenzelm@16656
   275
        t = f $ x,
wenzelm@16656
   276
        T = rty,
wenzelm@16656
   277
        maxidx = Int.max (maxidx1, maxidx2),
wenzelm@16601
   278
        sorts = Sorts.union sorts1 sorts2}
wenzelm@22584
   279
      else raise CTERM ("capply: types don't agree", [cf, cx])
wenzelm@22584
   280
  | capply cf cx = raise CTERM ("capply: first arg is not a function", [cf, cx]);
wenzelm@250
   281
wenzelm@16601
   282
fun cabs
wenzelm@16656
   283
  (ct1 as Cterm {t = t1, T = T1, maxidx = maxidx1, sorts = sorts1, ...})
wenzelm@16656
   284
  (ct2 as Cterm {t = t2, T = T2, maxidx = maxidx2, sorts = sorts2, ...}) =
wenzelm@21975
   285
    let val t = Term.lambda t1 t2 in
wenzelm@16656
   286
      Cterm {thy_ref = merge_thys0 ct1 ct2,
wenzelm@16656
   287
        t = t, T = T1 --> T2,
wenzelm@16656
   288
        maxidx = Int.max (maxidx1, maxidx2),
wenzelm@16656
   289
        sorts = Sorts.union sorts1 sorts2}
wenzelm@16601
   290
    end;
lcp@229
   291
wenzelm@20580
   292
wenzelm@22909
   293
(* indexes *)
wenzelm@22909
   294
wenzelm@20580
   295
fun adjust_maxidx_cterm i (ct as Cterm {thy_ref, t, T, maxidx, sorts}) =
wenzelm@20580
   296
  if maxidx = i then ct
wenzelm@20580
   297
  else if maxidx < i then
wenzelm@20580
   298
    Cterm {maxidx = i, thy_ref = thy_ref, t = t, T = T, sorts = sorts}
wenzelm@20580
   299
  else
wenzelm@20580
   300
    Cterm {maxidx = Int.max (maxidx_of_term t, i), thy_ref = thy_ref, t = t, T = T, sorts = sorts};
wenzelm@20580
   301
wenzelm@22909
   302
fun incr_indexes_cterm i (ct as Cterm {thy_ref, t, T, maxidx, sorts}) =
wenzelm@22909
   303
  if i < 0 then raise CTERM ("negative increment", [ct])
wenzelm@22909
   304
  else if i = 0 then ct
wenzelm@22909
   305
  else Cterm {thy_ref = thy_ref, t = Logic.incr_indexes ([], i) t,
wenzelm@22909
   306
    T = Logic.incr_tvar i T, maxidx = maxidx + i, sorts = sorts};
wenzelm@22909
   307
wenzelm@22909
   308
wenzelm@22909
   309
(* matching *)
wenzelm@22909
   310
wenzelm@22909
   311
local
wenzelm@22909
   312
wenzelm@22909
   313
fun gen_match match
wenzelm@20512
   314
    (ct1 as Cterm {t = t1, sorts = sorts1, ...},
wenzelm@20815
   315
     ct2 as Cterm {t = t2, sorts = sorts2, maxidx = maxidx2, ...}) =
berghofe@10416
   316
  let
wenzelm@24143
   317
    val thy = Theory.deref (merge_thys0 ct1 ct2);
wenzelm@24143
   318
    val (Tinsts, tinsts) = match thy (t1, t2) (Vartab.empty, Vartab.empty);
wenzelm@16601
   319
    val sorts = Sorts.union sorts1 sorts2;
wenzelm@20512
   320
    fun mk_cTinst ((a, i), (S, T)) =
wenzelm@24143
   321
      (Ctyp {T = TVar ((a, i), S), thy_ref = Theory.check_thy thy, maxidx = i, sorts = sorts},
wenzelm@24143
   322
       Ctyp {T = T, thy_ref = Theory.check_thy thy, maxidx = maxidx2, sorts = sorts});
wenzelm@20512
   323
    fun mk_ctinst ((x, i), (T, t)) =
wenzelm@16601
   324
      let val T = Envir.typ_subst_TVars Tinsts T in
wenzelm@24143
   325
        (Cterm {t = Var ((x, i), T), T = T, thy_ref = Theory.check_thy thy,
wenzelm@24143
   326
          maxidx = i, sorts = sorts},
wenzelm@24143
   327
         Cterm {t = t, T = T, thy_ref = Theory.check_thy thy, maxidx = maxidx2, sorts = sorts})
berghofe@10416
   328
      end;
wenzelm@16656
   329
  in (Vartab.fold (cons o mk_cTinst) Tinsts [], Vartab.fold (cons o mk_ctinst) tinsts []) end;
berghofe@10416
   330
wenzelm@22909
   331
in
berghofe@10416
   332
wenzelm@22909
   333
val match = gen_match Pattern.match;
wenzelm@22909
   334
val first_order_match = gen_match Pattern.first_order_match;
wenzelm@22909
   335
wenzelm@22909
   336
end;
berghofe@10416
   337
wenzelm@2509
   338
wenzelm@2509
   339
wenzelm@28321
   340
(*** Derivations and Theorems ***)
lcp@229
   341
wenzelm@28356
   342
datatype thm = Thm of
wenzelm@28378
   343
 deriv *                                        (*derivation*)
wenzelm@28378
   344
 {thy_ref: theory_ref,                          (*dynamic reference to theory*)
wenzelm@28378
   345
  tags: Properties.T,                           (*additional annotations/comments*)
wenzelm@28378
   346
  maxidx: int,                                  (*maximum index of any Var or TVar*)
wenzelm@28378
   347
  shyps: sort OrdList.T,                        (*sort hypotheses*)
wenzelm@28378
   348
  hyps: term OrdList.T,                         (*hypotheses*)
wenzelm@28378
   349
  tpairs: (term * term) list,                   (*flex-flex pairs*)
wenzelm@28378
   350
  prop: term}                                   (*conclusion*)
wenzelm@28378
   351
and deriv = Deriv of                     
wenzelm@28378
   352
 {oracle: bool,                                 (*oracle occurrence flag*)
wenzelm@28378
   353
  proof: Pt.proof,                              (*proof term*)
wenzelm@28378
   354
  promises: (serial * thm Future.T) OrdList.T}; (*promised derivations*)
clasohm@0
   355
wenzelm@23601
   356
type conv = cterm -> thm;
wenzelm@23601
   357
wenzelm@22365
   358
(*attributes subsume any kind of rules or context modifiers*)
wenzelm@22365
   359
type attribute = Context.generic * thm -> Context.generic * thm;
wenzelm@22365
   360
wenzelm@16725
   361
(*errors involving theorems*)
wenzelm@16725
   362
exception THM of string * int * thm list;
berghofe@13658
   363
wenzelm@28321
   364
fun rep_thm (Thm (_, args)) = args;
clasohm@0
   365
wenzelm@28321
   366
fun crep_thm (Thm (_, {thy_ref, tags, maxidx, shyps, hyps, tpairs, prop})) =
wenzelm@26631
   367
  let fun cterm max t = Cterm {thy_ref = thy_ref, t = t, T = propT, maxidx = max, sorts = shyps} in
wenzelm@28321
   368
   {thy_ref = thy_ref, tags = tags, maxidx = maxidx, shyps = shyps,
wenzelm@16425
   369
    hyps = map (cterm ~1) hyps,
wenzelm@16425
   370
    tpairs = map (pairself (cterm maxidx)) tpairs,
wenzelm@16425
   371
    prop = cterm maxidx prop}
clasohm@1517
   372
  end;
clasohm@1517
   373
wenzelm@16725
   374
fun terms_of_tpairs tpairs = fold_rev (fn (t, u) => cons t o cons u) tpairs [];
wenzelm@16725
   375
wenzelm@16725
   376
fun eq_tpairs ((t, u), (t', u')) = t aconv t' andalso u aconv u';
wenzelm@18944
   377
fun union_tpairs ts us = Library.merge eq_tpairs (ts, us);
wenzelm@16884
   378
val maxidx_tpairs = fold (fn (t, u) => Term.maxidx_term t #> Term.maxidx_term u);
wenzelm@16725
   379
wenzelm@16725
   380
fun attach_tpairs tpairs prop =
wenzelm@16725
   381
  Logic.list_implies (map Logic.mk_equals tpairs, prop);
wenzelm@16725
   382
wenzelm@28321
   383
fun full_prop_of (Thm (_, {tpairs, prop, ...})) = attach_tpairs tpairs prop;
wenzelm@16945
   384
wenzelm@22365
   385
val union_hyps = OrdList.union Term.fast_term_ord;
wenzelm@28354
   386
val insert_hyps = OrdList.insert Term.fast_term_ord;
wenzelm@28354
   387
val remove_hyps = OrdList.remove Term.fast_term_ord;
wenzelm@22365
   388
wenzelm@16945
   389
wenzelm@24143
   390
(* merge theories of cterms/thms -- trivial absorption only *)
wenzelm@16945
   391
wenzelm@28321
   392
fun merge_thys1 (Cterm {thy_ref = r1, ...}) (th as Thm (_, {thy_ref = r2, ...})) =
wenzelm@23601
   393
  Theory.merge_refs (r1, r2);
wenzelm@16945
   394
wenzelm@28321
   395
fun merge_thys2 (th1 as Thm (_, {thy_ref = r1, ...})) (th2 as Thm (_, {thy_ref = r2, ...})) =
wenzelm@23601
   396
  Theory.merge_refs (r1, r2);
wenzelm@16945
   397
clasohm@0
   398
wenzelm@22365
   399
(* basic components *)
wenzelm@16135
   400
wenzelm@28378
   401
fun rep_deriv (Thm (Deriv args, _)) = args;
wenzelm@28378
   402
val oracle_of = #oracle o rep_deriv;
wenzelm@28330
   403
wenzelm@28321
   404
val theory_of_thm = Theory.deref o #thy_ref o rep_thm;
wenzelm@28321
   405
val maxidx_of = #maxidx o rep_thm;
wenzelm@19910
   406
fun maxidx_thm th i = Int.max (maxidx_of th, i);
wenzelm@28321
   407
val hyps_of = #hyps o rep_thm;
wenzelm@28321
   408
val prop_of = #prop o rep_thm;
wenzelm@28321
   409
val tpairs_of = #tpairs o rep_thm;
clasohm@0
   410
wenzelm@16601
   411
val concl_of = Logic.strip_imp_concl o prop_of;
wenzelm@16601
   412
val prems_of = Logic.strip_imp_prems o prop_of;
wenzelm@21576
   413
val nprems_of = Logic.count_prems o prop_of;
wenzelm@19305
   414
fun no_prems th = nprems_of th = 0;
wenzelm@16601
   415
wenzelm@16601
   416
fun major_prem_of th =
wenzelm@16601
   417
  (case prems_of th of
wenzelm@16601
   418
    prem :: _ => Logic.strip_assums_concl prem
wenzelm@16601
   419
  | [] => raise THM ("major_prem_of: rule with no premises", 0, [th]));
wenzelm@16601
   420
wenzelm@16601
   421
(*the statement of any thm is a cterm*)
wenzelm@28321
   422
fun cprop_of (Thm (_, {thy_ref, maxidx, shyps, prop, ...})) =
wenzelm@16601
   423
  Cterm {thy_ref = thy_ref, maxidx = maxidx, T = propT, t = prop, sorts = shyps};
wenzelm@16601
   424
wenzelm@28321
   425
fun cprem_of (th as Thm (_, {thy_ref, maxidx, shyps, prop, ...})) i =
wenzelm@18035
   426
  Cterm {thy_ref = thy_ref, maxidx = maxidx, T = propT, sorts = shyps,
wenzelm@18145
   427
    t = Logic.nth_prem (i, prop) handle TERM _ => raise THM ("cprem_of", i, [th])};
wenzelm@18035
   428
wenzelm@16656
   429
(*explicit transfer to a super theory*)
wenzelm@16425
   430
fun transfer thy' thm =
wenzelm@3895
   431
  let
wenzelm@28321
   432
    val Thm (der, {thy_ref, tags, maxidx, shyps, hyps, tpairs, prop}) = thm;
wenzelm@16425
   433
    val thy = Theory.deref thy_ref;
wenzelm@26665
   434
    val _ = Theory.subthy (thy, thy') orelse raise THM ("transfer: not a super theory", 0, [thm]);
wenzelm@26665
   435
    val is_eq = Theory.eq_thy (thy, thy');
wenzelm@24143
   436
    val _ = Theory.check_thy thy;
wenzelm@3895
   437
  in
wenzelm@24143
   438
    if is_eq then thm
wenzelm@16945
   439
    else
wenzelm@28321
   440
      Thm (der,
wenzelm@28321
   441
       {thy_ref = Theory.check_thy thy',
wenzelm@21646
   442
        tags = tags,
wenzelm@16945
   443
        maxidx = maxidx,
wenzelm@16945
   444
        shyps = shyps,
wenzelm@16945
   445
        hyps = hyps,
wenzelm@16945
   446
        tpairs = tpairs,
wenzelm@28321
   447
        prop = prop})
wenzelm@3895
   448
  end;
wenzelm@387
   449
wenzelm@16945
   450
(*explicit weakening: maps |- B to A |- B*)
wenzelm@16945
   451
fun weaken raw_ct th =
wenzelm@16945
   452
  let
wenzelm@20261
   453
    val ct as Cterm {t = A, T, sorts, maxidx = maxidxA, ...} = adjust_maxidx_cterm ~1 raw_ct;
wenzelm@28321
   454
    val Thm (der, {tags, maxidx, shyps, hyps, tpairs, prop, ...}) = th;
wenzelm@16945
   455
  in
wenzelm@16945
   456
    if T <> propT then
wenzelm@16945
   457
      raise THM ("weaken: assumptions must have type prop", 0, [])
wenzelm@16945
   458
    else if maxidxA <> ~1 then
wenzelm@16945
   459
      raise THM ("weaken: assumptions may not contain schematic variables", maxidxA, [])
wenzelm@16945
   460
    else
wenzelm@28321
   461
      Thm (der,
wenzelm@28321
   462
       {thy_ref = merge_thys1 ct th,
wenzelm@21646
   463
        tags = tags,
wenzelm@16945
   464
        maxidx = maxidx,
wenzelm@16945
   465
        shyps = Sorts.union sorts shyps,
wenzelm@28354
   466
        hyps = insert_hyps A hyps,
wenzelm@16945
   467
        tpairs = tpairs,
wenzelm@28321
   468
        prop = prop})
wenzelm@16945
   469
  end;
wenzelm@16656
   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@26640
   486
        val shyps' = Sorts.subtract (map #2 (Sign.witness_sorts thy present extra)) shyps;
wenzelm@7642
   487
      in
wenzelm@28321
   488
        Thm (der, {thy_ref = Theory.check_thy thy, tags = tags, maxidx = maxidx,
wenzelm@28321
   489
          shyps = shyps', hyps = hyps, tpairs = tpairs, prop = prop})
wenzelm@7642
   490
      end;
wenzelm@1238
   491
wenzelm@16656
   492
(*dangling sort constraints of a thm*)
wenzelm@28321
   493
fun extra_shyps (th as Thm (_, {shyps, ...})) = Sorts.subtract (present_sorts th) shyps;
wenzelm@28321
   494
wenzelm@28321
   495
wenzelm@28321
   496
wenzelm@28321
   497
(** derivations **)
wenzelm@28321
   498
wenzelm@28321
   499
fun make_deriv oracle promises proof =
wenzelm@28321
   500
  Deriv {oracle = oracle, promises = promises, proof = proof};
wenzelm@28321
   501
wenzelm@28321
   502
val empty_deriv = make_deriv false [] Pt.min_proof;
wenzelm@28321
   503
wenzelm@28330
   504
wenzelm@28354
   505
(* inference rules *)
wenzelm@28321
   506
wenzelm@28378
   507
fun promise_ord ((i, _), (j, _)) = int_ord (j, i);
wenzelm@28330
   508
wenzelm@28321
   509
fun deriv_rule2 f
wenzelm@28321
   510
    (Deriv {oracle = ora1, promises = ps1, proof = prf1})
wenzelm@28321
   511
    (Deriv {oracle = ora2, promises = ps2, proof = prf2}) =
wenzelm@28321
   512
  let
wenzelm@28321
   513
    val ora = ora1 orelse ora2;
wenzelm@28330
   514
    val ps = OrdList.union promise_ord ps1 ps2;
wenzelm@28321
   515
    val prf =
wenzelm@28321
   516
      (case ! Pt.proofs of
wenzelm@28321
   517
        2 => f prf1 prf2
wenzelm@28321
   518
      | 1 => MinProof (([], [], []) |> Pt.mk_min_proof prf1 |> Pt.mk_min_proof prf2)
wenzelm@28321
   519
      | 0 =>
wenzelm@28330
   520
          if ora then MinProof ([], [], [] |> Pt.add_oracles ora1 prf1 |> Pt.add_oracles ora2 prf2)
wenzelm@28321
   521
          else Pt.min_proof
wenzelm@28321
   522
      | i => error ("Illegal level of detail for proof objects: " ^ string_of_int i));
wenzelm@28321
   523
  in make_deriv ora ps prf end;
wenzelm@28321
   524
wenzelm@28321
   525
fun deriv_rule1 f = deriv_rule2 (K f) empty_deriv;
wenzelm@28321
   526
fun deriv_rule0 prf = deriv_rule1 I (make_deriv false [] prf);
wenzelm@28321
   527
wenzelm@1238
   528
wenzelm@1238
   529
paulson@1529
   530
(** Axioms **)
wenzelm@387
   531
wenzelm@16425
   532
(*look up the named axiom in the theory or its ancestors*)
wenzelm@15672
   533
fun get_axiom_i theory name =
wenzelm@387
   534
  let
wenzelm@16425
   535
    fun get_ax thy =
wenzelm@22685
   536
      Symtab.lookup (Theory.axiom_table thy) name
wenzelm@16601
   537
      |> Option.map (fn prop =>
wenzelm@24143
   538
           let
wenzelm@28321
   539
             val der = deriv_rule0 (Pt.axm_proof name prop);
wenzelm@24143
   540
             val maxidx = maxidx_of_term prop;
wenzelm@26640
   541
             val shyps = Sorts.insert_term prop [];
wenzelm@24143
   542
           in
wenzelm@28321
   543
             Thm (der, {thy_ref = Theory.check_thy thy, tags = [],
wenzelm@28321
   544
               maxidx = maxidx, shyps = shyps, hyps = [], tpairs = [], prop = prop})
wenzelm@24143
   545
           end);
wenzelm@387
   546
  in
wenzelm@16425
   547
    (case get_first get_ax (theory :: Theory.ancestors_of theory) of
skalberg@15531
   548
      SOME thm => thm
skalberg@15531
   549
    | NONE => raise THEORY ("No axiom " ^ quote name, [theory]))
wenzelm@387
   550
  end;
wenzelm@387
   551
wenzelm@16352
   552
fun get_axiom thy =
wenzelm@16425
   553
  get_axiom_i thy o NameSpace.intern (Theory.axiom_space thy);
wenzelm@15672
   554
wenzelm@20884
   555
fun def_name c = c ^ "_def";
wenzelm@20884
   556
wenzelm@20884
   557
fun def_name_optional c "" = def_name c
wenzelm@20884
   558
  | def_name_optional _ name = name;
wenzelm@20884
   559
wenzelm@6368
   560
fun get_def thy = get_axiom thy o def_name;
wenzelm@4847
   561
paulson@1529
   562
wenzelm@776
   563
(*return additional axioms of this theory node*)
wenzelm@776
   564
fun axioms_of thy =
wenzelm@22685
   565
  map (fn s => (s, get_axiom_i thy s)) (Symtab.keys (Theory.axiom_table thy));
wenzelm@776
   566
wenzelm@6089
   567
wenzelm@21646
   568
(* official name and additional tags *)
wenzelm@6089
   569
wenzelm@28330
   570
fun get_name (Thm (Deriv {proof, ...}, {hyps, prop, ...})) = Pt.get_name hyps prop proof;
wenzelm@4018
   571
wenzelm@28330
   572
fun put_name name thm =
wenzelm@28330
   573
  let
wenzelm@28330
   574
    val Thm (Deriv {oracle, promises, proof}, args as {thy_ref, hyps, prop, tpairs, ...}) = thm;
wenzelm@28330
   575
    val _ = null tpairs orelse raise THM ("name_thm: unsolved flex-flex constraints", 0, [thm]);
wenzelm@28330
   576
    val thy = Theory.deref thy_ref;
wenzelm@28330
   577
    val der' = make_deriv oracle promises (Pt.thm_proof thy name hyps prop proof);
wenzelm@28330
   578
    val _ = Theory.check_thy thy;
wenzelm@28330
   579
  in Thm (der', args) end;
wenzelm@28321
   580
wenzelm@6089
   581
wenzelm@21646
   582
val get_tags = #tags o rep_thm;
wenzelm@6089
   583
wenzelm@28321
   584
fun map_tags f (Thm (der, {thy_ref, tags, maxidx, shyps, hyps, tpairs, prop})) =
wenzelm@28321
   585
  Thm (der, {thy_ref = thy_ref, tags = f tags, maxidx = maxidx,
wenzelm@28321
   586
    shyps = shyps, hyps = hyps, tpairs = tpairs, prop = prop});
clasohm@0
   587
clasohm@0
   588
wenzelm@28321
   589
fun norm_proof (Thm (der, args as {thy_ref, ...})) =
wenzelm@24143
   590
  let
wenzelm@24143
   591
    val thy = Theory.deref thy_ref;
wenzelm@28321
   592
    val der' = deriv_rule1 (Pt.rew_proof thy) der;
wenzelm@28321
   593
    val _ = Theory.check_thy thy;
wenzelm@28321
   594
  in Thm (der', args) end;
berghofe@23781
   595
wenzelm@28321
   596
fun adjust_maxidx_thm i (th as Thm (der, {thy_ref, tags, maxidx, shyps, hyps, tpairs, prop})) =
wenzelm@20261
   597
  if maxidx = i then th
wenzelm@20261
   598
  else if maxidx < i then
wenzelm@28321
   599
    Thm (der, {maxidx = i, thy_ref = thy_ref, tags = tags, shyps = shyps,
wenzelm@28321
   600
      hyps = hyps, tpairs = tpairs, prop = prop})
wenzelm@20261
   601
  else
wenzelm@28321
   602
    Thm (der, {maxidx = Int.max (maxidx_tpairs tpairs (maxidx_of_term prop), i), thy_ref = thy_ref,
wenzelm@28321
   603
      tags = tags, shyps = shyps, hyps = hyps, tpairs = tpairs, prop = prop});
wenzelm@564
   604
wenzelm@387
   605
wenzelm@2509
   606
paulson@1529
   607
(*** Meta rules ***)
clasohm@0
   608
wenzelm@16601
   609
(** primitive rules **)
clasohm@0
   610
wenzelm@16656
   611
(*The assumption rule A |- A*)
wenzelm@16601
   612
fun assume raw_ct =
wenzelm@20261
   613
  let val Cterm {thy_ref, t = prop, T, maxidx, sorts} = adjust_maxidx_cterm ~1 raw_ct in
wenzelm@16601
   614
    if T <> propT then
mengj@19230
   615
      raise THM ("assume: prop", 0, [])
wenzelm@16601
   616
    else if maxidx <> ~1 then
mengj@19230
   617
      raise THM ("assume: variables", maxidx, [])
wenzelm@28321
   618
    else Thm (deriv_rule0 (Pt.Hyp prop),
wenzelm@28321
   619
     {thy_ref = thy_ref,
wenzelm@21646
   620
      tags = [],
wenzelm@16601
   621
      maxidx = ~1,
wenzelm@16601
   622
      shyps = sorts,
wenzelm@16601
   623
      hyps = [prop],
wenzelm@16601
   624
      tpairs = [],
wenzelm@28321
   625
      prop = prop})
clasohm@0
   626
  end;
clasohm@0
   627
wenzelm@1220
   628
(*Implication introduction
wenzelm@3529
   629
    [A]
wenzelm@3529
   630
     :
wenzelm@3529
   631
     B
wenzelm@1220
   632
  -------
wenzelm@1220
   633
  A ==> B
wenzelm@1220
   634
*)
wenzelm@16601
   635
fun implies_intr
wenzelm@16679
   636
    (ct as Cterm {t = A, T, maxidx = maxidxA, sorts, ...})
wenzelm@28321
   637
    (th as Thm (der, {maxidx, hyps, shyps, tpairs, prop, ...})) =
wenzelm@16601
   638
  if T <> propT then
wenzelm@16601
   639
    raise THM ("implies_intr: assumptions must have type prop", 0, [th])
wenzelm@16601
   640
  else
wenzelm@28321
   641
    Thm (deriv_rule1 (Pt.implies_intr_proof A) der,
wenzelm@28321
   642
     {thy_ref = merge_thys1 ct th,
wenzelm@21646
   643
      tags = [],
wenzelm@16601
   644
      maxidx = Int.max (maxidxA, maxidx),
wenzelm@16601
   645
      shyps = Sorts.union sorts shyps,
wenzelm@28354
   646
      hyps = remove_hyps A hyps,
wenzelm@16601
   647
      tpairs = tpairs,
wenzelm@28321
   648
      prop = Logic.mk_implies (A, prop)});
clasohm@0
   649
paulson@1529
   650
wenzelm@1220
   651
(*Implication elimination
wenzelm@1220
   652
  A ==> B    A
wenzelm@1220
   653
  ------------
wenzelm@1220
   654
        B
wenzelm@1220
   655
*)
wenzelm@16601
   656
fun implies_elim thAB thA =
wenzelm@16601
   657
  let
wenzelm@28321
   658
    val Thm (derA, {maxidx = maxA, hyps = hypsA, shyps = shypsA, tpairs = tpairsA,
wenzelm@28321
   659
      prop = propA, ...}) = thA
wenzelm@28321
   660
    and Thm (der, {maxidx, hyps, shyps, tpairs, prop, ...}) = thAB;
wenzelm@16601
   661
    fun err () = raise THM ("implies_elim: major premise", 0, [thAB, thA]);
wenzelm@16601
   662
  in
wenzelm@16601
   663
    case prop of
wenzelm@20512
   664
      Const ("==>", _) $ A $ B =>
wenzelm@20512
   665
        if A aconv propA then
wenzelm@28321
   666
          Thm (deriv_rule2 (curry Pt.%%) der derA,
wenzelm@28321
   667
           {thy_ref = merge_thys2 thAB thA,
wenzelm@21646
   668
            tags = [],
wenzelm@16601
   669
            maxidx = Int.max (maxA, maxidx),
wenzelm@16601
   670
            shyps = Sorts.union shypsA shyps,
wenzelm@16601
   671
            hyps = union_hyps hypsA hyps,
wenzelm@16601
   672
            tpairs = union_tpairs tpairsA tpairs,
wenzelm@28321
   673
            prop = B})
wenzelm@16601
   674
        else err ()
wenzelm@16601
   675
    | _ => err ()
wenzelm@16601
   676
  end;
wenzelm@250
   677
wenzelm@1220
   678
(*Forall introduction.  The Free or Var x must not be free in the hypotheses.
wenzelm@16656
   679
    [x]
wenzelm@16656
   680
     :
wenzelm@16656
   681
     A
wenzelm@16656
   682
  ------
wenzelm@16656
   683
  !!x. A
wenzelm@1220
   684
*)
wenzelm@16601
   685
fun forall_intr
wenzelm@16601
   686
    (ct as Cterm {t = x, T, sorts, ...})
wenzelm@28321
   687
    (th as Thm (der, {maxidx, shyps, hyps, tpairs, prop, ...})) =
wenzelm@16601
   688
  let
wenzelm@16601
   689
    fun result a =
wenzelm@28321
   690
      Thm (deriv_rule1 (Pt.forall_intr_proof x a) der,
wenzelm@28321
   691
       {thy_ref = merge_thys1 ct th,
wenzelm@21646
   692
        tags = [],
wenzelm@16601
   693
        maxidx = maxidx,
wenzelm@16601
   694
        shyps = Sorts.union sorts shyps,
wenzelm@16601
   695
        hyps = hyps,
wenzelm@16601
   696
        tpairs = tpairs,
wenzelm@28321
   697
        prop = Term.all T $ Abs (a, T, abstract_over (x, prop))});
wenzelm@21798
   698
    fun check_occs a x ts =
wenzelm@16847
   699
      if exists (fn t => Logic.occs (x, t)) ts then
wenzelm@21798
   700
        raise THM ("forall_intr: variable " ^ quote a ^ " free in assumptions", 0, [th])
wenzelm@16601
   701
      else ();
wenzelm@16601
   702
  in
wenzelm@16601
   703
    case x of
wenzelm@21798
   704
      Free (a, _) => (check_occs a x hyps; check_occs a x (terms_of_tpairs tpairs); result a)
wenzelm@21798
   705
    | Var ((a, _), _) => (check_occs a x (terms_of_tpairs tpairs); result a)
wenzelm@16601
   706
    | _ => raise THM ("forall_intr: not a variable", 0, [th])
clasohm@0
   707
  end;
clasohm@0
   708
wenzelm@1220
   709
(*Forall elimination
wenzelm@16656
   710
  !!x. A
wenzelm@1220
   711
  ------
wenzelm@1220
   712
  A[t/x]
wenzelm@1220
   713
*)
wenzelm@16601
   714
fun forall_elim
wenzelm@16601
   715
    (ct as Cterm {t, T, maxidx = maxt, sorts, ...})
wenzelm@28321
   716
    (th as Thm (der, {maxidx, shyps, hyps, tpairs, prop, ...})) =
wenzelm@16601
   717
  (case prop of
wenzelm@16601
   718
    Const ("all", Type ("fun", [Type ("fun", [qary, _]), _])) $ A =>
wenzelm@16601
   719
      if T <> qary then
wenzelm@16601
   720
        raise THM ("forall_elim: type mismatch", 0, [th])
wenzelm@16601
   721
      else
wenzelm@28321
   722
        Thm (deriv_rule1 (Pt.% o rpair (SOME t)) der,
wenzelm@28321
   723
         {thy_ref = merge_thys1 ct th,
wenzelm@21646
   724
          tags = [],
wenzelm@16601
   725
          maxidx = Int.max (maxidx, maxt),
wenzelm@16601
   726
          shyps = Sorts.union sorts shyps,
wenzelm@16601
   727
          hyps = hyps,
wenzelm@16601
   728
          tpairs = tpairs,
wenzelm@28321
   729
          prop = Term.betapply (A, t)})
wenzelm@16601
   730
  | _ => raise THM ("forall_elim: not quantified", 0, [th]));
clasohm@0
   731
clasohm@0
   732
wenzelm@1220
   733
(* Equality *)
clasohm@0
   734
wenzelm@16601
   735
(*Reflexivity
wenzelm@16601
   736
  t == t
wenzelm@16601
   737
*)
wenzelm@16601
   738
fun reflexive (ct as Cterm {thy_ref, t, T, maxidx, sorts}) =
wenzelm@28321
   739
  Thm (deriv_rule0 Pt.reflexive,
wenzelm@28321
   740
   {thy_ref = thy_ref,
wenzelm@21646
   741
    tags = [],
wenzelm@16601
   742
    maxidx = maxidx,
wenzelm@16601
   743
    shyps = sorts,
wenzelm@16601
   744
    hyps = [],
wenzelm@16601
   745
    tpairs = [],
wenzelm@28321
   746
    prop = Logic.mk_equals (t, t)});
clasohm@0
   747
wenzelm@16601
   748
(*Symmetry
wenzelm@16601
   749
  t == u
wenzelm@16601
   750
  ------
wenzelm@16601
   751
  u == t
wenzelm@1220
   752
*)
wenzelm@28321
   753
fun symmetric (th as Thm (der, {thy_ref, maxidx, shyps, hyps, tpairs, prop, ...})) =
wenzelm@16601
   754
  (case prop of
wenzelm@16601
   755
    (eq as Const ("==", Type (_, [T, _]))) $ t $ u =>
wenzelm@28321
   756
      Thm (deriv_rule1 Pt.symmetric der,
wenzelm@28321
   757
       {thy_ref = thy_ref,
wenzelm@21646
   758
        tags = [],
wenzelm@16601
   759
        maxidx = maxidx,
wenzelm@16601
   760
        shyps = shyps,
wenzelm@16601
   761
        hyps = hyps,
wenzelm@16601
   762
        tpairs = tpairs,
wenzelm@28321
   763
        prop = eq $ u $ t})
wenzelm@16601
   764
    | _ => raise THM ("symmetric", 0, [th]));
clasohm@0
   765
wenzelm@16601
   766
(*Transitivity
wenzelm@16601
   767
  t1 == u    u == t2
wenzelm@16601
   768
  ------------------
wenzelm@16601
   769
       t1 == t2
wenzelm@1220
   770
*)
clasohm@0
   771
fun transitive th1 th2 =
wenzelm@16601
   772
  let
wenzelm@28321
   773
    val Thm (der1, {maxidx = max1, hyps = hyps1, shyps = shyps1, tpairs = tpairs1,
wenzelm@28321
   774
      prop = prop1, ...}) = th1
wenzelm@28321
   775
    and Thm (der2, {maxidx = max2, hyps = hyps2, shyps = shyps2, tpairs = tpairs2,
wenzelm@28321
   776
      prop = prop2, ...}) = th2;
wenzelm@16601
   777
    fun err msg = raise THM ("transitive: " ^ msg, 0, [th1, th2]);
wenzelm@16601
   778
  in
wenzelm@16601
   779
    case (prop1, prop2) of
wenzelm@16601
   780
      ((eq as Const ("==", Type (_, [T, _]))) $ t1 $ u, Const ("==", _) $ u' $ t2) =>
wenzelm@16601
   781
        if not (u aconv u') then err "middle term"
wenzelm@16601
   782
        else
wenzelm@28321
   783
          Thm (deriv_rule2 (Pt.transitive u T) der1 der2,
wenzelm@28321
   784
           {thy_ref = merge_thys2 th1 th2,
wenzelm@21646
   785
            tags = [],
wenzelm@16601
   786
            maxidx = Int.max (max1, max2),
wenzelm@16601
   787
            shyps = Sorts.union shyps1 shyps2,
wenzelm@16601
   788
            hyps = union_hyps hyps1 hyps2,
wenzelm@16601
   789
            tpairs = union_tpairs tpairs1 tpairs2,
wenzelm@28321
   790
            prop = eq $ t1 $ t2})
wenzelm@16601
   791
     | _ =>  err "premises"
clasohm@0
   792
  end;
clasohm@0
   793
wenzelm@16601
   794
(*Beta-conversion
wenzelm@16656
   795
  (%x. t)(u) == t[u/x]
wenzelm@16601
   796
  fully beta-reduces the term if full = true
berghofe@10416
   797
*)
wenzelm@16601
   798
fun beta_conversion full (Cterm {thy_ref, t, T, maxidx, sorts}) =
wenzelm@16601
   799
  let val t' =
wenzelm@16601
   800
    if full then Envir.beta_norm t
wenzelm@16601
   801
    else
wenzelm@16601
   802
      (case t of Abs (_, _, bodt) $ u => subst_bound (u, bodt)
wenzelm@16601
   803
      | _ => raise THM ("beta_conversion: not a redex", 0, []));
wenzelm@16601
   804
  in
wenzelm@28321
   805
    Thm (deriv_rule0 Pt.reflexive,
wenzelm@28321
   806
     {thy_ref = thy_ref,
wenzelm@21646
   807
      tags = [],
wenzelm@16601
   808
      maxidx = maxidx,
wenzelm@16601
   809
      shyps = sorts,
wenzelm@16601
   810
      hyps = [],
wenzelm@16601
   811
      tpairs = [],
wenzelm@28321
   812
      prop = Logic.mk_equals (t, t')})
berghofe@10416
   813
  end;
berghofe@10416
   814
wenzelm@16601
   815
fun eta_conversion (Cterm {thy_ref, t, T, maxidx, sorts}) =
wenzelm@28321
   816
  Thm (deriv_rule0 Pt.reflexive,
wenzelm@28321
   817
   {thy_ref = thy_ref,
wenzelm@21646
   818
    tags = [],
wenzelm@16601
   819
    maxidx = maxidx,
wenzelm@16601
   820
    shyps = sorts,
wenzelm@16601
   821
    hyps = [],
wenzelm@16601
   822
    tpairs = [],
wenzelm@28321
   823
    prop = Logic.mk_equals (t, Envir.eta_contract t)});
clasohm@0
   824
wenzelm@23493
   825
fun eta_long_conversion (Cterm {thy_ref, t, T, maxidx, sorts}) =
wenzelm@28321
   826
  Thm (deriv_rule0 Pt.reflexive,
wenzelm@28321
   827
   {thy_ref = thy_ref,
wenzelm@23493
   828
    tags = [],
wenzelm@23493
   829
    maxidx = maxidx,
wenzelm@23493
   830
    shyps = sorts,
wenzelm@23493
   831
    hyps = [],
wenzelm@23493
   832
    tpairs = [],
wenzelm@28321
   833
    prop = Logic.mk_equals (t, Pattern.eta_long [] t)});
wenzelm@23493
   834
clasohm@0
   835
(*The abstraction rule.  The Free or Var x must not be free in the hypotheses.
clasohm@0
   836
  The bound variable will be named "a" (since x will be something like x320)
wenzelm@16601
   837
      t == u
wenzelm@16601
   838
  --------------
wenzelm@16601
   839
  %x. t == %x. u
wenzelm@1220
   840
*)
wenzelm@16601
   841
fun abstract_rule a
wenzelm@16601
   842
    (Cterm {t = x, T, sorts, ...})
wenzelm@28321
   843
    (th as Thm (der, {thy_ref, maxidx, hyps, shyps, tpairs, prop, ...})) =
wenzelm@16601
   844
  let
wenzelm@16601
   845
    val (t, u) = Logic.dest_equals prop
wenzelm@16601
   846
      handle TERM _ => raise THM ("abstract_rule: premise not an equality", 0, [th]);
wenzelm@16601
   847
    val result =
wenzelm@28321
   848
      Thm (deriv_rule1 (Pt.abstract_rule x a) der,
wenzelm@28321
   849
       {thy_ref = thy_ref,
wenzelm@21646
   850
        tags = [],
wenzelm@16601
   851
        maxidx = maxidx,
wenzelm@16601
   852
        shyps = Sorts.union sorts shyps,
wenzelm@16601
   853
        hyps = hyps,
wenzelm@16601
   854
        tpairs = tpairs,
wenzelm@16601
   855
        prop = Logic.mk_equals
wenzelm@28321
   856
          (Abs (a, T, abstract_over (x, t)), Abs (a, T, abstract_over (x, u)))});
wenzelm@21798
   857
    fun check_occs a x ts =
wenzelm@16847
   858
      if exists (fn t => Logic.occs (x, t)) ts then
wenzelm@21798
   859
        raise THM ("abstract_rule: variable " ^ quote a ^ " free in assumptions", 0, [th])
wenzelm@16601
   860
      else ();
wenzelm@16601
   861
  in
wenzelm@16601
   862
    case x of
wenzelm@21798
   863
      Free (a, _) => (check_occs a x hyps; check_occs a x (terms_of_tpairs tpairs); result)
wenzelm@21798
   864
    | Var ((a, _), _) => (check_occs a x (terms_of_tpairs tpairs); result)
wenzelm@21798
   865
    | _ => raise THM ("abstract_rule: not a variable", 0, [th])
clasohm@0
   866
  end;
clasohm@0
   867
clasohm@0
   868
(*The combination rule
wenzelm@3529
   869
  f == g  t == u
wenzelm@3529
   870
  --------------
wenzelm@16601
   871
    f t == g u
wenzelm@1220
   872
*)
clasohm@0
   873
fun combination th1 th2 =
wenzelm@16601
   874
  let
wenzelm@28321
   875
    val Thm (der1, {maxidx = max1, shyps = shyps1, hyps = hyps1, tpairs = tpairs1,
wenzelm@28321
   876
      prop = prop1, ...}) = th1
wenzelm@28321
   877
    and Thm (der2, {maxidx = max2, shyps = shyps2, hyps = hyps2, tpairs = tpairs2,
wenzelm@28321
   878
      prop = prop2, ...}) = th2;
wenzelm@16601
   879
    fun chktypes fT tT =
wenzelm@16601
   880
      (case fT of
wenzelm@16601
   881
        Type ("fun", [T1, T2]) =>
wenzelm@16601
   882
          if T1 <> tT then
wenzelm@16601
   883
            raise THM ("combination: types", 0, [th1, th2])
wenzelm@16601
   884
          else ()
wenzelm@16601
   885
      | _ => raise THM ("combination: not function type", 0, [th1, th2]));
wenzelm@16601
   886
  in
wenzelm@16601
   887
    case (prop1, prop2) of
wenzelm@16601
   888
      (Const ("==", Type ("fun", [fT, _])) $ f $ g,
wenzelm@16601
   889
       Const ("==", Type ("fun", [tT, _])) $ t $ u) =>
wenzelm@16601
   890
        (chktypes fT tT;
wenzelm@28321
   891
          Thm (deriv_rule2 (Pt.combination f g t u fT) der1 der2,
wenzelm@28321
   892
           {thy_ref = merge_thys2 th1 th2,
wenzelm@21646
   893
            tags = [],
wenzelm@16601
   894
            maxidx = Int.max (max1, max2),
wenzelm@16601
   895
            shyps = Sorts.union shyps1 shyps2,
wenzelm@16601
   896
            hyps = union_hyps hyps1 hyps2,
wenzelm@16601
   897
            tpairs = union_tpairs tpairs1 tpairs2,
wenzelm@28321
   898
            prop = Logic.mk_equals (f $ t, g $ u)}))
wenzelm@16601
   899
     | _ => raise THM ("combination: premises", 0, [th1, th2])
clasohm@0
   900
  end;
clasohm@0
   901
wenzelm@16601
   902
(*Equality introduction
wenzelm@3529
   903
  A ==> B  B ==> A
wenzelm@3529
   904
  ----------------
wenzelm@3529
   905
       A == B
wenzelm@1220
   906
*)
clasohm@0
   907
fun equal_intr th1 th2 =
wenzelm@16601
   908
  let
wenzelm@28321
   909
    val Thm (der1, {maxidx = max1, shyps = shyps1, hyps = hyps1, tpairs = tpairs1,
wenzelm@28321
   910
      prop = prop1, ...}) = th1
wenzelm@28321
   911
    and Thm (der2, {maxidx = max2, shyps = shyps2, hyps = hyps2, tpairs = tpairs2,
wenzelm@28321
   912
      prop = prop2, ...}) = th2;
wenzelm@16601
   913
    fun err msg = raise THM ("equal_intr: " ^ msg, 0, [th1, th2]);
wenzelm@16601
   914
  in
wenzelm@16601
   915
    case (prop1, prop2) of
wenzelm@16601
   916
      (Const("==>", _) $ A $ B, Const("==>", _) $ B' $ A') =>
wenzelm@16601
   917
        if A aconv A' andalso B aconv B' then
wenzelm@28321
   918
          Thm (deriv_rule2 (Pt.equal_intr A B) der1 der2,
wenzelm@28321
   919
           {thy_ref = merge_thys2 th1 th2,
wenzelm@21646
   920
            tags = [],
wenzelm@16601
   921
            maxidx = Int.max (max1, max2),
wenzelm@16601
   922
            shyps = Sorts.union shyps1 shyps2,
wenzelm@16601
   923
            hyps = union_hyps hyps1 hyps2,
wenzelm@16601
   924
            tpairs = union_tpairs tpairs1 tpairs2,
wenzelm@28321
   925
            prop = Logic.mk_equals (A, B)})
wenzelm@16601
   926
        else err "not equal"
wenzelm@16601
   927
    | _ =>  err "premises"
paulson@1529
   928
  end;
paulson@1529
   929
paulson@1529
   930
(*The equal propositions rule
wenzelm@3529
   931
  A == B  A
paulson@1529
   932
  ---------
paulson@1529
   933
      B
paulson@1529
   934
*)
paulson@1529
   935
fun equal_elim th1 th2 =
wenzelm@16601
   936
  let
wenzelm@28321
   937
    val Thm (der1, {maxidx = max1, shyps = shyps1, hyps = hyps1,
wenzelm@28321
   938
      tpairs = tpairs1, prop = prop1, ...}) = th1
wenzelm@28321
   939
    and Thm (der2, {maxidx = max2, shyps = shyps2, hyps = hyps2,
wenzelm@28321
   940
      tpairs = tpairs2, prop = prop2, ...}) = th2;
wenzelm@16601
   941
    fun err msg = raise THM ("equal_elim: " ^ msg, 0, [th1, th2]);
wenzelm@16601
   942
  in
wenzelm@16601
   943
    case prop1 of
wenzelm@16601
   944
      Const ("==", _) $ A $ B =>
wenzelm@16601
   945
        if prop2 aconv A then
wenzelm@28321
   946
          Thm (deriv_rule2 (Pt.equal_elim A B) der1 der2,
wenzelm@28321
   947
           {thy_ref = merge_thys2 th1 th2,
wenzelm@21646
   948
            tags = [],
wenzelm@16601
   949
            maxidx = Int.max (max1, max2),
wenzelm@16601
   950
            shyps = Sorts.union shyps1 shyps2,
wenzelm@16601
   951
            hyps = union_hyps hyps1 hyps2,
wenzelm@16601
   952
            tpairs = union_tpairs tpairs1 tpairs2,
wenzelm@28321
   953
            prop = B})
wenzelm@16601
   954
        else err "not equal"
paulson@1529
   955
     | _ =>  err"major premise"
paulson@1529
   956
  end;
clasohm@0
   957
wenzelm@1220
   958
wenzelm@1220
   959
clasohm@0
   960
(**** Derived rules ****)
clasohm@0
   961
wenzelm@16601
   962
(*Smash unifies the list of term pairs leaving no flex-flex pairs.
wenzelm@24143
   963
  Instantiates the theorem and deletes trivial tpairs.  Resulting
wenzelm@24143
   964
  sequence may contain multiple elements if the tpairs are not all
wenzelm@24143
   965
  flex-flex.*)
wenzelm@28321
   966
fun flexflex_rule (th as Thm (der, {thy_ref, maxidx, shyps, hyps, tpairs, prop, ...})) =
wenzelm@24143
   967
  let val thy = Theory.deref thy_ref in
wenzelm@24143
   968
    Unify.smash_unifiers thy tpairs (Envir.empty maxidx)
wenzelm@24143
   969
    |> Seq.map (fn env =>
wenzelm@24143
   970
        if Envir.is_empty env then th
wenzelm@24143
   971
        else
wenzelm@24143
   972
          let
wenzelm@24143
   973
            val tpairs' = tpairs |> map (pairself (Envir.norm_term env))
wenzelm@24143
   974
              (*remove trivial tpairs, of the form t==t*)
wenzelm@24143
   975
              |> filter_out (op aconv);
wenzelm@28321
   976
            val der' = deriv_rule1 (Pt.norm_proof' env) der;
wenzelm@24143
   977
            val prop' = Envir.norm_term env prop;
wenzelm@24143
   978
            val maxidx = maxidx_tpairs tpairs' (maxidx_of_term prop');
wenzelm@26640
   979
            val shyps = Envir.insert_sorts env shyps;
wenzelm@24143
   980
          in
wenzelm@28321
   981
            Thm (der', {thy_ref = Theory.check_thy thy, tags = [], maxidx = maxidx,
wenzelm@28321
   982
              shyps = shyps, hyps = hyps, tpairs = tpairs', prop = prop'})
wenzelm@24143
   983
          end)
wenzelm@24143
   984
  end;
wenzelm@16601
   985
clasohm@0
   986
wenzelm@19910
   987
(*Generalization of fixed variables
wenzelm@19910
   988
           A
wenzelm@19910
   989
  --------------------
wenzelm@19910
   990
  A[?'a/'a, ?x/x, ...]
wenzelm@19910
   991
*)
wenzelm@19910
   992
wenzelm@19910
   993
fun generalize ([], []) _ th = th
wenzelm@19910
   994
  | generalize (tfrees, frees) idx th =
wenzelm@19910
   995
      let
wenzelm@28321
   996
        val Thm (der, {thy_ref, maxidx, shyps, hyps, tpairs, prop, ...}) = th;
wenzelm@19910
   997
        val _ = idx <= maxidx andalso raise THM ("generalize: bad index", idx, [th]);
wenzelm@19910
   998
wenzelm@19910
   999
        val bad_type = if null tfrees then K false else
wenzelm@19910
  1000
          Term.exists_subtype (fn TFree (a, _) => member (op =) tfrees a | _ => false);
wenzelm@19910
  1001
        fun bad_term (Free (x, T)) = bad_type T orelse member (op =) frees x
wenzelm@19910
  1002
          | bad_term (Var (_, T)) = bad_type T
wenzelm@19910
  1003
          | bad_term (Const (_, T)) = bad_type T
wenzelm@19910
  1004
          | bad_term (Abs (_, T, t)) = bad_type T orelse bad_term t
wenzelm@19910
  1005
          | bad_term (t $ u) = bad_term t orelse bad_term u
wenzelm@19910
  1006
          | bad_term (Bound _) = false;
wenzelm@19910
  1007
        val _ = exists bad_term hyps andalso
wenzelm@19910
  1008
          raise THM ("generalize: variable free in assumptions", 0, [th]);
wenzelm@19910
  1009
wenzelm@20512
  1010
        val gen = TermSubst.generalize (tfrees, frees) idx;
wenzelm@19910
  1011
        val prop' = gen prop;
wenzelm@19910
  1012
        val tpairs' = map (pairself gen) tpairs;
wenzelm@19910
  1013
        val maxidx' = maxidx_tpairs tpairs' (maxidx_of_term prop');
wenzelm@19910
  1014
      in
wenzelm@28321
  1015
        Thm (deriv_rule1 (Pt.generalize (tfrees, frees) idx) der,
wenzelm@28321
  1016
         {thy_ref = thy_ref,
wenzelm@21646
  1017
          tags = [],
wenzelm@19910
  1018
          maxidx = maxidx',
wenzelm@19910
  1019
          shyps = shyps,
wenzelm@19910
  1020
          hyps = hyps,
wenzelm@19910
  1021
          tpairs = tpairs',
wenzelm@28321
  1022
          prop = prop'})
wenzelm@19910
  1023
      end;
wenzelm@19910
  1024
wenzelm@19910
  1025
wenzelm@22584
  1026
(*Instantiation of schematic variables
wenzelm@16656
  1027
           A
wenzelm@16656
  1028
  --------------------
wenzelm@16656
  1029
  A[t1/v1, ..., tn/vn]
wenzelm@1220
  1030
*)
clasohm@0
  1031
wenzelm@6928
  1032
local
wenzelm@6928
  1033
wenzelm@26939
  1034
fun pretty_typing thy t T = Pretty.block
wenzelm@26939
  1035
  [Syntax.pretty_term_global thy t, Pretty.str " ::", Pretty.brk 1, Syntax.pretty_typ_global thy T];
berghofe@15797
  1036
wenzelm@16884
  1037
fun add_inst (ct, cu) (thy_ref, sorts) =
wenzelm@6928
  1038
  let
wenzelm@26939
  1039
    val Cterm {t = t, T = T, ...} = ct;
wenzelm@26939
  1040
    val Cterm {t = u, T = U, sorts = sorts_u, maxidx = maxidx_u, ...} = cu;
wenzelm@16884
  1041
    val thy_ref' = Theory.merge_refs (thy_ref, merge_thys0 ct cu);
wenzelm@16884
  1042
    val sorts' = Sorts.union sorts_u sorts;
wenzelm@3967
  1043
  in
wenzelm@16884
  1044
    (case t of Var v =>
wenzelm@20512
  1045
      if T = U then ((v, (u, maxidx_u)), (thy_ref', sorts'))
wenzelm@16884
  1046
      else raise TYPE (Pretty.string_of (Pretty.block
wenzelm@16884
  1047
       [Pretty.str "instantiate: type conflict",
wenzelm@16884
  1048
        Pretty.fbrk, pretty_typing (Theory.deref thy_ref') t T,
wenzelm@16884
  1049
        Pretty.fbrk, pretty_typing (Theory.deref thy_ref') u U]), [T, U], [t, u])
wenzelm@16884
  1050
    | _ => raise TYPE (Pretty.string_of (Pretty.block
wenzelm@16884
  1051
       [Pretty.str "instantiate: not a variable",
wenzelm@26939
  1052
        Pretty.fbrk, Syntax.pretty_term_global (Theory.deref thy_ref') t]), [], [t]))
clasohm@0
  1053
  end;
clasohm@0
  1054
wenzelm@16884
  1055
fun add_instT (cT, cU) (thy_ref, sorts) =
wenzelm@16656
  1056
  let
wenzelm@16884
  1057
    val Ctyp {T, thy_ref = thy_ref1, ...} = cT
wenzelm@20512
  1058
    and Ctyp {T = U, thy_ref = thy_ref2, sorts = sorts_U, maxidx = maxidx_U, ...} = cU;
wenzelm@24143
  1059
    val thy' = Theory.deref (Theory.merge_refs (thy_ref, Theory.merge_refs (thy_ref1, thy_ref2)));
wenzelm@16884
  1060
    val sorts' = Sorts.union sorts_U sorts;
wenzelm@16656
  1061
  in
wenzelm@16884
  1062
    (case T of TVar (v as (_, S)) =>
wenzelm@24143
  1063
      if Sign.of_sort thy' (U, S) then ((v, (U, maxidx_U)), (Theory.check_thy thy', sorts'))
wenzelm@26939
  1064
      else raise TYPE ("Type not of sort " ^ Syntax.string_of_sort_global thy' S, [U], [])
wenzelm@16656
  1065
    | _ => raise TYPE (Pretty.string_of (Pretty.block
berghofe@15797
  1066
        [Pretty.str "instantiate: not a type variable",
wenzelm@26939
  1067
         Pretty.fbrk, Syntax.pretty_typ_global thy' T]), [T], []))
wenzelm@16656
  1068
  end;
clasohm@0
  1069
wenzelm@6928
  1070
in
wenzelm@6928
  1071
wenzelm@16601
  1072
(*Left-to-right replacements: ctpairs = [..., (vi, ti), ...].
clasohm@0
  1073
  Instantiates distinct Vars by terms of same type.
wenzelm@16601
  1074
  Does NOT normalize the resulting theorem!*)
paulson@1529
  1075
fun instantiate ([], []) th = th
wenzelm@16884
  1076
  | instantiate (instT, inst) th =
wenzelm@16656
  1077
      let
wenzelm@28321
  1078
        val Thm (der, {thy_ref, hyps, shyps, tpairs, prop, ...}) = th;
wenzelm@16884
  1079
        val (inst', (instT', (thy_ref', shyps'))) =
wenzelm@16884
  1080
          (thy_ref, shyps) |> fold_map add_inst inst ||> fold_map add_instT instT;
wenzelm@20512
  1081
        val subst = TermSubst.instantiate_maxidx (instT', inst');
wenzelm@20512
  1082
        val (prop', maxidx1) = subst prop ~1;
wenzelm@20512
  1083
        val (tpairs', maxidx') =
wenzelm@20512
  1084
          fold_map (fn (t, u) => fn i => subst t i ||>> subst u) tpairs maxidx1;
wenzelm@16656
  1085
      in
wenzelm@28321
  1086
        Thm (deriv_rule1 (fn d => Pt.instantiate (map (apsnd #1) instT', map (apsnd #1) inst') d) der,
wenzelm@28321
  1087
         {thy_ref = thy_ref',
wenzelm@21646
  1088
          tags = [],
wenzelm@20545
  1089
          maxidx = maxidx',
wenzelm@20545
  1090
          shyps = shyps',
wenzelm@20545
  1091
          hyps = hyps,
wenzelm@20545
  1092
          tpairs = tpairs',
wenzelm@28321
  1093
          prop = prop'})
wenzelm@16656
  1094
      end
wenzelm@16656
  1095
      handle TYPE (msg, _, _) => raise THM (msg, 0, [th]);
wenzelm@6928
  1096
wenzelm@22584
  1097
fun instantiate_cterm ([], []) ct = ct
wenzelm@22584
  1098
  | instantiate_cterm (instT, inst) ct =
wenzelm@22584
  1099
      let
wenzelm@22584
  1100
        val Cterm {thy_ref, t, T, sorts, ...} = ct;
wenzelm@22584
  1101
        val (inst', (instT', (thy_ref', sorts'))) =
wenzelm@22584
  1102
          (thy_ref, sorts) |> fold_map add_inst inst ||> fold_map add_instT instT;
wenzelm@22584
  1103
        val subst = TermSubst.instantiate_maxidx (instT', inst');
wenzelm@22584
  1104
        val substT = TermSubst.instantiateT_maxidx instT';
wenzelm@22584
  1105
        val (t', maxidx1) = subst t ~1;
wenzelm@22584
  1106
        val (T', maxidx') = substT T maxidx1;
wenzelm@22584
  1107
      in Cterm {thy_ref = thy_ref', t = t', T = T', sorts = sorts', maxidx = maxidx'} end
wenzelm@22584
  1108
      handle TYPE (msg, _, _) => raise CTERM (msg, [ct]);
wenzelm@22584
  1109
wenzelm@6928
  1110
end;
wenzelm@6928
  1111
clasohm@0
  1112
wenzelm@16601
  1113
(*The trivial implication A ==> A, justified by assume and forall rules.
wenzelm@16601
  1114
  A can contain Vars, not so for assume!*)
wenzelm@16601
  1115
fun trivial (Cterm {thy_ref, t =A, T, maxidx, sorts}) =
wenzelm@16601
  1116
  if T <> propT then
wenzelm@16601
  1117
    raise THM ("trivial: the term must have type prop", 0, [])
wenzelm@16601
  1118
  else
wenzelm@28321
  1119
    Thm (deriv_rule0 (Pt.AbsP ("H", NONE, Pt.PBound 0)),
wenzelm@28321
  1120
     {thy_ref = thy_ref,
wenzelm@21646
  1121
      tags = [],
wenzelm@16601
  1122
      maxidx = maxidx,
wenzelm@16601
  1123
      shyps = sorts,
wenzelm@16601
  1124
      hyps = [],
wenzelm@16601
  1125
      tpairs = [],
wenzelm@28321
  1126
      prop = Logic.mk_implies (A, A)});
clasohm@0
  1127
paulson@1503
  1128
(*Axiom-scheme reflecting signature contents: "OFCLASS(?'a::c, c_class)" *)
wenzelm@16425
  1129
fun class_triv thy c =
wenzelm@24143
  1130
  let
wenzelm@24143
  1131
    val Cterm {t, maxidx, sorts, ...} =
wenzelm@24848
  1132
      cterm_of thy (Logic.mk_inclass (TVar ((Name.aT, 0), [c]), Sign.certify_class thy c))
wenzelm@24143
  1133
        handle TERM (msg, _) => raise THM ("class_triv: " ^ msg, 0, []);
wenzelm@28321
  1134
    val der = deriv_rule0 (Pt.PAxm ("Pure.class_triv:" ^ c, t, SOME []));
wenzelm@399
  1135
  in
wenzelm@28321
  1136
    Thm (der, {thy_ref = Theory.check_thy thy, tags = [], maxidx = maxidx,
wenzelm@28321
  1137
      shyps = sorts, hyps = [], tpairs = [], prop = t})
wenzelm@399
  1138
  end;
wenzelm@399
  1139
wenzelm@19505
  1140
(*Internalize sort constraints of type variable*)
wenzelm@19505
  1141
fun unconstrainT
wenzelm@19505
  1142
    (Ctyp {thy_ref = thy_ref1, T, ...})
wenzelm@28321
  1143
    (th as Thm (_, {thy_ref = thy_ref2, maxidx, shyps, hyps, tpairs, prop, ...})) =
wenzelm@19505
  1144
  let
wenzelm@19505
  1145
    val ((x, i), S) = Term.dest_TVar T handle TYPE _ =>
wenzelm@19505
  1146
      raise THM ("unconstrainT: not a type variable", 0, [th]);
wenzelm@19505
  1147
    val T' = TVar ((x, i), []);
wenzelm@20548
  1148
    val unconstrain = Term.map_types (Term.map_atyps (fn U => if U = T then T' else U));
wenzelm@19505
  1149
    val constraints = map (curry Logic.mk_inclass T') S;
wenzelm@19505
  1150
  in
wenzelm@28321
  1151
    Thm (deriv_rule0 (Pt.PAxm ("Pure.unconstrainT", prop, SOME [])),
wenzelm@28321
  1152
     {thy_ref = Theory.merge_refs (thy_ref1, thy_ref2),
wenzelm@21646
  1153
      tags = [],
wenzelm@19505
  1154
      maxidx = Int.max (maxidx, i),
wenzelm@19505
  1155
      shyps = Sorts.remove_sort S shyps,
wenzelm@19505
  1156
      hyps = hyps,
wenzelm@19505
  1157
      tpairs = map (pairself unconstrain) tpairs,
wenzelm@28321
  1158
      prop = Logic.list_implies (constraints, unconstrain prop)})
wenzelm@19505
  1159
  end;
wenzelm@399
  1160
wenzelm@6786
  1161
(* Replace all TFrees not fixed or in the hyps by new TVars *)
wenzelm@28321
  1162
fun varifyT' fixed (Thm (der, {thy_ref, maxidx, shyps, hyps, tpairs, prop, ...})) =
wenzelm@12500
  1163
  let
wenzelm@23178
  1164
    val tfrees = List.foldr add_term_tfrees fixed hyps;
berghofe@13658
  1165
    val prop1 = attach_tpairs tpairs prop;
haftmann@21116
  1166
    val (al, prop2) = Type.varify tfrees prop1;
wenzelm@16601
  1167
    val (ts, prop3) = Logic.strip_prems (length tpairs, [], prop2);
wenzelm@16601
  1168
  in
wenzelm@28321
  1169
    (al, Thm (deriv_rule1 (Pt.varify_proof prop tfrees) der,
wenzelm@28321
  1170
     {thy_ref = thy_ref,
wenzelm@21646
  1171
      tags = [],
wenzelm@16601
  1172
      maxidx = Int.max (0, maxidx),
wenzelm@16601
  1173
      shyps = shyps,
wenzelm@16601
  1174
      hyps = hyps,
wenzelm@16601
  1175
      tpairs = rev (map Logic.dest_equals ts),
wenzelm@28321
  1176
      prop = prop3}))
wenzelm@28321
  1177
  end;
wenzelm@28321
  1178
wenzelm@28321
  1179
val varifyT = #2 o varifyT' [];
wenzelm@28321
  1180
wenzelm@28321
  1181
(* Replace all TVars by new TFrees *)
wenzelm@28321
  1182
fun freezeT (Thm (der, {thy_ref, maxidx, shyps, hyps, tpairs, prop, ...})) =
wenzelm@28321
  1183
  let
wenzelm@28321
  1184
    val prop1 = attach_tpairs tpairs prop;
wenzelm@28321
  1185
    val prop2 = Type.freeze prop1;
wenzelm@28321
  1186
    val (ts, prop3) = Logic.strip_prems (length tpairs, [], prop2);
wenzelm@28321
  1187
  in
wenzelm@28321
  1188
    Thm (deriv_rule1 (Pt.freezeT prop1) der,
wenzelm@28321
  1189
     {thy_ref = thy_ref,
wenzelm@28321
  1190
      tags = [],
wenzelm@28321
  1191
      maxidx = maxidx_of_term prop2,
wenzelm@28321
  1192
      shyps = shyps,
wenzelm@28321
  1193
      hyps = hyps,
wenzelm@28321
  1194
      tpairs = rev (map Logic.dest_equals ts),
wenzelm@18127
  1195
      prop = prop3})
clasohm@0
  1196
  end;
clasohm@0
  1197
clasohm@0
  1198
clasohm@0
  1199
(*** Inference rules for tactics ***)
clasohm@0
  1200
clasohm@0
  1201
(*Destruct proof state into constraints, other goals, goal(i), rest *)
wenzelm@28321
  1202
fun dest_state (state as Thm (_, {prop,tpairs,...}), i) =
berghofe@13658
  1203
  (case  Logic.strip_prems(i, [], prop) of
berghofe@13658
  1204
      (B::rBs, C) => (tpairs, rev rBs, B, C)
berghofe@13658
  1205
    | _ => raise THM("dest_state", i, [state]))
clasohm@0
  1206
  handle TERM _ => raise THM("dest_state", i, [state]);
clasohm@0
  1207
lcp@309
  1208
(*Increment variables and parameters of orule as required for
wenzelm@18035
  1209
  resolution with a goal.*)
wenzelm@18035
  1210
fun lift_rule goal orule =
wenzelm@16601
  1211
  let
wenzelm@18035
  1212
    val Cterm {t = gprop, T, maxidx = gmax, sorts, ...} = goal;
wenzelm@18035
  1213
    val inc = gmax + 1;
wenzelm@18035
  1214
    val lift_abs = Logic.lift_abs inc gprop;
wenzelm@18035
  1215
    val lift_all = Logic.lift_all inc gprop;
wenzelm@28321
  1216
    val Thm (der, {maxidx, shyps, hyps, tpairs, prop, ...}) = orule;
wenzelm@16601
  1217
    val (As, B) = Logic.strip_horn prop;
wenzelm@16601
  1218
  in
wenzelm@18035
  1219
    if T <> propT then raise THM ("lift_rule: the term must have type prop", 0, [])
wenzelm@18035
  1220
    else
wenzelm@28321
  1221
      Thm (deriv_rule1 (Pt.lift_proof gprop inc prop) der,
wenzelm@28321
  1222
       {thy_ref = merge_thys1 goal orule,
wenzelm@21646
  1223
        tags = [],
wenzelm@18035
  1224
        maxidx = maxidx + inc,
wenzelm@18035
  1225
        shyps = Sorts.union shyps sorts,  (*sic!*)
wenzelm@18035
  1226
        hyps = hyps,
wenzelm@18035
  1227
        tpairs = map (pairself lift_abs) tpairs,
wenzelm@28321
  1228
        prop = Logic.list_implies (map lift_all As, lift_all B)})
clasohm@0
  1229
  end;
clasohm@0
  1230
wenzelm@28321
  1231
fun incr_indexes i (thm as Thm (der, {thy_ref, maxidx, shyps, hyps, tpairs, prop, ...})) =
wenzelm@16601
  1232
  if i < 0 then raise THM ("negative increment", 0, [thm])
wenzelm@16601
  1233
  else if i = 0 then thm
wenzelm@16601
  1234
  else
wenzelm@28321
  1235
    Thm (deriv_rule1 (Pt.map_proof_terms (Logic.incr_indexes ([], i)) (Logic.incr_tvar i)) der,
wenzelm@28321
  1236
     {thy_ref = thy_ref,
wenzelm@21646
  1237
      tags = [],
wenzelm@16601
  1238
      maxidx = maxidx + i,
wenzelm@16601
  1239
      shyps = shyps,
wenzelm@16601
  1240
      hyps = hyps,
wenzelm@16601
  1241
      tpairs = map (pairself (Logic.incr_indexes ([], i))) tpairs,
wenzelm@28321
  1242
      prop = Logic.incr_indexes ([], i) prop});
berghofe@10416
  1243
clasohm@0
  1244
(*Solve subgoal Bi of proof state B1...Bn/C by assumption. *)
clasohm@0
  1245
fun assumption i state =
wenzelm@16601
  1246
  let
wenzelm@28321
  1247
    val Thm (der, {thy_ref, maxidx, shyps, hyps, prop, ...}) = state;
wenzelm@16656
  1248
    val thy = Theory.deref thy_ref;
wenzelm@16601
  1249
    val (tpairs, Bs, Bi, C) = dest_state (state, i);
wenzelm@16601
  1250
    fun newth n (env as Envir.Envir {maxidx, ...}, tpairs) =
wenzelm@28321
  1251
      Thm (deriv_rule1
wenzelm@16601
  1252
          ((if Envir.is_empty env then I else (Pt.norm_proof' env)) o
wenzelm@16601
  1253
            Pt.assumption_proof Bs Bi n) der,
wenzelm@28321
  1254
       {tags = [],
wenzelm@16601
  1255
        maxidx = maxidx,
wenzelm@26640
  1256
        shyps = Envir.insert_sorts env shyps,
wenzelm@16601
  1257
        hyps = hyps,
wenzelm@16601
  1258
        tpairs =
wenzelm@16601
  1259
          if Envir.is_empty env then tpairs
wenzelm@16601
  1260
          else map (pairself (Envir.norm_term env)) tpairs,
wenzelm@16601
  1261
        prop =
wenzelm@16601
  1262
          if Envir.is_empty env then (*avoid wasted normalizations*)
wenzelm@16601
  1263
            Logic.list_implies (Bs, C)
wenzelm@16601
  1264
          else (*normalize the new rule fully*)
wenzelm@24143
  1265
            Envir.norm_term env (Logic.list_implies (Bs, C)),
wenzelm@28321
  1266
        thy_ref = Theory.check_thy thy});
wenzelm@16601
  1267
    fun addprfs [] _ = Seq.empty
wenzelm@16601
  1268
      | addprfs ((t, u) :: apairs) n = Seq.make (fn () => Seq.pull
wenzelm@16601
  1269
          (Seq.mapp (newth n)
wenzelm@16656
  1270
            (Unify.unifiers (thy, Envir.empty maxidx, (t, u) :: tpairs))
wenzelm@16601
  1271
            (addprfs apairs (n + 1))))
wenzelm@16601
  1272
  in addprfs (Logic.assum_pairs (~1, Bi)) 1 end;
clasohm@0
  1273
wenzelm@250
  1274
(*Solve subgoal Bi of proof state B1...Bn/C by assumption.
clasohm@0
  1275
  Checks if Bi's conclusion is alpha-convertible to one of its assumptions*)
clasohm@0
  1276
fun eq_assumption i state =
wenzelm@16601
  1277
  let
wenzelm@28321
  1278
    val Thm (der, {thy_ref, maxidx, shyps, hyps, prop, ...}) = state;
wenzelm@16601
  1279
    val (tpairs, Bs, Bi, C) = dest_state (state, i);
wenzelm@16601
  1280
  in
berghofe@26832
  1281
    (case find_index Pattern.aeconv (Logic.assum_pairs (~1, Bi)) of
wenzelm@16601
  1282
      ~1 => raise THM ("eq_assumption", 0, [state])
wenzelm@16601
  1283
    | n =>
wenzelm@28321
  1284
        Thm (deriv_rule1 (Pt.assumption_proof Bs Bi (n + 1)) der,
wenzelm@28321
  1285
         {thy_ref = thy_ref,
wenzelm@21646
  1286
          tags = [],
wenzelm@16601
  1287
          maxidx = maxidx,
wenzelm@16601
  1288
          shyps = shyps,
wenzelm@16601
  1289
          hyps = hyps,
wenzelm@16601
  1290
          tpairs = tpairs,
wenzelm@28321
  1291
          prop = Logic.list_implies (Bs, C)}))
clasohm@0
  1292
  end;
clasohm@0
  1293
clasohm@0
  1294
paulson@2671
  1295
(*For rotate_tac: fast rotation of assumptions of subgoal i*)
paulson@2671
  1296
fun rotate_rule k i state =
wenzelm@16601
  1297
  let
wenzelm@28321
  1298
    val Thm (der, {thy_ref, maxidx, shyps, hyps, prop, ...}) = state;
wenzelm@16601
  1299
    val (tpairs, Bs, Bi, C) = dest_state (state, i);
wenzelm@16601
  1300
    val params = Term.strip_all_vars Bi
wenzelm@16601
  1301
    and rest   = Term.strip_all_body Bi;
wenzelm@16601
  1302
    val asms   = Logic.strip_imp_prems rest
wenzelm@16601
  1303
    and concl  = Logic.strip_imp_concl rest;
wenzelm@16601
  1304
    val n = length asms;
wenzelm@16601
  1305
    val m = if k < 0 then n + k else k;
wenzelm@16601
  1306
    val Bi' =
wenzelm@16601
  1307
      if 0 = m orelse m = n then Bi
wenzelm@16601
  1308
      else if 0 < m andalso m < n then
wenzelm@19012
  1309
        let val (ps, qs) = chop m asms
wenzelm@16601
  1310
        in list_all (params, Logic.list_implies (qs @ ps, concl)) end
wenzelm@16601
  1311
      else raise THM ("rotate_rule", k, [state]);
wenzelm@16601
  1312
  in
wenzelm@28321
  1313
    Thm (deriv_rule1 (Pt.rotate_proof Bs Bi m) der,
wenzelm@28321
  1314
     {thy_ref = thy_ref,
wenzelm@21646
  1315
      tags = [],
wenzelm@16601
  1316
      maxidx = maxidx,
wenzelm@16601
  1317
      shyps = shyps,
wenzelm@16601
  1318
      hyps = hyps,
wenzelm@16601
  1319
      tpairs = tpairs,
wenzelm@28321
  1320
      prop = Logic.list_implies (Bs @ [Bi'], C)})
paulson@2671
  1321
  end;
paulson@2671
  1322
paulson@2671
  1323
paulson@7248
  1324
(*Rotates a rule's premises to the left by k, leaving the first j premises
paulson@7248
  1325
  unchanged.  Does nothing if k=0 or if k equals n-j, where n is the
wenzelm@16656
  1326
  number of premises.  Useful with etac and underlies defer_tac*)
paulson@7248
  1327
fun permute_prems j k rl =
wenzelm@16601
  1328
  let
wenzelm@28321
  1329
    val Thm (der, {thy_ref, maxidx, shyps, hyps, tpairs, prop, ...}) = rl;
wenzelm@16601
  1330
    val prems = Logic.strip_imp_prems prop
wenzelm@16601
  1331
    and concl = Logic.strip_imp_concl prop;
wenzelm@16601
  1332
    val moved_prems = List.drop (prems, j)
wenzelm@16601
  1333
    and fixed_prems = List.take (prems, j)
wenzelm@16601
  1334
      handle Subscript => raise THM ("permute_prems: j", j, [rl]);
wenzelm@16601
  1335
    val n_j = length moved_prems;
wenzelm@16601
  1336
    val m = if k < 0 then n_j + k else k;
wenzelm@16601
  1337
    val prop' =
wenzelm@16601
  1338
      if 0 = m orelse m = n_j then prop
wenzelm@16601
  1339
      else if 0 < m andalso m < n_j then
wenzelm@19012
  1340
        let val (ps, qs) = chop m moved_prems
wenzelm@16601
  1341
        in Logic.list_implies (fixed_prems @ qs @ ps, concl) end
wenzelm@16725
  1342
      else raise THM ("permute_prems: k", k, [rl]);
wenzelm@16601
  1343
  in
wenzelm@28321
  1344
    Thm (deriv_rule1 (Pt.permute_prems_prf prems j m) der,
wenzelm@28321
  1345
     {thy_ref = thy_ref,
wenzelm@21646
  1346
      tags = [],
wenzelm@16601
  1347
      maxidx = maxidx,
wenzelm@16601
  1348
      shyps = shyps,
wenzelm@16601
  1349
      hyps = hyps,
wenzelm@16601
  1350
      tpairs = tpairs,
wenzelm@28321
  1351
      prop = prop'})
paulson@7248
  1352
  end;
paulson@7248
  1353
paulson@7248
  1354
clasohm@0
  1355
(** User renaming of parameters in a subgoal **)
clasohm@0
  1356
clasohm@0
  1357
(*Calls error rather than raising an exception because it is intended
clasohm@0
  1358
  for top-level use -- exception handling would not make sense here.
clasohm@0
  1359
  The names in cs, if distinct, are used for the innermost parameters;
wenzelm@17868
  1360
  preceding parameters may be renamed to make all params distinct.*)
clasohm@0
  1361
fun rename_params_rule (cs, i) state =
wenzelm@16601
  1362
  let
wenzelm@28321
  1363
    val Thm (der, {thy_ref, tags, maxidx, shyps, hyps, ...}) = state;
wenzelm@16601
  1364
    val (tpairs, Bs, Bi, C) = dest_state (state, i);
wenzelm@16601
  1365
    val iparams = map #1 (Logic.strip_params Bi);
wenzelm@16601
  1366
    val short = length iparams - length cs;
wenzelm@16601
  1367
    val newnames =
wenzelm@16601
  1368
      if short < 0 then error "More names than abstractions!"
wenzelm@20071
  1369
      else Name.variant_list cs (Library.take (short, iparams)) @ cs;
wenzelm@20330
  1370
    val freenames = Term.fold_aterms (fn Free (x, _) => insert (op =) x | _ => I) Bi [];
wenzelm@16601
  1371
    val newBi = Logic.list_rename_params (newnames, Bi);
wenzelm@250
  1372
  in
wenzelm@21182
  1373
    (case duplicates (op =) cs of
wenzelm@21182
  1374
      a :: _ => (warning ("Can't rename.  Bound variables not distinct: " ^ a); state)
wenzelm@21182
  1375
    | [] =>
wenzelm@16601
  1376
      (case cs inter_string freenames of
wenzelm@16601
  1377
        a :: _ => (warning ("Can't rename.  Bound/Free variable clash: " ^ a); state)
wenzelm@16601
  1378
      | [] =>
wenzelm@28321
  1379
        Thm (der,
wenzelm@28321
  1380
         {thy_ref = thy_ref,
wenzelm@21646
  1381
          tags = tags,
wenzelm@16601
  1382
          maxidx = maxidx,
wenzelm@16601
  1383
          shyps = shyps,
wenzelm@16601
  1384
          hyps = hyps,
wenzelm@16601
  1385
          tpairs = tpairs,
wenzelm@28321
  1386
          prop = Logic.list_implies (Bs @ [newBi], C)})))
clasohm@0
  1387
  end;
clasohm@0
  1388
wenzelm@12982
  1389
clasohm@0
  1390
(*** Preservation of bound variable names ***)
clasohm@0
  1391
wenzelm@28321
  1392
fun rename_boundvars pat obj (thm as Thm (der, {thy_ref, tags, maxidx, shyps, hyps, tpairs, prop})) =
wenzelm@12982
  1393
  (case Term.rename_abs pat obj prop of
skalberg@15531
  1394
    NONE => thm
wenzelm@28321
  1395
  | SOME prop' => Thm (der,
wenzelm@16425
  1396
      {thy_ref = thy_ref,
wenzelm@21646
  1397
       tags = tags,
wenzelm@12982
  1398
       maxidx = maxidx,
wenzelm@12982
  1399
       hyps = hyps,
wenzelm@12982
  1400
       shyps = shyps,
berghofe@13658
  1401
       tpairs = tpairs,
wenzelm@28321
  1402
       prop = prop'}));
berghofe@10416
  1403
clasohm@0
  1404
wenzelm@16656
  1405
(* strip_apply f (A, B) strips off all assumptions/parameters from A
clasohm@0
  1406
   introduced by lifting over B, and applies f to remaining part of A*)
clasohm@0
  1407
fun strip_apply f =
clasohm@0
  1408
  let fun strip(Const("==>",_)$ A1 $ B1,
wenzelm@27336
  1409
                Const("==>",_)$ _  $ B2) = Logic.mk_implies (A1, strip(B1,B2))
wenzelm@250
  1410
        | strip((c as Const("all",_)) $ Abs(a,T,t1),
wenzelm@250
  1411
                      Const("all",_)  $ Abs(_,_,t2)) = c$Abs(a,T,strip(t1,t2))
wenzelm@250
  1412
        | strip(A,_) = f A
clasohm@0
  1413
  in strip end;
clasohm@0
  1414
clasohm@0
  1415
(*Use the alist to rename all bound variables and some unknowns in a term
clasohm@0
  1416
  dpairs = current disagreement pairs;  tpairs = permanent ones (flexflex);
clasohm@0
  1417
  Preserves unknowns in tpairs and on lhs of dpairs. *)
clasohm@0
  1418
fun rename_bvs([],_,_,_) = I
clasohm@0
  1419
  | rename_bvs(al,dpairs,tpairs,B) =
wenzelm@20330
  1420
      let
wenzelm@20330
  1421
        val add_var = fold_aterms (fn Var ((x, _), _) => insert (op =) x | _ => I);
wenzelm@20330
  1422
        val vids = []
wenzelm@20330
  1423
          |> fold (add_var o fst) dpairs
wenzelm@20330
  1424
          |> fold (add_var o fst) tpairs
wenzelm@20330
  1425
          |> fold (add_var o snd) tpairs;
wenzelm@250
  1426
        (*unknowns appearing elsewhere be preserved!*)
wenzelm@250
  1427
        fun rename(t as Var((x,i),T)) =
wenzelm@20330
  1428
              (case AList.lookup (op =) al x of
wenzelm@20330
  1429
                SOME y =>
wenzelm@20330
  1430
                  if member (op =) vids x orelse member (op =) vids y then t
wenzelm@20330
  1431
                  else Var((y,i),T)
wenzelm@20330
  1432
              | NONE=> t)
clasohm@0
  1433
          | rename(Abs(x,T,t)) =
wenzelm@18944
  1434
              Abs (the_default x (AList.lookup (op =) al x), T, rename t)
clasohm@0
  1435
          | rename(f$t) = rename f $ rename t
clasohm@0
  1436
          | rename(t) = t;
wenzelm@250
  1437
        fun strip_ren Ai = strip_apply rename (Ai,B)
wenzelm@20330
  1438
      in strip_ren end;
clasohm@0
  1439
clasohm@0
  1440
(*Function to rename bounds/unknowns in the argument, lifted over B*)
clasohm@0
  1441
fun rename_bvars(dpairs, tpairs, B) =
wenzelm@23178
  1442
        rename_bvs(List.foldr Term.match_bvars [] dpairs, dpairs, tpairs, B);
clasohm@0
  1443
clasohm@0
  1444
clasohm@0
  1445
(*** RESOLUTION ***)
clasohm@0
  1446
lcp@721
  1447
(** Lifting optimizations **)
lcp@721
  1448
clasohm@0
  1449
(*strip off pairs of assumptions/parameters in parallel -- they are
clasohm@0
  1450
  identical because of lifting*)
wenzelm@250
  1451
fun strip_assums2 (Const("==>", _) $ _ $ B1,
wenzelm@250
  1452
                   Const("==>", _) $ _ $ B2) = strip_assums2 (B1,B2)
clasohm@0
  1453
  | strip_assums2 (Const("all",_)$Abs(a,T,t1),
wenzelm@250
  1454
                   Const("all",_)$Abs(_,_,t2)) =
clasohm@0
  1455
      let val (B1,B2) = strip_assums2 (t1,t2)
clasohm@0
  1456
      in  (Abs(a,T,B1), Abs(a,T,B2))  end
clasohm@0
  1457
  | strip_assums2 BB = BB;
clasohm@0
  1458
clasohm@0
  1459
lcp@721
  1460
(*Faster normalization: skip assumptions that were lifted over*)
lcp@721
  1461
fun norm_term_skip env 0 t = Envir.norm_term env t
lcp@721
  1462
  | norm_term_skip env n (Const("all",_)$Abs(a,T,t)) =
lcp@721
  1463
        let val Envir.Envir{iTs, ...} = env
berghofe@15797
  1464
            val T' = Envir.typ_subst_TVars iTs T
wenzelm@1238
  1465
            (*Must instantiate types of parameters because they are flattened;
lcp@721
  1466
              this could be a NEW parameter*)
wenzelm@27336
  1467
        in Term.all T' $ Abs(a, T', norm_term_skip env n t)  end
lcp@721
  1468
  | norm_term_skip env n (Const("==>", _) $ A $ B) =
wenzelm@27336
  1469
        Logic.mk_implies (A, norm_term_skip env (n-1) B)
lcp@721
  1470
  | norm_term_skip env n t = error"norm_term_skip: too few assumptions??";
lcp@721
  1471
lcp@721
  1472
clasohm@0
  1473
(*Composition of object rule r=(A1...Am/B) with proof state s=(B1...Bn/C)
wenzelm@250
  1474
  Unifies B with Bi, replacing subgoal i    (1 <= i <= n)
clasohm@0
  1475
  If match then forbid instantiations in proof state
clasohm@0
  1476
  If lifted then shorten the dpair using strip_assums2.
clasohm@0
  1477
  If eres_flg then simultaneously proves A1 by assumption.
wenzelm@250
  1478
  nsubgoal is the number of new subgoals (written m above).
clasohm@0
  1479
  Curried so that resolution calls dest_state only once.
clasohm@0
  1480
*)
wenzelm@4270
  1481
local exception COMPOSE
clasohm@0
  1482
in
wenzelm@18486
  1483
fun bicompose_aux flatten match (state, (stpairs, Bs, Bi, C), lifted)
clasohm@0
  1484
                        (eres_flg, orule, nsubgoal) =
wenzelm@28321
  1485
 let val Thm (sder, {maxidx=smax, shyps=sshyps, hyps=shyps, ...}) = state
wenzelm@28321
  1486
     and Thm (rder, {maxidx=rmax, shyps=rshyps, hyps=rhyps,
wenzelm@28321
  1487
             tpairs=rtpairs, prop=rprop,...}) = orule
paulson@1529
  1488
         (*How many hyps to skip over during normalization*)
wenzelm@21576
  1489
     and nlift = Logic.count_prems (strip_all_body Bi) + (if eres_flg then ~1 else 0)
wenzelm@24143
  1490
     val thy = Theory.deref (merge_thys2 state orule);
clasohm@0
  1491
     (** Add new theorem with prop = '[| Bs; As |] ==> C' to thq **)
berghofe@11518
  1492
     fun addth A (As, oldAs, rder', n) ((env as Envir.Envir {maxidx, ...}, tpairs), thq) =
wenzelm@250
  1493
       let val normt = Envir.norm_term env;
wenzelm@250
  1494
           (*perform minimal copying here by examining env*)
berghofe@13658
  1495
           val (ntpairs, normp) =
berghofe@13658
  1496
             if Envir.is_empty env then (tpairs, (Bs @ As, C))
wenzelm@250
  1497
             else
wenzelm@250
  1498
             let val ntps = map (pairself normt) tpairs
wenzelm@19861
  1499
             in if Envir.above env smax then
wenzelm@1238
  1500
                  (*no assignments in state; normalize the rule only*)
wenzelm@1238
  1501
                  if lifted
berghofe@13658
  1502
                  then (ntps, (Bs @ map (norm_term_skip env nlift) As, C))
berghofe@13658
  1503
                  else (ntps, (Bs @ map normt As, C))
paulson@1529
  1504
                else if match then raise COMPOSE
wenzelm@250
  1505
                else (*normalize the new rule fully*)
berghofe@13658
  1506
                  (ntps, (map normt (Bs @ As), normt C))
wenzelm@250
  1507
             end
wenzelm@16601
  1508
           val th =
wenzelm@28321
  1509
             Thm (deriv_rule2
berghofe@11518
  1510
                   ((if Envir.is_empty env then I
wenzelm@19861
  1511
                     else if Envir.above env smax then
berghofe@11518
  1512
                       (fn f => fn der => f (Pt.norm_proof' env der))
berghofe@11518
  1513
                     else
berghofe@11518
  1514
                       curry op oo (Pt.norm_proof' env))
berghofe@23296
  1515
                    (Pt.bicompose_proof flatten Bs oldAs As A n (nlift+1))) rder' sder,
wenzelm@28321
  1516
                {tags = [],
wenzelm@2386
  1517
                 maxidx = maxidx,
wenzelm@26640
  1518
                 shyps = Envir.insert_sorts env (Sorts.union rshyps sshyps),
wenzelm@16601
  1519
                 hyps = union_hyps rhyps shyps,
berghofe@13658
  1520
                 tpairs = ntpairs,
wenzelm@24143
  1521
                 prop = Logic.list_implies normp,
wenzelm@28321
  1522
                 thy_ref = Theory.check_thy thy})
wenzelm@19475
  1523
        in  Seq.cons th thq  end  handle COMPOSE => thq;
berghofe@13658
  1524
     val (rAs,B) = Logic.strip_prems(nsubgoal, [], rprop)
clasohm@0
  1525
       handle TERM _ => raise THM("bicompose: rule", 0, [orule,state]);
clasohm@0
  1526
     (*Modify assumptions, deleting n-th if n>0 for e-resolution*)
clasohm@0
  1527
     fun newAs(As0, n, dpairs, tpairs) =
berghofe@11518
  1528
       let val (As1, rder') =
berghofe@25939
  1529
         if not lifted then (As0, rder)
berghofe@11518
  1530
         else (map (rename_bvars(dpairs,tpairs,B)) As0,
wenzelm@28321
  1531
           deriv_rule1 (Pt.map_proof_terms
berghofe@11518
  1532
             (rename_bvars (dpairs, tpairs, Bound 0)) I) rder);
wenzelm@18486
  1533
       in (map (if flatten then (Logic.flatten_params n) else I) As1, As1, rder', n)
wenzelm@250
  1534
          handle TERM _ =>
wenzelm@250
  1535
          raise THM("bicompose: 1st premise", 0, [orule])
clasohm@0
  1536
       end;
paulson@2147
  1537
     val env = Envir.empty(Int.max(rmax,smax));
clasohm@0
  1538
     val BBi = if lifted then strip_assums2(B,Bi) else (B,Bi);
clasohm@0
  1539
     val dpairs = BBi :: (rtpairs@stpairs);
clasohm@0
  1540
     (*elim-resolution: try each assumption in turn.  Initially n=1*)
berghofe@11518
  1541
     fun tryasms (_, _, _, []) = Seq.empty
berghofe@11518
  1542
       | tryasms (A, As, n, (t,u)::apairs) =
wenzelm@16425
  1543
          (case Seq.pull(Unify.unifiers(thy, env, (t,u)::dpairs))  of
wenzelm@16425
  1544
              NONE                   => tryasms (A, As, n+1, apairs)
wenzelm@16425
  1545
            | cell as SOME((_,tpairs),_) =>
wenzelm@16425
  1546
                Seq.it_right (addth A (newAs(As, n, [BBi,(u,t)], tpairs)))
wenzelm@16425
  1547
                    (Seq.make(fn()=> cell),
wenzelm@16425
  1548
                     Seq.make(fn()=> Seq.pull (tryasms(A, As, n+1, apairs)))))
clasohm@0
  1549
     fun eres [] = raise THM("bicompose: no premises", 0, [orule,state])
skalberg@15531
  1550
       | eres (A1::As) = tryasms(SOME A1, As, 1, Logic.assum_pairs(nlift+1,A1))
clasohm@0
  1551
     (*ordinary resolution*)
skalberg@15531
  1552
     fun res(NONE) = Seq.empty
skalberg@15531
  1553
       | res(cell as SOME((_,tpairs),_)) =
skalberg@15531
  1554
             Seq.it_right (addth NONE (newAs(rev rAs, 0, [BBi], tpairs)))
wenzelm@4270
  1555
                       (Seq.make (fn()=> cell), Seq.empty)
clasohm@0
  1556
 in  if eres_flg then eres(rev rAs)
wenzelm@16425
  1557
     else res(Seq.pull(Unify.unifiers(thy, env, dpairs)))
clasohm@0
  1558
 end;
wenzelm@7528
  1559
end;
clasohm@0
  1560
wenzelm@18501
  1561
fun compose_no_flatten match (orule, nsubgoal) i state =
wenzelm@18501
  1562
  bicompose_aux false match (state, dest_state (state, i), false) (false, orule, nsubgoal);
clasohm@0
  1563
wenzelm@18501
  1564
fun bicompose match arg i state =
wenzelm@18501
  1565
  bicompose_aux true match (state, dest_state (state,i), false) arg;
clasohm@0
  1566
clasohm@0
  1567
(*Quick test whether rule is resolvable with the subgoal with hyps Hs
clasohm@0
  1568
  and conclusion B.  If eres_flg then checks 1st premise of rule also*)
clasohm@0
  1569
fun could_bires (Hs, B, eres_flg, rule) =
wenzelm@16847
  1570
    let fun could_reshyp (A1::_) = exists (fn H => could_unify (A1, H)) Hs
wenzelm@250
  1571
          | could_reshyp [] = false;  (*no premise -- illegal*)
wenzelm@250
  1572
    in  could_unify(concl_of rule, B) andalso
wenzelm@250
  1573
        (not eres_flg  orelse  could_reshyp (prems_of rule))
clasohm@0
  1574
    end;
clasohm@0
  1575
clasohm@0
  1576
(*Bi-resolution of a state with a list of (flag,rule) pairs.
clasohm@0
  1577
  Puts the rule above:  rule/state.  Renames vars in the rules. *)
wenzelm@250
  1578
fun biresolution match brules i state =
wenzelm@18035
  1579
    let val (stpairs, Bs, Bi, C) = dest_state(state,i);
wenzelm@18145
  1580
        val lift = lift_rule (cprem_of state i);
wenzelm@250
  1581
        val B = Logic.strip_assums_concl Bi;
wenzelm@250
  1582
        val Hs = Logic.strip_assums_hyp Bi;
wenzelm@22573
  1583
        val compose = bicompose_aux true match (state, (stpairs, Bs, Bi, C), true);
wenzelm@4270
  1584
        fun res [] = Seq.empty
wenzelm@250
  1585
          | res ((eres_flg, rule)::brules) =
nipkow@13642
  1586
              if !Pattern.trace_unify_fail orelse
nipkow@13642
  1587
                 could_bires (Hs, B, eres_flg, rule)
wenzelm@4270
  1588
              then Seq.make (*delay processing remainder till needed*)
wenzelm@22573
  1589
                  (fn()=> SOME(compose (eres_flg, lift rule, nprems_of rule),
wenzelm@250
  1590
                               res brules))
wenzelm@250
  1591
              else res brules
wenzelm@4270
  1592
    in  Seq.flat (res brules)  end;
clasohm@0
  1593
clasohm@0
  1594
wenzelm@28321
  1595
wenzelm@28321
  1596
(*** Promises ***)
wenzelm@28321
  1597
wenzelm@28356
  1598
(* pending future derivations *)
wenzelm@28356
  1599
wenzelm@28356
  1600
structure Futures = TheoryDataFun
wenzelm@28356
  1601
(
wenzelm@28356
  1602
  type T = thm Future.T list ref;
wenzelm@28356
  1603
  val empty : T = ref [];
wenzelm@28378
  1604
  val copy = I;  (*shared ref within whole theory body*)
wenzelm@28356
  1605
  fun extend _ : T = ref [];
wenzelm@28356
  1606
  fun merge _ _ : T = ref [];
wenzelm@28356
  1607
);
wenzelm@28356
  1608
wenzelm@28356
  1609
fun add_future thy future = CRITICAL (fn () => change (Futures.get thy) (cons future));
wenzelm@28356
  1610
wenzelm@28356
  1611
fun join_futures thy =
wenzelm@28356
  1612
  let
wenzelm@28356
  1613
    val futures = Futures.get thy;
wenzelm@28356
  1614
    val results = Future.join_results (! futures);
wenzelm@28364
  1615
    val done = CRITICAL (fn () =>
wenzelm@28364
  1616
      (change futures (filter_out Future.is_finished); null (! futures)));
wenzelm@28381
  1617
    val _ = Future.release_results results;
wenzelm@28364
  1618
  in if done then NONE else SOME thy end;
wenzelm@28356
  1619
wenzelm@28356
  1620
val _ = Context.>> (Context.map_theory (Futures.init #> Theory.at_end join_futures));
wenzelm@28356
  1621
wenzelm@28356
  1622
wenzelm@28330
  1623
(* promise *)
wenzelm@28330
  1624
wenzelm@28389
  1625
fun promise_result i orig_thy orig_shyps orig_prop raw_thm =
wenzelm@28378
  1626
  let
wenzelm@28378
  1627
    val _ = Theory.check_thy orig_thy;
wenzelm@28378
  1628
    val thm = strip_shyps (transfer orig_thy raw_thm);
wenzelm@28378
  1629
    val _ = Theory.check_thy orig_thy;
wenzelm@28378
  1630
    fun err msg = raise THM ("promise_result: " ^ msg, 0, [thm]);
wenzelm@28378
  1631
wenzelm@28389
  1632
    val Thm (Deriv {promises, ...}, {shyps, hyps, tpairs, prop, ...}) = thm;
wenzelm@28378
  1633
    val _ = prop aconv orig_prop orelse err "bad prop";
wenzelm@28378
  1634
    val _ = null tpairs orelse err "bad tpairs";
wenzelm@28378
  1635
    val _ = null hyps orelse err "bad hyps";
wenzelm@28378
  1636
    val _ = Sorts.subset (shyps, orig_shyps) orelse err "bad shyps";
wenzelm@28389
  1637
    val _ = forall (fn (j, _) => j < i) promises orelse err "bad dependencies";
wenzelm@28378
  1638
  in thm end;
wenzelm@28378
  1639
wenzelm@28364
  1640
fun promise make_result ct =
wenzelm@28321
  1641
  let
wenzelm@28321
  1642
    val {thy_ref = thy_ref, t = prop, T, maxidx, sorts} = rep_cterm ct;
wenzelm@28321
  1643
    val thy = Context.reject_draft (Theory.deref thy_ref);
wenzelm@28321
  1644
    val _ = T <> propT andalso raise CTERM ("promise: prop expected", [ct]);
wenzelm@28378
  1645
wenzelm@28389
  1646
    val i = serial ();
wenzelm@28389
  1647
    val future = Future.fork_irrelevant (promise_result i thy sorts prop o make_result);
wenzelm@28356
  1648
    val _ = add_future thy future;
wenzelm@28321
  1649
  in
wenzelm@28378
  1650
    Thm (make_deriv false [(i, future)] (Pt.promise_proof i prop),
wenzelm@28321
  1651
     {thy_ref = thy_ref,
wenzelm@28321
  1652
      tags = [],
wenzelm@28321
  1653
      maxidx = maxidx,
wenzelm@28321
  1654
      shyps = sorts,
wenzelm@28321
  1655
      hyps = [],
wenzelm@28321
  1656
      tpairs = [],
wenzelm@28321
  1657
      prop = prop})
wenzelm@28321
  1658
  end;
wenzelm@28321
  1659
wenzelm@28330
  1660
wenzelm@28330
  1661
(* fulfill *)
wenzelm@28330
  1662
wenzelm@28330
  1663
fun fulfill (thm as Thm (Deriv {oracle, proof, promises}, args)) =
wenzelm@28330
  1664
  let
wenzelm@28381
  1665
    val _ = Future.release_results (Future.join_results (map #2 promises));
wenzelm@28378
  1666
    val results = map (apsnd Future.join) promises;
wenzelm@28378
  1667
    val proofs = fold (fn (i, Thm (Deriv {proof = prf, ...}, _)) => Inttab.update (i, prf))
wenzelm@28378
  1668
      results Inttab.empty;
wenzelm@28378
  1669
    val ora = oracle orelse exists (oracle_of o #2) results;
wenzelm@28378
  1670
  in Thm (make_deriv ora [] (Pt.fulfill proofs proof), args) end;
wenzelm@28330
  1671
wenzelm@28330
  1672
val proof_of = fulfill #> (fn Thm (Deriv {proof, ...}, _) => proof);
wenzelm@28330
  1673
wenzelm@28321
  1674
wenzelm@28321
  1675
wenzelm@2509
  1676
(*** Oracles ***)
wenzelm@2509
  1677
wenzelm@28290
  1678
(* oracle rule *)
wenzelm@28290
  1679
wenzelm@28290
  1680
fun invoke_oracle thy_ref1 name oracle arg =
wenzelm@28290
  1681
  let val {thy_ref = thy_ref2, t = prop, T, maxidx, sorts} = rep_cterm (oracle arg) in
wenzelm@28290
  1682
    if T <> propT then
wenzelm@28290
  1683
      raise THM ("Oracle's result must have type prop: " ^ name, 0, [])
wenzelm@28290
  1684
    else
wenzelm@28330
  1685
      Thm (make_deriv true [] (Pt.oracle_proof name prop),
wenzelm@28321
  1686
       {thy_ref = Theory.merge_refs (thy_ref1, thy_ref2),
wenzelm@28290
  1687
        tags = [],
wenzelm@28290
  1688
        maxidx = maxidx,
wenzelm@28290
  1689
        shyps = sorts,
wenzelm@28290
  1690
        hyps = [],
wenzelm@28290
  1691
        tpairs = [],
wenzelm@28321
  1692
        prop = prop})
wenzelm@3812
  1693
  end;
wenzelm@3812
  1694
wenzelm@28290
  1695
wenzelm@28290
  1696
(* authentic derivation names *)
wenzelm@28290
  1697
wenzelm@28290
  1698
fun err_dup_ora dup = error ("Duplicate oracle: " ^ quote dup);
wenzelm@28290
  1699
wenzelm@28290
  1700
structure Oracles = TheoryDataFun
wenzelm@28290
  1701
(
wenzelm@28290
  1702
  type T = stamp NameSpace.table;
wenzelm@28290
  1703
  val empty = NameSpace.empty_table;
wenzelm@28290
  1704
  val copy = I;
wenzelm@28290
  1705
  val extend = I;
wenzelm@28290
  1706
  fun merge _ oracles = NameSpace.merge_tables (op =) oracles
wenzelm@28290
  1707
    handle Symtab.DUP dup => err_dup_ora dup;
wenzelm@28290
  1708
);
wenzelm@28290
  1709
wenzelm@28290
  1710
val extern_oracles = map #1 o NameSpace.extern_table o Oracles.get;
wenzelm@28290
  1711
wenzelm@28290
  1712
fun add_oracle (bname, oracle) thy =
wenzelm@28290
  1713
  let
wenzelm@28290
  1714
    val naming = Sign.naming_of thy;
wenzelm@28290
  1715
    val name = NameSpace.full naming bname;
wenzelm@28290
  1716
    val thy' = thy |> Oracles.map (fn (space, tab) =>
wenzelm@28290
  1717
      (NameSpace.declare naming name space,
wenzelm@28290
  1718
        Symtab.update_new (name, stamp ()) tab handle Symtab.DUP dup => err_dup_ora dup));
wenzelm@28290
  1719
  in ((name, invoke_oracle (Theory.check_thy thy') name oracle), thy') end;
wenzelm@28290
  1720
clasohm@0
  1721
end;
paulson@1503
  1722
wenzelm@6089
  1723
structure BasicThm: BASIC_THM = Thm;
wenzelm@6089
  1724
open BasicThm;