src/Pure/thm.ML
author wenzelm
Wed Apr 26 22:38:16 2006 +0200 (2006-04-26)
changeset 19475 8aa2b380614a
parent 19429 e425e74b01af
child 19505 0b345cf953c4
permissions -rw-r--r--
curried Seq.cons;
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@16425
     7
meta theorems, meta rules (including lifting and resolution).
clasohm@0
     8
*)
clasohm@0
     9
wenzelm@6089
    10
signature BASIC_THM =
paulson@1503
    11
  sig
wenzelm@1160
    12
  (*certified types*)
wenzelm@387
    13
  type ctyp
wenzelm@16656
    14
  val rep_ctyp: ctyp ->
wenzelm@16656
    15
   {thy: theory,
wenzelm@16656
    16
    sign: theory,       (*obsolete*)
wenzelm@16656
    17
    T: typ,
wenzelm@16656
    18
    sorts: sort list}
wenzelm@16425
    19
  val theory_of_ctyp: ctyp -> theory
wenzelm@16425
    20
  val typ_of: ctyp -> typ
wenzelm@16425
    21
  val ctyp_of: theory -> typ -> ctyp
wenzelm@16425
    22
  val read_ctyp: theory -> string -> ctyp
wenzelm@1160
    23
wenzelm@1160
    24
  (*certified terms*)
wenzelm@1160
    25
  type cterm
clasohm@1493
    26
  exception CTERM of string
wenzelm@16601
    27
  val rep_cterm: cterm ->
wenzelm@16656
    28
   {thy: theory,
wenzelm@16656
    29
    sign: theory,       (*obsolete*)
wenzelm@16656
    30
    t: term,
wenzelm@16656
    31
    T: typ,
wenzelm@16656
    32
    maxidx: int,
wenzelm@16656
    33
    sorts: sort list}
wenzelm@16601
    34
  val crep_cterm: cterm ->
wenzelm@16601
    35
    {thy: theory, sign: theory, t: term, T: ctyp, maxidx: int, sorts: sort list}
wenzelm@16425
    36
  val theory_of_cterm: cterm -> theory
wenzelm@16425
    37
  val term_of: cterm -> term
wenzelm@16425
    38
  val cterm_of: theory -> term -> cterm
wenzelm@16425
    39
  val ctyp_of_term: cterm -> ctyp
wenzelm@16425
    40
  val read_cterm: theory -> string * typ -> cterm
wenzelm@16425
    41
  val adjust_maxidx: cterm -> cterm
wenzelm@16425
    42
  val read_def_cterm:
wenzelm@16425
    43
    theory * (indexname -> typ option) * (indexname -> sort option) ->
wenzelm@1160
    44
    string list -> bool -> string * typ -> cterm * (indexname * typ) list
wenzelm@16425
    45
  val read_def_cterms:
wenzelm@16425
    46
    theory * (indexname -> typ option) * (indexname -> sort option) ->
nipkow@4281
    47
    string list -> bool -> (string * typ)list
nipkow@4281
    48
    -> cterm list * (indexname * typ)list
wenzelm@1160
    49
wenzelm@16425
    50
  type tag              (* = string * string list *)
paulson@1529
    51
wenzelm@1160
    52
  (*meta theorems*)
wenzelm@1160
    53
  type thm
wenzelm@16425
    54
  val rep_thm: thm ->
wenzelm@16656
    55
   {thy: theory,
wenzelm@16656
    56
    sign: theory,       (*obsolete*)
wenzelm@16425
    57
    der: bool * Proofterm.proof,
wenzelm@16425
    58
    maxidx: int,
wenzelm@16425
    59
    shyps: sort list,
wenzelm@16425
    60
    hyps: term list,
wenzelm@16425
    61
    tpairs: (term * term) list,
wenzelm@16425
    62
    prop: term}
wenzelm@16425
    63
  val crep_thm: thm ->
wenzelm@16656
    64
   {thy: theory,
wenzelm@16656
    65
    sign: theory,       (*obsolete*)
wenzelm@16425
    66
    der: bool * Proofterm.proof,
wenzelm@16425
    67
    maxidx: int,
wenzelm@16425
    68
    shyps: sort list,
wenzelm@16425
    69
    hyps: cterm list,
wenzelm@16425
    70
    tpairs: (cterm * cterm) list,
wenzelm@16425
    71
    prop: cterm}
wenzelm@6089
    72
  exception THM of string * int * thm list
wenzelm@18733
    73
  type attribute     (* = Context.generic * thm -> Context.generic * thm *)
wenzelm@16425
    74
  val eq_thm: thm * thm -> bool
wenzelm@16425
    75
  val eq_thms: thm list * thm list -> bool
wenzelm@16425
    76
  val theory_of_thm: thm -> theory
wenzelm@16425
    77
  val sign_of_thm: thm -> theory    (*obsolete*)
wenzelm@19429
    78
  val maxidx_of: thm -> int
wenzelm@16425
    79
  val prop_of: thm -> term
wenzelm@16425
    80
  val proof_of: thm -> Proofterm.proof
wenzelm@16425
    81
  val tpairs_of: thm -> (term * term) list
wenzelm@16656
    82
  val concl_of: thm -> term
wenzelm@16425
    83
  val prems_of: thm -> term list
wenzelm@16425
    84
  val nprems_of: thm -> int
wenzelm@16425
    85
  val cprop_of: thm -> cterm
wenzelm@18145
    86
  val cprem_of: thm -> int -> cterm
wenzelm@16656
    87
  val transfer: theory -> thm -> thm
wenzelm@16945
    88
  val weaken: cterm -> thm -> thm
wenzelm@16425
    89
  val extra_shyps: thm -> sort list
wenzelm@16425
    90
  val strip_shyps: thm -> thm
wenzelm@16425
    91
  val get_axiom_i: theory -> string -> thm
wenzelm@16425
    92
  val get_axiom: theory -> xstring -> thm
wenzelm@16425
    93
  val def_name: string -> string
wenzelm@16425
    94
  val get_def: theory -> xstring -> thm
wenzelm@16425
    95
  val axioms_of: theory -> (string * thm) list
wenzelm@1160
    96
wenzelm@1160
    97
  (*meta rules*)
wenzelm@16425
    98
  val assume: cterm -> thm
wenzelm@16425
    99
  val implies_intr: cterm -> thm -> thm
wenzelm@16425
   100
  val implies_elim: thm -> thm -> thm
wenzelm@16425
   101
  val forall_intr: cterm -> thm -> thm
wenzelm@16425
   102
  val forall_elim: cterm -> thm -> thm
wenzelm@16425
   103
  val reflexive: cterm -> thm
wenzelm@16425
   104
  val symmetric: thm -> thm
wenzelm@16425
   105
  val transitive: thm -> thm -> thm
wenzelm@16425
   106
  val beta_conversion: bool -> cterm -> thm
wenzelm@16425
   107
  val eta_conversion: cterm -> thm
wenzelm@16425
   108
  val abstract_rule: string -> cterm -> thm -> thm
wenzelm@16425
   109
  val combination: thm -> thm -> thm
wenzelm@16425
   110
  val equal_intr: thm -> thm -> thm
wenzelm@16425
   111
  val equal_elim: thm -> thm -> thm
wenzelm@16425
   112
  val flexflex_rule: thm -> thm Seq.seq
wenzelm@16425
   113
  val instantiate: (ctyp * ctyp) list * (cterm * cterm) list -> thm -> thm
wenzelm@16425
   114
  val trivial: cterm -> thm
wenzelm@16425
   115
  val class_triv: theory -> class -> thm
wenzelm@16425
   116
  val varifyT: thm -> thm
wenzelm@18127
   117
  val varifyT': (string * sort) list -> thm -> ((string * sort) * indexname) list * thm
wenzelm@16425
   118
  val freezeT: thm -> thm
wenzelm@16425
   119
  val dest_state: thm * int -> (term * term) list * term list * term * term
wenzelm@18035
   120
  val lift_rule: cterm -> thm -> thm
wenzelm@16425
   121
  val incr_indexes: int -> thm -> thm
wenzelm@16425
   122
  val assumption: int -> thm -> thm Seq.seq
wenzelm@16425
   123
  val eq_assumption: int -> thm -> thm
wenzelm@16425
   124
  val rotate_rule: int -> int -> thm -> thm
wenzelm@16425
   125
  val permute_prems: int -> int -> thm -> thm
wenzelm@1160
   126
  val rename_params_rule: string list * int -> thm -> thm
wenzelm@18501
   127
  val compose_no_flatten: bool -> thm * int -> int -> thm -> thm Seq.seq
wenzelm@16425
   128
  val bicompose: bool -> bool * thm * int -> int -> thm -> thm Seq.seq
wenzelm@16425
   129
  val biresolution: bool -> (bool * thm) list -> int -> thm -> thm Seq.seq
wenzelm@16425
   130
  val invoke_oracle: theory -> xstring -> theory * Object.T -> thm
wenzelm@16425
   131
  val invoke_oracle_i: theory -> string -> theory * Object.T -> thm
wenzelm@250
   132
end;
clasohm@0
   133
wenzelm@6089
   134
signature THM =
wenzelm@6089
   135
sig
wenzelm@6089
   136
  include BASIC_THM
wenzelm@16425
   137
  val dest_ctyp: ctyp -> ctyp list
wenzelm@16425
   138
  val dest_comb: cterm -> cterm * cterm
wenzelm@16425
   139
  val dest_abs: string option -> cterm -> cterm * cterm
wenzelm@16425
   140
  val capply: cterm -> cterm -> cterm
wenzelm@16425
   141
  val cabs: cterm -> cterm -> cterm
wenzelm@16425
   142
  val major_prem_of: thm -> term
wenzelm@16425
   143
  val no_prems: thm -> bool
wenzelm@18733
   144
  val rule_attribute: (Context.generic -> thm -> thm) -> attribute
wenzelm@18733
   145
  val declaration_attribute: (thm -> Context.generic -> Context.generic) -> attribute
wenzelm@18733
   146
  val theory_attributes: attribute list -> theory * thm -> theory * thm
wenzelm@18733
   147
  val proof_attributes: attribute list -> Context.proof * thm -> Context.proof * thm
wenzelm@17345
   148
  val no_attributes: 'a -> 'a * 'b list
wenzelm@17345
   149
  val simple_fact: 'a -> ('a * 'b list) list
wenzelm@16945
   150
  val terms_of_tpairs: (term * term) list -> term list
wenzelm@16945
   151
  val full_prop_of: thm -> term
wenzelm@16425
   152
  val get_name_tags: thm -> string * tag list
wenzelm@16425
   153
  val put_name_tags: string * tag list -> thm -> thm
wenzelm@16425
   154
  val name_of_thm: thm -> string
wenzelm@16425
   155
  val tags_of_thm: thm -> tag list
wenzelm@16425
   156
  val name_thm: string * thm -> thm
wenzelm@16945
   157
  val compress: thm -> thm
wenzelm@16945
   158
  val adjust_maxidx_thm: thm -> thm
wenzelm@16425
   159
  val rename_boundvars: term -> term -> thm -> thm
wenzelm@16425
   160
  val cterm_match: cterm * cterm -> (ctyp * ctyp) list * (cterm * cterm) list
wenzelm@16425
   161
  val cterm_first_order_match: cterm * cterm -> (ctyp * ctyp) list * (cterm * cterm) list
wenzelm@16425
   162
  val cterm_incr_indexes: int -> cterm -> cterm
wenzelm@6089
   163
end;
wenzelm@6089
   164
wenzelm@3550
   165
structure Thm: THM =
clasohm@0
   166
struct
wenzelm@250
   167
wenzelm@16656
   168
wenzelm@387
   169
(*** Certified terms and types ***)
wenzelm@387
   170
wenzelm@16656
   171
(** collect occurrences of sorts -- unless all sorts non-empty **)
wenzelm@16656
   172
wenzelm@16679
   173
fun may_insert_typ_sorts thy T = if Sign.all_sorts_nonempty thy then I else Sorts.insert_typ T;
wenzelm@16679
   174
fun may_insert_term_sorts thy t = if Sign.all_sorts_nonempty thy then I else Sorts.insert_term t;
wenzelm@16656
   175
wenzelm@16656
   176
(*NB: type unification may invent new sorts*)
wenzelm@16656
   177
fun may_insert_env_sorts thy (env as Envir.Envir {iTs, ...}) =
wenzelm@16656
   178
  if Sign.all_sorts_nonempty thy then I
wenzelm@16656
   179
  else Vartab.fold (fn (_, (_, T)) => Sorts.insert_typ T) iTs;
wenzelm@16656
   180
wenzelm@16656
   181
wenzelm@16656
   182
wenzelm@250
   183
(** certified types **)
wenzelm@250
   184
wenzelm@16656
   185
datatype ctyp = Ctyp of {thy_ref: theory_ref, T: typ, sorts: sort list};
wenzelm@250
   186
wenzelm@16656
   187
fun rep_ctyp (Ctyp {thy_ref, T, sorts}) =
wenzelm@16425
   188
  let val thy = Theory.deref thy_ref
wenzelm@16656
   189
  in {thy = thy, sign = thy, T = T, sorts = sorts} end;
wenzelm@250
   190
wenzelm@16656
   191
fun theory_of_ctyp (Ctyp {thy_ref, ...}) = Theory.deref thy_ref;
wenzelm@16425
   192
wenzelm@250
   193
fun typ_of (Ctyp {T, ...}) = T;
wenzelm@250
   194
wenzelm@16656
   195
fun ctyp_of thy raw_T =
wenzelm@16656
   196
  let val T = Sign.certify_typ thy raw_T
wenzelm@16656
   197
  in Ctyp {thy_ref = Theory.self_ref thy, T = T, sorts = may_insert_typ_sorts thy T []} end;
wenzelm@250
   198
wenzelm@16425
   199
fun read_ctyp thy s =
wenzelm@16656
   200
  let val T = Sign.read_typ (thy, K NONE) s
wenzelm@16656
   201
  in Ctyp {thy_ref = Theory.self_ref thy, T = T, sorts = may_insert_typ_sorts thy T []} end;
lcp@229
   202
wenzelm@16656
   203
fun dest_ctyp (Ctyp {thy_ref, T = Type (s, Ts), sorts}) =
wenzelm@16656
   204
      map (fn T => Ctyp {thy_ref = thy_ref, T = T, sorts = sorts}) Ts
wenzelm@16679
   205
  | dest_ctyp cT = raise TYPE ("dest_ctyp", [typ_of cT], []);
berghofe@15087
   206
lcp@229
   207
lcp@229
   208
wenzelm@250
   209
(** certified terms **)
lcp@229
   210
wenzelm@16601
   211
(*certified terms with checked typ, maxidx, and sorts*)
wenzelm@16601
   212
datatype cterm = Cterm of
wenzelm@16601
   213
 {thy_ref: theory_ref,
wenzelm@16601
   214
  t: term,
wenzelm@16601
   215
  T: typ,
wenzelm@16601
   216
  maxidx: int,
wenzelm@16601
   217
  sorts: sort list};
wenzelm@16425
   218
wenzelm@16679
   219
exception CTERM of string;
wenzelm@16679
   220
wenzelm@16601
   221
fun rep_cterm (Cterm {thy_ref, t, T, maxidx, sorts}) =
wenzelm@16425
   222
  let val thy =  Theory.deref thy_ref
wenzelm@16601
   223
  in {thy = thy, sign = thy, t = t, T = T, maxidx = maxidx, sorts = sorts} end;
lcp@229
   224
wenzelm@16601
   225
fun crep_cterm (Cterm {thy_ref, t, T, maxidx, sorts}) =
wenzelm@16425
   226
  let val thy = Theory.deref thy_ref in
wenzelm@16656
   227
   {thy = thy, sign = thy, t = t, T = Ctyp {thy_ref = thy_ref, T = T, sorts = sorts},
wenzelm@16601
   228
    maxidx = maxidx, sorts = sorts}
wenzelm@16425
   229
  end;
wenzelm@3967
   230
wenzelm@16425
   231
fun theory_of_cterm (Cterm {thy_ref, ...}) = Theory.deref thy_ref;
wenzelm@250
   232
fun term_of (Cterm {t, ...}) = t;
lcp@229
   233
wenzelm@16656
   234
fun ctyp_of_term (Cterm {thy_ref, T, sorts, ...}) =
wenzelm@16656
   235
  Ctyp {thy_ref = thy_ref, T = T, sorts = sorts};
paulson@2671
   236
wenzelm@16425
   237
fun cterm_of thy tm =
wenzelm@16601
   238
  let
wenzelm@18969
   239
    val (t, T, maxidx) = Sign.certify_term thy tm;
wenzelm@16656
   240
    val sorts = may_insert_term_sorts thy t [];
wenzelm@16601
   241
  in Cterm {thy_ref = Theory.self_ref thy, t = t, T = T, maxidx = maxidx, sorts = sorts} end;
lcp@229
   242
wenzelm@16656
   243
fun merge_thys0 (Cterm {thy_ref = r1, ...}) (Cterm {thy_ref = r2, ...}) =
wenzelm@16656
   244
  Theory.merge_refs (r1, r2);
wenzelm@16656
   245
clasohm@1493
   246
(*Destruct application in cterms*)
wenzelm@16679
   247
fun dest_comb (Cterm {t = t $ u, T, thy_ref, maxidx, sorts}) =
wenzelm@16679
   248
      let val A = Term.argument_type_of t in
wenzelm@16679
   249
        (Cterm {t = t, T = A --> T, thy_ref = thy_ref, maxidx = maxidx, sorts = sorts},
wenzelm@16679
   250
         Cterm {t = u, T = A, thy_ref = thy_ref, maxidx = maxidx, sorts = sorts})
clasohm@1493
   251
      end
clasohm@1493
   252
  | dest_comb _ = raise CTERM "dest_comb";
clasohm@1493
   253
clasohm@1493
   254
(*Destruct abstraction in cterms*)
wenzelm@16679
   255
fun dest_abs a (Cterm {t = Abs (x, T, t), T = Type ("fun", [_, U]), thy_ref, maxidx, sorts}) =
wenzelm@18944
   256
      let val (y', t') = Term.dest_abs (the_default x a, T, t) in
wenzelm@16679
   257
        (Cterm {t = Free (y', T), T = T, thy_ref = thy_ref, maxidx = maxidx, sorts = sorts},
wenzelm@16679
   258
          Cterm {t = t', T = U, thy_ref = thy_ref, maxidx = maxidx, sorts = sorts})
clasohm@1493
   259
      end
berghofe@10416
   260
  | dest_abs _ _ = raise CTERM "dest_abs";
clasohm@1493
   261
paulson@2147
   262
(*Makes maxidx precise: it is often too big*)
wenzelm@16601
   263
fun adjust_maxidx (ct as Cterm {thy_ref, t, T, maxidx, sorts}) =
wenzelm@16425
   264
  if maxidx = ~1 then ct
wenzelm@16601
   265
  else Cterm {thy_ref = thy_ref, t = t, T = T, maxidx = maxidx_of_term t, sorts = sorts};
clasohm@1703
   266
clasohm@1516
   267
(*Form cterm out of a function and an argument*)
wenzelm@16601
   268
fun capply
wenzelm@16656
   269
  (cf as Cterm {t = f, T = Type ("fun", [dty, rty]), maxidx = maxidx1, sorts = sorts1, ...})
wenzelm@16656
   270
  (cx as Cterm {t = x, T, maxidx = maxidx2, sorts = sorts2, ...}) =
wenzelm@16601
   271
    if T = dty then
wenzelm@16656
   272
      Cterm {thy_ref = merge_thys0 cf cx,
wenzelm@16656
   273
        t = f $ x,
wenzelm@16656
   274
        T = rty,
wenzelm@16656
   275
        maxidx = Int.max (maxidx1, maxidx2),
wenzelm@16601
   276
        sorts = Sorts.union sorts1 sorts2}
clasohm@1516
   277
      else raise CTERM "capply: types don't agree"
clasohm@1516
   278
  | capply _ _ = raise CTERM "capply: first arg is not a function"
wenzelm@250
   279
wenzelm@16601
   280
fun cabs
wenzelm@16656
   281
  (ct1 as Cterm {t = t1, T = T1, maxidx = maxidx1, sorts = sorts1, ...})
wenzelm@16656
   282
  (ct2 as Cterm {t = t2, T = T2, maxidx = maxidx2, sorts = sorts2, ...}) =
wenzelm@18944
   283
    let val t = lambda t1 t2 handle TERM _ => raise CTERM "cabs: malformed first argument" in
wenzelm@16656
   284
      Cterm {thy_ref = merge_thys0 ct1 ct2,
wenzelm@16656
   285
        t = t, T = T1 --> T2,
wenzelm@16656
   286
        maxidx = Int.max (maxidx1, maxidx2),
wenzelm@16656
   287
        sorts = Sorts.union sorts1 sorts2}
wenzelm@16601
   288
    end;
lcp@229
   289
berghofe@10416
   290
(*Matching of cterms*)
wenzelm@16656
   291
fun gen_cterm_match match
wenzelm@16656
   292
    (ct1 as Cterm {t = t1, maxidx = maxidx1, sorts = sorts1, ...},
wenzelm@16656
   293
     ct2 as Cterm {t = t2, maxidx = maxidx2, sorts = sorts2, ...}) =
berghofe@10416
   294
  let
wenzelm@16656
   295
    val thy_ref = merge_thys0 ct1 ct2;
wenzelm@18184
   296
    val (Tinsts, tinsts) = match (Theory.deref thy_ref) (t1, t2) (Vartab.empty, Vartab.empty);
berghofe@10416
   297
    val maxidx = Int.max (maxidx1, maxidx2);
wenzelm@16601
   298
    val sorts = Sorts.union sorts1 sorts2;
wenzelm@16656
   299
    fun mk_cTinst (ixn, (S, T)) =
wenzelm@16656
   300
      (Ctyp {T = TVar (ixn, S), thy_ref = thy_ref, sorts = sorts},
wenzelm@16656
   301
       Ctyp {T = T, thy_ref = thy_ref, sorts = sorts});
wenzelm@16656
   302
    fun mk_ctinst (ixn, (T, t)) =
wenzelm@16601
   303
      let val T = Envir.typ_subst_TVars Tinsts T in
wenzelm@16656
   304
        (Cterm {t = Var (ixn, T), T = T, thy_ref = thy_ref, maxidx = maxidx, sorts = sorts},
wenzelm@16656
   305
         Cterm {t = t, T = T, thy_ref = thy_ref, maxidx = maxidx, sorts = sorts})
berghofe@10416
   306
      end;
wenzelm@16656
   307
  in (Vartab.fold (cons o mk_cTinst) Tinsts [], Vartab.fold (cons o mk_ctinst) tinsts []) end;
berghofe@10416
   308
berghofe@10416
   309
val cterm_match = gen_cterm_match Pattern.match;
berghofe@10416
   310
val cterm_first_order_match = gen_cterm_match Pattern.first_order_match;
berghofe@10416
   311
berghofe@10416
   312
(*Incrementing indexes*)
wenzelm@16601
   313
fun cterm_incr_indexes i (ct as Cterm {thy_ref, t, T, maxidx, sorts}) =
wenzelm@16601
   314
  if i < 0 then raise CTERM "negative increment"
wenzelm@16601
   315
  else if i = 0 then ct
wenzelm@16601
   316
  else Cterm {thy_ref = thy_ref, t = Logic.incr_indexes ([], i) t,
wenzelm@16884
   317
    T = Logic.incr_tvar i T, maxidx = maxidx + i, sorts = sorts};
berghofe@10416
   318
wenzelm@2509
   319
wenzelm@2509
   320
wenzelm@574
   321
(** read cterms **)   (*exception ERROR*)
wenzelm@250
   322
nipkow@4281
   323
(*read terms, infer types, certify terms*)
wenzelm@16425
   324
fun read_def_cterms (thy, types, sorts) used freeze sTs =
wenzelm@250
   325
  let
wenzelm@16425
   326
    val (ts', tye) = Sign.read_def_terms (thy, types, sorts) used freeze sTs;
wenzelm@16425
   327
    val cts = map (cterm_of thy) ts'
wenzelm@2979
   328
      handle TYPE (msg, _, _) => error msg
wenzelm@2386
   329
           | TERM (msg, _) => error msg;
nipkow@4281
   330
  in (cts, tye) end;
nipkow@4281
   331
nipkow@4281
   332
(*read term, infer types, certify term*)
nipkow@4281
   333
fun read_def_cterm args used freeze aT =
nipkow@4281
   334
  let val ([ct],tye) = read_def_cterms args used freeze [aT]
nipkow@4281
   335
  in (ct,tye) end;
lcp@229
   336
wenzelm@16425
   337
fun read_cterm thy = #1 o read_def_cterm (thy, K NONE, K NONE) [] true;
lcp@229
   338
wenzelm@250
   339
wenzelm@6089
   340
(*tags provide additional comment, apart from the axiom/theorem name*)
wenzelm@6089
   341
type tag = string * string list;
wenzelm@6089
   342
wenzelm@2509
   343
wenzelm@387
   344
(*** Meta theorems ***)
lcp@229
   345
berghofe@11518
   346
structure Pt = Proofterm;
berghofe@11518
   347
clasohm@0
   348
datatype thm = Thm of
wenzelm@16425
   349
 {thy_ref: theory_ref,         (*dynamic reference to theory*)
berghofe@11518
   350
  der: bool * Pt.proof,        (*derivation*)
wenzelm@3967
   351
  maxidx: int,                 (*maximum index of any Var or TVar*)
wenzelm@16601
   352
  shyps: sort list,            (*sort hypotheses as ordered list*)
wenzelm@16601
   353
  hyps: term list,             (*hypotheses as ordered list*)
berghofe@13658
   354
  tpairs: (term * term) list,  (*flex-flex pairs*)
wenzelm@3967
   355
  prop: term};                 (*conclusion*)
clasohm@0
   356
wenzelm@16725
   357
(*errors involving theorems*)
wenzelm@16725
   358
exception THM of string * int * thm list;
berghofe@13658
   359
wenzelm@16425
   360
fun rep_thm (Thm {thy_ref, der, maxidx, shyps, hyps, tpairs, prop}) =
wenzelm@16425
   361
  let val thy = Theory.deref thy_ref in
wenzelm@16425
   362
   {thy = thy, sign = thy, der = der, maxidx = maxidx,
wenzelm@16425
   363
    shyps = shyps, hyps = hyps, tpairs = tpairs, prop = prop}
wenzelm@16425
   364
  end;
clasohm@0
   365
wenzelm@16425
   366
(*version of rep_thm returning cterms instead of terms*)
wenzelm@16425
   367
fun crep_thm (Thm {thy_ref, der, maxidx, shyps, hyps, tpairs, prop}) =
wenzelm@16425
   368
  let
wenzelm@16425
   369
    val thy = Theory.deref thy_ref;
wenzelm@16601
   370
    fun cterm max t = Cterm {thy_ref = thy_ref, t = t, T = propT, maxidx = max, sorts = shyps};
wenzelm@16425
   371
  in
wenzelm@16425
   372
   {thy = thy, sign = thy, der = der, maxidx = maxidx, shyps = shyps,
wenzelm@16425
   373
    hyps = map (cterm ~1) hyps,
wenzelm@16425
   374
    tpairs = map (pairself (cterm maxidx)) tpairs,
wenzelm@16425
   375
    prop = cterm maxidx prop}
clasohm@1517
   376
  end;
clasohm@1517
   377
wenzelm@16725
   378
fun terms_of_tpairs tpairs = fold_rev (fn (t, u) => cons t o cons u) tpairs [];
wenzelm@16725
   379
wenzelm@16725
   380
fun eq_tpairs ((t, u), (t', u')) = t aconv t' andalso u aconv u';
wenzelm@18944
   381
fun union_tpairs ts us = Library.merge eq_tpairs (ts, us);
wenzelm@16884
   382
val maxidx_tpairs = fold (fn (t, u) => Term.maxidx_term t #> Term.maxidx_term u);
wenzelm@16725
   383
wenzelm@16725
   384
fun attach_tpairs tpairs prop =
wenzelm@16725
   385
  Logic.list_implies (map Logic.mk_equals tpairs, prop);
wenzelm@16725
   386
wenzelm@16725
   387
fun full_prop_of (Thm {tpairs, prop, ...}) = attach_tpairs tpairs prop;
wenzelm@16945
   388
wenzelm@16945
   389
wenzelm@16945
   390
(* merge theories of cterms/thms; raise exception if incompatible *)
wenzelm@16945
   391
wenzelm@16945
   392
fun merge_thys1 (Cterm {thy_ref = r1, ...}) (th as Thm {thy_ref = r2, ...}) =
wenzelm@16945
   393
  Theory.merge_refs (r1, r2) handle TERM (msg, _) => raise THM (msg, 0, [th]);
wenzelm@16945
   394
wenzelm@16945
   395
fun merge_thys2 (th1 as Thm {thy_ref = r1, ...}) (th2 as Thm {thy_ref = r2, ...}) =
wenzelm@16945
   396
  Theory.merge_refs (r1, r2) handle TERM (msg, _) => raise THM (msg, 0, [th1, th2]);
wenzelm@16945
   397
clasohm@0
   398
wenzelm@16425
   399
(*attributes subsume any kind of rules or context modifiers*)
wenzelm@18733
   400
type attribute = Context.generic * thm -> Context.generic * thm;
wenzelm@18733
   401
wenzelm@18733
   402
fun rule_attribute f (x, th) = (x, f x th);
wenzelm@18733
   403
fun declaration_attribute f (x, th) = (f th x, th);
wenzelm@18733
   404
wenzelm@18733
   405
fun apply_attributes mk dest =
wenzelm@18733
   406
  let
wenzelm@18733
   407
    fun app [] = I
wenzelm@18733
   408
      | app ((f: attribute) :: fs) = fn (x, th) => f (mk x, th) |>> dest |> app fs;
wenzelm@18733
   409
  in app end;
wenzelm@18733
   410
wenzelm@18733
   411
val theory_attributes = apply_attributes Context.Theory Context.the_theory;
wenzelm@18733
   412
val proof_attributes = apply_attributes Context.Proof Context.the_proof;
wenzelm@17708
   413
wenzelm@6089
   414
fun no_attributes x = (x, []);
wenzelm@17345
   415
fun simple_fact x = [(x, [])];
wenzelm@6089
   416
wenzelm@16601
   417
wenzelm@16656
   418
(* hyps *)
wenzelm@16601
   419
wenzelm@16945
   420
val insert_hyps = OrdList.insert Term.fast_term_ord;
wenzelm@16679
   421
val remove_hyps = OrdList.remove Term.fast_term_ord;
wenzelm@16679
   422
val union_hyps = OrdList.union Term.fast_term_ord;
wenzelm@16679
   423
val eq_set_hyps = OrdList.eq_set Term.fast_term_ord;
wenzelm@16601
   424
wenzelm@16601
   425
wenzelm@16601
   426
(* eq_thm(s) *)
wenzelm@16601
   427
wenzelm@3994
   428
fun eq_thm (th1, th2) =
wenzelm@3994
   429
  let
wenzelm@16425
   430
    val {thy = thy1, shyps = shyps1, hyps = hyps1, tpairs = tpairs1, prop = prop1, ...} =
wenzelm@9031
   431
      rep_thm th1;
wenzelm@16425
   432
    val {thy = thy2, shyps = shyps2, hyps = hyps2, tpairs = tpairs2, prop = prop2, ...} =
wenzelm@9031
   433
      rep_thm th2;
wenzelm@3994
   434
  in
wenzelm@16601
   435
    Context.joinable (thy1, thy2) andalso
wenzelm@16601
   436
    Sorts.eq_set (shyps1, shyps2) andalso
wenzelm@16601
   437
    eq_set_hyps (hyps1, hyps2) andalso
wenzelm@16656
   438
    equal_lists eq_tpairs (tpairs1, tpairs2) andalso
wenzelm@3994
   439
    prop1 aconv prop2
wenzelm@3994
   440
  end;
wenzelm@387
   441
wenzelm@16135
   442
val eq_thms = Library.equal_lists eq_thm;
wenzelm@16135
   443
wenzelm@16425
   444
fun theory_of_thm (Thm {thy_ref, ...}) = Theory.deref thy_ref;
wenzelm@16425
   445
val sign_of_thm = theory_of_thm;
wenzelm@16425
   446
wenzelm@19429
   447
fun maxidx_of (Thm {maxidx, ...}) = maxidx;
wenzelm@12803
   448
fun prop_of (Thm {prop, ...}) = prop;
wenzelm@13528
   449
fun proof_of (Thm {der = (_, proof), ...}) = proof;
wenzelm@16601
   450
fun tpairs_of (Thm {tpairs, ...}) = tpairs;
clasohm@0
   451
wenzelm@16601
   452
val concl_of = Logic.strip_imp_concl o prop_of;
wenzelm@16601
   453
val prems_of = Logic.strip_imp_prems o prop_of;
wenzelm@16601
   454
fun nprems_of th = Logic.count_prems (prop_of th, 0);
wenzelm@19305
   455
fun no_prems th = nprems_of th = 0;
wenzelm@16601
   456
wenzelm@16601
   457
fun major_prem_of th =
wenzelm@16601
   458
  (case prems_of th of
wenzelm@16601
   459
    prem :: _ => Logic.strip_assums_concl prem
wenzelm@16601
   460
  | [] => raise THM ("major_prem_of: rule with no premises", 0, [th]));
wenzelm@16601
   461
wenzelm@16601
   462
(*the statement of any thm is a cterm*)
wenzelm@16601
   463
fun cprop_of (Thm {thy_ref, maxidx, shyps, prop, ...}) =
wenzelm@16601
   464
  Cterm {thy_ref = thy_ref, maxidx = maxidx, T = propT, t = prop, sorts = shyps};
wenzelm@16601
   465
wenzelm@18145
   466
fun cprem_of (th as Thm {thy_ref, maxidx, shyps, prop, ...}) i =
wenzelm@18035
   467
  Cterm {thy_ref = thy_ref, maxidx = maxidx, T = propT, sorts = shyps,
wenzelm@18145
   468
    t = Logic.nth_prem (i, prop) handle TERM _ => raise THM ("cprem_of", i, [th])};
wenzelm@18035
   469
wenzelm@16656
   470
(*explicit transfer to a super theory*)
wenzelm@16425
   471
fun transfer thy' thm =
wenzelm@3895
   472
  let
wenzelm@16425
   473
    val Thm {thy_ref, der, maxidx, shyps, hyps, tpairs, prop} = thm;
wenzelm@16425
   474
    val thy = Theory.deref thy_ref;
wenzelm@3895
   475
  in
wenzelm@16945
   476
    if not (subthy (thy, thy')) then
wenzelm@16945
   477
      raise THM ("transfer: not a super theory", 0, [thm])
wenzelm@16945
   478
    else if eq_thy (thy, thy') then thm
wenzelm@16945
   479
    else
wenzelm@16945
   480
      Thm {thy_ref = Theory.self_ref thy',
wenzelm@16945
   481
        der = der,
wenzelm@16945
   482
        maxidx = maxidx,
wenzelm@16945
   483
        shyps = shyps,
wenzelm@16945
   484
        hyps = hyps,
wenzelm@16945
   485
        tpairs = tpairs,
wenzelm@16945
   486
        prop = prop}
wenzelm@3895
   487
  end;
wenzelm@387
   488
wenzelm@16945
   489
(*explicit weakening: maps |- B to A |- B*)
wenzelm@16945
   490
fun weaken raw_ct th =
wenzelm@16945
   491
  let
wenzelm@16945
   492
    val ct as Cterm {t = A, T, sorts, maxidx = maxidxA, ...} = adjust_maxidx raw_ct;
wenzelm@16945
   493
    val Thm {der, maxidx, shyps, hyps, tpairs, prop, ...} = th;
wenzelm@16945
   494
  in
wenzelm@16945
   495
    if T <> propT then
wenzelm@16945
   496
      raise THM ("weaken: assumptions must have type prop", 0, [])
wenzelm@16945
   497
    else if maxidxA <> ~1 then
wenzelm@16945
   498
      raise THM ("weaken: assumptions may not contain schematic variables", maxidxA, [])
wenzelm@16945
   499
    else
wenzelm@16945
   500
      Thm {thy_ref = merge_thys1 ct th,
wenzelm@16945
   501
        der = der,
wenzelm@16945
   502
        maxidx = maxidx,
wenzelm@16945
   503
        shyps = Sorts.union sorts shyps,
wenzelm@16945
   504
        hyps = insert_hyps A hyps,
wenzelm@16945
   505
        tpairs = tpairs,
wenzelm@16945
   506
        prop = prop}
wenzelm@16945
   507
  end;
wenzelm@16656
   508
wenzelm@16656
   509
clasohm@0
   510
wenzelm@1238
   511
(** sort contexts of theorems **)
wenzelm@1238
   512
wenzelm@16656
   513
fun present_sorts (Thm {hyps, tpairs, prop, ...}) =
wenzelm@16656
   514
  fold (fn (t, u) => Sorts.insert_term t o Sorts.insert_term u) tpairs
wenzelm@16656
   515
    (Sorts.insert_terms hyps (Sorts.insert_term prop []));
wenzelm@1238
   516
wenzelm@7642
   517
(*remove extra sorts that are non-empty by virtue of type signature information*)
wenzelm@7642
   518
fun strip_shyps (thm as Thm {shyps = [], ...}) = thm
wenzelm@16425
   519
  | strip_shyps (thm as Thm {thy_ref, der, maxidx, shyps, hyps, tpairs, prop}) =
wenzelm@7642
   520
      let
wenzelm@16425
   521
        val thy = Theory.deref thy_ref;
wenzelm@16656
   522
        val shyps' =
wenzelm@16656
   523
          if Sign.all_sorts_nonempty thy then []
wenzelm@16656
   524
          else
wenzelm@16656
   525
            let
wenzelm@16656
   526
              val present = present_sorts thm;
wenzelm@16656
   527
              val extra = Sorts.subtract present shyps;
wenzelm@16656
   528
              val witnessed = map #2 (Sign.witness_sorts thy present extra);
wenzelm@16656
   529
            in Sorts.subtract witnessed shyps end;
wenzelm@7642
   530
      in
wenzelm@16425
   531
        Thm {thy_ref = thy_ref, der = der, maxidx = maxidx,
wenzelm@16656
   532
          shyps = shyps', hyps = hyps, tpairs = tpairs, prop = prop}
wenzelm@7642
   533
      end;
wenzelm@1238
   534
wenzelm@16656
   535
(*dangling sort constraints of a thm*)
wenzelm@16656
   536
fun extra_shyps (th as Thm {shyps, ...}) = Sorts.subtract (present_sorts th) shyps;
wenzelm@16656
   537
wenzelm@1238
   538
wenzelm@1238
   539
paulson@1529
   540
(** Axioms **)
wenzelm@387
   541
wenzelm@16425
   542
(*look up the named axiom in the theory or its ancestors*)
wenzelm@15672
   543
fun get_axiom_i theory name =
wenzelm@387
   544
  let
wenzelm@16425
   545
    fun get_ax thy =
wenzelm@17412
   546
      Symtab.lookup (#2 (#axioms (Theory.rep_theory thy))) name
wenzelm@16601
   547
      |> Option.map (fn prop =>
wenzelm@16601
   548
          Thm {thy_ref = Theory.self_ref thy,
wenzelm@16601
   549
            der = Pt.infer_derivs' I (false, Pt.axm_proof name prop),
wenzelm@16601
   550
            maxidx = maxidx_of_term prop,
wenzelm@16656
   551
            shyps = may_insert_term_sorts thy prop [],
wenzelm@16601
   552
            hyps = [],
wenzelm@16601
   553
            tpairs = [],
wenzelm@16601
   554
            prop = prop});
wenzelm@387
   555
  in
wenzelm@16425
   556
    (case get_first get_ax (theory :: Theory.ancestors_of theory) of
skalberg@15531
   557
      SOME thm => thm
skalberg@15531
   558
    | NONE => raise THEORY ("No axiom " ^ quote name, [theory]))
wenzelm@387
   559
  end;
wenzelm@387
   560
wenzelm@16352
   561
fun get_axiom thy =
wenzelm@16425
   562
  get_axiom_i thy o NameSpace.intern (Theory.axiom_space thy);
wenzelm@15672
   563
wenzelm@6368
   564
fun def_name name = name ^ "_def";
wenzelm@6368
   565
fun get_def thy = get_axiom thy o def_name;
wenzelm@4847
   566
paulson@1529
   567
wenzelm@776
   568
(*return additional axioms of this theory node*)
wenzelm@776
   569
fun axioms_of thy =
wenzelm@776
   570
  map (fn (s, _) => (s, get_axiom thy s))
wenzelm@16352
   571
    (Symtab.dest (#2 (#axioms (Theory.rep_theory thy))));
wenzelm@776
   572
wenzelm@6089
   573
wenzelm@6089
   574
(* name and tags -- make proof objects more readable *)
wenzelm@6089
   575
wenzelm@12923
   576
fun get_name_tags (Thm {hyps, prop, der = (_, prf), ...}) =
wenzelm@12923
   577
  Pt.get_name_tags hyps prop prf;
wenzelm@4018
   578
wenzelm@16425
   579
fun put_name_tags x (Thm {thy_ref, der = (ora, prf), maxidx,
wenzelm@16425
   580
      shyps, hyps, tpairs = [], prop}) = Thm {thy_ref = thy_ref,
wenzelm@16425
   581
        der = (ora, Pt.thm_proof (Theory.deref thy_ref) x hyps prop prf),
berghofe@13658
   582
        maxidx = maxidx, shyps = shyps, hyps = hyps, tpairs = [], prop = prop}
berghofe@13658
   583
  | put_name_tags _ thm =
berghofe@13658
   584
      raise THM ("put_name_tags: unsolved flex-flex constraints", 0, [thm]);
wenzelm@6089
   585
wenzelm@6089
   586
val name_of_thm = #1 o get_name_tags;
wenzelm@6089
   587
val tags_of_thm = #2 o get_name_tags;
wenzelm@6089
   588
wenzelm@6089
   589
fun name_thm (name, thm) = put_name_tags (name, tags_of_thm thm) thm;
clasohm@0
   590
clasohm@0
   591
paulson@1529
   592
(*Compression of theorems -- a separate rule, not integrated with the others,
paulson@1529
   593
  as it could be slow.*)
wenzelm@16425
   594
fun compress (Thm {thy_ref, der, maxidx, shyps, hyps, tpairs, prop}) =
wenzelm@16991
   595
  let val thy = Theory.deref thy_ref in
wenzelm@16991
   596
    Thm {thy_ref = thy_ref,
wenzelm@16991
   597
      der = der,
wenzelm@16991
   598
      maxidx = maxidx,
wenzelm@16991
   599
      shyps = shyps,
wenzelm@16991
   600
      hyps = map (Compress.term thy) hyps,
wenzelm@16991
   601
      tpairs = map (pairself (Compress.term thy)) tpairs,
wenzelm@16991
   602
      prop = Compress.term thy prop}
wenzelm@16991
   603
  end;
wenzelm@16945
   604
wenzelm@16945
   605
fun adjust_maxidx_thm (Thm {thy_ref, der, shyps, hyps, tpairs, prop, ...}) =
wenzelm@16945
   606
  Thm {thy_ref = thy_ref,
wenzelm@16945
   607
    der = der,
wenzelm@16945
   608
    maxidx = maxidx_tpairs tpairs (maxidx_of_term prop),
wenzelm@16945
   609
    shyps = shyps,
wenzelm@16945
   610
    hyps = hyps,
wenzelm@16945
   611
    tpairs = tpairs,
wenzelm@16945
   612
    prop = prop};
wenzelm@564
   613
wenzelm@387
   614
wenzelm@2509
   615
paulson@1529
   616
(*** Meta rules ***)
clasohm@0
   617
wenzelm@16601
   618
(** primitive rules **)
clasohm@0
   619
wenzelm@16656
   620
(*The assumption rule A |- A*)
wenzelm@16601
   621
fun assume raw_ct =
wenzelm@16601
   622
  let val Cterm {thy_ref, t = prop, T, maxidx, sorts} = adjust_maxidx raw_ct in
wenzelm@16601
   623
    if T <> propT then
mengj@19230
   624
      raise THM ("assume: prop", 0, [])
wenzelm@16601
   625
    else if maxidx <> ~1 then
mengj@19230
   626
      raise THM ("assume: variables", maxidx, [])
wenzelm@16601
   627
    else Thm {thy_ref = thy_ref,
wenzelm@16601
   628
      der = Pt.infer_derivs' I (false, Pt.Hyp prop),
wenzelm@16601
   629
      maxidx = ~1,
wenzelm@16601
   630
      shyps = sorts,
wenzelm@16601
   631
      hyps = [prop],
wenzelm@16601
   632
      tpairs = [],
wenzelm@16601
   633
      prop = prop}
clasohm@0
   634
  end;
clasohm@0
   635
wenzelm@1220
   636
(*Implication introduction
wenzelm@3529
   637
    [A]
wenzelm@3529
   638
     :
wenzelm@3529
   639
     B
wenzelm@1220
   640
  -------
wenzelm@1220
   641
  A ==> B
wenzelm@1220
   642
*)
wenzelm@16601
   643
fun implies_intr
wenzelm@16679
   644
    (ct as Cterm {t = A, T, maxidx = maxidxA, sorts, ...})
wenzelm@16679
   645
    (th as Thm {der, maxidx, hyps, shyps, tpairs, prop, ...}) =
wenzelm@16601
   646
  if T <> propT then
wenzelm@16601
   647
    raise THM ("implies_intr: assumptions must have type prop", 0, [th])
wenzelm@16601
   648
  else
wenzelm@16601
   649
    Thm {thy_ref = merge_thys1 ct th,
wenzelm@16601
   650
      der = Pt.infer_derivs' (Pt.implies_intr_proof A) der,
wenzelm@16601
   651
      maxidx = Int.max (maxidxA, maxidx),
wenzelm@16601
   652
      shyps = Sorts.union sorts shyps,
wenzelm@16601
   653
      hyps = remove_hyps A hyps,
wenzelm@16601
   654
      tpairs = tpairs,
wenzelm@16601
   655
      prop = implies $ A $ prop};
clasohm@0
   656
paulson@1529
   657
wenzelm@1220
   658
(*Implication elimination
wenzelm@1220
   659
  A ==> B    A
wenzelm@1220
   660
  ------------
wenzelm@1220
   661
        B
wenzelm@1220
   662
*)
wenzelm@16601
   663
fun implies_elim thAB thA =
wenzelm@16601
   664
  let
wenzelm@16601
   665
    val Thm {maxidx = maxA, der = derA, hyps = hypsA, shyps = shypsA, tpairs = tpairsA,
wenzelm@16601
   666
      prop = propA, ...} = thA
wenzelm@16601
   667
    and Thm {der, maxidx, hyps, shyps, tpairs, prop, ...} = thAB;
wenzelm@16601
   668
    fun err () = raise THM ("implies_elim: major premise", 0, [thAB, thA]);
wenzelm@16601
   669
  in
wenzelm@16601
   670
    case prop of
wenzelm@16601
   671
      imp $ A $ B =>
wenzelm@16601
   672
        if imp = Term.implies andalso A aconv propA then
wenzelm@16656
   673
          Thm {thy_ref = merge_thys2 thAB thA,
wenzelm@16601
   674
            der = Pt.infer_derivs (curry Pt.%%) der derA,
wenzelm@16601
   675
            maxidx = Int.max (maxA, maxidx),
wenzelm@16601
   676
            shyps = Sorts.union shypsA shyps,
wenzelm@16601
   677
            hyps = union_hyps hypsA hyps,
wenzelm@16601
   678
            tpairs = union_tpairs tpairsA tpairs,
wenzelm@16601
   679
            prop = B}
wenzelm@16601
   680
        else err ()
wenzelm@16601
   681
    | _ => err ()
wenzelm@16601
   682
  end;
wenzelm@250
   683
wenzelm@1220
   684
(*Forall introduction.  The Free or Var x must not be free in the hypotheses.
wenzelm@16656
   685
    [x]
wenzelm@16656
   686
     :
wenzelm@16656
   687
     A
wenzelm@16656
   688
  ------
wenzelm@16656
   689
  !!x. A
wenzelm@1220
   690
*)
wenzelm@16601
   691
fun forall_intr
wenzelm@16601
   692
    (ct as Cterm {t = x, T, sorts, ...})
wenzelm@16679
   693
    (th as Thm {der, maxidx, shyps, hyps, tpairs, prop, ...}) =
wenzelm@16601
   694
  let
wenzelm@16601
   695
    fun result a =
wenzelm@16601
   696
      Thm {thy_ref = merge_thys1 ct th,
wenzelm@16601
   697
        der = Pt.infer_derivs' (Pt.forall_intr_proof x a) der,
wenzelm@16601
   698
        maxidx = maxidx,
wenzelm@16601
   699
        shyps = Sorts.union sorts shyps,
wenzelm@16601
   700
        hyps = hyps,
wenzelm@16601
   701
        tpairs = tpairs,
wenzelm@16601
   702
        prop = all T $ Abs (a, T, abstract_over (x, prop))};
wenzelm@16601
   703
    fun check_occs x ts =
wenzelm@16847
   704
      if exists (fn t => Logic.occs (x, t)) ts then
wenzelm@16601
   705
        raise THM("forall_intr: variable free in assumptions", 0, [th])
wenzelm@16601
   706
      else ();
wenzelm@16601
   707
  in
wenzelm@16601
   708
    case x of
wenzelm@16601
   709
      Free (a, _) => (check_occs x hyps; check_occs x (terms_of_tpairs tpairs); result a)
wenzelm@16601
   710
    | Var ((a, _), _) => (check_occs x (terms_of_tpairs tpairs); result a)
wenzelm@16601
   711
    | _ => raise THM ("forall_intr: not a variable", 0, [th])
clasohm@0
   712
  end;
clasohm@0
   713
wenzelm@1220
   714
(*Forall elimination
wenzelm@16656
   715
  !!x. A
wenzelm@1220
   716
  ------
wenzelm@1220
   717
  A[t/x]
wenzelm@1220
   718
*)
wenzelm@16601
   719
fun forall_elim
wenzelm@16601
   720
    (ct as Cterm {t, T, maxidx = maxt, sorts, ...})
wenzelm@16601
   721
    (th as Thm {der, maxidx, shyps, hyps, tpairs, prop, ...}) =
wenzelm@16601
   722
  (case prop of
wenzelm@16601
   723
    Const ("all", Type ("fun", [Type ("fun", [qary, _]), _])) $ A =>
wenzelm@16601
   724
      if T <> qary then
wenzelm@16601
   725
        raise THM ("forall_elim: type mismatch", 0, [th])
wenzelm@16601
   726
      else
wenzelm@16601
   727
        Thm {thy_ref = merge_thys1 ct th,
wenzelm@16601
   728
          der = Pt.infer_derivs' (Pt.% o rpair (SOME t)) der,
wenzelm@16601
   729
          maxidx = Int.max (maxidx, maxt),
wenzelm@16601
   730
          shyps = Sorts.union sorts shyps,
wenzelm@16601
   731
          hyps = hyps,
wenzelm@16601
   732
          tpairs = tpairs,
wenzelm@16601
   733
          prop = Term.betapply (A, t)}
wenzelm@16601
   734
  | _ => raise THM ("forall_elim: not quantified", 0, [th]));
clasohm@0
   735
clasohm@0
   736
wenzelm@1220
   737
(* Equality *)
clasohm@0
   738
wenzelm@16601
   739
(*Reflexivity
wenzelm@16601
   740
  t == t
wenzelm@16601
   741
*)
wenzelm@16601
   742
fun reflexive (ct as Cterm {thy_ref, t, T, maxidx, sorts}) =
wenzelm@16656
   743
  Thm {thy_ref = thy_ref,
wenzelm@16601
   744
    der = Pt.infer_derivs' I (false, Pt.reflexive),
wenzelm@16601
   745
    maxidx = maxidx,
wenzelm@16601
   746
    shyps = sorts,
wenzelm@16601
   747
    hyps = [],
wenzelm@16601
   748
    tpairs = [],
wenzelm@16601
   749
    prop = Logic.mk_equals (t, t)};
clasohm@0
   750
wenzelm@16601
   751
(*Symmetry
wenzelm@16601
   752
  t == u
wenzelm@16601
   753
  ------
wenzelm@16601
   754
  u == t
wenzelm@1220
   755
*)
wenzelm@16601
   756
fun symmetric (th as Thm {thy_ref, der, maxidx, shyps, hyps, tpairs, prop}) =
wenzelm@16601
   757
  (case prop of
wenzelm@16601
   758
    (eq as Const ("==", Type (_, [T, _]))) $ t $ u =>
wenzelm@16601
   759
      Thm {thy_ref = thy_ref,
wenzelm@16601
   760
        der = Pt.infer_derivs' Pt.symmetric der,
wenzelm@16601
   761
        maxidx = maxidx,
wenzelm@16601
   762
        shyps = shyps,
wenzelm@16601
   763
        hyps = hyps,
wenzelm@16601
   764
        tpairs = tpairs,
wenzelm@16601
   765
        prop = eq $ u $ t}
wenzelm@16601
   766
    | _ => raise THM ("symmetric", 0, [th]));
clasohm@0
   767
wenzelm@16601
   768
(*Transitivity
wenzelm@16601
   769
  t1 == u    u == t2
wenzelm@16601
   770
  ------------------
wenzelm@16601
   771
       t1 == t2
wenzelm@1220
   772
*)
clasohm@0
   773
fun transitive th1 th2 =
wenzelm@16601
   774
  let
wenzelm@16601
   775
    val Thm {der = der1, maxidx = max1, hyps = hyps1, shyps = shyps1, tpairs = tpairs1,
wenzelm@16601
   776
      prop = prop1, ...} = th1
wenzelm@16601
   777
    and Thm {der = der2, maxidx = max2, hyps = hyps2, shyps = shyps2, tpairs = tpairs2,
wenzelm@16601
   778
      prop = prop2, ...} = th2;
wenzelm@16601
   779
    fun err msg = raise THM ("transitive: " ^ msg, 0, [th1, th2]);
wenzelm@16601
   780
  in
wenzelm@16601
   781
    case (prop1, prop2) of
wenzelm@16601
   782
      ((eq as Const ("==", Type (_, [T, _]))) $ t1 $ u, Const ("==", _) $ u' $ t2) =>
wenzelm@16601
   783
        if not (u aconv u') then err "middle term"
wenzelm@16601
   784
        else
wenzelm@16656
   785
          Thm {thy_ref = merge_thys2 th1 th2,
wenzelm@16601
   786
            der = Pt.infer_derivs (Pt.transitive u T) der1 der2,
wenzelm@16601
   787
            maxidx = Int.max (max1, max2),
wenzelm@16601
   788
            shyps = Sorts.union shyps1 shyps2,
wenzelm@16601
   789
            hyps = union_hyps hyps1 hyps2,
wenzelm@16601
   790
            tpairs = union_tpairs tpairs1 tpairs2,
wenzelm@16601
   791
            prop = eq $ t1 $ t2}
wenzelm@16601
   792
     | _ =>  err "premises"
clasohm@0
   793
  end;
clasohm@0
   794
wenzelm@16601
   795
(*Beta-conversion
wenzelm@16656
   796
  (%x. t)(u) == t[u/x]
wenzelm@16601
   797
  fully beta-reduces the term if full = true
berghofe@10416
   798
*)
wenzelm@16601
   799
fun beta_conversion full (Cterm {thy_ref, t, T, maxidx, sorts}) =
wenzelm@16601
   800
  let val t' =
wenzelm@16601
   801
    if full then Envir.beta_norm t
wenzelm@16601
   802
    else
wenzelm@16601
   803
      (case t of Abs (_, _, bodt) $ u => subst_bound (u, bodt)
wenzelm@16601
   804
      | _ => raise THM ("beta_conversion: not a redex", 0, []));
wenzelm@16601
   805
  in
wenzelm@16601
   806
    Thm {thy_ref = thy_ref,
wenzelm@16601
   807
      der = Pt.infer_derivs' I (false, Pt.reflexive),
wenzelm@16601
   808
      maxidx = maxidx,
wenzelm@16601
   809
      shyps = sorts,
wenzelm@16601
   810
      hyps = [],
wenzelm@16601
   811
      tpairs = [],
wenzelm@16601
   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@16601
   816
  Thm {thy_ref = thy_ref,
wenzelm@16601
   817
    der = Pt.infer_derivs' I (false, Pt.reflexive),
wenzelm@16601
   818
    maxidx = maxidx,
wenzelm@16601
   819
    shyps = sorts,
wenzelm@16601
   820
    hyps = [],
wenzelm@16601
   821
    tpairs = [],
wenzelm@18944
   822
    prop = Logic.mk_equals (t, Envir.eta_contract t)};
clasohm@0
   823
clasohm@0
   824
(*The abstraction rule.  The Free or Var x must not be free in the hypotheses.
clasohm@0
   825
  The bound variable will be named "a" (since x will be something like x320)
wenzelm@16601
   826
      t == u
wenzelm@16601
   827
  --------------
wenzelm@16601
   828
  %x. t == %x. u
wenzelm@1220
   829
*)
wenzelm@16601
   830
fun abstract_rule a
wenzelm@16601
   831
    (Cterm {t = x, T, sorts, ...})
wenzelm@16601
   832
    (th as Thm {thy_ref, der, maxidx, hyps, shyps, tpairs, prop}) =
wenzelm@16601
   833
  let
wenzelm@17708
   834
    val string_of = Sign.string_of_term (Theory.deref thy_ref);
wenzelm@16601
   835
    val (t, u) = Logic.dest_equals prop
wenzelm@16601
   836
      handle TERM _ => raise THM ("abstract_rule: premise not an equality", 0, [th]);
wenzelm@16601
   837
    val result =
wenzelm@16601
   838
      Thm {thy_ref = thy_ref,
wenzelm@16601
   839
        der = Pt.infer_derivs' (Pt.abstract_rule x a) der,
wenzelm@16601
   840
        maxidx = maxidx,
wenzelm@16601
   841
        shyps = Sorts.union sorts shyps,
wenzelm@16601
   842
        hyps = hyps,
wenzelm@16601
   843
        tpairs = tpairs,
wenzelm@16601
   844
        prop = Logic.mk_equals
wenzelm@16601
   845
          (Abs (a, T, abstract_over (x, t)), Abs (a, T, abstract_over (x, u)))};
wenzelm@16601
   846
    fun check_occs x ts =
wenzelm@16847
   847
      if exists (fn t => Logic.occs (x, t)) ts then
wenzelm@17708
   848
        raise THM ("abstract_rule: variable free in assumptions " ^ string_of x, 0, [th])
wenzelm@16601
   849
      else ();
wenzelm@16601
   850
  in
wenzelm@16601
   851
    case x of
wenzelm@16601
   852
      Free _ => (check_occs x hyps; check_occs x (terms_of_tpairs tpairs); result)
wenzelm@16601
   853
    | Var _ => (check_occs x (terms_of_tpairs tpairs); result)
wenzelm@17708
   854
    | _ => raise THM ("abstract_rule: not a variable " ^ string_of x, 0, [th])
clasohm@0
   855
  end;
clasohm@0
   856
clasohm@0
   857
(*The combination rule
wenzelm@3529
   858
  f == g  t == u
wenzelm@3529
   859
  --------------
wenzelm@16601
   860
    f t == g u
wenzelm@1220
   861
*)
clasohm@0
   862
fun combination th1 th2 =
wenzelm@16601
   863
  let
wenzelm@16601
   864
    val Thm {der = der1, maxidx = max1, shyps = shyps1, hyps = hyps1, tpairs = tpairs1,
wenzelm@16601
   865
      prop = prop1, ...} = th1
wenzelm@16601
   866
    and Thm {der = der2, maxidx = max2, shyps = shyps2, hyps = hyps2, tpairs = tpairs2,
wenzelm@16601
   867
      prop = prop2, ...} = th2;
wenzelm@16601
   868
    fun chktypes fT tT =
wenzelm@16601
   869
      (case fT of
wenzelm@16601
   870
        Type ("fun", [T1, T2]) =>
wenzelm@16601
   871
          if T1 <> tT then
wenzelm@16601
   872
            raise THM ("combination: types", 0, [th1, th2])
wenzelm@16601
   873
          else ()
wenzelm@16601
   874
      | _ => raise THM ("combination: not function type", 0, [th1, th2]));
wenzelm@16601
   875
  in
wenzelm@16601
   876
    case (prop1, prop2) of
wenzelm@16601
   877
      (Const ("==", Type ("fun", [fT, _])) $ f $ g,
wenzelm@16601
   878
       Const ("==", Type ("fun", [tT, _])) $ t $ u) =>
wenzelm@16601
   879
        (chktypes fT tT;
wenzelm@16601
   880
          Thm {thy_ref = merge_thys2 th1 th2,
wenzelm@16601
   881
            der = Pt.infer_derivs (Pt.combination f g t u fT) der1 der2,
wenzelm@16601
   882
            maxidx = Int.max (max1, max2),
wenzelm@16601
   883
            shyps = Sorts.union shyps1 shyps2,
wenzelm@16601
   884
            hyps = union_hyps hyps1 hyps2,
wenzelm@16601
   885
            tpairs = union_tpairs tpairs1 tpairs2,
wenzelm@16601
   886
            prop = Logic.mk_equals (f $ t, g $ u)})
wenzelm@16601
   887
     | _ => raise THM ("combination: premises", 0, [th1, th2])
clasohm@0
   888
  end;
clasohm@0
   889
wenzelm@16601
   890
(*Equality introduction
wenzelm@3529
   891
  A ==> B  B ==> A
wenzelm@3529
   892
  ----------------
wenzelm@3529
   893
       A == B
wenzelm@1220
   894
*)
clasohm@0
   895
fun equal_intr th1 th2 =
wenzelm@16601
   896
  let
wenzelm@16601
   897
    val Thm {der = der1, maxidx = max1, shyps = shyps1, hyps = hyps1, tpairs = tpairs1,
wenzelm@16601
   898
      prop = prop1, ...} = th1
wenzelm@16601
   899
    and Thm {der = der2, maxidx = max2, shyps = shyps2, hyps = hyps2, tpairs = tpairs2,
wenzelm@16601
   900
      prop = prop2, ...} = th2;
wenzelm@16601
   901
    fun err msg = raise THM ("equal_intr: " ^ msg, 0, [th1, th2]);
wenzelm@16601
   902
  in
wenzelm@16601
   903
    case (prop1, prop2) of
wenzelm@16601
   904
      (Const("==>", _) $ A $ B, Const("==>", _) $ B' $ A') =>
wenzelm@16601
   905
        if A aconv A' andalso B aconv B' then
wenzelm@16601
   906
          Thm {thy_ref = merge_thys2 th1 th2,
wenzelm@16601
   907
            der = Pt.infer_derivs (Pt.equal_intr A B) der1 der2,
wenzelm@16601
   908
            maxidx = Int.max (max1, max2),
wenzelm@16601
   909
            shyps = Sorts.union shyps1 shyps2,
wenzelm@16601
   910
            hyps = union_hyps hyps1 hyps2,
wenzelm@16601
   911
            tpairs = union_tpairs tpairs1 tpairs2,
wenzelm@16601
   912
            prop = Logic.mk_equals (A, B)}
wenzelm@16601
   913
        else err "not equal"
wenzelm@16601
   914
    | _ =>  err "premises"
paulson@1529
   915
  end;
paulson@1529
   916
paulson@1529
   917
(*The equal propositions rule
wenzelm@3529
   918
  A == B  A
paulson@1529
   919
  ---------
paulson@1529
   920
      B
paulson@1529
   921
*)
paulson@1529
   922
fun equal_elim th1 th2 =
wenzelm@16601
   923
  let
wenzelm@16601
   924
    val Thm {der = der1, maxidx = max1, shyps = shyps1, hyps = hyps1,
wenzelm@16601
   925
      tpairs = tpairs1, prop = prop1, ...} = th1
wenzelm@16601
   926
    and Thm {der = der2, maxidx = max2, shyps = shyps2, hyps = hyps2,
wenzelm@16601
   927
      tpairs = tpairs2, prop = prop2, ...} = th2;
wenzelm@16601
   928
    fun err msg = raise THM ("equal_elim: " ^ msg, 0, [th1, th2]);
wenzelm@16601
   929
  in
wenzelm@16601
   930
    case prop1 of
wenzelm@16601
   931
      Const ("==", _) $ A $ B =>
wenzelm@16601
   932
        if prop2 aconv A then
wenzelm@16601
   933
          Thm {thy_ref = merge_thys2 th1 th2,
wenzelm@16601
   934
            der = Pt.infer_derivs (Pt.equal_elim A B) der1 der2,
wenzelm@16601
   935
            maxidx = Int.max (max1, max2),
wenzelm@16601
   936
            shyps = Sorts.union shyps1 shyps2,
wenzelm@16601
   937
            hyps = union_hyps hyps1 hyps2,
wenzelm@16601
   938
            tpairs = union_tpairs tpairs1 tpairs2,
wenzelm@16601
   939
            prop = B}
wenzelm@16601
   940
        else err "not equal"
paulson@1529
   941
     | _ =>  err"major premise"
paulson@1529
   942
  end;
clasohm@0
   943
wenzelm@1220
   944
wenzelm@1220
   945
clasohm@0
   946
(**** Derived rules ****)
clasohm@0
   947
wenzelm@16601
   948
(*Smash unifies the list of term pairs leaving no flex-flex pairs.
wenzelm@250
   949
  Instantiates the theorem and deletes trivial tpairs.
clasohm@0
   950
  Resulting sequence may contain multiple elements if the tpairs are
clasohm@0
   951
    not all flex-flex. *)
wenzelm@16601
   952
fun flexflex_rule (th as Thm {thy_ref, der, maxidx, shyps, hyps, tpairs, prop}) =
wenzelm@16601
   953
  Unify.smash_unifiers (Theory.deref thy_ref, Envir.empty maxidx, tpairs)
wenzelm@16601
   954
  |> Seq.map (fn env =>
wenzelm@16601
   955
      if Envir.is_empty env then th
wenzelm@16601
   956
      else
wenzelm@16601
   957
        let
wenzelm@16601
   958
          val tpairs' = tpairs |> map (pairself (Envir.norm_term env))
wenzelm@16601
   959
            (*remove trivial tpairs, of the form t==t*)
wenzelm@16884
   960
            |> filter_out (op aconv);
wenzelm@16601
   961
          val prop' = Envir.norm_term env prop;
wenzelm@16601
   962
        in
wenzelm@16601
   963
          Thm {thy_ref = thy_ref,
wenzelm@16601
   964
            der = Pt.infer_derivs' (Pt.norm_proof' env) der,
wenzelm@16711
   965
            maxidx = maxidx_tpairs tpairs' (maxidx_of_term prop'),
wenzelm@16656
   966
            shyps = may_insert_env_sorts (Theory.deref thy_ref) env shyps,
wenzelm@16601
   967
            hyps = hyps,
wenzelm@16601
   968
            tpairs = tpairs',
wenzelm@16601
   969
            prop = prop'}
wenzelm@16601
   970
        end);
wenzelm@16601
   971
clasohm@0
   972
clasohm@0
   973
(*Instantiation of Vars
wenzelm@16656
   974
           A
wenzelm@16656
   975
  --------------------
wenzelm@16656
   976
  A[t1/v1, ..., tn/vn]
wenzelm@1220
   977
*)
clasohm@0
   978
wenzelm@6928
   979
local
wenzelm@6928
   980
wenzelm@16425
   981
fun pretty_typing thy t T =
wenzelm@16425
   982
  Pretty.block [Sign.pretty_term thy t, Pretty.str " ::", Pretty.brk 1, Sign.pretty_typ thy T];
berghofe@15797
   983
wenzelm@16884
   984
fun add_inst (ct, cu) (thy_ref, sorts) =
wenzelm@6928
   985
  let
wenzelm@16884
   986
    val Cterm {t = t, T = T, ...} = ct
wenzelm@16884
   987
    and Cterm {t = u, T = U, sorts = sorts_u, ...} = cu;
wenzelm@16884
   988
    val thy_ref' = Theory.merge_refs (thy_ref, merge_thys0 ct cu);
wenzelm@16884
   989
    val sorts' = Sorts.union sorts_u sorts;
wenzelm@3967
   990
  in
wenzelm@16884
   991
    (case t of Var v =>
wenzelm@16884
   992
      if T = U then ((v, u), (thy_ref', sorts'))
wenzelm@16884
   993
      else raise TYPE (Pretty.string_of (Pretty.block
wenzelm@16884
   994
       [Pretty.str "instantiate: type conflict",
wenzelm@16884
   995
        Pretty.fbrk, pretty_typing (Theory.deref thy_ref') t T,
wenzelm@16884
   996
        Pretty.fbrk, pretty_typing (Theory.deref thy_ref') u U]), [T, U], [t, u])
wenzelm@16884
   997
    | _ => raise TYPE (Pretty.string_of (Pretty.block
wenzelm@16884
   998
       [Pretty.str "instantiate: not a variable",
wenzelm@16884
   999
        Pretty.fbrk, Sign.pretty_term (Theory.deref thy_ref') t]), [], [t]))
clasohm@0
  1000
  end;
clasohm@0
  1001
wenzelm@16884
  1002
fun add_instT (cT, cU) (thy_ref, sorts) =
wenzelm@16656
  1003
  let
wenzelm@16884
  1004
    val Ctyp {T, thy_ref = thy_ref1, ...} = cT
wenzelm@16884
  1005
    and Ctyp {T = U, thy_ref = thy_ref2, sorts = sorts_U, ...} = cU;
wenzelm@16884
  1006
    val thy_ref' = Theory.merge_refs (thy_ref, Theory.merge_refs (thy_ref1, thy_ref2));
wenzelm@16884
  1007
    val thy' = Theory.deref thy_ref';
wenzelm@16884
  1008
    val sorts' = Sorts.union sorts_U sorts;
wenzelm@16656
  1009
  in
wenzelm@16884
  1010
    (case T of TVar (v as (_, S)) =>
wenzelm@17203
  1011
      if Sign.of_sort thy' (U, S) then ((v, U), (thy_ref', sorts'))
wenzelm@16656
  1012
      else raise TYPE ("Type not of sort " ^ Sign.string_of_sort thy' S, [U], [])
wenzelm@16656
  1013
    | _ => raise TYPE (Pretty.string_of (Pretty.block
berghofe@15797
  1014
        [Pretty.str "instantiate: not a type variable",
wenzelm@16656
  1015
         Pretty.fbrk, Sign.pretty_typ thy' T]), [T], []))
wenzelm@16656
  1016
  end;
clasohm@0
  1017
wenzelm@6928
  1018
in
wenzelm@6928
  1019
wenzelm@16601
  1020
(*Left-to-right replacements: ctpairs = [..., (vi, ti), ...].
clasohm@0
  1021
  Instantiates distinct Vars by terms of same type.
wenzelm@16601
  1022
  Does NOT normalize the resulting theorem!*)
paulson@1529
  1023
fun instantiate ([], []) th = th
wenzelm@16884
  1024
  | instantiate (instT, inst) th =
wenzelm@16656
  1025
      let
wenzelm@16884
  1026
        val Thm {thy_ref, der, hyps, shyps, tpairs, prop, ...} = th;
wenzelm@16884
  1027
        val (inst', (instT', (thy_ref', shyps'))) =
wenzelm@16884
  1028
          (thy_ref, shyps) |> fold_map add_inst inst ||> fold_map add_instT instT;
wenzelm@16884
  1029
        val subst = Term.instantiate (instT', inst');
wenzelm@16656
  1030
        val prop' = subst prop;
wenzelm@16884
  1031
        val tpairs' = map (pairself subst) tpairs;
wenzelm@16656
  1032
      in
wenzelm@16884
  1033
        if has_duplicates (fn ((v, _), (v', _)) => Term.eq_var (v, v')) inst' then
wenzelm@16656
  1034
          raise THM ("instantiate: variables not distinct", 0, [th])
wenzelm@16884
  1035
        else if has_duplicates (fn ((v, _), (v', _)) => Term.eq_tvar (v, v')) instT' then
wenzelm@16656
  1036
          raise THM ("instantiate: type variables not distinct", 0, [th])
wenzelm@16656
  1037
        else
wenzelm@16884
  1038
          Thm {thy_ref = thy_ref',
wenzelm@16884
  1039
            der = Pt.infer_derivs' (Pt.instantiate (instT', inst')) der,
wenzelm@16884
  1040
            maxidx = maxidx_tpairs tpairs' (maxidx_of_term prop'),
wenzelm@16656
  1041
            shyps = shyps',
wenzelm@16656
  1042
            hyps = hyps,
wenzelm@16884
  1043
            tpairs = tpairs',
wenzelm@16656
  1044
            prop = prop'}
wenzelm@16656
  1045
      end
wenzelm@16656
  1046
      handle TYPE (msg, _, _) => raise THM (msg, 0, [th]);
wenzelm@6928
  1047
wenzelm@6928
  1048
end;
wenzelm@6928
  1049
clasohm@0
  1050
wenzelm@16601
  1051
(*The trivial implication A ==> A, justified by assume and forall rules.
wenzelm@16601
  1052
  A can contain Vars, not so for assume!*)
wenzelm@16601
  1053
fun trivial (Cterm {thy_ref, t =A, T, maxidx, sorts}) =
wenzelm@16601
  1054
  if T <> propT then
wenzelm@16601
  1055
    raise THM ("trivial: the term must have type prop", 0, [])
wenzelm@16601
  1056
  else
wenzelm@16601
  1057
    Thm {thy_ref = thy_ref,
wenzelm@16601
  1058
      der = Pt.infer_derivs' I (false, Pt.AbsP ("H", NONE, Pt.PBound 0)),
wenzelm@16601
  1059
      maxidx = maxidx,
wenzelm@16601
  1060
      shyps = sorts,
wenzelm@16601
  1061
      hyps = [],
wenzelm@16601
  1062
      tpairs = [],
wenzelm@16601
  1063
      prop = implies $ A $ A};
clasohm@0
  1064
paulson@1503
  1065
(*Axiom-scheme reflecting signature contents: "OFCLASS(?'a::c, c_class)" *)
wenzelm@16425
  1066
fun class_triv thy c =
wenzelm@16601
  1067
  let val Cterm {thy_ref, t, maxidx, sorts, ...} =
wenzelm@16425
  1068
    cterm_of thy (Logic.mk_inclass (TVar (("'a", 0), [c]), c))
wenzelm@6368
  1069
      handle TERM (msg, _) => raise THM ("class_triv: " ^ msg, 0, []);
wenzelm@399
  1070
  in
wenzelm@16601
  1071
    Thm {thy_ref = thy_ref,
wenzelm@16601
  1072
      der = Pt.infer_derivs' I (false, Pt.PAxm ("ProtoPure.class_triv:" ^ c, t, SOME [])),
wenzelm@16601
  1073
      maxidx = maxidx,
wenzelm@16601
  1074
      shyps = sorts,
wenzelm@16601
  1075
      hyps = [],
wenzelm@16601
  1076
      tpairs = [],
wenzelm@16601
  1077
      prop = t}
wenzelm@399
  1078
  end;
wenzelm@399
  1079
wenzelm@399
  1080
wenzelm@6786
  1081
(* Replace all TFrees not fixed or in the hyps by new TVars *)
wenzelm@16601
  1082
fun varifyT' fixed (Thm {thy_ref, der, maxidx, shyps, hyps, tpairs, prop}) =
wenzelm@12500
  1083
  let
berghofe@15797
  1084
    val tfrees = foldr add_term_tfrees fixed hyps;
berghofe@13658
  1085
    val prop1 = attach_tpairs tpairs prop;
berghofe@13658
  1086
    val (prop2, al) = Type.varify (prop1, tfrees);
wenzelm@16601
  1087
    val (ts, prop3) = Logic.strip_prems (length tpairs, [], prop2);
wenzelm@16601
  1088
  in
wenzelm@18127
  1089
    (al, Thm {thy_ref = thy_ref,
wenzelm@16601
  1090
      der = Pt.infer_derivs' (Pt.varify_proof prop tfrees) der,
wenzelm@16601
  1091
      maxidx = Int.max (0, maxidx),
wenzelm@16601
  1092
      shyps = shyps,
wenzelm@16601
  1093
      hyps = hyps,
wenzelm@16601
  1094
      tpairs = rev (map Logic.dest_equals ts),
wenzelm@18127
  1095
      prop = prop3})
clasohm@0
  1096
  end;
clasohm@0
  1097
wenzelm@18127
  1098
val varifyT = #2 o varifyT' [];
wenzelm@6786
  1099
clasohm@0
  1100
(* Replace all TVars by new TFrees *)
wenzelm@16601
  1101
fun freezeT (Thm {thy_ref, der, maxidx, shyps, hyps, tpairs, prop}) =
berghofe@13658
  1102
  let
berghofe@13658
  1103
    val prop1 = attach_tpairs tpairs prop;
wenzelm@16287
  1104
    val prop2 = Type.freeze prop1;
wenzelm@16601
  1105
    val (ts, prop3) = Logic.strip_prems (length tpairs, [], prop2);
wenzelm@16601
  1106
  in
wenzelm@16601
  1107
    Thm {thy_ref = thy_ref,
wenzelm@16601
  1108
      der = Pt.infer_derivs' (Pt.freezeT prop1) der,
wenzelm@16601
  1109
      maxidx = maxidx_of_term prop2,
wenzelm@16601
  1110
      shyps = shyps,
wenzelm@16601
  1111
      hyps = hyps,
wenzelm@16601
  1112
      tpairs = rev (map Logic.dest_equals ts),
wenzelm@16601
  1113
      prop = prop3}
wenzelm@1220
  1114
  end;
clasohm@0
  1115
clasohm@0
  1116
clasohm@0
  1117
(*** Inference rules for tactics ***)
clasohm@0
  1118
clasohm@0
  1119
(*Destruct proof state into constraints, other goals, goal(i), rest *)
berghofe@13658
  1120
fun dest_state (state as Thm{prop,tpairs,...}, i) =
berghofe@13658
  1121
  (case  Logic.strip_prems(i, [], prop) of
berghofe@13658
  1122
      (B::rBs, C) => (tpairs, rev rBs, B, C)
berghofe@13658
  1123
    | _ => raise THM("dest_state", i, [state]))
clasohm@0
  1124
  handle TERM _ => raise THM("dest_state", i, [state]);
clasohm@0
  1125
lcp@309
  1126
(*Increment variables and parameters of orule as required for
wenzelm@18035
  1127
  resolution with a goal.*)
wenzelm@18035
  1128
fun lift_rule goal orule =
wenzelm@16601
  1129
  let
wenzelm@18035
  1130
    val Cterm {t = gprop, T, maxidx = gmax, sorts, ...} = goal;
wenzelm@18035
  1131
    val inc = gmax + 1;
wenzelm@18035
  1132
    val lift_abs = Logic.lift_abs inc gprop;
wenzelm@18035
  1133
    val lift_all = Logic.lift_all inc gprop;
wenzelm@18035
  1134
    val Thm {der, maxidx, shyps, hyps, tpairs, prop, ...} = orule;
wenzelm@16601
  1135
    val (As, B) = Logic.strip_horn prop;
wenzelm@16601
  1136
  in
wenzelm@18035
  1137
    if T <> propT then raise THM ("lift_rule: the term must have type prop", 0, [])
wenzelm@18035
  1138
    else
wenzelm@18035
  1139
      Thm {thy_ref = merge_thys1 goal orule,
wenzelm@18035
  1140
        der = Pt.infer_derivs' (Pt.lift_proof gprop inc prop) der,
wenzelm@18035
  1141
        maxidx = maxidx + inc,
wenzelm@18035
  1142
        shyps = Sorts.union shyps sorts,  (*sic!*)
wenzelm@18035
  1143
        hyps = hyps,
wenzelm@18035
  1144
        tpairs = map (pairself lift_abs) tpairs,
wenzelm@18035
  1145
        prop = Logic.list_implies (map lift_all As, lift_all B)}
clasohm@0
  1146
  end;
clasohm@0
  1147
wenzelm@16425
  1148
fun incr_indexes i (thm as Thm {thy_ref, der, maxidx, shyps, hyps, tpairs, prop}) =
wenzelm@16601
  1149
  if i < 0 then raise THM ("negative increment", 0, [thm])
wenzelm@16601
  1150
  else if i = 0 then thm
wenzelm@16601
  1151
  else
wenzelm@16425
  1152
    Thm {thy_ref = thy_ref,
wenzelm@16884
  1153
      der = Pt.infer_derivs'
wenzelm@16884
  1154
        (Pt.map_proof_terms (Logic.incr_indexes ([], i)) (Logic.incr_tvar i)) der,
wenzelm@16601
  1155
      maxidx = maxidx + i,
wenzelm@16601
  1156
      shyps = shyps,
wenzelm@16601
  1157
      hyps = hyps,
wenzelm@16601
  1158
      tpairs = map (pairself (Logic.incr_indexes ([], i))) tpairs,
wenzelm@16601
  1159
      prop = Logic.incr_indexes ([], i) prop};
berghofe@10416
  1160
clasohm@0
  1161
(*Solve subgoal Bi of proof state B1...Bn/C by assumption. *)
clasohm@0
  1162
fun assumption i state =
wenzelm@16601
  1163
  let
wenzelm@16601
  1164
    val Thm {thy_ref, der, maxidx, shyps, hyps, prop, ...} = state;
wenzelm@16656
  1165
    val thy = Theory.deref thy_ref;
wenzelm@16601
  1166
    val (tpairs, Bs, Bi, C) = dest_state (state, i);
wenzelm@16601
  1167
    fun newth n (env as Envir.Envir {maxidx, ...}, tpairs) =
wenzelm@16601
  1168
      Thm {thy_ref = thy_ref,
wenzelm@16601
  1169
        der = Pt.infer_derivs'
wenzelm@16601
  1170
          ((if Envir.is_empty env then I else (Pt.norm_proof' env)) o
wenzelm@16601
  1171
            Pt.assumption_proof Bs Bi n) der,
wenzelm@16601
  1172
        maxidx = maxidx,
wenzelm@16656
  1173
        shyps = may_insert_env_sorts thy env shyps,
wenzelm@16601
  1174
        hyps = hyps,
wenzelm@16601
  1175
        tpairs =
wenzelm@16601
  1176
          if Envir.is_empty env then tpairs
wenzelm@16601
  1177
          else map (pairself (Envir.norm_term env)) tpairs,
wenzelm@16601
  1178
        prop =
wenzelm@16601
  1179
          if Envir.is_empty env then (*avoid wasted normalizations*)
wenzelm@16601
  1180
            Logic.list_implies (Bs, C)
wenzelm@16601
  1181
          else (*normalize the new rule fully*)
wenzelm@16601
  1182
            Envir.norm_term env (Logic.list_implies (Bs, C))};
wenzelm@16601
  1183
    fun addprfs [] _ = Seq.empty
wenzelm@16601
  1184
      | addprfs ((t, u) :: apairs) n = Seq.make (fn () => Seq.pull
wenzelm@16601
  1185
          (Seq.mapp (newth n)
wenzelm@16656
  1186
            (Unify.unifiers (thy, Envir.empty maxidx, (t, u) :: tpairs))
wenzelm@16601
  1187
            (addprfs apairs (n + 1))))
wenzelm@16601
  1188
  in addprfs (Logic.assum_pairs (~1, Bi)) 1 end;
clasohm@0
  1189
wenzelm@250
  1190
(*Solve subgoal Bi of proof state B1...Bn/C by assumption.
clasohm@0
  1191
  Checks if Bi's conclusion is alpha-convertible to one of its assumptions*)
clasohm@0
  1192
fun eq_assumption i state =
wenzelm@16601
  1193
  let
wenzelm@16601
  1194
    val Thm {thy_ref, der, maxidx, shyps, hyps, prop, ...} = state;
wenzelm@16601
  1195
    val (tpairs, Bs, Bi, C) = dest_state (state, i);
wenzelm@16601
  1196
  in
wenzelm@16601
  1197
    (case find_index (op aconv) (Logic.assum_pairs (~1, Bi)) of
wenzelm@16601
  1198
      ~1 => raise THM ("eq_assumption", 0, [state])
wenzelm@16601
  1199
    | n =>
wenzelm@16601
  1200
        Thm {thy_ref = thy_ref,
wenzelm@16601
  1201
          der = Pt.infer_derivs' (Pt.assumption_proof Bs Bi (n + 1)) der,
wenzelm@16601
  1202
          maxidx = maxidx,
wenzelm@16601
  1203
          shyps = shyps,
wenzelm@16601
  1204
          hyps = hyps,
wenzelm@16601
  1205
          tpairs = tpairs,
wenzelm@16601
  1206
          prop = Logic.list_implies (Bs, C)})
clasohm@0
  1207
  end;
clasohm@0
  1208
clasohm@0
  1209
paulson@2671
  1210
(*For rotate_tac: fast rotation of assumptions of subgoal i*)
paulson@2671
  1211
fun rotate_rule k i state =
wenzelm@16601
  1212
  let
wenzelm@16601
  1213
    val Thm {thy_ref, der, maxidx, shyps, hyps, prop, ...} = state;
wenzelm@16601
  1214
    val (tpairs, Bs, Bi, C) = dest_state (state, i);
wenzelm@16601
  1215
    val params = Term.strip_all_vars Bi
wenzelm@16601
  1216
    and rest   = Term.strip_all_body Bi;
wenzelm@16601
  1217
    val asms   = Logic.strip_imp_prems rest
wenzelm@16601
  1218
    and concl  = Logic.strip_imp_concl rest;
wenzelm@16601
  1219
    val n = length asms;
wenzelm@16601
  1220
    val m = if k < 0 then n + k else k;
wenzelm@16601
  1221
    val Bi' =
wenzelm@16601
  1222
      if 0 = m orelse m = n then Bi
wenzelm@16601
  1223
      else if 0 < m andalso m < n then
wenzelm@19012
  1224
        let val (ps, qs) = chop m asms
wenzelm@16601
  1225
        in list_all (params, Logic.list_implies (qs @ ps, concl)) end
wenzelm@16601
  1226
      else raise THM ("rotate_rule", k, [state]);
wenzelm@16601
  1227
  in
wenzelm@16601
  1228
    Thm {thy_ref = thy_ref,
wenzelm@16601
  1229
      der = Pt.infer_derivs' (Pt.rotate_proof Bs Bi m) der,
wenzelm@16601
  1230
      maxidx = maxidx,
wenzelm@16601
  1231
      shyps = shyps,
wenzelm@16601
  1232
      hyps = hyps,
wenzelm@16601
  1233
      tpairs = tpairs,
wenzelm@16601
  1234
      prop = Logic.list_implies (Bs @ [Bi'], C)}
paulson@2671
  1235
  end;
paulson@2671
  1236
paulson@2671
  1237
paulson@7248
  1238
(*Rotates a rule's premises to the left by k, leaving the first j premises
paulson@7248
  1239
  unchanged.  Does nothing if k=0 or if k equals n-j, where n is the
wenzelm@16656
  1240
  number of premises.  Useful with etac and underlies defer_tac*)
paulson@7248
  1241
fun permute_prems j k rl =
wenzelm@16601
  1242
  let
wenzelm@16601
  1243
    val Thm {thy_ref, der, maxidx, shyps, hyps, tpairs, prop} = rl;
wenzelm@16601
  1244
    val prems = Logic.strip_imp_prems prop
wenzelm@16601
  1245
    and concl = Logic.strip_imp_concl prop;
wenzelm@16601
  1246
    val moved_prems = List.drop (prems, j)
wenzelm@16601
  1247
    and fixed_prems = List.take (prems, j)
wenzelm@16601
  1248
      handle Subscript => raise THM ("permute_prems: j", j, [rl]);
wenzelm@16601
  1249
    val n_j = length moved_prems;
wenzelm@16601
  1250
    val m = if k < 0 then n_j + k else k;
wenzelm@16601
  1251
    val prop' =
wenzelm@16601
  1252
      if 0 = m orelse m = n_j then prop
wenzelm@16601
  1253
      else if 0 < m andalso m < n_j then
wenzelm@19012
  1254
        let val (ps, qs) = chop m moved_prems
wenzelm@16601
  1255
        in Logic.list_implies (fixed_prems @ qs @ ps, concl) end
wenzelm@16725
  1256
      else raise THM ("permute_prems: k", k, [rl]);
wenzelm@16601
  1257
  in
wenzelm@16601
  1258
    Thm {thy_ref = thy_ref,
wenzelm@16601
  1259
      der = Pt.infer_derivs' (Pt.permute_prems_prf prems j m) der,
wenzelm@16601
  1260
      maxidx = maxidx,
wenzelm@16601
  1261
      shyps = shyps,
wenzelm@16601
  1262
      hyps = hyps,
wenzelm@16601
  1263
      tpairs = tpairs,
wenzelm@16601
  1264
      prop = prop'}
paulson@7248
  1265
  end;
paulson@7248
  1266
paulson@7248
  1267
clasohm@0
  1268
(** User renaming of parameters in a subgoal **)
clasohm@0
  1269
clasohm@0
  1270
(*Calls error rather than raising an exception because it is intended
clasohm@0
  1271
  for top-level use -- exception handling would not make sense here.
clasohm@0
  1272
  The names in cs, if distinct, are used for the innermost parameters;
wenzelm@17868
  1273
  preceding parameters may be renamed to make all params distinct.*)
clasohm@0
  1274
fun rename_params_rule (cs, i) state =
wenzelm@16601
  1275
  let
wenzelm@16601
  1276
    val Thm {thy_ref, der, maxidx, shyps, hyps, ...} = state;
wenzelm@16601
  1277
    val (tpairs, Bs, Bi, C) = dest_state (state, i);
wenzelm@16601
  1278
    val iparams = map #1 (Logic.strip_params Bi);
wenzelm@16601
  1279
    val short = length iparams - length cs;
wenzelm@16601
  1280
    val newnames =
wenzelm@16601
  1281
      if short < 0 then error "More names than abstractions!"
wenzelm@16601
  1282
      else variantlist (Library.take (short, iparams), cs) @ cs;
wenzelm@16601
  1283
    val freenames = map (#1 o dest_Free) (term_frees Bi);
wenzelm@16601
  1284
    val newBi = Logic.list_rename_params (newnames, Bi);
wenzelm@250
  1285
  in
wenzelm@16601
  1286
    case findrep cs of
wenzelm@16601
  1287
      c :: _ => (warning ("Can't rename.  Bound variables not distinct: " ^ c); state)
wenzelm@16601
  1288
    | [] =>
wenzelm@16601
  1289
      (case cs inter_string freenames of
wenzelm@16601
  1290
        a :: _ => (warning ("Can't rename.  Bound/Free variable clash: " ^ a); state)
wenzelm@16601
  1291
      | [] =>
wenzelm@16601
  1292
        Thm {thy_ref = thy_ref,
wenzelm@16601
  1293
          der = der,
wenzelm@16601
  1294
          maxidx = maxidx,
wenzelm@16601
  1295
          shyps = shyps,
wenzelm@16601
  1296
          hyps = hyps,
wenzelm@16601
  1297
          tpairs = tpairs,
wenzelm@16601
  1298
          prop = Logic.list_implies (Bs @ [newBi], C)})
clasohm@0
  1299
  end;
clasohm@0
  1300
wenzelm@12982
  1301
clasohm@0
  1302
(*** Preservation of bound variable names ***)
clasohm@0
  1303
wenzelm@16601
  1304
fun rename_boundvars pat obj (thm as Thm {thy_ref, der, maxidx, shyps, hyps, tpairs, prop}) =
wenzelm@12982
  1305
  (case Term.rename_abs pat obj prop of
skalberg@15531
  1306
    NONE => thm
skalberg@15531
  1307
  | SOME prop' => Thm
wenzelm@16425
  1308
      {thy_ref = thy_ref,
wenzelm@12982
  1309
       der = der,
wenzelm@12982
  1310
       maxidx = maxidx,
wenzelm@12982
  1311
       hyps = hyps,
wenzelm@12982
  1312
       shyps = shyps,
berghofe@13658
  1313
       tpairs = tpairs,
wenzelm@12982
  1314
       prop = prop'});
berghofe@10416
  1315
clasohm@0
  1316
wenzelm@16656
  1317
(* strip_apply f (A, B) strips off all assumptions/parameters from A
clasohm@0
  1318
   introduced by lifting over B, and applies f to remaining part of A*)
clasohm@0
  1319
fun strip_apply f =
clasohm@0
  1320
  let fun strip(Const("==>",_)$ A1 $ B1,
wenzelm@250
  1321
                Const("==>",_)$ _  $ B2) = implies $ A1 $ strip(B1,B2)
wenzelm@250
  1322
        | strip((c as Const("all",_)) $ Abs(a,T,t1),
wenzelm@250
  1323
                      Const("all",_)  $ Abs(_,_,t2)) = c$Abs(a,T,strip(t1,t2))
wenzelm@250
  1324
        | strip(A,_) = f A
clasohm@0
  1325
  in strip end;
clasohm@0
  1326
clasohm@0
  1327
(*Use the alist to rename all bound variables and some unknowns in a term
clasohm@0
  1328
  dpairs = current disagreement pairs;  tpairs = permanent ones (flexflex);
clasohm@0
  1329
  Preserves unknowns in tpairs and on lhs of dpairs. *)
clasohm@0
  1330
fun rename_bvs([],_,_,_) = I
clasohm@0
  1331
  | rename_bvs(al,dpairs,tpairs,B) =
skalberg@15574
  1332
    let val vars = foldr add_term_vars []
skalberg@15574
  1333
                        (map fst dpairs @ map fst tpairs @ map snd tpairs)
wenzelm@250
  1334
        (*unknowns appearing elsewhere be preserved!*)
wenzelm@250
  1335
        val vids = map (#1 o #1 o dest_Var) vars;
wenzelm@250
  1336
        fun rename(t as Var((x,i),T)) =
wenzelm@17184
  1337
                (case AList.lookup (op =) al x of
skalberg@15531
  1338
                   SOME(y) => if x mem_string vids orelse y mem_string vids then t
wenzelm@250
  1339
                              else Var((y,i),T)
skalberg@15531
  1340
                 | NONE=> t)
clasohm@0
  1341
          | rename(Abs(x,T,t)) =
wenzelm@18944
  1342
              Abs (the_default x (AList.lookup (op =) al x), T, rename t)
clasohm@0
  1343
          | rename(f$t) = rename f $ rename t
clasohm@0
  1344
          | rename(t) = t;
wenzelm@250
  1345
        fun strip_ren Ai = strip_apply rename (Ai,B)
clasohm@0
  1346
    in strip_ren end;
clasohm@0
  1347
clasohm@0
  1348
(*Function to rename bounds/unknowns in the argument, lifted over B*)
clasohm@0
  1349
fun rename_bvars(dpairs, tpairs, B) =
skalberg@15574
  1350
        rename_bvs(foldr Term.match_bvars [] dpairs, dpairs, tpairs, B);
clasohm@0
  1351
clasohm@0
  1352
clasohm@0
  1353
(*** RESOLUTION ***)
clasohm@0
  1354
lcp@721
  1355
(** Lifting optimizations **)
lcp@721
  1356
clasohm@0
  1357
(*strip off pairs of assumptions/parameters in parallel -- they are
clasohm@0
  1358
  identical because of lifting*)
wenzelm@250
  1359
fun strip_assums2 (Const("==>", _) $ _ $ B1,
wenzelm@250
  1360
                   Const("==>", _) $ _ $ B2) = strip_assums2 (B1,B2)
clasohm@0
  1361
  | strip_assums2 (Const("all",_)$Abs(a,T,t1),
wenzelm@250
  1362
                   Const("all",_)$Abs(_,_,t2)) =
clasohm@0
  1363
      let val (B1,B2) = strip_assums2 (t1,t2)
clasohm@0
  1364
      in  (Abs(a,T,B1), Abs(a,T,B2))  end
clasohm@0
  1365
  | strip_assums2 BB = BB;
clasohm@0
  1366
clasohm@0
  1367
lcp@721
  1368
(*Faster normalization: skip assumptions that were lifted over*)
lcp@721
  1369
fun norm_term_skip env 0 t = Envir.norm_term env t
lcp@721
  1370
  | norm_term_skip env n (Const("all",_)$Abs(a,T,t)) =
lcp@721
  1371
        let val Envir.Envir{iTs, ...} = env
berghofe@15797
  1372
            val T' = Envir.typ_subst_TVars iTs T
wenzelm@1238
  1373
            (*Must instantiate types of parameters because they are flattened;
lcp@721
  1374
              this could be a NEW parameter*)
lcp@721
  1375
        in  all T' $ Abs(a, T', norm_term_skip env n t)  end
lcp@721
  1376
  | norm_term_skip env n (Const("==>", _) $ A $ B) =
wenzelm@1238
  1377
        implies $ A $ norm_term_skip env (n-1) B
lcp@721
  1378
  | norm_term_skip env n t = error"norm_term_skip: too few assumptions??";
lcp@721
  1379
lcp@721
  1380
clasohm@0
  1381
(*Composition of object rule r=(A1...Am/B) with proof state s=(B1...Bn/C)
wenzelm@250
  1382
  Unifies B with Bi, replacing subgoal i    (1 <= i <= n)
clasohm@0
  1383
  If match then forbid instantiations in proof state
clasohm@0
  1384
  If lifted then shorten the dpair using strip_assums2.
clasohm@0
  1385
  If eres_flg then simultaneously proves A1 by assumption.
wenzelm@250
  1386
  nsubgoal is the number of new subgoals (written m above).
clasohm@0
  1387
  Curried so that resolution calls dest_state only once.
clasohm@0
  1388
*)
wenzelm@4270
  1389
local exception COMPOSE
clasohm@0
  1390
in
wenzelm@18486
  1391
fun bicompose_aux flatten match (state, (stpairs, Bs, Bi, C), lifted)
clasohm@0
  1392
                        (eres_flg, orule, nsubgoal) =
paulson@1529
  1393
 let val Thm{der=sder, maxidx=smax, shyps=sshyps, hyps=shyps, ...} = state
wenzelm@16425
  1394
     and Thm{der=rder, maxidx=rmax, shyps=rshyps, hyps=rhyps,
berghofe@13658
  1395
             tpairs=rtpairs, prop=rprop,...} = orule
paulson@1529
  1396
         (*How many hyps to skip over during normalization*)
wenzelm@1238
  1397
     and nlift = Logic.count_prems(strip_all_body Bi,
wenzelm@1238
  1398
                                   if eres_flg then ~1 else 0)
wenzelm@16601
  1399
     val thy_ref = merge_thys2 state orule;
wenzelm@16425
  1400
     val thy = Theory.deref thy_ref;
clasohm@0
  1401
     (** Add new theorem with prop = '[| Bs; As |] ==> C' to thq **)
berghofe@11518
  1402
     fun addth A (As, oldAs, rder', n) ((env as Envir.Envir {maxidx, ...}, tpairs), thq) =
wenzelm@250
  1403
       let val normt = Envir.norm_term env;
wenzelm@250
  1404
           (*perform minimal copying here by examining env*)
berghofe@13658
  1405
           val (ntpairs, normp) =
berghofe@13658
  1406
             if Envir.is_empty env then (tpairs, (Bs @ As, C))
wenzelm@250
  1407
             else
wenzelm@250
  1408
             let val ntps = map (pairself normt) tpairs
paulson@2147
  1409
             in if Envir.above (smax, env) then
wenzelm@1238
  1410
                  (*no assignments in state; normalize the rule only*)
wenzelm@1238
  1411
                  if lifted
berghofe@13658
  1412
                  then (ntps, (Bs @ map (norm_term_skip env nlift) As, C))
berghofe@13658
  1413
                  else (ntps, (Bs @ map normt As, C))
paulson@1529
  1414
                else if match then raise COMPOSE
wenzelm@250
  1415
                else (*normalize the new rule fully*)
berghofe@13658
  1416
                  (ntps, (map normt (Bs @ As), normt C))
wenzelm@250
  1417
             end
wenzelm@16601
  1418
           val th =
wenzelm@16425
  1419
             Thm{thy_ref = thy_ref,
berghofe@11518
  1420
                 der = Pt.infer_derivs
berghofe@11518
  1421
                   ((if Envir.is_empty env then I
berghofe@11518
  1422
                     else if Envir.above (smax, env) then
berghofe@11518
  1423
                       (fn f => fn der => f (Pt.norm_proof' env der))
berghofe@11518
  1424
                     else
berghofe@11518
  1425
                       curry op oo (Pt.norm_proof' env))
wenzelm@18486
  1426
                    (Pt.bicompose_proof flatten Bs oldAs As A n)) rder' sder,
wenzelm@2386
  1427
                 maxidx = maxidx,
wenzelm@16656
  1428
                 shyps = may_insert_env_sorts thy env (Sorts.union rshyps sshyps),
wenzelm@16601
  1429
                 hyps = union_hyps rhyps shyps,
berghofe@13658
  1430
                 tpairs = ntpairs,
berghofe@13658
  1431
                 prop = Logic.list_implies normp}
wenzelm@19475
  1432
        in  Seq.cons th thq  end  handle COMPOSE => thq;
berghofe@13658
  1433
     val (rAs,B) = Logic.strip_prems(nsubgoal, [], rprop)
clasohm@0
  1434
       handle TERM _ => raise THM("bicompose: rule", 0, [orule,state]);
clasohm@0
  1435
     (*Modify assumptions, deleting n-th if n>0 for e-resolution*)
clasohm@0
  1436
     fun newAs(As0, n, dpairs, tpairs) =
berghofe@11518
  1437
       let val (As1, rder') =
berghofe@11518
  1438
         if !Logic.auto_rename orelse not lifted then (As0, rder)
berghofe@11518
  1439
         else (map (rename_bvars(dpairs,tpairs,B)) As0,
berghofe@11518
  1440
           Pt.infer_derivs' (Pt.map_proof_terms
berghofe@11518
  1441
             (rename_bvars (dpairs, tpairs, Bound 0)) I) rder);
wenzelm@18486
  1442
       in (map (if flatten then (Logic.flatten_params n) else I) As1, As1, rder', n)
wenzelm@250
  1443
          handle TERM _ =>
wenzelm@250
  1444
          raise THM("bicompose: 1st premise", 0, [orule])
clasohm@0
  1445
       end;
paulson@2147
  1446
     val env = Envir.empty(Int.max(rmax,smax));
clasohm@0
  1447
     val BBi = if lifted then strip_assums2(B,Bi) else (B,Bi);
clasohm@0
  1448
     val dpairs = BBi :: (rtpairs@stpairs);
clasohm@0
  1449
     (*elim-resolution: try each assumption in turn.  Initially n=1*)
berghofe@11518
  1450
     fun tryasms (_, _, _, []) = Seq.empty
berghofe@11518
  1451
       | tryasms (A, As, n, (t,u)::apairs) =
wenzelm@16425
  1452
          (case Seq.pull(Unify.unifiers(thy, env, (t,u)::dpairs))  of
wenzelm@16425
  1453
              NONE                   => tryasms (A, As, n+1, apairs)
wenzelm@16425
  1454
            | cell as SOME((_,tpairs),_) =>
wenzelm@16425
  1455
                Seq.it_right (addth A (newAs(As, n, [BBi,(u,t)], tpairs)))
wenzelm@16425
  1456
                    (Seq.make(fn()=> cell),
wenzelm@16425
  1457
                     Seq.make(fn()=> Seq.pull (tryasms(A, As, n+1, apairs)))))
clasohm@0
  1458
     fun eres [] = raise THM("bicompose: no premises", 0, [orule,state])
skalberg@15531
  1459
       | eres (A1::As) = tryasms(SOME A1, As, 1, Logic.assum_pairs(nlift+1,A1))
clasohm@0
  1460
     (*ordinary resolution*)
skalberg@15531
  1461
     fun res(NONE) = Seq.empty
skalberg@15531
  1462
       | res(cell as SOME((_,tpairs),_)) =
skalberg@15531
  1463
             Seq.it_right (addth NONE (newAs(rev rAs, 0, [BBi], tpairs)))
wenzelm@4270
  1464
                       (Seq.make (fn()=> cell), Seq.empty)
clasohm@0
  1465
 in  if eres_flg then eres(rev rAs)
wenzelm@16425
  1466
     else res(Seq.pull(Unify.unifiers(thy, env, dpairs)))
clasohm@0
  1467
 end;
wenzelm@7528
  1468
end;
clasohm@0
  1469
wenzelm@18501
  1470
fun compose_no_flatten match (orule, nsubgoal) i state =
wenzelm@18501
  1471
  bicompose_aux false match (state, dest_state (state, i), false) (false, orule, nsubgoal);
clasohm@0
  1472
wenzelm@18501
  1473
fun bicompose match arg i state =
wenzelm@18501
  1474
  bicompose_aux true match (state, dest_state (state,i), false) arg;
clasohm@0
  1475
clasohm@0
  1476
(*Quick test whether rule is resolvable with the subgoal with hyps Hs
clasohm@0
  1477
  and conclusion B.  If eres_flg then checks 1st premise of rule also*)
clasohm@0
  1478
fun could_bires (Hs, B, eres_flg, rule) =
wenzelm@16847
  1479
    let fun could_reshyp (A1::_) = exists (fn H => could_unify (A1, H)) Hs
wenzelm@250
  1480
          | could_reshyp [] = false;  (*no premise -- illegal*)
wenzelm@250
  1481
    in  could_unify(concl_of rule, B) andalso
wenzelm@250
  1482
        (not eres_flg  orelse  could_reshyp (prems_of rule))
clasohm@0
  1483
    end;
clasohm@0
  1484
clasohm@0
  1485
(*Bi-resolution of a state with a list of (flag,rule) pairs.
clasohm@0
  1486
  Puts the rule above:  rule/state.  Renames vars in the rules. *)
wenzelm@250
  1487
fun biresolution match brules i state =
wenzelm@18035
  1488
    let val (stpairs, Bs, Bi, C) = dest_state(state,i);
wenzelm@18145
  1489
        val lift = lift_rule (cprem_of state i);
wenzelm@250
  1490
        val B = Logic.strip_assums_concl Bi;
wenzelm@250
  1491
        val Hs = Logic.strip_assums_hyp Bi;
wenzelm@18486
  1492
        val comp = bicompose_aux true match (state, (stpairs, Bs, Bi, C), true);
wenzelm@4270
  1493
        fun res [] = Seq.empty
wenzelm@250
  1494
          | res ((eres_flg, rule)::brules) =
nipkow@13642
  1495
              if !Pattern.trace_unify_fail orelse
nipkow@13642
  1496
                 could_bires (Hs, B, eres_flg, rule)
wenzelm@4270
  1497
              then Seq.make (*delay processing remainder till needed*)
skalberg@15531
  1498
                  (fn()=> SOME(comp (eres_flg, lift rule, nprems_of rule),
wenzelm@250
  1499
                               res brules))
wenzelm@250
  1500
              else res brules
wenzelm@4270
  1501
    in  Seq.flat (res brules)  end;
clasohm@0
  1502
clasohm@0
  1503
wenzelm@2509
  1504
(*** Oracles ***)
wenzelm@2509
  1505
wenzelm@16425
  1506
fun invoke_oracle_i thy1 name =
wenzelm@3812
  1507
  let
wenzelm@3812
  1508
    val oracle =
wenzelm@17412
  1509
      (case Symtab.lookup (#2 (#oracles (Theory.rep_theory thy1))) name of
skalberg@15531
  1510
        NONE => raise THM ("Unknown oracle: " ^ name, 0, [])
skalberg@15531
  1511
      | SOME (f, _) => f);
wenzelm@16847
  1512
    val thy_ref1 = Theory.self_ref thy1;
wenzelm@3812
  1513
  in
wenzelm@16425
  1514
    fn (thy2, data) =>
wenzelm@3812
  1515
      let
wenzelm@16847
  1516
        val thy' = Theory.merge (Theory.deref thy_ref1, thy2);
wenzelm@18969
  1517
        val (prop, T, maxidx) = Sign.certify_term thy' (oracle (thy', data));
wenzelm@3812
  1518
      in
wenzelm@3812
  1519
        if T <> propT then
wenzelm@3812
  1520
          raise THM ("Oracle's result must have type prop: " ^ name, 0, [])
wenzelm@16601
  1521
        else
wenzelm@16601
  1522
          Thm {thy_ref = Theory.self_ref thy',
berghofe@11518
  1523
            der = (true, Pt.oracle_proof name prop),
wenzelm@3812
  1524
            maxidx = maxidx,
wenzelm@16656
  1525
            shyps = may_insert_term_sorts thy' prop [],
wenzelm@16425
  1526
            hyps = [],
berghofe@13658
  1527
            tpairs = [],
wenzelm@16601
  1528
            prop = prop}
wenzelm@3812
  1529
      end
wenzelm@3812
  1530
  end;
wenzelm@3812
  1531
wenzelm@15672
  1532
fun invoke_oracle thy =
wenzelm@16425
  1533
  invoke_oracle_i thy o NameSpace.intern (Theory.oracle_space thy);
wenzelm@15672
  1534
clasohm@0
  1535
end;
paulson@1503
  1536
wenzelm@6089
  1537
structure BasicThm: BASIC_THM = Thm;
wenzelm@6089
  1538
open BasicThm;