src/Pure/drule.ML
author wenzelm
Tue Aug 01 17:20:42 1995 +0200 (1995-08-01 ago)
changeset 1218 59ed8ef1a3a1
parent 1194 563ecd14c1d8
child 1237 45ac644b0052
permissions -rw-r--r--
modified pretty_thm, standard, eq_thm to handle shyps;
wenzelm@252
     1
(*  Title:      Pure/drule.ML
clasohm@0
     2
    ID:         $Id$
wenzelm@252
     3
    Author:     Lawrence C Paulson, Cambridge University Computer Laboratory
clasohm@0
     4
    Copyright   1993  University of Cambridge
clasohm@0
     5
clasohm@0
     6
Derived rules and other operations on theorems and theories
clasohm@0
     7
*)
clasohm@0
     8
lcp@11
     9
infix 0 RS RSN RL RLN MRS MRL COMP;
clasohm@0
    10
clasohm@0
    11
signature DRULE =
clasohm@0
    12
  sig
clasohm@0
    13
  structure Thm : THM
clasohm@0
    14
  local open Thm  in
lcp@668
    15
  val add_defs		: (string * string) list -> theory -> theory
lcp@668
    16
  val add_defs_i	: (string * term) list -> theory -> theory
lcp@668
    17
  val asm_rl		: thm
lcp@668
    18
  val assume_ax		: theory -> string -> thm
lcp@668
    19
  val COMP		: thm * thm -> thm
lcp@668
    20
  val compose		: thm * int * thm -> thm list
lcp@708
    21
  val cprems_of		: thm -> cterm list
lcp@708
    22
  val cskip_flexpairs	: cterm -> cterm
lcp@708
    23
  val cstrip_imp_prems	: cterm -> cterm list
lcp@668
    24
  val cterm_instantiate	: (cterm*cterm)list -> thm -> thm
lcp@668
    25
  val cut_rl		: thm
lcp@668
    26
  val equal_abs_elim	: cterm  -> thm -> thm
lcp@229
    27
  val equal_abs_elim_list: cterm list -> thm -> thm
lcp@668
    28
  val eq_thm		: thm * thm -> bool
lcp@668
    29
  val eq_thm_sg		: thm * thm -> bool
lcp@229
    30
  val flexpair_abs_elim_list: cterm list -> thm -> thm
lcp@668
    31
  val forall_intr_list	: cterm list -> thm -> thm
lcp@668
    32
  val forall_intr_frees	: thm -> thm
lcp@1194
    33
  val forall_intr_vars	: thm -> thm
lcp@668
    34
  val forall_elim_list	: cterm list -> thm -> thm
lcp@668
    35
  val forall_elim_var	: int -> thm -> thm
lcp@668
    36
  val forall_elim_vars	: int -> thm -> thm
lcp@668
    37
  val implies_elim_list	: thm -> thm list -> thm
lcp@668
    38
  val implies_intr_list	: cterm list -> thm -> thm
lcp@668
    39
  val MRL		: thm list list * thm list -> thm list
lcp@668
    40
  val MRS		: thm list * thm -> thm
lcp@668
    41
  val pprint_cterm	: cterm -> pprint_args -> unit
lcp@668
    42
  val pprint_ctyp	: ctyp -> pprint_args -> unit
lcp@668
    43
  val pprint_theory	: theory -> pprint_args -> unit
lcp@668
    44
  val pprint_thm	: thm -> pprint_args -> unit
lcp@668
    45
  val pretty_thm	: thm -> Sign.Syntax.Pretty.T
lcp@668
    46
  val print_cterm	: cterm -> unit
lcp@668
    47
  val print_ctyp	: ctyp -> unit
lcp@668
    48
  val print_goals	: int -> thm -> unit
lcp@668
    49
  val print_goals_ref	: (int -> thm -> unit) ref
lcp@668
    50
  val print_syntax	: theory -> unit
lcp@668
    51
  val print_theory	: theory -> unit
lcp@668
    52
  val print_thm		: thm -> unit
lcp@668
    53
  val prth		: thm -> thm
lcp@668
    54
  val prthq		: thm Sequence.seq -> thm Sequence.seq
lcp@668
    55
  val prths		: thm list -> thm list
lcp@668
    56
  val read_instantiate	: (string*string)list -> thm -> thm
clasohm@0
    57
  val read_instantiate_sg: Sign.sg -> (string*string)list -> thm -> thm
lcp@668
    58
  val read_insts	:
lcp@229
    59
          Sign.sg -> (indexname -> typ option) * (indexname -> sort option)
lcp@229
    60
                  -> (indexname -> typ option) * (indexname -> sort option)
nipkow@949
    61
                  -> string list -> (string*string)list
lcp@229
    62
                  -> (indexname*ctyp)list * (cterm*cterm)list
lcp@668
    63
  val reflexive_thm	: thm
lcp@668
    64
  val revcut_rl		: thm
lcp@668
    65
  val rewrite_goal_rule	: bool*bool -> (meta_simpset -> thm -> thm option)
nipkow@214
    66
        -> meta_simpset -> int -> thm -> thm
clasohm@0
    67
  val rewrite_goals_rule: thm list -> thm -> thm
lcp@668
    68
  val rewrite_rule	: thm list -> thm -> thm
lcp@668
    69
  val RS		: thm * thm -> thm
lcp@668
    70
  val RSN		: thm * (int * thm) -> thm
lcp@668
    71
  val RL		: thm list * thm list -> thm list
lcp@668
    72
  val RLN		: thm list * (int * thm list) -> thm list
lcp@668
    73
  val show_hyps		: bool ref
lcp@668
    74
  val size_of_thm	: thm -> int
lcp@668
    75
  val standard		: thm -> thm
lcp@668
    76
  val string_of_cterm	: cterm -> string
lcp@668
    77
  val string_of_ctyp	: ctyp -> string
lcp@668
    78
  val string_of_thm	: thm -> string
lcp@668
    79
  val symmetric_thm	: thm
lcp@668
    80
  val thin_rl		: thm
lcp@668
    81
  val transitive_thm	: thm
clasohm@0
    82
  val triv_forall_equality: thm
clasohm@0
    83
  val types_sorts: thm -> (indexname-> typ option) * (indexname-> sort option)
lcp@668
    84
  val zero_var_indexes	: thm -> thm
clasohm@0
    85
  end
clasohm@0
    86
  end;
clasohm@0
    87
lcp@668
    88
wenzelm@252
    89
functor DruleFun (structure Logic: LOGIC and Thm: THM): DRULE =
clasohm@0
    90
struct
clasohm@0
    91
structure Thm = Thm;
clasohm@0
    92
structure Sign = Thm.Sign;
clasohm@0
    93
structure Type = Sign.Type;
wenzelm@575
    94
structure Syntax = Sign.Syntax;
wenzelm@575
    95
structure Pretty = Syntax.Pretty
wenzelm@400
    96
structure Symtab = Sign.Symtab;
wenzelm@400
    97
clasohm@0
    98
local open Thm
clasohm@0
    99
in
clasohm@0
   100
wenzelm@561
   101
(**** Extend Theories ****)
wenzelm@561
   102
wenzelm@561
   103
(** add constant definitions **)
wenzelm@561
   104
wenzelm@561
   105
(* all_axioms_of *)
wenzelm@561
   106
wenzelm@561
   107
(*results may contain duplicates!*)
wenzelm@561
   108
wenzelm@561
   109
fun ancestry_of thy =
wenzelm@561
   110
  thy :: flat (map ancestry_of (parents_of thy));
wenzelm@561
   111
wenzelm@776
   112
val all_axioms_of = 
wenzelm@776
   113
  flat o map (Symtab.dest o #new_axioms o rep_theory) o ancestry_of;
wenzelm@561
   114
wenzelm@561
   115
wenzelm@561
   116
(* clash_types, clash_consts *)
wenzelm@561
   117
wenzelm@561
   118
(*check if types have common instance (ignoring sorts)*)
wenzelm@561
   119
wenzelm@561
   120
fun clash_types ty1 ty2 =
wenzelm@561
   121
  let
wenzelm@561
   122
    val ty1' = Type.varifyT ty1;
wenzelm@561
   123
    val ty2' = incr_tvar (maxidx_of_typ ty1' + 1) (Type.varifyT ty2);
wenzelm@561
   124
  in
wenzelm@561
   125
    Type.raw_unify (ty1', ty2')
wenzelm@561
   126
  end;
wenzelm@561
   127
wenzelm@561
   128
fun clash_consts (c1, ty1) (c2, ty2) =
wenzelm@561
   129
  c1 = c2 andalso clash_types ty1 ty2;
wenzelm@561
   130
wenzelm@561
   131
wenzelm@561
   132
(* clash_defns *)
wenzelm@561
   133
wenzelm@561
   134
fun clash_defn c_ty (name, tm) =
wenzelm@561
   135
  let val (c, ty') = dest_Const (head_of (fst (Logic.dest_equals tm))) in
wenzelm@561
   136
    if clash_consts c_ty (c, ty') then Some (name, ty') else None
wenzelm@561
   137
  end handle TERM _ => None;
wenzelm@561
   138
wenzelm@561
   139
fun clash_defns c_ty axms =
wenzelm@561
   140
  distinct (mapfilter (clash_defn c_ty) axms);
wenzelm@561
   141
wenzelm@561
   142
wenzelm@561
   143
(* dest_defn *)
wenzelm@561
   144
wenzelm@561
   145
fun dest_defn tm =
wenzelm@561
   146
  let
wenzelm@561
   147
    fun err msg = raise_term msg [tm];
wenzelm@561
   148
wenzelm@561
   149
    val (lhs, rhs) = Logic.dest_equals tm
wenzelm@561
   150
      handle TERM _ => err "Not a meta-equality (==)";
wenzelm@561
   151
    val (head, args) = strip_comb lhs;
wenzelm@561
   152
    val (c, ty) = dest_Const head
wenzelm@561
   153
      handle TERM _ => err "Head of lhs not a constant";
wenzelm@561
   154
wenzelm@655
   155
    fun occs_const (Const c_ty') = (c_ty' = (c, ty))
wenzelm@561
   156
      | occs_const (Abs (_, _, t)) = occs_const t
wenzelm@561
   157
      | occs_const (t $ u) = occs_const t orelse occs_const u
wenzelm@561
   158
      | occs_const _ = false;
wenzelm@641
   159
wenzelm@641
   160
    val show_frees = commas_quote o map (fst o dest_Free);
wenzelm@641
   161
    val show_tfrees = commas_quote o map fst;
wenzelm@641
   162
wenzelm@641
   163
    val lhs_dups = duplicates args;
wenzelm@641
   164
    val rhs_extras = gen_rems (op =) (term_frees rhs, args);
wenzelm@641
   165
    val rhs_extrasT = gen_rems (op =) (term_tfrees rhs, typ_tfrees ty);
wenzelm@561
   166
  in
wenzelm@561
   167
    if not (forall is_Free args) then
wenzelm@561
   168
      err "Arguments of lhs have to be variables"
wenzelm@641
   169
    else if not (null lhs_dups) then
wenzelm@641
   170
      err ("Duplicate variables on lhs: " ^ show_frees lhs_dups)
wenzelm@641
   171
    else if not (null rhs_extras) then
wenzelm@641
   172
      err ("Extra variables on rhs: " ^ show_frees rhs_extras)
wenzelm@641
   173
    else if not (null rhs_extrasT) then
wenzelm@641
   174
      err ("Extra type variables on rhs: " ^ show_tfrees rhs_extrasT)
wenzelm@561
   175
    else if occs_const rhs then
wenzelm@655
   176
      err ("Constant to be defined occurs on rhs")
wenzelm@561
   177
    else (c, ty)
wenzelm@561
   178
  end;
wenzelm@561
   179
wenzelm@561
   180
wenzelm@561
   181
(* check_defn *)
wenzelm@561
   182
wenzelm@641
   183
fun err_in_defn name msg =
wenzelm@641
   184
  (writeln msg; error ("The error(s) above occurred in definition " ^ quote name));
wenzelm@561
   185
wenzelm@561
   186
fun check_defn sign (axms, (name, tm)) =
wenzelm@561
   187
  let
wenzelm@561
   188
    fun show_const (c, ty) = quote (Pretty.string_of (Pretty.block
wenzelm@561
   189
      [Pretty.str (c ^ " ::"), Pretty.brk 1, Sign.pretty_typ sign ty]));
wenzelm@561
   190
wenzelm@561
   191
    fun show_defn c (dfn, ty') = show_const (c, ty') ^ " in " ^ dfn;
wenzelm@561
   192
    fun show_defns c = commas o map (show_defn c);
wenzelm@561
   193
wenzelm@561
   194
    val (c, ty) = dest_defn tm
wenzelm@641
   195
      handle TERM (msg, _) => err_in_defn name msg;
wenzelm@561
   196
    val defns = clash_defns (c, ty) axms;
wenzelm@561
   197
  in
wenzelm@561
   198
    if not (null defns) then
wenzelm@641
   199
      err_in_defn name ("Definition of " ^ show_const (c, ty) ^
wenzelm@561
   200
        " clashes with " ^ show_defns c defns)
wenzelm@561
   201
    else (name, tm) :: axms
wenzelm@561
   202
  end;
wenzelm@561
   203
wenzelm@561
   204
wenzelm@561
   205
(* add_defs *)
wenzelm@561
   206
wenzelm@561
   207
fun ext_defns prep_axm raw_axms thy =
wenzelm@561
   208
  let
wenzelm@561
   209
    val axms = map (prep_axm (sign_of thy)) raw_axms;
wenzelm@561
   210
    val all_axms = all_axioms_of thy;
wenzelm@561
   211
  in
wenzelm@561
   212
    foldl (check_defn (sign_of thy)) (all_axms, axms);
wenzelm@561
   213
    add_axioms_i axms thy
wenzelm@561
   214
  end;
wenzelm@561
   215
wenzelm@561
   216
val add_defs_i = ext_defns cert_axm;
wenzelm@561
   217
val add_defs = ext_defns read_axm;
wenzelm@561
   218
wenzelm@561
   219
wenzelm@561
   220
clasohm@0
   221
(**** More derived rules and operations on theorems ****)
clasohm@0
   222
lcp@708
   223
(** some cterm->cterm operations: much faster than calling cterm_of! **)
lcp@708
   224
lcp@708
   225
(*Discard flexflex pairs; return a cterm*)
lcp@708
   226
fun cskip_flexpairs ct =
lcp@708
   227
    case term_of ct of
lcp@708
   228
	(Const("==>", _) $ (Const("=?=",_)$_$_) $ _) =>
lcp@708
   229
	    cskip_flexpairs (#2 (dest_cimplies ct))
lcp@708
   230
      | _ => ct;
lcp@708
   231
lcp@708
   232
(* A1==>...An==>B  goes to  [A1,...,An], where B is not an implication *)
lcp@708
   233
fun cstrip_imp_prems ct =
lcp@708
   234
    let val (cA,cB) = dest_cimplies ct
lcp@708
   235
    in  cA :: cstrip_imp_prems cB  end
lcp@708
   236
    handle TERM _ => [];
lcp@708
   237
lcp@708
   238
(*The premises of a theorem, as a cterm list*)
lcp@708
   239
val cprems_of = cstrip_imp_prems o cskip_flexpairs o cprop_of;
lcp@708
   240
lcp@708
   241
lcp@229
   242
(** reading of instantiations **)
lcp@229
   243
lcp@229
   244
fun indexname cs = case Syntax.scan_varname cs of (v,[]) => v
lcp@229
   245
        | _ => error("Lexical error in variable name " ^ quote (implode cs));
lcp@229
   246
lcp@229
   247
fun absent ixn =
lcp@229
   248
  error("No such variable in term: " ^ Syntax.string_of_vname ixn);
lcp@229
   249
lcp@229
   250
fun inst_failure ixn =
lcp@229
   251
  error("Instantiation of " ^ Syntax.string_of_vname ixn ^ " fails");
lcp@229
   252
nipkow@952
   253
(* this code is a bit of a mess. add_cterm could be simplified greatly if
nipkow@952
   254
   simultaneous instantiations were read or at least type checked
nipkow@952
   255
   simultaneously rather than one after the other. This would make the tricky
nipkow@952
   256
   composition of implicit type instantiations (parameter tye) superfluous.
nipkow@952
   257
*)
nipkow@949
   258
fun read_insts sign (rtypes,rsorts) (types,sorts) used insts =
lcp@229
   259
let val {tsig,...} = Sign.rep_sg sign
lcp@229
   260
    fun split([],tvs,vs) = (tvs,vs)
lcp@229
   261
      | split((sv,st)::l,tvs,vs) = (case explode sv of
lcp@229
   262
                  "'"::cs => split(l,(indexname cs,st)::tvs,vs)
lcp@229
   263
                | cs => split(l,tvs,(indexname cs,st)::vs));
lcp@229
   264
    val (tvs,vs) = split(insts,[],[]);
lcp@229
   265
    fun readT((a,i),st) =
lcp@229
   266
        let val ixn = ("'" ^ a,i);
lcp@229
   267
            val S = case rsorts ixn of Some S => S | None => absent ixn;
lcp@229
   268
            val T = Sign.read_typ (sign,sorts) st;
lcp@229
   269
        in if Type.typ_instance(tsig,T,TVar(ixn,S)) then (ixn,T)
lcp@229
   270
           else inst_failure ixn
lcp@229
   271
        end
lcp@229
   272
    val tye = map readT tvs;
nipkow@949
   273
    fun add_cterm ((cts,tye,used), (ixn,st)) =
lcp@229
   274
        let val T = case rtypes ixn of
lcp@229
   275
                      Some T => typ_subst_TVars tye T
lcp@229
   276
                    | None => absent ixn;
nipkow@949
   277
            val (ct,tye2) = read_def_cterm(sign,types,sorts) used false (st,T);
nipkow@952
   278
            val cts' = (ixn,T,ct)::cts
nipkow@952
   279
            fun inst(ixn,T,ct) = (ixn,typ_subst_TVars tye2 T,ct)
nipkow@949
   280
            val used' = add_term_tvarnames(term_of ct,used);
nipkow@952
   281
        in (map inst cts',tye2 @ tye,used') end
nipkow@949
   282
    val (cterms,tye',_) = foldl add_cterm (([],tye,used), vs);
nipkow@952
   283
in (map (fn (ixn,T) => (ixn,ctyp_of sign T)) tye',
nipkow@952
   284
    map (fn (ixn,T,ct) => (cterm_of sign (Var(ixn,T)), ct)) cterms)
nipkow@952
   285
end;
lcp@229
   286
lcp@229
   287
wenzelm@252
   288
wenzelm@252
   289
(*** Printing of theories, theorems, etc. ***)
lcp@229
   290
lcp@229
   291
(*If false, hypotheses are printed as dots*)
lcp@229
   292
val show_hyps = ref true;
lcp@229
   293
lcp@229
   294
fun pretty_thm th =
wenzelm@1218
   295
  let
wenzelm@1218
   296
    val {sign, shyps, hyps, prop, ...} = rep_thm th;
wenzelm@1218
   297
    val hlen = length shyps + length hyps;
wenzelm@1218
   298
    val hsymbs =
wenzelm@1218
   299
      if hlen = 0 then []
wenzelm@1218
   300
      else if ! show_hyps then
wenzelm@1218
   301
        [Pretty.brk 2, Pretty.list "[" "]"
wenzelm@1218
   302
          (map (Sign.pretty_term sign) hyps @ map Sign.pretty_sort shyps)]
wenzelm@1218
   303
      else
wenzelm@1218
   304
        [Pretty.brk 2, Pretty.str ("[" ^ implode (replicate hlen ".") ^ "]")];
wenzelm@1218
   305
  in
wenzelm@1218
   306
    Pretty.block (Sign.pretty_term sign prop :: hsymbs)
wenzelm@1218
   307
  end;
lcp@229
   308
lcp@229
   309
val string_of_thm = Pretty.string_of o pretty_thm;
lcp@229
   310
val pprint_thm = Pretty.pprint o Pretty.quote o pretty_thm;
lcp@229
   311
lcp@229
   312
lcp@229
   313
(** Top-level commands for printing theorems **)
lcp@229
   314
val print_thm = writeln o string_of_thm;
lcp@229
   315
lcp@229
   316
fun prth th = (print_thm th; th);
lcp@229
   317
lcp@229
   318
(*Print and return a sequence of theorems, separated by blank lines. *)
lcp@229
   319
fun prthq thseq =
wenzelm@252
   320
  (Sequence.prints (fn _ => print_thm) 100000 thseq; thseq);
lcp@229
   321
lcp@229
   322
(*Print and return a list of theorems, separated by blank lines. *)
lcp@229
   323
fun prths ths = (print_list_ln print_thm ths; ths);
lcp@229
   324
wenzelm@252
   325
wenzelm@252
   326
(* other printing commands *)
lcp@229
   327
wenzelm@252
   328
fun pprint_ctyp cT =
wenzelm@252
   329
  let val {sign, T} = rep_ctyp cT in Sign.pprint_typ sign T end;
wenzelm@252
   330
wenzelm@252
   331
fun string_of_ctyp cT =
wenzelm@252
   332
  let val {sign, T} = rep_ctyp cT in Sign.string_of_typ sign T end;
lcp@229
   333
lcp@229
   334
val print_ctyp = writeln o string_of_ctyp;
lcp@229
   335
wenzelm@252
   336
fun pprint_cterm ct =
wenzelm@252
   337
  let val {sign, t, ...} = rep_cterm ct in Sign.pprint_term sign t end;
lcp@229
   338
wenzelm@252
   339
fun string_of_cterm ct =
wenzelm@252
   340
  let val {sign, t, ...} = rep_cterm ct in Sign.string_of_term sign t end;
lcp@229
   341
lcp@229
   342
val print_cterm = writeln o string_of_cterm;
lcp@229
   343
wenzelm@252
   344
wenzelm@252
   345
(* print theory *)
wenzelm@252
   346
wenzelm@252
   347
val pprint_theory = Sign.pprint_sg o sign_of;
lcp@229
   348
wenzelm@575
   349
val print_syntax = Syntax.print_syntax o syn_of;
wenzelm@575
   350
wenzelm@385
   351
fun print_axioms thy =
wenzelm@252
   352
  let
wenzelm@400
   353
    val {sign, new_axioms, ...} = rep_theory thy;
wenzelm@400
   354
    val axioms = Symtab.dest new_axioms;
lcp@229
   355
wenzelm@385
   356
    fun prt_axm (a, t) = Pretty.block [Pretty.str (a ^ ":"), Pretty.brk 1,
wenzelm@385
   357
      Pretty.quote (Sign.pretty_term sign t)];
wenzelm@252
   358
  in
wenzelm@385
   359
    Pretty.writeln (Pretty.big_list "additional axioms:" (map prt_axm axioms))
wenzelm@252
   360
  end;
lcp@229
   361
wenzelm@843
   362
fun print_theory thy = (Sign.print_sg (sign_of thy); print_axioms thy);
wenzelm@385
   363
lcp@229
   364
lcp@229
   365
lcp@229
   366
(** Print thm A1,...,An/B in "goal style" -- premises as numbered subgoals **)
lcp@229
   367
wenzelm@641
   368
(* get type_env, sort_env of term *)
wenzelm@641
   369
wenzelm@641
   370
local
wenzelm@641
   371
  open Syntax;
wenzelm@641
   372
wenzelm@641
   373
  fun ins_entry (x, y) [] = [(x, [y])]
wenzelm@641
   374
    | ins_entry (x, y) ((pair as (x', ys')) :: pairs) =
wenzelm@641
   375
        if x = x' then (x', y ins ys') :: pairs
wenzelm@641
   376
        else pair :: ins_entry (x, y) pairs;
wenzelm@641
   377
wenzelm@641
   378
  fun add_type_env (Free (x, T), env) = ins_entry (T, x) env
wenzelm@641
   379
    | add_type_env (Var (xi, T), env) = ins_entry (T, string_of_vname xi) env
wenzelm@641
   380
    | add_type_env (Abs (_, _, t), env) = add_type_env (t, env)
wenzelm@641
   381
    | add_type_env (t $ u, env) = add_type_env (u, add_type_env (t, env))
wenzelm@641
   382
    | add_type_env (_, env) = env;
wenzelm@641
   383
wenzelm@641
   384
  fun add_sort_env (Type (_, Ts), env) = foldr add_sort_env (Ts, env)
wenzelm@641
   385
    | add_sort_env (TFree (x, S), env) = ins_entry (S, x) env
wenzelm@641
   386
    | add_sort_env (TVar (xi, S), env) = ins_entry (S, string_of_vname xi) env;
wenzelm@641
   387
wenzelm@641
   388
  val sort = map (apsnd sort_strings);
wenzelm@641
   389
in
wenzelm@641
   390
  fun type_env t = sort (add_type_env (t, []));
wenzelm@641
   391
  fun sort_env t = rev (sort (it_term_types add_sort_env (t, [])));
wenzelm@641
   392
end;
wenzelm@641
   393
wenzelm@641
   394
wenzelm@641
   395
(* print_goals *)
wenzelm@641
   396
wenzelm@641
   397
fun print_goals maxgoals state =
wenzelm@641
   398
  let
wenzelm@641
   399
    open Syntax;
wenzelm@641
   400
wenzelm@641
   401
    val {sign, prop, ...} = rep_thm state;
wenzelm@641
   402
wenzelm@641
   403
    val pretty_term = Sign.pretty_term sign;
wenzelm@641
   404
    val pretty_typ = Sign.pretty_typ sign;
wenzelm@641
   405
    val pretty_sort = Sign.pretty_sort;
wenzelm@641
   406
wenzelm@641
   407
    fun pretty_vars prtf (X, vs) = Pretty.block
wenzelm@641
   408
      [Pretty.block (Pretty.commas (map Pretty.str vs)),
wenzelm@641
   409
        Pretty.str " ::", Pretty.brk 1, prtf X];
lcp@229
   410
wenzelm@641
   411
    fun print_list _ _ [] = ()
wenzelm@641
   412
      | print_list name prtf lst =
wenzelm@641
   413
          (writeln ""; Pretty.writeln (Pretty.big_list name (map prtf lst)));
wenzelm@641
   414
wenzelm@641
   415
wenzelm@641
   416
    fun print_goals (_, []) = ()
wenzelm@641
   417
      | print_goals (n, A :: As) = (Pretty.writeln (Pretty.blk (0,
wenzelm@641
   418
          [Pretty.str (" " ^ string_of_int n ^ ". "), pretty_term A]));
wenzelm@641
   419
            print_goals (n + 1, As));
wenzelm@641
   420
wenzelm@641
   421
    val print_ffpairs =
wenzelm@641
   422
      print_list "Flex-flex pairs:" (pretty_term o Logic.mk_flexpair);
wenzelm@641
   423
wenzelm@641
   424
    val print_types = print_list "Types:" (pretty_vars pretty_typ) o type_env;
wenzelm@641
   425
    val print_sorts = print_list "Sorts:" (pretty_vars pretty_sort) o sort_env;
wenzelm@641
   426
wenzelm@641
   427
wenzelm@641
   428
    val (tpairs, As, B) = Logic.strip_horn prop;
wenzelm@641
   429
    val ngoals = length As;
wenzelm@641
   430
wenzelm@641
   431
    val orig_no_freeTs = ! show_no_free_types;
wenzelm@641
   432
    val orig_sorts = ! show_sorts;
wenzelm@641
   433
wenzelm@641
   434
    fun restore () =
wenzelm@641
   435
      (show_no_free_types := orig_no_freeTs; show_sorts := orig_sorts);
wenzelm@641
   436
  in
wenzelm@641
   437
    (show_no_free_types := true; show_sorts := false;
wenzelm@641
   438
      Pretty.writeln (pretty_term B);
wenzelm@641
   439
      if ngoals = 0 then writeln "No subgoals!"
wenzelm@641
   440
      else if ngoals > maxgoals then
wenzelm@641
   441
        (print_goals (1, take (maxgoals, As));
wenzelm@641
   442
          writeln ("A total of " ^ string_of_int ngoals ^ " subgoals..."))
wenzelm@641
   443
      else print_goals (1, As);
wenzelm@641
   444
wenzelm@641
   445
      print_ffpairs tpairs;
wenzelm@641
   446
wenzelm@641
   447
      if orig_sorts then
wenzelm@641
   448
        (print_types prop; print_sorts prop)
wenzelm@641
   449
      else if ! show_types then
wenzelm@641
   450
        print_types prop
wenzelm@641
   451
      else ())
wenzelm@641
   452
    handle exn => (restore (); raise exn);
wenzelm@641
   453
    restore ()
wenzelm@641
   454
  end;
wenzelm@641
   455
lcp@229
   456
lcp@229
   457
(*"hook" for user interfaces: allows print_goals to be replaced*)
lcp@229
   458
val print_goals_ref = ref print_goals;
lcp@229
   459
wenzelm@252
   460
(*** Find the type (sort) associated with a (T)Var or (T)Free in a term
clasohm@0
   461
     Used for establishing default types (of variables) and sorts (of
clasohm@0
   462
     type variables) when reading another term.
clasohm@0
   463
     Index -1 indicates that a (T)Free rather than a (T)Var is wanted.
clasohm@0
   464
***)
clasohm@0
   465
clasohm@0
   466
fun types_sorts thm =
clasohm@0
   467
    let val {prop,hyps,...} = rep_thm thm;
wenzelm@252
   468
        val big = list_comb(prop,hyps); (* bogus term! *)
wenzelm@252
   469
        val vars = map dest_Var (term_vars big);
wenzelm@252
   470
        val frees = map dest_Free (term_frees big);
wenzelm@252
   471
        val tvars = term_tvars big;
wenzelm@252
   472
        val tfrees = term_tfrees big;
wenzelm@252
   473
        fun typ(a,i) = if i<0 then assoc(frees,a) else assoc(vars,(a,i));
wenzelm@252
   474
        fun sort(a,i) = if i<0 then assoc(tfrees,a) else assoc(tvars,(a,i));
clasohm@0
   475
    in (typ,sort) end;
clasohm@0
   476
clasohm@0
   477
(** Standardization of rules **)
clasohm@0
   478
clasohm@0
   479
(*Generalization over a list of variables, IGNORING bad ones*)
clasohm@0
   480
fun forall_intr_list [] th = th
clasohm@0
   481
  | forall_intr_list (y::ys) th =
wenzelm@252
   482
        let val gth = forall_intr_list ys th
wenzelm@252
   483
        in  forall_intr y gth   handle THM _ =>  gth  end;
clasohm@0
   484
clasohm@0
   485
(*Generalization over all suitable Free variables*)
clasohm@0
   486
fun forall_intr_frees th =
clasohm@0
   487
    let val {prop,sign,...} = rep_thm th
clasohm@0
   488
    in  forall_intr_list
wenzelm@252
   489
         (map (cterm_of sign) (sort atless (term_frees prop)))
clasohm@0
   490
         th
clasohm@0
   491
    end;
clasohm@0
   492
clasohm@0
   493
(*Replace outermost quantified variable by Var of given index.
clasohm@0
   494
    Could clash with Vars already present.*)
wenzelm@252
   495
fun forall_elim_var i th =
clasohm@0
   496
    let val {prop,sign,...} = rep_thm th
clasohm@0
   497
    in case prop of
wenzelm@252
   498
          Const("all",_) $ Abs(a,T,_) =>
wenzelm@252
   499
              forall_elim (cterm_of sign (Var((a,i), T)))  th
wenzelm@252
   500
        | _ => raise THM("forall_elim_var", i, [th])
clasohm@0
   501
    end;
clasohm@0
   502
clasohm@0
   503
(*Repeat forall_elim_var until all outer quantifiers are removed*)
wenzelm@252
   504
fun forall_elim_vars i th =
clasohm@0
   505
    forall_elim_vars i (forall_elim_var i th)
wenzelm@252
   506
        handle THM _ => th;
clasohm@0
   507
clasohm@0
   508
(*Specialization over a list of cterms*)
clasohm@0
   509
fun forall_elim_list cts th = foldr (uncurry forall_elim) (rev cts, th);
clasohm@0
   510
clasohm@0
   511
(* maps [A1,...,An], B   to   [| A1;...;An |] ==> B  *)
clasohm@0
   512
fun implies_intr_list cAs th = foldr (uncurry implies_intr) (cAs,th);
clasohm@0
   513
clasohm@0
   514
(* maps [| A1;...;An |] ==> B and [A1,...,An]   to   B *)
clasohm@0
   515
fun implies_elim_list impth ths = foldl (uncurry implies_elim) (impth,ths);
clasohm@0
   516
clasohm@0
   517
(*Reset Var indexes to zero, renaming to preserve distinctness*)
wenzelm@252
   518
fun zero_var_indexes th =
clasohm@0
   519
    let val {prop,sign,...} = rep_thm th;
clasohm@0
   520
        val vars = term_vars prop
clasohm@0
   521
        val bs = foldl add_new_id ([], map (fn Var((a,_),_)=>a) vars)
wenzelm@252
   522
        val inrs = add_term_tvars(prop,[]);
wenzelm@252
   523
        val nms' = rev(foldl add_new_id ([], map (#1 o #1) inrs));
wenzelm@252
   524
        val tye = map (fn ((v,rs),a) => (v, TVar((a,0),rs))) (inrs ~~ nms')
wenzelm@252
   525
        val ctye = map (fn (v,T) => (v,ctyp_of sign T)) tye;
wenzelm@252
   526
        fun varpairs([],[]) = []
wenzelm@252
   527
          | varpairs((var as Var(v,T)) :: vars, b::bs) =
wenzelm@252
   528
                let val T' = typ_subst_TVars tye T
wenzelm@252
   529
                in (cterm_of sign (Var(v,T')),
wenzelm@252
   530
                    cterm_of sign (Var((b,0),T'))) :: varpairs(vars,bs)
wenzelm@252
   531
                end
wenzelm@252
   532
          | varpairs _ = raise TERM("varpairs", []);
clasohm@0
   533
    in instantiate (ctye, varpairs(vars,rev bs)) th end;
clasohm@0
   534
clasohm@0
   535
clasohm@0
   536
(*Standard form of object-rule: no hypotheses, Frees, or outer quantifiers;
clasohm@0
   537
    all generality expressed by Vars having index 0.*)
clasohm@0
   538
fun standard th =
wenzelm@1218
   539
  let val {maxidx,...} = rep_thm th
wenzelm@1218
   540
  in  
wenzelm@1218
   541
    th |> implies_intr_hyps
wenzelm@1218
   542
    |> strip_shyps |> implies_intr_shyps
wenzelm@1218
   543
    |> forall_intr_frees |> forall_elim_vars (maxidx + 1)
wenzelm@1218
   544
    |> zero_var_indexes |> varifyT
wenzelm@1218
   545
  end;
wenzelm@1218
   546
clasohm@0
   547
wenzelm@252
   548
(*Assume a new formula, read following the same conventions as axioms.
clasohm@0
   549
  Generalizes over Free variables,
clasohm@0
   550
  creates the assumption, and then strips quantifiers.
clasohm@0
   551
  Example is [| ALL x:?A. ?P(x) |] ==> [| ?P(?a) |]
wenzelm@252
   552
             [ !(A,P,a)[| ALL x:A. P(x) |] ==> [| P(a) |] ]    *)
clasohm@0
   553
fun assume_ax thy sP =
clasohm@0
   554
    let val sign = sign_of thy
wenzelm@252
   555
        val prop = Logic.close_form (term_of (read_cterm sign
wenzelm@252
   556
                         (sP, propT)))
lcp@229
   557
    in forall_elim_vars 0 (assume (cterm_of sign prop))  end;
clasohm@0
   558
wenzelm@252
   559
(*Resolution: exactly one resolvent must be produced.*)
clasohm@0
   560
fun tha RSN (i,thb) =
clasohm@0
   561
  case Sequence.chop (2, biresolution false [(false,tha)] i thb) of
clasohm@0
   562
      ([th],_) => th
clasohm@0
   563
    | ([],_)   => raise THM("RSN: no unifiers", i, [tha,thb])
clasohm@0
   564
    |      _   => raise THM("RSN: multiple unifiers", i, [tha,thb]);
clasohm@0
   565
clasohm@0
   566
(*resolution: P==>Q, Q==>R gives P==>R. *)
clasohm@0
   567
fun tha RS thb = tha RSN (1,thb);
clasohm@0
   568
clasohm@0
   569
(*For joining lists of rules*)
wenzelm@252
   570
fun thas RLN (i,thbs) =
clasohm@0
   571
  let val resolve = biresolution false (map (pair false) thas) i
clasohm@0
   572
      fun resb thb = Sequence.list_of_s (resolve thb) handle THM _ => []
clasohm@0
   573
  in  flat (map resb thbs)  end;
clasohm@0
   574
clasohm@0
   575
fun thas RL thbs = thas RLN (1,thbs);
clasohm@0
   576
lcp@11
   577
(*Resolve a list of rules against bottom_rl from right to left;
lcp@11
   578
  makes proof trees*)
wenzelm@252
   579
fun rls MRS bottom_rl =
lcp@11
   580
  let fun rs_aux i [] = bottom_rl
wenzelm@252
   581
        | rs_aux i (rl::rls) = rl RSN (i, rs_aux (i+1) rls)
lcp@11
   582
  in  rs_aux 1 rls  end;
lcp@11
   583
lcp@11
   584
(*As above, but for rule lists*)
wenzelm@252
   585
fun rlss MRL bottom_rls =
lcp@11
   586
  let fun rs_aux i [] = bottom_rls
wenzelm@252
   587
        | rs_aux i (rls::rlss) = rls RLN (i, rs_aux (i+1) rlss)
lcp@11
   588
  in  rs_aux 1 rlss  end;
lcp@11
   589
wenzelm@252
   590
(*compose Q and [...,Qi,Q(i+1),...]==>R to [...,Q(i+1),...]==>R
clasohm@0
   591
  with no lifting or renaming!  Q may contain ==> or meta-quants
clasohm@0
   592
  ALWAYS deletes premise i *)
wenzelm@252
   593
fun compose(tha,i,thb) =
clasohm@0
   594
    Sequence.list_of_s (bicompose false (false,tha,0) i thb);
clasohm@0
   595
clasohm@0
   596
(*compose Q and [Q1,Q2,...,Qk]==>R to [Q2,...,Qk]==>R getting unique result*)
clasohm@0
   597
fun tha COMP thb =
clasohm@0
   598
    case compose(tha,1,thb) of
wenzelm@252
   599
        [th] => th
clasohm@0
   600
      | _ =>   raise THM("COMP", 1, [tha,thb]);
clasohm@0
   601
clasohm@0
   602
(*Instantiate theorem th, reading instantiations under signature sg*)
clasohm@0
   603
fun read_instantiate_sg sg sinsts th =
clasohm@0
   604
    let val ts = types_sorts th;
nipkow@952
   605
        val used = add_term_tvarnames(#prop(rep_thm th),[]);
nipkow@952
   606
    in  instantiate (read_insts sg ts ts used sinsts) th  end;
clasohm@0
   607
clasohm@0
   608
(*Instantiate theorem th, reading instantiations under theory of th*)
clasohm@0
   609
fun read_instantiate sinsts th =
clasohm@0
   610
    read_instantiate_sg (#sign (rep_thm th)) sinsts th;
clasohm@0
   611
clasohm@0
   612
clasohm@0
   613
(*Left-to-right replacements: tpairs = [...,(vi,ti),...].
clasohm@0
   614
  Instantiates distinct Vars by terms, inferring type instantiations. *)
clasohm@0
   615
local
clasohm@0
   616
  fun add_types ((ct,cu), (sign,tye)) =
lcp@229
   617
    let val {sign=signt, t=t, T= T, ...} = rep_cterm ct
lcp@229
   618
        and {sign=signu, t=u, T= U, ...} = rep_cterm cu
clasohm@0
   619
        val sign' = Sign.merge(sign, Sign.merge(signt, signu))
wenzelm@252
   620
        val tye' = Type.unify (#tsig(Sign.rep_sg sign')) ((T,U), tye)
wenzelm@252
   621
          handle Type.TUNIFY => raise TYPE("add_types", [T,U], [t,u])
clasohm@0
   622
    in  (sign', tye')  end;
clasohm@0
   623
in
wenzelm@252
   624
fun cterm_instantiate ctpairs0 th =
clasohm@0
   625
  let val (sign,tye) = foldr add_types (ctpairs0, (#sign(rep_thm th),[]))
clasohm@0
   626
      val tsig = #tsig(Sign.rep_sg sign);
clasohm@0
   627
      fun instT(ct,cu) = let val inst = subst_TVars tye
wenzelm@252
   628
                         in (cterm_fun inst ct, cterm_fun inst cu) end
lcp@229
   629
      fun ctyp2 (ix,T) = (ix, ctyp_of sign T)
clasohm@0
   630
  in  instantiate (map ctyp2 tye, map instT ctpairs0) th  end
wenzelm@252
   631
  handle TERM _ =>
clasohm@0
   632
           raise THM("cterm_instantiate: incompatible signatures",0,[th])
clasohm@0
   633
       | TYPE _ => raise THM("cterm_instantiate: types", 0, [th])
clasohm@0
   634
end;
clasohm@0
   635
clasohm@0
   636
clasohm@0
   637
(** theorem equality test is exported and used by BEST_FIRST **)
clasohm@0
   638
wenzelm@252
   639
(*equality of theorems uses equality of signatures and
clasohm@0
   640
  the a-convertible test for terms*)
wenzelm@252
   641
fun eq_thm (th1,th2) =
wenzelm@1218
   642
    let val {sign=sg1, shyps=shyps1, hyps=hyps1, prop=prop1, ...} = rep_thm th1
wenzelm@1218
   643
        and {sign=sg2, shyps=shyps2, hyps=hyps2, prop=prop2, ...} = rep_thm th2
wenzelm@252
   644
    in  Sign.eq_sg (sg1,sg2) andalso
wenzelm@1218
   645
        eq_set (shyps1, shyps2) andalso
wenzelm@252
   646
        aconvs(hyps1,hyps2) andalso
wenzelm@252
   647
        prop1 aconv prop2
clasohm@0
   648
    end;
clasohm@0
   649
clasohm@0
   650
(*Do the two theorems have the same signature?*)
wenzelm@252
   651
fun eq_thm_sg (th1,th2) = Sign.eq_sg(#sign(rep_thm th1), #sign(rep_thm th2));
clasohm@0
   652
clasohm@0
   653
(*Useful "distance" function for BEST_FIRST*)
clasohm@0
   654
val size_of_thm = size_of_term o #prop o rep_thm;
clasohm@0
   655
clasohm@0
   656
lcp@1194
   657
(** Mark Staples's weaker version of eq_thm: ignores variable renaming and
lcp@1194
   658
    (some) type variable renaming **)
lcp@1194
   659
lcp@1194
   660
 (* Can't use term_vars, because it sorts the resulting list of variable names.
lcp@1194
   661
    We instead need the unique list noramlised by the order of appearance
lcp@1194
   662
    in the term. *)
lcp@1194
   663
fun term_vars' (t as Var(v,T)) = [t]
lcp@1194
   664
  | term_vars' (Abs(_,_,b)) = term_vars' b
lcp@1194
   665
  | term_vars' (f$a) = (term_vars' f) @ (term_vars' a)
lcp@1194
   666
  | term_vars' _ = [];
lcp@1194
   667
lcp@1194
   668
fun forall_intr_vars th =
lcp@1194
   669
  let val {prop,sign,...} = rep_thm th;
lcp@1194
   670
      val vars = distinct (term_vars' prop);
lcp@1194
   671
  in forall_intr_list (map (cterm_of sign) vars) th end;
lcp@1194
   672
lcp@1194
   673
fun weak_eq_thm (tha,thb) = 
lcp@1194
   674
    eq_thm(forall_intr_vars (freezeT tha), forall_intr_vars (freezeT thb));
lcp@1194
   675
lcp@1194
   676
lcp@1194
   677
clasohm@0
   678
(*** Meta-Rewriting Rules ***)
clasohm@0
   679
clasohm@0
   680
clasohm@0
   681
val reflexive_thm =
clasohm@922
   682
  let val cx = cterm_of Sign.proto_pure (Var(("x",0),TVar(("'a",0),logicS)))
clasohm@0
   683
  in Thm.reflexive cx end;
clasohm@0
   684
clasohm@0
   685
val symmetric_thm =
clasohm@922
   686
  let val xy = read_cterm Sign.proto_pure ("x::'a::logic == y",propT)
clasohm@0
   687
  in standard(Thm.implies_intr_hyps(Thm.symmetric(Thm.assume xy))) end;
clasohm@0
   688
clasohm@0
   689
val transitive_thm =
clasohm@922
   690
  let val xy = read_cterm Sign.proto_pure ("x::'a::logic == y",propT)
clasohm@922
   691
      val yz = read_cterm Sign.proto_pure ("y::'a::logic == z",propT)
clasohm@0
   692
      val xythm = Thm.assume xy and yzthm = Thm.assume yz
clasohm@0
   693
  in standard(Thm.implies_intr yz (Thm.transitive xythm yzthm)) end;
clasohm@0
   694
lcp@229
   695
(** Below, a "conversion" has type cterm -> thm **)
lcp@229
   696
clasohm@922
   697
val refl_cimplies = reflexive (cterm_of Sign.proto_pure implies);
clasohm@0
   698
clasohm@0
   699
(*In [A1,...,An]==>B, rewrite the selected A's only -- for rewrite_goals_tac*)
nipkow@214
   700
(*Do not rewrite flex-flex pairs*)
wenzelm@252
   701
fun goals_conv pred cv =
lcp@229
   702
  let fun gconv i ct =
lcp@229
   703
        let val (A,B) = Thm.dest_cimplies ct
lcp@229
   704
            val (thA,j) = case term_of A of
lcp@229
   705
                  Const("=?=",_)$_$_ => (reflexive A, i)
lcp@229
   706
                | _ => (if pred i then cv A else reflexive A, i+1)
wenzelm@252
   707
        in  combination (combination refl_cimplies thA) (gconv j B) end
lcp@229
   708
        handle TERM _ => reflexive ct
clasohm@0
   709
  in gconv 1 end;
clasohm@0
   710
clasohm@0
   711
(*Use a conversion to transform a theorem*)
lcp@229
   712
fun fconv_rule cv th = equal_elim (cv (cprop_of th)) th;
clasohm@0
   713
clasohm@0
   714
(*rewriting conversion*)
lcp@229
   715
fun rew_conv mode prover mss = rewrite_cterm mode mss prover;
clasohm@0
   716
clasohm@0
   717
(*Rewrite a theorem*)
nipkow@214
   718
fun rewrite_rule thms =
nipkow@214
   719
  fconv_rule (rew_conv (true,false) (K(K None)) (Thm.mss_of thms));
clasohm@0
   720
clasohm@0
   721
(*Rewrite the subgoals of a proof state (represented by a theorem) *)
clasohm@0
   722
fun rewrite_goals_rule thms =
nipkow@214
   723
  fconv_rule (goals_conv (K true) (rew_conv (true,false) (K(K None))
nipkow@214
   724
             (Thm.mss_of thms)));
clasohm@0
   725
clasohm@0
   726
(*Rewrite the subgoal of a proof state (represented by a theorem) *)
nipkow@214
   727
fun rewrite_goal_rule mode prover mss i thm =
nipkow@214
   728
  if 0 < i  andalso  i <= nprems_of thm
nipkow@214
   729
  then fconv_rule (goals_conv (fn j => j=i) (rew_conv mode prover mss)) thm
nipkow@214
   730
  else raise THM("rewrite_goal_rule",i,[thm]);
clasohm@0
   731
clasohm@0
   732
clasohm@0
   733
(** Derived rules mainly for METAHYPS **)
clasohm@0
   734
clasohm@0
   735
(*Given the term "a", takes (%x.t)==(%x.u) to t[a/x]==u[a/x]*)
clasohm@0
   736
fun equal_abs_elim ca eqth =
lcp@229
   737
  let val {sign=signa, t=a, ...} = rep_cterm ca
clasohm@0
   738
      and combth = combination eqth (reflexive ca)
clasohm@0
   739
      val {sign,prop,...} = rep_thm eqth
clasohm@0
   740
      val (abst,absu) = Logic.dest_equals prop
lcp@229
   741
      val cterm = cterm_of (Sign.merge (sign,signa))
clasohm@0
   742
  in  transitive (symmetric (beta_conversion (cterm (abst$a))))
clasohm@0
   743
           (transitive combth (beta_conversion (cterm (absu$a))))
clasohm@0
   744
  end
clasohm@0
   745
  handle THM _ => raise THM("equal_abs_elim", 0, [eqth]);
clasohm@0
   746
clasohm@0
   747
(*Calling equal_abs_elim with multiple terms*)
clasohm@0
   748
fun equal_abs_elim_list cts th = foldr (uncurry equal_abs_elim) (rev cts, th);
clasohm@0
   749
clasohm@0
   750
local
clasohm@0
   751
  open Logic
clasohm@0
   752
  val alpha = TVar(("'a",0), [])     (*  type ?'a::{}  *)
clasohm@0
   753
  fun err th = raise THM("flexpair_inst: ", 0, [th])
clasohm@0
   754
  fun flexpair_inst def th =
clasohm@0
   755
    let val {prop = Const _ $ t $ u,  sign,...} = rep_thm th
wenzelm@252
   756
        val cterm = cterm_of sign
wenzelm@252
   757
        fun cvar a = cterm(Var((a,0),alpha))
wenzelm@252
   758
        val def' = cterm_instantiate [(cvar"t", cterm t), (cvar"u", cterm u)]
wenzelm@252
   759
                   def
clasohm@0
   760
    in  equal_elim def' th
clasohm@0
   761
    end
clasohm@0
   762
    handle THM _ => err th | bind => err th
clasohm@0
   763
in
clasohm@0
   764
val flexpair_intr = flexpair_inst (symmetric flexpair_def)
clasohm@0
   765
and flexpair_elim = flexpair_inst flexpair_def
clasohm@0
   766
end;
clasohm@0
   767
clasohm@0
   768
(*Version for flexflex pairs -- this supports lifting.*)
wenzelm@252
   769
fun flexpair_abs_elim_list cts =
clasohm@0
   770
    flexpair_intr o equal_abs_elim_list cts o flexpair_elim;
clasohm@0
   771
clasohm@0
   772
clasohm@0
   773
(*** Some useful meta-theorems ***)
clasohm@0
   774
clasohm@0
   775
(*The rule V/V, obtains assumption solving for eresolve_tac*)
clasohm@922
   776
val asm_rl = trivial(read_cterm Sign.proto_pure ("PROP ?psi",propT));
clasohm@0
   777
clasohm@0
   778
(*Meta-level cut rule: [| V==>W; V |] ==> W *)
clasohm@922
   779
val cut_rl = trivial(read_cterm Sign.proto_pure
wenzelm@252
   780
        ("PROP ?psi ==> PROP ?theta", propT));
clasohm@0
   781
wenzelm@252
   782
(*Generalized elim rule for one conclusion; cut_rl with reversed premises:
clasohm@0
   783
     [| PROP V;  PROP V ==> PROP W |] ==> PROP W *)
clasohm@0
   784
val revcut_rl =
clasohm@922
   785
  let val V = read_cterm Sign.proto_pure ("PROP V", propT)
clasohm@922
   786
      and VW = read_cterm Sign.proto_pure ("PROP V ==> PROP W", propT);
wenzelm@252
   787
  in  standard (implies_intr V
wenzelm@252
   788
                (implies_intr VW
wenzelm@252
   789
                 (implies_elim (assume VW) (assume V))))
clasohm@0
   790
  end;
clasohm@0
   791
lcp@668
   792
(*for deleting an unwanted assumption*)
lcp@668
   793
val thin_rl =
clasohm@922
   794
  let val V = read_cterm Sign.proto_pure ("PROP V", propT)
clasohm@922
   795
      and W = read_cterm Sign.proto_pure ("PROP W", propT);
lcp@668
   796
  in  standard (implies_intr V (implies_intr W (assume W)))
lcp@668
   797
  end;
lcp@668
   798
clasohm@0
   799
(* (!!x. PROP ?V) == PROP ?V       Allows removal of redundant parameters*)
clasohm@0
   800
val triv_forall_equality =
clasohm@922
   801
  let val V  = read_cterm Sign.proto_pure ("PROP V", propT)
clasohm@922
   802
      and QV = read_cterm Sign.proto_pure ("!!x::'a. PROP V", propT)
clasohm@922
   803
      and x  = read_cterm Sign.proto_pure ("x", TFree("'a",logicS));
clasohm@0
   804
  in  standard (equal_intr (implies_intr QV (forall_elim x (assume QV)))
wenzelm@252
   805
                           (implies_intr V  (forall_intr x (assume V))))
clasohm@0
   806
  end;
clasohm@0
   807
clasohm@0
   808
end
clasohm@0
   809
end;
wenzelm@252
   810