src/Pure/drule.ML
author wenzelm
Thu May 19 16:17:46 1994 +0200 (1994-05-19)
changeset 385 921f87897a76
parent 252 7532f95d7f44
child 400 3c2c40c87112
permissions -rw-r--r--
added print_sign, print_axioms: theory -> unit;
replaced ["logic"] by logicS;
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
clasohm@0
    15
  val asm_rl: thm
clasohm@0
    16
  val assume_ax: theory -> string -> thm
clasohm@0
    17
  val COMP: thm * thm -> thm
clasohm@0
    18
  val compose: thm * int * thm -> thm list
lcp@229
    19
  val cterm_instantiate: (cterm*cterm)list -> thm -> thm
clasohm@0
    20
  val cut_rl: thm
lcp@229
    21
  val equal_abs_elim: cterm  -> thm -> thm
lcp@229
    22
  val equal_abs_elim_list: cterm list -> thm -> thm
clasohm@0
    23
  val eq_thm: thm * thm -> bool
clasohm@0
    24
  val eq_thm_sg: thm * thm -> bool
lcp@229
    25
  val flexpair_abs_elim_list: cterm list -> thm -> thm
lcp@229
    26
  val forall_intr_list: cterm list -> thm -> thm
clasohm@0
    27
  val forall_intr_frees: thm -> thm
lcp@229
    28
  val forall_elim_list: cterm list -> thm -> thm
clasohm@0
    29
  val forall_elim_var: int -> thm -> thm
clasohm@0
    30
  val forall_elim_vars: int -> thm -> thm
clasohm@0
    31
  val implies_elim_list: thm -> thm list -> thm
lcp@229
    32
  val implies_intr_list: cterm list -> thm -> thm
lcp@11
    33
  val MRL: thm list list * thm list -> thm list
lcp@11
    34
  val MRS: thm list * thm -> thm
lcp@229
    35
  val pprint_cterm: cterm -> pprint_args -> unit
lcp@229
    36
  val pprint_ctyp: ctyp -> pprint_args -> unit
lcp@229
    37
  val pprint_theory: theory -> pprint_args -> unit
lcp@229
    38
  val pprint_thm: thm -> pprint_args -> unit
lcp@229
    39
  val pretty_thm: thm -> Sign.Syntax.Pretty.T
lcp@229
    40
  val print_cterm: cterm -> unit
lcp@229
    41
  val print_ctyp: ctyp -> unit
clasohm@0
    42
  val print_goals: int -> thm -> unit
lcp@67
    43
  val print_goals_ref: (int -> thm -> unit) ref
wenzelm@385
    44
  val print_sign: theory -> unit
wenzelm@385
    45
  val print_axioms: theory -> unit
clasohm@0
    46
  val print_theory: theory -> unit
clasohm@0
    47
  val print_thm: thm -> unit
clasohm@0
    48
  val prth: thm -> thm
clasohm@0
    49
  val prthq: thm Sequence.seq -> thm Sequence.seq
clasohm@0
    50
  val prths: thm list -> thm list
clasohm@0
    51
  val read_instantiate: (string*string)list -> thm -> thm
clasohm@0
    52
  val read_instantiate_sg: Sign.sg -> (string*string)list -> thm -> thm
wenzelm@252
    53
  val read_insts:
lcp@229
    54
          Sign.sg -> (indexname -> typ option) * (indexname -> sort option)
lcp@229
    55
                  -> (indexname -> typ option) * (indexname -> sort option)
lcp@229
    56
                  -> (string*string)list
lcp@229
    57
                  -> (indexname*ctyp)list * (cterm*cterm)list
clasohm@0
    58
  val reflexive_thm: thm
clasohm@0
    59
  val revcut_rl: thm
nipkow@214
    60
  val rewrite_goal_rule: bool*bool -> (meta_simpset -> thm -> thm option)
nipkow@214
    61
        -> meta_simpset -> int -> thm -> thm
clasohm@0
    62
  val rewrite_goals_rule: thm list -> thm -> thm
clasohm@0
    63
  val rewrite_rule: thm list -> thm -> thm
clasohm@0
    64
  val RS: thm * thm -> thm
clasohm@0
    65
  val RSN: thm * (int * thm) -> thm
clasohm@0
    66
  val RL: thm list * thm list -> thm list
clasohm@0
    67
  val RLN: thm list * (int * thm list) -> thm list
clasohm@0
    68
  val show_hyps: bool ref
clasohm@0
    69
  val size_of_thm: thm -> int
clasohm@0
    70
  val standard: thm -> thm
lcp@229
    71
  val string_of_cterm: cterm -> string
lcp@229
    72
  val string_of_ctyp: ctyp -> string
clasohm@0
    73
  val string_of_thm: thm -> string
clasohm@0
    74
  val symmetric_thm: thm
clasohm@0
    75
  val transitive_thm: thm
clasohm@0
    76
  val triv_forall_equality: thm
clasohm@0
    77
  val types_sorts: thm -> (indexname-> typ option) * (indexname-> sort option)
clasohm@0
    78
  val zero_var_indexes: thm -> thm
clasohm@0
    79
  end
clasohm@0
    80
  end;
clasohm@0
    81
wenzelm@252
    82
functor DruleFun (structure Logic: LOGIC and Thm: THM): DRULE =
clasohm@0
    83
struct
clasohm@0
    84
structure Thm = Thm;
clasohm@0
    85
structure Sign = Thm.Sign;
clasohm@0
    86
structure Type = Sign.Type;
clasohm@0
    87
structure Pretty = Sign.Syntax.Pretty
clasohm@0
    88
local open Thm
clasohm@0
    89
in
clasohm@0
    90
clasohm@0
    91
(**** More derived rules and operations on theorems ****)
clasohm@0
    92
lcp@229
    93
(** reading of instantiations **)
lcp@229
    94
lcp@229
    95
fun indexname cs = case Syntax.scan_varname cs of (v,[]) => v
lcp@229
    96
        | _ => error("Lexical error in variable name " ^ quote (implode cs));
lcp@229
    97
lcp@229
    98
fun absent ixn =
lcp@229
    99
  error("No such variable in term: " ^ Syntax.string_of_vname ixn);
lcp@229
   100
lcp@229
   101
fun inst_failure ixn =
lcp@229
   102
  error("Instantiation of " ^ Syntax.string_of_vname ixn ^ " fails");
lcp@229
   103
lcp@229
   104
fun read_insts sign (rtypes,rsorts) (types,sorts) insts =
lcp@229
   105
let val {tsig,...} = Sign.rep_sg sign
lcp@229
   106
    fun split([],tvs,vs) = (tvs,vs)
lcp@229
   107
      | split((sv,st)::l,tvs,vs) = (case explode sv of
lcp@229
   108
                  "'"::cs => split(l,(indexname cs,st)::tvs,vs)
lcp@229
   109
                | cs => split(l,tvs,(indexname cs,st)::vs));
lcp@229
   110
    val (tvs,vs) = split(insts,[],[]);
lcp@229
   111
    fun readT((a,i),st) =
lcp@229
   112
        let val ixn = ("'" ^ a,i);
lcp@229
   113
            val S = case rsorts ixn of Some S => S | None => absent ixn;
lcp@229
   114
            val T = Sign.read_typ (sign,sorts) st;
lcp@229
   115
        in if Type.typ_instance(tsig,T,TVar(ixn,S)) then (ixn,T)
lcp@229
   116
           else inst_failure ixn
lcp@229
   117
        end
lcp@229
   118
    val tye = map readT tvs;
lcp@229
   119
    fun add_cterm ((cts,tye), (ixn,st)) =
lcp@229
   120
        let val T = case rtypes ixn of
lcp@229
   121
                      Some T => typ_subst_TVars tye T
lcp@229
   122
                    | None => absent ixn;
lcp@229
   123
            val (ct,tye2) = read_def_cterm (sign,types,sorts) (st,T);
lcp@229
   124
            val cv = cterm_of sign (Var(ixn,typ_subst_TVars tye2 T))
lcp@229
   125
        in ((cv,ct)::cts,tye2 @ tye) end
lcp@229
   126
    val (cterms,tye') = foldl add_cterm (([],tye), vs);
lcp@229
   127
in (map (fn (ixn,T) => (ixn,ctyp_of sign T)) tye', cterms) end;
lcp@229
   128
lcp@229
   129
wenzelm@252
   130
wenzelm@252
   131
(*** Printing of theories, theorems, etc. ***)
lcp@229
   132
lcp@229
   133
(*If false, hypotheses are printed as dots*)
lcp@229
   134
val show_hyps = ref true;
lcp@229
   135
lcp@229
   136
fun pretty_thm th =
lcp@229
   137
let val {sign, hyps, prop,...} = rep_thm th
lcp@229
   138
    val hsymbs = if null hyps then []
wenzelm@252
   139
                 else if !show_hyps then
wenzelm@252
   140
                      [Pretty.brk 2,
wenzelm@252
   141
                       Pretty.lst("[","]") (map (Sign.pretty_term sign) hyps)]
wenzelm@252
   142
                 else Pretty.str" [" :: map (fn _ => Pretty.str".") hyps @
wenzelm@252
   143
                      [Pretty.str"]"];
lcp@229
   144
in Pretty.blk(0, Sign.pretty_term sign prop :: hsymbs) end;
lcp@229
   145
lcp@229
   146
val string_of_thm = Pretty.string_of o pretty_thm;
lcp@229
   147
lcp@229
   148
val pprint_thm = Pretty.pprint o Pretty.quote o pretty_thm;
lcp@229
   149
lcp@229
   150
lcp@229
   151
(** Top-level commands for printing theorems **)
lcp@229
   152
val print_thm = writeln o string_of_thm;
lcp@229
   153
lcp@229
   154
fun prth th = (print_thm th; th);
lcp@229
   155
lcp@229
   156
(*Print and return a sequence of theorems, separated by blank lines. *)
lcp@229
   157
fun prthq thseq =
wenzelm@252
   158
  (Sequence.prints (fn _ => print_thm) 100000 thseq; thseq);
lcp@229
   159
lcp@229
   160
(*Print and return a list of theorems, separated by blank lines. *)
lcp@229
   161
fun prths ths = (print_list_ln print_thm ths; ths);
lcp@229
   162
wenzelm@252
   163
wenzelm@252
   164
(* other printing commands *)
lcp@229
   165
wenzelm@252
   166
fun pprint_ctyp cT =
wenzelm@252
   167
  let val {sign, T} = rep_ctyp cT in Sign.pprint_typ sign T end;
wenzelm@252
   168
wenzelm@252
   169
fun string_of_ctyp cT =
wenzelm@252
   170
  let val {sign, T} = rep_ctyp cT in Sign.string_of_typ sign T end;
lcp@229
   171
lcp@229
   172
val print_ctyp = writeln o string_of_ctyp;
lcp@229
   173
wenzelm@252
   174
fun pprint_cterm ct =
wenzelm@252
   175
  let val {sign, t, ...} = rep_cterm ct in Sign.pprint_term sign t end;
lcp@229
   176
wenzelm@252
   177
fun string_of_cterm ct =
wenzelm@252
   178
  let val {sign, t, ...} = rep_cterm ct in Sign.string_of_term sign t end;
lcp@229
   179
lcp@229
   180
val print_cterm = writeln o string_of_cterm;
lcp@229
   181
wenzelm@252
   182
wenzelm@252
   183
(* print theory *)
wenzelm@252
   184
wenzelm@252
   185
val pprint_theory = Sign.pprint_sg o sign_of;
lcp@229
   186
wenzelm@385
   187
val print_sign = Sign.print_sg o sign_of;
wenzelm@385
   188
wenzelm@385
   189
fun print_axioms thy =
wenzelm@252
   190
  let
wenzelm@385
   191
    val {sign, ext_axtab, ...} = rep_theory thy;
wenzelm@385
   192
    val axioms = Symtab.dest ext_axtab;
lcp@229
   193
wenzelm@385
   194
    fun prt_axm (a, t) = Pretty.block [Pretty.str (a ^ ":"), Pretty.brk 1,
wenzelm@385
   195
      Pretty.quote (Sign.pretty_term sign t)];
wenzelm@252
   196
  in
wenzelm@385
   197
    Pretty.writeln (Pretty.big_list "additional axioms:" (map prt_axm axioms))
wenzelm@252
   198
  end;
lcp@229
   199
wenzelm@385
   200
fun print_theory thy = (print_sign thy; print_axioms thy);
wenzelm@385
   201
lcp@229
   202
lcp@229
   203
lcp@229
   204
(** Print thm A1,...,An/B in "goal style" -- premises as numbered subgoals **)
lcp@229
   205
lcp@229
   206
fun prettyprints es = writeln(Pretty.string_of(Pretty.blk(0,es)));
lcp@229
   207
lcp@229
   208
fun print_goals maxgoals th : unit =
lcp@229
   209
let val {sign, hyps, prop,...} = rep_thm th;
lcp@229
   210
    fun printgoals (_, []) = ()
lcp@229
   211
      | printgoals (n, A::As) =
wenzelm@252
   212
        let val prettyn = Pretty.str(" " ^ string_of_int n ^ ". ");
wenzelm@252
   213
            val prettyA = Sign.pretty_term sign A
wenzelm@252
   214
        in prettyprints[prettyn,prettyA];
wenzelm@252
   215
           printgoals (n+1,As)
lcp@229
   216
        end;
lcp@229
   217
    fun prettypair(t,u) =
lcp@229
   218
        Pretty.blk(0, [Sign.pretty_term sign t, Pretty.str" =?=", Pretty.brk 1,
wenzelm@252
   219
                       Sign.pretty_term sign u]);
lcp@229
   220
    fun printff [] = ()
lcp@229
   221
      | printff tpairs =
wenzelm@252
   222
         writeln("\nFlex-flex pairs:\n" ^
wenzelm@252
   223
                 Pretty.string_of(Pretty.lst("","") (map prettypair tpairs)))
lcp@229
   224
    val (tpairs,As,B) = Logic.strip_horn(prop);
lcp@229
   225
    val ngoals = length As
wenzelm@252
   226
in
lcp@229
   227
   writeln (Sign.string_of_term sign B);
lcp@229
   228
   if ngoals=0 then writeln"No subgoals!"
wenzelm@252
   229
   else if ngoals>maxgoals
lcp@229
   230
        then (printgoals (1, take(maxgoals,As));
wenzelm@252
   231
              writeln("A total of " ^ string_of_int ngoals ^ " subgoals..."))
lcp@229
   232
        else printgoals (1, As);
lcp@229
   233
   printff tpairs
lcp@229
   234
end;
lcp@229
   235
lcp@229
   236
(*"hook" for user interfaces: allows print_goals to be replaced*)
lcp@229
   237
val print_goals_ref = ref print_goals;
lcp@229
   238
wenzelm@252
   239
(*** Find the type (sort) associated with a (T)Var or (T)Free in a term
clasohm@0
   240
     Used for establishing default types (of variables) and sorts (of
clasohm@0
   241
     type variables) when reading another term.
clasohm@0
   242
     Index -1 indicates that a (T)Free rather than a (T)Var is wanted.
clasohm@0
   243
***)
clasohm@0
   244
clasohm@0
   245
fun types_sorts thm =
clasohm@0
   246
    let val {prop,hyps,...} = rep_thm thm;
wenzelm@252
   247
        val big = list_comb(prop,hyps); (* bogus term! *)
wenzelm@252
   248
        val vars = map dest_Var (term_vars big);
wenzelm@252
   249
        val frees = map dest_Free (term_frees big);
wenzelm@252
   250
        val tvars = term_tvars big;
wenzelm@252
   251
        val tfrees = term_tfrees big;
wenzelm@252
   252
        fun typ(a,i) = if i<0 then assoc(frees,a) else assoc(vars,(a,i));
wenzelm@252
   253
        fun sort(a,i) = if i<0 then assoc(tfrees,a) else assoc(tvars,(a,i));
clasohm@0
   254
    in (typ,sort) end;
clasohm@0
   255
clasohm@0
   256
(** Standardization of rules **)
clasohm@0
   257
clasohm@0
   258
(*Generalization over a list of variables, IGNORING bad ones*)
clasohm@0
   259
fun forall_intr_list [] th = th
clasohm@0
   260
  | forall_intr_list (y::ys) th =
wenzelm@252
   261
        let val gth = forall_intr_list ys th
wenzelm@252
   262
        in  forall_intr y gth   handle THM _ =>  gth  end;
clasohm@0
   263
clasohm@0
   264
(*Generalization over all suitable Free variables*)
clasohm@0
   265
fun forall_intr_frees th =
clasohm@0
   266
    let val {prop,sign,...} = rep_thm th
clasohm@0
   267
    in  forall_intr_list
wenzelm@252
   268
         (map (cterm_of sign) (sort atless (term_frees prop)))
clasohm@0
   269
         th
clasohm@0
   270
    end;
clasohm@0
   271
clasohm@0
   272
(*Replace outermost quantified variable by Var of given index.
clasohm@0
   273
    Could clash with Vars already present.*)
wenzelm@252
   274
fun forall_elim_var i th =
clasohm@0
   275
    let val {prop,sign,...} = rep_thm th
clasohm@0
   276
    in case prop of
wenzelm@252
   277
          Const("all",_) $ Abs(a,T,_) =>
wenzelm@252
   278
              forall_elim (cterm_of sign (Var((a,i), T)))  th
wenzelm@252
   279
        | _ => raise THM("forall_elim_var", i, [th])
clasohm@0
   280
    end;
clasohm@0
   281
clasohm@0
   282
(*Repeat forall_elim_var until all outer quantifiers are removed*)
wenzelm@252
   283
fun forall_elim_vars i th =
clasohm@0
   284
    forall_elim_vars i (forall_elim_var i th)
wenzelm@252
   285
        handle THM _ => th;
clasohm@0
   286
clasohm@0
   287
(*Specialization over a list of cterms*)
clasohm@0
   288
fun forall_elim_list cts th = foldr (uncurry forall_elim) (rev cts, th);
clasohm@0
   289
clasohm@0
   290
(* maps [A1,...,An], B   to   [| A1;...;An |] ==> B  *)
clasohm@0
   291
fun implies_intr_list cAs th = foldr (uncurry implies_intr) (cAs,th);
clasohm@0
   292
clasohm@0
   293
(* maps [| A1;...;An |] ==> B and [A1,...,An]   to   B *)
clasohm@0
   294
fun implies_elim_list impth ths = foldl (uncurry implies_elim) (impth,ths);
clasohm@0
   295
clasohm@0
   296
(*Reset Var indexes to zero, renaming to preserve distinctness*)
wenzelm@252
   297
fun zero_var_indexes th =
clasohm@0
   298
    let val {prop,sign,...} = rep_thm th;
clasohm@0
   299
        val vars = term_vars prop
clasohm@0
   300
        val bs = foldl add_new_id ([], map (fn Var((a,_),_)=>a) vars)
wenzelm@252
   301
        val inrs = add_term_tvars(prop,[]);
wenzelm@252
   302
        val nms' = rev(foldl add_new_id ([], map (#1 o #1) inrs));
wenzelm@252
   303
        val tye = map (fn ((v,rs),a) => (v, TVar((a,0),rs))) (inrs ~~ nms')
wenzelm@252
   304
        val ctye = map (fn (v,T) => (v,ctyp_of sign T)) tye;
wenzelm@252
   305
        fun varpairs([],[]) = []
wenzelm@252
   306
          | varpairs((var as Var(v,T)) :: vars, b::bs) =
wenzelm@252
   307
                let val T' = typ_subst_TVars tye T
wenzelm@252
   308
                in (cterm_of sign (Var(v,T')),
wenzelm@252
   309
                    cterm_of sign (Var((b,0),T'))) :: varpairs(vars,bs)
wenzelm@252
   310
                end
wenzelm@252
   311
          | varpairs _ = raise TERM("varpairs", []);
clasohm@0
   312
    in instantiate (ctye, varpairs(vars,rev bs)) th end;
clasohm@0
   313
clasohm@0
   314
clasohm@0
   315
(*Standard form of object-rule: no hypotheses, Frees, or outer quantifiers;
clasohm@0
   316
    all generality expressed by Vars having index 0.*)
clasohm@0
   317
fun standard th =
clasohm@0
   318
    let val {maxidx,...} = rep_thm th
wenzelm@252
   319
    in  varifyT (zero_var_indexes (forall_elim_vars(maxidx+1)
clasohm@0
   320
                         (forall_intr_frees(implies_intr_hyps th))))
clasohm@0
   321
    end;
clasohm@0
   322
wenzelm@252
   323
(*Assume a new formula, read following the same conventions as axioms.
clasohm@0
   324
  Generalizes over Free variables,
clasohm@0
   325
  creates the assumption, and then strips quantifiers.
clasohm@0
   326
  Example is [| ALL x:?A. ?P(x) |] ==> [| ?P(?a) |]
wenzelm@252
   327
             [ !(A,P,a)[| ALL x:A. P(x) |] ==> [| P(a) |] ]    *)
clasohm@0
   328
fun assume_ax thy sP =
clasohm@0
   329
    let val sign = sign_of thy
wenzelm@252
   330
        val prop = Logic.close_form (term_of (read_cterm sign
wenzelm@252
   331
                         (sP, propT)))
lcp@229
   332
    in forall_elim_vars 0 (assume (cterm_of sign prop))  end;
clasohm@0
   333
wenzelm@252
   334
(*Resolution: exactly one resolvent must be produced.*)
clasohm@0
   335
fun tha RSN (i,thb) =
clasohm@0
   336
  case Sequence.chop (2, biresolution false [(false,tha)] i thb) of
clasohm@0
   337
      ([th],_) => th
clasohm@0
   338
    | ([],_)   => raise THM("RSN: no unifiers", i, [tha,thb])
clasohm@0
   339
    |      _   => raise THM("RSN: multiple unifiers", i, [tha,thb]);
clasohm@0
   340
clasohm@0
   341
(*resolution: P==>Q, Q==>R gives P==>R. *)
clasohm@0
   342
fun tha RS thb = tha RSN (1,thb);
clasohm@0
   343
clasohm@0
   344
(*For joining lists of rules*)
wenzelm@252
   345
fun thas RLN (i,thbs) =
clasohm@0
   346
  let val resolve = biresolution false (map (pair false) thas) i
clasohm@0
   347
      fun resb thb = Sequence.list_of_s (resolve thb) handle THM _ => []
clasohm@0
   348
  in  flat (map resb thbs)  end;
clasohm@0
   349
clasohm@0
   350
fun thas RL thbs = thas RLN (1,thbs);
clasohm@0
   351
lcp@11
   352
(*Resolve a list of rules against bottom_rl from right to left;
lcp@11
   353
  makes proof trees*)
wenzelm@252
   354
fun rls MRS bottom_rl =
lcp@11
   355
  let fun rs_aux i [] = bottom_rl
wenzelm@252
   356
        | rs_aux i (rl::rls) = rl RSN (i, rs_aux (i+1) rls)
lcp@11
   357
  in  rs_aux 1 rls  end;
lcp@11
   358
lcp@11
   359
(*As above, but for rule lists*)
wenzelm@252
   360
fun rlss MRL bottom_rls =
lcp@11
   361
  let fun rs_aux i [] = bottom_rls
wenzelm@252
   362
        | rs_aux i (rls::rlss) = rls RLN (i, rs_aux (i+1) rlss)
lcp@11
   363
  in  rs_aux 1 rlss  end;
lcp@11
   364
wenzelm@252
   365
(*compose Q and [...,Qi,Q(i+1),...]==>R to [...,Q(i+1),...]==>R
clasohm@0
   366
  with no lifting or renaming!  Q may contain ==> or meta-quants
clasohm@0
   367
  ALWAYS deletes premise i *)
wenzelm@252
   368
fun compose(tha,i,thb) =
clasohm@0
   369
    Sequence.list_of_s (bicompose false (false,tha,0) i thb);
clasohm@0
   370
clasohm@0
   371
(*compose Q and [Q1,Q2,...,Qk]==>R to [Q2,...,Qk]==>R getting unique result*)
clasohm@0
   372
fun tha COMP thb =
clasohm@0
   373
    case compose(tha,1,thb) of
wenzelm@252
   374
        [th] => th
clasohm@0
   375
      | _ =>   raise THM("COMP", 1, [tha,thb]);
clasohm@0
   376
clasohm@0
   377
(*Instantiate theorem th, reading instantiations under signature sg*)
clasohm@0
   378
fun read_instantiate_sg sg sinsts th =
clasohm@0
   379
    let val ts = types_sorts th;
lcp@229
   380
    in  instantiate (read_insts sg ts ts sinsts) th  end;
clasohm@0
   381
clasohm@0
   382
(*Instantiate theorem th, reading instantiations under theory of th*)
clasohm@0
   383
fun read_instantiate sinsts th =
clasohm@0
   384
    read_instantiate_sg (#sign (rep_thm th)) sinsts th;
clasohm@0
   385
clasohm@0
   386
clasohm@0
   387
(*Left-to-right replacements: tpairs = [...,(vi,ti),...].
clasohm@0
   388
  Instantiates distinct Vars by terms, inferring type instantiations. *)
clasohm@0
   389
local
clasohm@0
   390
  fun add_types ((ct,cu), (sign,tye)) =
lcp@229
   391
    let val {sign=signt, t=t, T= T, ...} = rep_cterm ct
lcp@229
   392
        and {sign=signu, t=u, T= U, ...} = rep_cterm cu
clasohm@0
   393
        val sign' = Sign.merge(sign, Sign.merge(signt, signu))
wenzelm@252
   394
        val tye' = Type.unify (#tsig(Sign.rep_sg sign')) ((T,U), tye)
wenzelm@252
   395
          handle Type.TUNIFY => raise TYPE("add_types", [T,U], [t,u])
clasohm@0
   396
    in  (sign', tye')  end;
clasohm@0
   397
in
wenzelm@252
   398
fun cterm_instantiate ctpairs0 th =
clasohm@0
   399
  let val (sign,tye) = foldr add_types (ctpairs0, (#sign(rep_thm th),[]))
clasohm@0
   400
      val tsig = #tsig(Sign.rep_sg sign);
clasohm@0
   401
      fun instT(ct,cu) = let val inst = subst_TVars tye
wenzelm@252
   402
                         in (cterm_fun inst ct, cterm_fun inst cu) end
lcp@229
   403
      fun ctyp2 (ix,T) = (ix, ctyp_of sign T)
clasohm@0
   404
  in  instantiate (map ctyp2 tye, map instT ctpairs0) th  end
wenzelm@252
   405
  handle TERM _ =>
clasohm@0
   406
           raise THM("cterm_instantiate: incompatible signatures",0,[th])
clasohm@0
   407
       | TYPE _ => raise THM("cterm_instantiate: types", 0, [th])
clasohm@0
   408
end;
clasohm@0
   409
clasohm@0
   410
clasohm@0
   411
(** theorem equality test is exported and used by BEST_FIRST **)
clasohm@0
   412
wenzelm@252
   413
(*equality of theorems uses equality of signatures and
clasohm@0
   414
  the a-convertible test for terms*)
wenzelm@252
   415
fun eq_thm (th1,th2) =
clasohm@0
   416
    let val {sign=sg1, hyps=hyps1, prop=prop1, ...} = rep_thm th1
wenzelm@252
   417
        and {sign=sg2, hyps=hyps2, prop=prop2, ...} = rep_thm th2
wenzelm@252
   418
    in  Sign.eq_sg (sg1,sg2) andalso
wenzelm@252
   419
        aconvs(hyps1,hyps2) andalso
wenzelm@252
   420
        prop1 aconv prop2
clasohm@0
   421
    end;
clasohm@0
   422
clasohm@0
   423
(*Do the two theorems have the same signature?*)
wenzelm@252
   424
fun eq_thm_sg (th1,th2) = Sign.eq_sg(#sign(rep_thm th1), #sign(rep_thm th2));
clasohm@0
   425
clasohm@0
   426
(*Useful "distance" function for BEST_FIRST*)
clasohm@0
   427
val size_of_thm = size_of_term o #prop o rep_thm;
clasohm@0
   428
clasohm@0
   429
clasohm@0
   430
(*** Meta-Rewriting Rules ***)
clasohm@0
   431
clasohm@0
   432
clasohm@0
   433
val reflexive_thm =
wenzelm@385
   434
  let val cx = cterm_of Sign.pure (Var(("x",0),TVar(("'a",0),logicS)))
clasohm@0
   435
  in Thm.reflexive cx end;
clasohm@0
   436
clasohm@0
   437
val symmetric_thm =
lcp@229
   438
  let val xy = read_cterm Sign.pure ("x::'a::logic == y",propT)
clasohm@0
   439
  in standard(Thm.implies_intr_hyps(Thm.symmetric(Thm.assume xy))) end;
clasohm@0
   440
clasohm@0
   441
val transitive_thm =
lcp@229
   442
  let val xy = read_cterm Sign.pure ("x::'a::logic == y",propT)
lcp@229
   443
      val yz = read_cterm Sign.pure ("y::'a::logic == z",propT)
clasohm@0
   444
      val xythm = Thm.assume xy and yzthm = Thm.assume yz
clasohm@0
   445
  in standard(Thm.implies_intr yz (Thm.transitive xythm yzthm)) end;
clasohm@0
   446
lcp@229
   447
(** Below, a "conversion" has type cterm -> thm **)
lcp@229
   448
lcp@229
   449
val refl_cimplies = reflexive (cterm_of Sign.pure implies);
clasohm@0
   450
clasohm@0
   451
(*In [A1,...,An]==>B, rewrite the selected A's only -- for rewrite_goals_tac*)
nipkow@214
   452
(*Do not rewrite flex-flex pairs*)
wenzelm@252
   453
fun goals_conv pred cv =
lcp@229
   454
  let fun gconv i ct =
lcp@229
   455
        let val (A,B) = Thm.dest_cimplies ct
lcp@229
   456
            val (thA,j) = case term_of A of
lcp@229
   457
                  Const("=?=",_)$_$_ => (reflexive A, i)
lcp@229
   458
                | _ => (if pred i then cv A else reflexive A, i+1)
wenzelm@252
   459
        in  combination (combination refl_cimplies thA) (gconv j B) end
lcp@229
   460
        handle TERM _ => reflexive ct
clasohm@0
   461
  in gconv 1 end;
clasohm@0
   462
clasohm@0
   463
(*Use a conversion to transform a theorem*)
lcp@229
   464
fun fconv_rule cv th = equal_elim (cv (cprop_of th)) th;
clasohm@0
   465
clasohm@0
   466
(*rewriting conversion*)
lcp@229
   467
fun rew_conv mode prover mss = rewrite_cterm mode mss prover;
clasohm@0
   468
clasohm@0
   469
(*Rewrite a theorem*)
nipkow@214
   470
fun rewrite_rule thms =
nipkow@214
   471
  fconv_rule (rew_conv (true,false) (K(K None)) (Thm.mss_of thms));
clasohm@0
   472
clasohm@0
   473
(*Rewrite the subgoals of a proof state (represented by a theorem) *)
clasohm@0
   474
fun rewrite_goals_rule thms =
nipkow@214
   475
  fconv_rule (goals_conv (K true) (rew_conv (true,false) (K(K None))
nipkow@214
   476
             (Thm.mss_of thms)));
clasohm@0
   477
clasohm@0
   478
(*Rewrite the subgoal of a proof state (represented by a theorem) *)
nipkow@214
   479
fun rewrite_goal_rule mode prover mss i thm =
nipkow@214
   480
  if 0 < i  andalso  i <= nprems_of thm
nipkow@214
   481
  then fconv_rule (goals_conv (fn j => j=i) (rew_conv mode prover mss)) thm
nipkow@214
   482
  else raise THM("rewrite_goal_rule",i,[thm]);
clasohm@0
   483
clasohm@0
   484
clasohm@0
   485
(** Derived rules mainly for METAHYPS **)
clasohm@0
   486
clasohm@0
   487
(*Given the term "a", takes (%x.t)==(%x.u) to t[a/x]==u[a/x]*)
clasohm@0
   488
fun equal_abs_elim ca eqth =
lcp@229
   489
  let val {sign=signa, t=a, ...} = rep_cterm ca
clasohm@0
   490
      and combth = combination eqth (reflexive ca)
clasohm@0
   491
      val {sign,prop,...} = rep_thm eqth
clasohm@0
   492
      val (abst,absu) = Logic.dest_equals prop
lcp@229
   493
      val cterm = cterm_of (Sign.merge (sign,signa))
clasohm@0
   494
  in  transitive (symmetric (beta_conversion (cterm (abst$a))))
clasohm@0
   495
           (transitive combth (beta_conversion (cterm (absu$a))))
clasohm@0
   496
  end
clasohm@0
   497
  handle THM _ => raise THM("equal_abs_elim", 0, [eqth]);
clasohm@0
   498
clasohm@0
   499
(*Calling equal_abs_elim with multiple terms*)
clasohm@0
   500
fun equal_abs_elim_list cts th = foldr (uncurry equal_abs_elim) (rev cts, th);
clasohm@0
   501
clasohm@0
   502
local
clasohm@0
   503
  open Logic
clasohm@0
   504
  val alpha = TVar(("'a",0), [])     (*  type ?'a::{}  *)
clasohm@0
   505
  fun err th = raise THM("flexpair_inst: ", 0, [th])
clasohm@0
   506
  fun flexpair_inst def th =
clasohm@0
   507
    let val {prop = Const _ $ t $ u,  sign,...} = rep_thm th
wenzelm@252
   508
        val cterm = cterm_of sign
wenzelm@252
   509
        fun cvar a = cterm(Var((a,0),alpha))
wenzelm@252
   510
        val def' = cterm_instantiate [(cvar"t", cterm t), (cvar"u", cterm u)]
wenzelm@252
   511
                   def
clasohm@0
   512
    in  equal_elim def' th
clasohm@0
   513
    end
clasohm@0
   514
    handle THM _ => err th | bind => err th
clasohm@0
   515
in
clasohm@0
   516
val flexpair_intr = flexpair_inst (symmetric flexpair_def)
clasohm@0
   517
and flexpair_elim = flexpair_inst flexpair_def
clasohm@0
   518
end;
clasohm@0
   519
clasohm@0
   520
(*Version for flexflex pairs -- this supports lifting.*)
wenzelm@252
   521
fun flexpair_abs_elim_list cts =
clasohm@0
   522
    flexpair_intr o equal_abs_elim_list cts o flexpair_elim;
clasohm@0
   523
clasohm@0
   524
clasohm@0
   525
(*** Some useful meta-theorems ***)
clasohm@0
   526
clasohm@0
   527
(*The rule V/V, obtains assumption solving for eresolve_tac*)
lcp@229
   528
val asm_rl = trivial(read_cterm Sign.pure ("PROP ?psi",propT));
clasohm@0
   529
clasohm@0
   530
(*Meta-level cut rule: [| V==>W; V |] ==> W *)
wenzelm@252
   531
val cut_rl = trivial(read_cterm Sign.pure
wenzelm@252
   532
        ("PROP ?psi ==> PROP ?theta", propT));
clasohm@0
   533
wenzelm@252
   534
(*Generalized elim rule for one conclusion; cut_rl with reversed premises:
clasohm@0
   535
     [| PROP V;  PROP V ==> PROP W |] ==> PROP W *)
clasohm@0
   536
val revcut_rl =
lcp@229
   537
  let val V = read_cterm Sign.pure ("PROP V", propT)
lcp@229
   538
      and VW = read_cterm Sign.pure ("PROP V ==> PROP W", propT);
wenzelm@252
   539
  in  standard (implies_intr V
wenzelm@252
   540
                (implies_intr VW
wenzelm@252
   541
                 (implies_elim (assume VW) (assume V))))
clasohm@0
   542
  end;
clasohm@0
   543
clasohm@0
   544
(* (!!x. PROP ?V) == PROP ?V       Allows removal of redundant parameters*)
clasohm@0
   545
val triv_forall_equality =
lcp@229
   546
  let val V  = read_cterm Sign.pure ("PROP V", propT)
lcp@229
   547
      and QV = read_cterm Sign.pure ("!!x::'a. PROP V", propT)
wenzelm@385
   548
      and x  = read_cterm Sign.pure ("x", TFree("'a",logicS));
clasohm@0
   549
  in  standard (equal_intr (implies_intr QV (forall_elim x (assume QV)))
wenzelm@252
   550
                           (implies_intr V  (forall_intr x (assume V))))
clasohm@0
   551
  end;
clasohm@0
   552
clasohm@0
   553
end
clasohm@0
   554
end;
wenzelm@252
   555