src/Pure/thm.ML
author lcp
Wed Apr 06 16:36:34 1994 +0200 (1994-04-06)
changeset 309 3751567696bf
parent 305 4c2bbb5de471
child 387 69f4356d915d
permissions -rw-r--r--
restored the signature constraint :THM
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@250
     6
The abstract types "theory" and "thm".
wenzelm@250
     7
Also "cterm" / "ctyp" (certified terms / typs under a signature).
clasohm@0
     8
*)
clasohm@0
     9
wenzelm@250
    10
signature THM =
wenzelm@250
    11
sig
clasohm@0
    12
  structure Envir : ENVIR
clasohm@0
    13
  structure Sequence : SEQUENCE
clasohm@0
    14
  structure Sign : SIGN
lcp@229
    15
  type cterm
lcp@229
    16
  type ctyp
clasohm@0
    17
  type meta_simpset
clasohm@0
    18
  type theory
clasohm@0
    19
  type thm
clasohm@0
    20
  exception THM of string * int * thm list
clasohm@0
    21
  exception THEORY of string * theory list
clasohm@0
    22
  exception SIMPLIFIER of string * thm
lcp@229
    23
  (*Certified terms/types; previously in sign.ML*)
lcp@229
    24
  val cterm_of: Sign.sg -> term -> cterm
lcp@229
    25
  val ctyp_of: Sign.sg -> typ -> ctyp
wenzelm@250
    26
  val read_ctyp: Sign.sg -> string -> ctyp
lcp@229
    27
  val read_cterm: Sign.sg -> string * typ -> cterm
lcp@229
    28
  val rep_cterm: cterm -> {T: typ, t: term, sign: Sign.sg, maxidx: int}
lcp@229
    29
  val rep_ctyp: ctyp -> {T: typ, sign: Sign.sg}
lcp@229
    30
  val term_of: cterm -> term
lcp@229
    31
  val typ_of: ctyp -> typ
wenzelm@250
    32
  val cterm_fun: (term -> term) -> (cterm -> cterm)
wenzelm@250
    33
  (*End of cterm/ctyp functions*)
lcp@229
    34
  val abstract_rule: string -> cterm -> thm -> thm
clasohm@0
    35
  val add_congs: meta_simpset * thm list -> meta_simpset
clasohm@0
    36
  val add_prems: meta_simpset * thm list -> meta_simpset
clasohm@0
    37
  val add_simps: meta_simpset * thm list -> meta_simpset
lcp@229
    38
  val assume: cterm -> thm
wenzelm@250
    39
  val assumption: int -> thm -> thm Sequence.seq
clasohm@0
    40
  val axioms_of: theory -> (string * thm) list
wenzelm@250
    41
  val beta_conversion: cterm -> thm
wenzelm@250
    42
  val bicompose: bool -> bool * thm * int -> int -> thm -> thm Sequence.seq
wenzelm@250
    43
  val biresolution: bool -> (bool*thm)list -> int -> thm -> thm Sequence.seq
wenzelm@250
    44
  val combination: thm -> thm -> thm
wenzelm@250
    45
  val concl_of: thm -> term
lcp@229
    46
  val cprop_of: thm -> cterm
nipkow@87
    47
  val del_simps: meta_simpset * thm list -> meta_simpset
lcp@229
    48
  val dest_cimplies: cterm -> cterm*cterm
clasohm@0
    49
  val dest_state: thm * int -> (term*term)list * term list * term * term
clasohm@0
    50
  val empty_mss: meta_simpset
wenzelm@250
    51
  val eq_assumption: int -> thm -> thm
clasohm@0
    52
  val equal_intr: thm -> thm -> thm
clasohm@0
    53
  val equal_elim: thm -> thm -> thm
clasohm@0
    54
  val extend_theory: theory -> string
wenzelm@250
    55
        -> (class * class list) list * sort
wenzelm@250
    56
           * (string list * int)list
wenzelm@250
    57
           * (string * string list * string) list
wenzelm@250
    58
           * (string list * (sort list * class))list
wenzelm@250
    59
           * (string list * string)list * Sign.Syntax.sext option
wenzelm@250
    60
        -> (string*string)list -> theory
wenzelm@250
    61
  val extensional: thm -> thm
wenzelm@250
    62
  val flexflex_rule: thm -> thm Sequence.seq
wenzelm@250
    63
  val flexpair_def: thm
lcp@229
    64
  val forall_elim: cterm -> thm -> thm
lcp@229
    65
  val forall_intr: cterm -> thm -> thm
clasohm@0
    66
  val freezeT: thm -> thm
clasohm@0
    67
  val get_axiom: theory -> string -> thm
clasohm@0
    68
  val implies_elim: thm -> thm -> thm
lcp@229
    69
  val implies_intr: cterm -> thm -> thm
clasohm@0
    70
  val implies_intr_hyps: thm -> thm
wenzelm@250
    71
  val instantiate: (indexname*ctyp)list * (cterm*cterm)list
clasohm@0
    72
                   -> thm -> thm
clasohm@0
    73
  val lift_rule: (thm * int) -> thm -> thm
clasohm@0
    74
  val merge_theories: theory * theory -> theory
clasohm@0
    75
  val mk_rews_of_mss: meta_simpset -> thm -> thm list
clasohm@0
    76
  val mss_of: thm list -> meta_simpset
clasohm@0
    77
  val nprems_of: thm -> int
clasohm@0
    78
  val parents_of: theory -> theory list
clasohm@0
    79
  val prems_of: thm -> term list
clasohm@0
    80
  val prems_of_mss: meta_simpset -> thm list
clasohm@0
    81
  val pure_thy: theory
lcp@229
    82
  val read_def_cterm :
lcp@229
    83
         Sign.sg * (indexname -> typ option) * (indexname -> sort option) ->
lcp@229
    84
         string * typ -> cterm * (indexname * typ) list
wenzelm@250
    85
   val reflexive: cterm -> thm
clasohm@0
    86
  val rename_params_rule: string list * int -> thm -> thm
clasohm@0
    87
  val rep_thm: thm -> {prop: term, hyps: term list, maxidx: int, sign: Sign.sg}
nipkow@214
    88
  val rewrite_cterm:
nipkow@214
    89
         bool*bool -> meta_simpset -> (meta_simpset -> thm -> thm option)
lcp@229
    90
           -> cterm -> thm
clasohm@0
    91
  val set_mk_rews: meta_simpset * (thm -> thm list) -> meta_simpset
wenzelm@250
    92
  val sign_of: theory -> Sign.sg
clasohm@0
    93
  val syn_of: theory -> Sign.Syntax.syntax
clasohm@0
    94
  val stamps_of_thm: thm -> string ref list
clasohm@0
    95
  val stamps_of_thy: theory -> string ref list
wenzelm@250
    96
  val symmetric: thm -> thm
clasohm@0
    97
  val tpairs_of: thm -> (term*term)list
clasohm@0
    98
  val trace_simp: bool ref
clasohm@0
    99
  val transitive: thm -> thm -> thm
lcp@229
   100
  val trivial: cterm -> thm
clasohm@0
   101
  val varifyT: thm -> thm
wenzelm@250
   102
end;
clasohm@0
   103
wenzelm@250
   104
functor ThmFun (structure Logic: LOGIC and Unify: UNIFY and Pattern: PATTERN
lcp@309
   105
  and Net:NET sharing type Pattern.type_sig = Unify.Sign.Type.type_sig) : THM =
clasohm@0
   106
struct
wenzelm@250
   107
clasohm@0
   108
structure Sequence = Unify.Sequence;
clasohm@0
   109
structure Envir = Unify.Envir;
clasohm@0
   110
structure Sign = Unify.Sign;
clasohm@0
   111
structure Type = Sign.Type;
clasohm@0
   112
structure Syntax = Sign.Syntax;
clasohm@0
   113
structure Symtab = Sign.Symtab;
clasohm@0
   114
clasohm@0
   115
wenzelm@250
   116
(** certified types **)
wenzelm@250
   117
wenzelm@250
   118
(*certified typs under a signature*)
wenzelm@250
   119
wenzelm@250
   120
datatype ctyp = Ctyp of {sign: Sign.sg, T: typ};
wenzelm@250
   121
wenzelm@250
   122
fun rep_ctyp (Ctyp args) = args;
wenzelm@250
   123
fun typ_of (Ctyp {T, ...}) = T;
wenzelm@250
   124
wenzelm@250
   125
fun ctyp_of sign T =
wenzelm@250
   126
  Ctyp {sign = sign, T = Sign.certify_typ sign T};
wenzelm@250
   127
wenzelm@250
   128
fun read_ctyp sign s =
wenzelm@250
   129
  Ctyp {sign = sign, T = Sign.read_typ (sign, K None) s};
lcp@229
   130
lcp@229
   131
lcp@229
   132
wenzelm@250
   133
(** certified terms **)
lcp@229
   134
wenzelm@250
   135
(*certified terms under a signature, with checked typ and maxidx of Vars*)
lcp@229
   136
wenzelm@250
   137
datatype cterm = Cterm of {sign: Sign.sg, t: term, T: typ, maxidx: int};
lcp@229
   138
lcp@229
   139
fun rep_cterm (Cterm args) = args;
wenzelm@250
   140
fun term_of (Cterm {t, ...}) = t;
lcp@229
   141
wenzelm@250
   142
(*create a cterm by checking a "raw" term with respect to a signature*)
wenzelm@250
   143
fun cterm_of sign tm =
wenzelm@250
   144
  let val (t, T, maxidx) = Sign.certify_term sign tm
wenzelm@250
   145
  in Cterm {sign = sign, t = t, T = T, maxidx = maxidx}
wenzelm@250
   146
  end handle TYPE (msg, _, _)
wenzelm@250
   147
    => raise TERM ("Term not in signature\n" ^ msg, [tm]);
lcp@229
   148
wenzelm@250
   149
fun cterm_fun f (Cterm {sign, t, ...}) = cterm_of sign (f t);
wenzelm@250
   150
lcp@229
   151
wenzelm@250
   152
(*dest_implies for cterms. Note T=prop below*)
wenzelm@250
   153
fun dest_cimplies (Cterm{sign, T, maxidx, t=Const("==>", _) $ A $ B}) =
lcp@229
   154
       (Cterm{sign=sign, T=T, maxidx=maxidx, t=A},
wenzelm@250
   155
        Cterm{sign=sign, T=T, maxidx=maxidx, t=B})
wenzelm@250
   156
  | dest_cimplies ct = raise TERM ("dest_cimplies", [term_of ct]);
lcp@229
   157
wenzelm@250
   158
lcp@229
   159
wenzelm@250
   160
(** read cterms **)
wenzelm@250
   161
wenzelm@250
   162
(*read term, infer types, certify term*)
wenzelm@250
   163
wenzelm@250
   164
fun read_def_cterm (sign, types, sorts) (a, T) =
wenzelm@250
   165
  let
wenzelm@250
   166
    val {tsig, const_tab, syn, ...} = Sign.rep_sg sign;
wenzelm@250
   167
    val showtyp = Sign.string_of_typ sign;
wenzelm@250
   168
    val showterm = Sign.string_of_term sign;
wenzelm@250
   169
wenzelm@250
   170
    fun termerr [] = ""
wenzelm@250
   171
      | termerr [t] = "\nInvolving this term:\n" ^ showterm t
wenzelm@250
   172
      | termerr ts = "\nInvolving these terms:\n" ^ cat_lines (map showterm ts);
wenzelm@250
   173
wenzelm@250
   174
    val T' = Sign.certify_typ sign T
wenzelm@250
   175
      handle TYPE (msg, _, _) => error msg;
wenzelm@250
   176
    val t = Syntax.read syn T' a;
wenzelm@250
   177
    val (t', tye) = Type.infer_types (tsig, const_tab, types, sorts, T', t)
wenzelm@250
   178
      handle TYPE (msg, Ts, ts) => error ("Type checking error: " ^ msg ^ "\n"
wenzelm@250
   179
        ^ cat_lines (map showtyp Ts) ^ termerr ts);
wenzelm@250
   180
    val ct = cterm_of sign t' handle TERM (msg, _) => error msg;
wenzelm@250
   181
  in (ct, tye) end;
lcp@229
   182
lcp@229
   183
fun read_cterm sign = #1 o (read_def_cterm (sign, K None, K None));
lcp@229
   184
wenzelm@250
   185
wenzelm@250
   186
lcp@229
   187
(**** META-THEOREMS ****)
lcp@229
   188
clasohm@0
   189
datatype thm = Thm of
wenzelm@250
   190
  {sign: Sign.sg, maxidx: int, hyps: term list, prop: term};
clasohm@0
   191
wenzelm@250
   192
fun rep_thm (Thm args) = args;
clasohm@0
   193
clasohm@0
   194
(*Errors involving theorems*)
clasohm@0
   195
exception THM of string * int * thm list;
clasohm@0
   196
clasohm@0
   197
(*maps object-rule to tpairs *)
clasohm@0
   198
fun tpairs_of (Thm{prop,...}) = #1 (Logic.strip_flexpairs prop);
clasohm@0
   199
clasohm@0
   200
(*maps object-rule to premises *)
clasohm@0
   201
fun prems_of (Thm{prop,...}) =
clasohm@0
   202
    Logic.strip_imp_prems (Logic.skip_flexpairs prop);
clasohm@0
   203
clasohm@0
   204
(*counts premises in a rule*)
clasohm@0
   205
fun nprems_of (Thm{prop,...}) =
clasohm@0
   206
    Logic.count_prems (Logic.skip_flexpairs prop, 0);
clasohm@0
   207
clasohm@0
   208
(*maps object-rule to conclusion *)
clasohm@0
   209
fun concl_of (Thm{prop,...}) = Logic.strip_imp_concl prop;
clasohm@0
   210
lcp@229
   211
(*The statement of any Thm is a Cterm*)
wenzelm@250
   212
fun cprop_of (Thm{sign,maxidx,hyps,prop}) =
wenzelm@250
   213
        Cterm{sign=sign, maxidx=maxidx, T=propT, t=prop};
lcp@229
   214
clasohm@0
   215
(*Stamps associated with a signature*)
clasohm@0
   216
val stamps_of_thm = #stamps o Sign.rep_sg o #sign o rep_thm;
clasohm@0
   217
clasohm@0
   218
(*Theories.  There is one pure theory.
clasohm@0
   219
  A theory can be extended.  Two theories can be merged.*)
clasohm@0
   220
datatype theory =
clasohm@0
   221
    Pure of {sign: Sign.sg}
clasohm@0
   222
  | Extend of {sign: Sign.sg,  axioms: thm Symtab.table,  thy: theory}
clasohm@0
   223
  | Merge of {sign: Sign.sg,  thy1: theory,  thy2: theory};
clasohm@0
   224
clasohm@0
   225
(*Errors involving theories*)
clasohm@0
   226
exception THEORY of string * theory list;
clasohm@0
   227
clasohm@0
   228
fun sign_of (Pure {sign}) = sign
clasohm@0
   229
  | sign_of (Extend {sign,...}) = sign
clasohm@0
   230
  | sign_of (Merge {sign,...}) = sign;
clasohm@0
   231
clasohm@0
   232
val syn_of = #syn o Sign.rep_sg o sign_of;
clasohm@0
   233
clasohm@0
   234
(*return the axioms of a theory and its ancestors*)
clasohm@0
   235
fun axioms_of (Pure _) = []
wenzelm@250
   236
  | axioms_of (Extend {axioms, thy, ...}) =
wenzelm@250
   237
      axioms_of thy @ Symtab.alist_of axioms
wenzelm@250
   238
  | axioms_of (Merge {thy1, thy2, ...}) = axioms_of thy1 @ axioms_of thy2;
clasohm@0
   239
clasohm@0
   240
(*return the immediate ancestors -- also distinguishes the kinds of theories*)
clasohm@0
   241
fun parents_of (Pure _) = []
clasohm@0
   242
  | parents_of (Extend{thy,...}) = [thy]
clasohm@0
   243
  | parents_of (Merge{thy1,thy2,...}) = [thy1,thy2];
clasohm@0
   244
clasohm@0
   245
clasohm@0
   246
(*Merge theories of two theorems.  Raise exception if incompatible.
clasohm@0
   247
  Prefers (via Sign.merge) the signature of th1.  *)
clasohm@0
   248
fun merge_theories(th1,th2) =
clasohm@0
   249
  let val Thm{sign=sign1,...} = th1 and Thm{sign=sign2,...} = th2
clasohm@0
   250
  in  Sign.merge (sign1,sign2)  end
clasohm@0
   251
  handle TERM _ => raise THM("incompatible signatures", 0, [th1,th2]);
clasohm@0
   252
clasohm@0
   253
(*Stamps associated with a theory*)
clasohm@0
   254
val stamps_of_thy = #stamps o Sign.rep_sg o sign_of;
clasohm@0
   255
clasohm@0
   256
clasohm@0
   257
(**** Primitive rules ****)
clasohm@0
   258
clasohm@0
   259
(* discharge all assumptions t from ts *)
clasohm@0
   260
val disch = gen_rem (op aconv);
clasohm@0
   261
clasohm@0
   262
(*The assumption rule A|-A in a theory  *)
wenzelm@250
   263
fun assume ct : thm =
lcp@229
   264
  let val {sign, t=prop, T, maxidx} = rep_cterm ct
wenzelm@250
   265
  in  if T<>propT then
wenzelm@250
   266
        raise THM("assume: assumptions must have type prop", 0, [])
clasohm@0
   267
      else if maxidx <> ~1 then
wenzelm@250
   268
        raise THM("assume: assumptions may not contain scheme variables",
wenzelm@250
   269
                  maxidx, [])
clasohm@0
   270
      else Thm{sign = sign, maxidx = ~1, hyps = [prop], prop = prop}
clasohm@0
   271
  end;
clasohm@0
   272
wenzelm@250
   273
(* Implication introduction
wenzelm@250
   274
              A |- B
wenzelm@250
   275
              -------
wenzelm@250
   276
              A ==> B    *)
clasohm@0
   277
fun implies_intr cA (thB as Thm{sign,maxidx,hyps,prop}) : thm =
lcp@229
   278
  let val {sign=signA, t=A, T, maxidx=maxidxA} = rep_cterm cA
clasohm@0
   279
  in  if T<>propT then
wenzelm@250
   280
        raise THM("implies_intr: assumptions must have type prop", 0, [thB])
wenzelm@250
   281
      else Thm{sign= Sign.merge (sign,signA),  maxidx= max[maxidxA, maxidx],
wenzelm@250
   282
             hyps= disch(hyps,A),  prop= implies$A$prop}
clasohm@0
   283
      handle TERM _ =>
clasohm@0
   284
        raise THM("implies_intr: incompatible signatures", 0, [thB])
clasohm@0
   285
  end;
clasohm@0
   286
clasohm@0
   287
(* Implication elimination
wenzelm@250
   288
        A ==> B       A
wenzelm@250
   289
        ---------------
wenzelm@250
   290
                B      *)
clasohm@0
   291
fun implies_elim thAB thA : thm =
clasohm@0
   292
    let val Thm{maxidx=maxA, hyps=hypsA, prop=propA,...} = thA
wenzelm@250
   293
        and Thm{sign, maxidx, hyps, prop,...} = thAB;
wenzelm@250
   294
        fun err(a) = raise THM("implies_elim: "^a, 0, [thAB,thA])
clasohm@0
   295
    in  case prop of
wenzelm@250
   296
            imp$A$B =>
wenzelm@250
   297
                if imp=implies andalso  A aconv propA
wenzelm@250
   298
                then  Thm{sign= merge_theories(thAB,thA),
wenzelm@250
   299
                          maxidx= max[maxA,maxidx],
wenzelm@250
   300
                          hyps= hypsA union hyps,  (*dups suppressed*)
wenzelm@250
   301
                          prop= B}
wenzelm@250
   302
                else err("major premise")
wenzelm@250
   303
          | _ => err("major premise")
clasohm@0
   304
    end;
wenzelm@250
   305
clasohm@0
   306
(* Forall introduction.  The Free or Var x must not be free in the hypotheses.
clasohm@0
   307
     A
clasohm@0
   308
   ------
clasohm@0
   309
   !!x.A       *)
clasohm@0
   310
fun forall_intr cx (th as Thm{sign,maxidx,hyps,prop}) =
lcp@229
   311
  let val x = term_of cx;
clasohm@0
   312
      fun result(a,T) = Thm{sign= sign, maxidx= maxidx, hyps= hyps,
wenzelm@250
   313
                            prop= all(T) $ Abs(a, T, abstract_over (x,prop))}
clasohm@0
   314
  in  case x of
wenzelm@250
   315
        Free(a,T) =>
wenzelm@250
   316
          if exists (apl(x, Logic.occs)) hyps
wenzelm@250
   317
          then  raise THM("forall_intr: variable free in assumptions", 0, [th])
wenzelm@250
   318
          else  result(a,T)
clasohm@0
   319
      | Var((a,_),T) => result(a,T)
clasohm@0
   320
      | _ => raise THM("forall_intr: not a variable", 0, [th])
clasohm@0
   321
  end;
clasohm@0
   322
clasohm@0
   323
(* Forall elimination
wenzelm@250
   324
              !!x.A
wenzelm@250
   325
             --------
wenzelm@250
   326
              A[t/x]     *)
clasohm@0
   327
fun forall_elim ct (th as Thm{sign,maxidx,hyps,prop}) : thm =
lcp@229
   328
  let val {sign=signt, t, T, maxidx=maxt} = rep_cterm ct
clasohm@0
   329
  in  case prop of
wenzelm@250
   330
          Const("all",Type("fun",[Type("fun",[qary,_]),_])) $ A =>
wenzelm@250
   331
            if T<>qary then
wenzelm@250
   332
                raise THM("forall_elim: type mismatch", 0, [th])
wenzelm@250
   333
            else Thm{sign= Sign.merge(sign,signt),
wenzelm@250
   334
                     maxidx= max[maxidx, maxt],
wenzelm@250
   335
                     hyps= hyps,  prop= betapply(A,t)}
wenzelm@250
   336
        | _ => raise THM("forall_elim: not quantified", 0, [th])
clasohm@0
   337
  end
clasohm@0
   338
  handle TERM _ =>
wenzelm@250
   339
         raise THM("forall_elim: incompatible signatures", 0, [th]);
clasohm@0
   340
clasohm@0
   341
clasohm@0
   342
(*** Equality ***)
clasohm@0
   343
clasohm@0
   344
(*Definition of the relation =?= *)
clasohm@0
   345
val flexpair_def =
wenzelm@250
   346
  Thm{sign= Sign.pure, hyps= [], maxidx= 0,
wenzelm@250
   347
      prop= term_of
wenzelm@250
   348
              (read_cterm Sign.pure
wenzelm@250
   349
                 ("(?t =?= ?u) == (?t == ?u::?'a::{})", propT))};
clasohm@0
   350
clasohm@0
   351
(*The reflexivity rule: maps  t   to the theorem   t==t   *)
wenzelm@250
   352
fun reflexive ct =
lcp@229
   353
  let val {sign, t, T, maxidx} = rep_cterm ct
clasohm@0
   354
  in  Thm{sign= sign, hyps= [], maxidx= maxidx, prop= Logic.mk_equals(t,t)}
clasohm@0
   355
  end;
clasohm@0
   356
clasohm@0
   357
(*The symmetry rule
clasohm@0
   358
    t==u
clasohm@0
   359
    ----
clasohm@0
   360
    u==t         *)
clasohm@0
   361
fun symmetric (th as Thm{sign,hyps,prop,maxidx}) =
clasohm@0
   362
  case prop of
clasohm@0
   363
      (eq as Const("==",_)) $ t $ u =>
wenzelm@250
   364
          Thm{sign=sign, hyps=hyps, maxidx=maxidx, prop= eq$u$t}
clasohm@0
   365
    | _ => raise THM("symmetric", 0, [th]);
clasohm@0
   366
clasohm@0
   367
(*The transitive rule
clasohm@0
   368
    t1==u    u==t2
clasohm@0
   369
    ------------
clasohm@0
   370
        t1==t2      *)
clasohm@0
   371
fun transitive th1 th2 =
clasohm@0
   372
  let val Thm{maxidx=max1, hyps=hyps1, prop=prop1,...} = th1
clasohm@0
   373
      and Thm{maxidx=max2, hyps=hyps2, prop=prop2,...} = th2;
clasohm@0
   374
      fun err(msg) = raise THM("transitive: "^msg, 0, [th1,th2])
clasohm@0
   375
  in case (prop1,prop2) of
clasohm@0
   376
       ((eq as Const("==",_)) $ t1 $ u, Const("==",_) $ u' $ t2) =>
wenzelm@250
   377
          if not (u aconv u') then err"middle term"  else
wenzelm@250
   378
              Thm{sign= merge_theories(th1,th2), hyps= hyps1 union hyps2,
wenzelm@250
   379
                  maxidx= max[max1,max2], prop= eq$t1$t2}
clasohm@0
   380
     | _ =>  err"premises"
clasohm@0
   381
  end;
clasohm@0
   382
clasohm@0
   383
(*Beta-conversion: maps (%(x)t)(u) to the theorem  (%(x)t)(u) == t[u/x]   *)
wenzelm@250
   384
fun beta_conversion ct =
lcp@229
   385
  let val {sign, t, T, maxidx} = rep_cterm ct
clasohm@0
   386
  in  case t of
wenzelm@250
   387
          Abs(_,_,bodt) $ u =>
wenzelm@250
   388
            Thm{sign= sign,  hyps= [],
wenzelm@250
   389
                maxidx= maxidx_of_term t,
wenzelm@250
   390
                prop= Logic.mk_equals(t, subst_bounds([u],bodt))}
wenzelm@250
   391
        | _ =>  raise THM("beta_conversion: not a redex", 0, [])
clasohm@0
   392
  end;
clasohm@0
   393
clasohm@0
   394
(*The extensionality rule   (proviso: x not free in f, g, or hypotheses)
clasohm@0
   395
    f(x) == g(x)
clasohm@0
   396
    ------------
clasohm@0
   397
       f == g    *)
clasohm@0
   398
fun extensional (th as Thm{sign,maxidx,hyps,prop}) =
clasohm@0
   399
  case prop of
clasohm@0
   400
    (Const("==",_)) $ (f$x) $ (g$y) =>
wenzelm@250
   401
      let fun err(msg) = raise THM("extensional: "^msg, 0, [th])
clasohm@0
   402
      in (if x<>y then err"different variables" else
clasohm@0
   403
          case y of
wenzelm@250
   404
                Free _ =>
wenzelm@250
   405
                  if exists (apl(y, Logic.occs)) (f::g::hyps)
wenzelm@250
   406
                  then err"variable free in hyps or functions"    else  ()
wenzelm@250
   407
              | Var _ =>
wenzelm@250
   408
                  if Logic.occs(y,f)  orelse  Logic.occs(y,g)
wenzelm@250
   409
                  then err"variable free in functions"   else  ()
wenzelm@250
   410
              | _ => err"not a variable");
wenzelm@250
   411
          Thm{sign=sign, hyps=hyps, maxidx=maxidx,
wenzelm@250
   412
              prop= Logic.mk_equals(f,g)}
clasohm@0
   413
      end
clasohm@0
   414
 | _ =>  raise THM("extensional: premise", 0, [th]);
clasohm@0
   415
clasohm@0
   416
(*The abstraction rule.  The Free or Var x must not be free in the hypotheses.
clasohm@0
   417
  The bound variable will be named "a" (since x will be something like x320)
clasohm@0
   418
          t == u
clasohm@0
   419
    ----------------
clasohm@0
   420
      %(x)t == %(x)u     *)
clasohm@0
   421
fun abstract_rule a cx (th as Thm{sign,maxidx,hyps,prop}) =
lcp@229
   422
  let val x = term_of cx;
wenzelm@250
   423
      val (t,u) = Logic.dest_equals prop
wenzelm@250
   424
            handle TERM _ =>
wenzelm@250
   425
                raise THM("abstract_rule: premise not an equality", 0, [th])
clasohm@0
   426
      fun result T =
clasohm@0
   427
            Thm{sign= sign, maxidx= maxidx, hyps= hyps,
wenzelm@250
   428
                prop= Logic.mk_equals(Abs(a, T, abstract_over (x,t)),
wenzelm@250
   429
                                      Abs(a, T, abstract_over (x,u)))}
clasohm@0
   430
  in  case x of
wenzelm@250
   431
        Free(_,T) =>
wenzelm@250
   432
         if exists (apl(x, Logic.occs)) hyps
wenzelm@250
   433
         then raise THM("abstract_rule: variable free in assumptions", 0, [th])
wenzelm@250
   434
         else result T
clasohm@0
   435
      | Var(_,T) => result T
clasohm@0
   436
      | _ => raise THM("abstract_rule: not a variable", 0, [th])
clasohm@0
   437
  end;
clasohm@0
   438
clasohm@0
   439
(*The combination rule
clasohm@0
   440
    f==g    t==u
clasohm@0
   441
    ------------
clasohm@0
   442
     f(t)==g(u)      *)
clasohm@0
   443
fun combination th1 th2 =
clasohm@0
   444
  let val Thm{maxidx=max1, hyps=hyps1, prop=prop1,...} = th1
clasohm@0
   445
      and Thm{maxidx=max2, hyps=hyps2, prop=prop2,...} = th2
clasohm@0
   446
  in  case (prop1,prop2)  of
clasohm@0
   447
       (Const("==",_) $ f $ g, Const("==",_) $ t $ u) =>
wenzelm@250
   448
              Thm{sign= merge_theories(th1,th2), hyps= hyps1 union hyps2,
wenzelm@250
   449
                  maxidx= max[max1,max2], prop= Logic.mk_equals(f$t, g$u)}
clasohm@0
   450
     | _ =>  raise THM("combination: premises", 0, [th1,th2])
clasohm@0
   451
  end;
clasohm@0
   452
clasohm@0
   453
clasohm@0
   454
(*The equal propositions rule
clasohm@0
   455
    A==B    A
clasohm@0
   456
    ---------
clasohm@0
   457
        B          *)
clasohm@0
   458
fun equal_elim th1 th2 =
clasohm@0
   459
  let val Thm{maxidx=max1, hyps=hyps1, prop=prop1,...} = th1
clasohm@0
   460
      and Thm{maxidx=max2, hyps=hyps2, prop=prop2,...} = th2;
clasohm@0
   461
      fun err(msg) = raise THM("equal_elim: "^msg, 0, [th1,th2])
clasohm@0
   462
  in  case prop1  of
clasohm@0
   463
       Const("==",_) $ A $ B =>
wenzelm@250
   464
          if not (prop2 aconv A) then err"not equal"  else
wenzelm@250
   465
              Thm{sign= merge_theories(th1,th2), hyps= hyps1 union hyps2,
wenzelm@250
   466
                  maxidx= max[max1,max2], prop= B}
clasohm@0
   467
     | _ =>  err"major premise"
clasohm@0
   468
  end;
clasohm@0
   469
clasohm@0
   470
clasohm@0
   471
(* Equality introduction
clasohm@0
   472
    A==>B    B==>A
clasohm@0
   473
    -------------
clasohm@0
   474
         A==B            *)
clasohm@0
   475
fun equal_intr th1 th2 =
clasohm@0
   476
let val Thm{maxidx=max1, hyps=hyps1, prop=prop1,...} = th1
clasohm@0
   477
    and Thm{maxidx=max2, hyps=hyps2, prop=prop2,...} = th2;
clasohm@0
   478
    fun err(msg) = raise THM("equal_intr: "^msg, 0, [th1,th2])
clasohm@0
   479
in case (prop1,prop2) of
clasohm@0
   480
     (Const("==>",_) $ A $ B, Const("==>",_) $ B' $ A')  =>
wenzelm@250
   481
        if A aconv A' andalso B aconv B'
wenzelm@250
   482
        then Thm{sign= merge_theories(th1,th2), hyps= hyps1 union hyps2,
wenzelm@250
   483
                 maxidx= max[max1,max2], prop= Logic.mk_equals(A,B)}
wenzelm@250
   484
        else err"not equal"
clasohm@0
   485
   | _ =>  err"premises"
clasohm@0
   486
end;
clasohm@0
   487
clasohm@0
   488
(**** Derived rules ****)
clasohm@0
   489
clasohm@0
   490
(*Discharge all hypotheses (need not verify cterms)
clasohm@0
   491
  Repeated hypotheses are discharged only once;  fold cannot do this*)
clasohm@0
   492
fun implies_intr_hyps (Thm{sign, maxidx, hyps=A::As, prop}) =
clasohm@0
   493
      implies_intr_hyps
wenzelm@250
   494
            (Thm{sign=sign,  maxidx=maxidx,
wenzelm@250
   495
                 hyps= disch(As,A),  prop= implies$A$prop})
clasohm@0
   496
  | implies_intr_hyps th = th;
clasohm@0
   497
clasohm@0
   498
(*Smash" unifies the list of term pairs leaving no flex-flex pairs.
wenzelm@250
   499
  Instantiates the theorem and deletes trivial tpairs.
clasohm@0
   500
  Resulting sequence may contain multiple elements if the tpairs are
clasohm@0
   501
    not all flex-flex. *)
clasohm@0
   502
fun flexflex_rule (Thm{sign,maxidx,hyps,prop}) =
wenzelm@250
   503
  let fun newthm env =
wenzelm@250
   504
          let val (tpairs,horn) =
wenzelm@250
   505
                        Logic.strip_flexpairs (Envir.norm_term env prop)
wenzelm@250
   506
                (*Remove trivial tpairs, of the form t=t*)
wenzelm@250
   507
              val distpairs = filter (not o op aconv) tpairs
wenzelm@250
   508
              val newprop = Logic.list_flexpairs(distpairs, horn)
wenzelm@250
   509
          in  Thm{sign= sign, hyps= hyps,
wenzelm@250
   510
                  maxidx= maxidx_of_term newprop, prop= newprop}
wenzelm@250
   511
          end;
clasohm@0
   512
      val (tpairs,_) = Logic.strip_flexpairs prop
clasohm@0
   513
  in Sequence.maps newthm
wenzelm@250
   514
            (Unify.smash_unifiers(sign, Envir.empty maxidx, tpairs))
clasohm@0
   515
  end;
clasohm@0
   516
clasohm@0
   517
(*Instantiation of Vars
wenzelm@250
   518
                      A
wenzelm@250
   519
             --------------------
wenzelm@250
   520
              A[t1/v1,....,tn/vn]     *)
clasohm@0
   521
clasohm@0
   522
(*Check that all the terms are Vars and are distinct*)
clasohm@0
   523
fun instl_ok ts = forall is_Var ts andalso null(findrep ts);
clasohm@0
   524
clasohm@0
   525
(*For instantiate: process pair of cterms, merge theories*)
clasohm@0
   526
fun add_ctpair ((ct,cu), (sign,tpairs)) =
lcp@229
   527
  let val {sign=signt, t=t, T= T, ...} = rep_cterm ct
lcp@229
   528
      and {sign=signu, t=u, T= U, ...} = rep_cterm cu
clasohm@0
   529
  in  if T=U  then (Sign.merge(sign, Sign.merge(signt, signu)), (t,u)::tpairs)
clasohm@0
   530
      else raise TYPE("add_ctpair", [T,U], [t,u])
clasohm@0
   531
  end;
clasohm@0
   532
clasohm@0
   533
fun add_ctyp ((v,ctyp), (sign',vTs)) =
lcp@229
   534
  let val {T,sign} = rep_ctyp ctyp
clasohm@0
   535
  in (Sign.merge(sign,sign'), (v,T)::vTs) end;
clasohm@0
   536
clasohm@0
   537
(*Left-to-right replacements: ctpairs = [...,(vi,ti),...].
clasohm@0
   538
  Instantiates distinct Vars by terms of same type.
clasohm@0
   539
  Normalizes the new theorem! *)
wenzelm@250
   540
fun instantiate (vcTs,ctpairs)  (th as Thm{sign,maxidx,hyps,prop}) =
clasohm@0
   541
  let val (newsign,tpairs) = foldr add_ctpair (ctpairs, (sign,[]));
clasohm@0
   542
      val (newsign,vTs) = foldr add_ctyp (vcTs, (newsign,[]));
wenzelm@250
   543
      val newprop =
wenzelm@250
   544
            Envir.norm_term (Envir.empty 0)
wenzelm@250
   545
              (subst_atomic tpairs
wenzelm@250
   546
               (Type.inst_term_tvars(#tsig(Sign.rep_sg newsign),vTs) prop))
clasohm@0
   547
      val newth = Thm{sign= newsign, hyps= hyps,
wenzelm@250
   548
                      maxidx= maxidx_of_term newprop, prop= newprop}
wenzelm@250
   549
  in  if not(instl_ok(map #1 tpairs))
nipkow@193
   550
      then raise THM("instantiate: variables not distinct", 0, [th])
nipkow@193
   551
      else if not(null(findrep(map #1 vTs)))
nipkow@193
   552
      then raise THM("instantiate: type variables not distinct", 0, [th])
nipkow@193
   553
      else (*Check types of Vars for agreement*)
nipkow@193
   554
      case findrep (map (#1 o dest_Var) (term_vars newprop)) of
wenzelm@250
   555
          ix::_ => raise THM("instantiate: conflicting types for variable " ^
wenzelm@250
   556
                             Syntax.string_of_vname ix ^ "\n", 0, [newth])
wenzelm@250
   557
        | [] =>
wenzelm@250
   558
             case findrep (map #1 (term_tvars newprop)) of
wenzelm@250
   559
             ix::_ => raise THM
wenzelm@250
   560
                    ("instantiate: conflicting sorts for type variable " ^
wenzelm@250
   561
                     Syntax.string_of_vname ix ^ "\n", 0, [newth])
nipkow@193
   562
        | [] => newth
clasohm@0
   563
  end
wenzelm@250
   564
  handle TERM _ =>
clasohm@0
   565
           raise THM("instantiate: incompatible signatures",0,[th])
nipkow@193
   566
       | TYPE _ => raise THM("instantiate: type conflict", 0, [th]);
clasohm@0
   567
clasohm@0
   568
(*The trivial implication A==>A, justified by assume and forall rules.
clasohm@0
   569
  A can contain Vars, not so for assume!   *)
wenzelm@250
   570
fun trivial ct : thm =
lcp@229
   571
  let val {sign, t=A, T, maxidx} = rep_cterm ct
wenzelm@250
   572
  in  if T<>propT then
wenzelm@250
   573
            raise THM("trivial: the term must have type prop", 0, [])
clasohm@0
   574
      else Thm{sign= sign, maxidx= maxidx, hyps= [], prop= implies$A$A}
clasohm@0
   575
  end;
clasohm@0
   576
clasohm@0
   577
(* Replace all TFrees not in the hyps by new TVars *)
clasohm@0
   578
fun varifyT(Thm{sign,maxidx,hyps,prop}) =
clasohm@0
   579
  let val tfrees = foldr add_term_tfree_names (hyps,[])
clasohm@0
   580
  in Thm{sign=sign, maxidx=max[0,maxidx], hyps=hyps,
wenzelm@250
   581
         prop= Type.varify(prop,tfrees)}
clasohm@0
   582
  end;
clasohm@0
   583
clasohm@0
   584
(* Replace all TVars by new TFrees *)
clasohm@0
   585
fun freezeT(Thm{sign,maxidx,hyps,prop}) =
clasohm@0
   586
  let val prop' = Type.freeze (K true) prop
clasohm@0
   587
  in Thm{sign=sign, maxidx=maxidx_of_term prop', hyps=hyps, prop=prop'} end;
clasohm@0
   588
clasohm@0
   589
clasohm@0
   590
(*** Inference rules for tactics ***)
clasohm@0
   591
clasohm@0
   592
(*Destruct proof state into constraints, other goals, goal(i), rest *)
clasohm@0
   593
fun dest_state (state as Thm{prop,...}, i) =
clasohm@0
   594
  let val (tpairs,horn) = Logic.strip_flexpairs prop
clasohm@0
   595
  in  case  Logic.strip_prems(i, [], horn) of
clasohm@0
   596
          (B::rBs, C) => (tpairs, rev rBs, B, C)
clasohm@0
   597
        | _ => raise THM("dest_state", i, [state])
clasohm@0
   598
  end
clasohm@0
   599
  handle TERM _ => raise THM("dest_state", i, [state]);
clasohm@0
   600
lcp@309
   601
(*Increment variables and parameters of orule as required for
clasohm@0
   602
  resolution with goal i of state. *)
clasohm@0
   603
fun lift_rule (state, i) orule =
clasohm@0
   604
  let val Thm{prop=sprop,maxidx=smax,...} = state;
clasohm@0
   605
      val (Bi::_, _) = Logic.strip_prems(i, [], Logic.skip_flexpairs sprop)
wenzelm@250
   606
        handle TERM _ => raise THM("lift_rule", i, [orule,state]);
clasohm@0
   607
      val (lift_abs,lift_all) = Logic.lift_fns(Bi,smax+1);
clasohm@0
   608
      val (Thm{sign,maxidx,hyps,prop}) = orule
clasohm@0
   609
      val (tpairs,As,B) = Logic.strip_horn prop
clasohm@0
   610
  in  Thm{hyps=hyps, sign= merge_theories(state,orule),
wenzelm@250
   611
          maxidx= maxidx+smax+1,
wenzelm@250
   612
          prop= Logic.rule_of(map (pairself lift_abs) tpairs,
wenzelm@250
   613
                              map lift_all As,    lift_all B)}
clasohm@0
   614
  end;
clasohm@0
   615
clasohm@0
   616
(*Solve subgoal Bi of proof state B1...Bn/C by assumption. *)
clasohm@0
   617
fun assumption i state =
clasohm@0
   618
  let val Thm{sign,maxidx,hyps,prop} = state;
clasohm@0
   619
      val (tpairs, Bs, Bi, C) = dest_state(state,i)
wenzelm@250
   620
      fun newth (env as Envir.Envir{maxidx, ...}, tpairs) =
wenzelm@250
   621
          Thm{sign=sign, hyps=hyps, maxidx=maxidx, prop=
wenzelm@250
   622
            if Envir.is_empty env then (*avoid wasted normalizations*)
wenzelm@250
   623
              Logic.rule_of (tpairs, Bs, C)
wenzelm@250
   624
            else (*normalize the new rule fully*)
wenzelm@250
   625
              Envir.norm_term env (Logic.rule_of (tpairs, Bs, C))};
clasohm@0
   626
      fun addprfs [] = Sequence.null
clasohm@0
   627
        | addprfs ((t,u)::apairs) = Sequence.seqof (fn()=> Sequence.pull
clasohm@0
   628
             (Sequence.mapp newth
wenzelm@250
   629
                (Unify.unifiers(sign,Envir.empty maxidx, (t,u)::tpairs))
wenzelm@250
   630
                (addprfs apairs)))
clasohm@0
   631
  in  addprfs (Logic.assum_pairs Bi)  end;
clasohm@0
   632
wenzelm@250
   633
(*Solve subgoal Bi of proof state B1...Bn/C by assumption.
clasohm@0
   634
  Checks if Bi's conclusion is alpha-convertible to one of its assumptions*)
clasohm@0
   635
fun eq_assumption i state =
clasohm@0
   636
  let val Thm{sign,maxidx,hyps,prop} = state;
clasohm@0
   637
      val (tpairs, Bs, Bi, C) = dest_state(state,i)
clasohm@0
   638
  in  if exists (op aconv) (Logic.assum_pairs Bi)
wenzelm@250
   639
      then Thm{sign=sign, hyps=hyps, maxidx=maxidx,
wenzelm@250
   640
               prop=Logic.rule_of(tpairs, Bs, C)}
clasohm@0
   641
      else  raise THM("eq_assumption", 0, [state])
clasohm@0
   642
  end;
clasohm@0
   643
clasohm@0
   644
clasohm@0
   645
(** User renaming of parameters in a subgoal **)
clasohm@0
   646
clasohm@0
   647
(*Calls error rather than raising an exception because it is intended
clasohm@0
   648
  for top-level use -- exception handling would not make sense here.
clasohm@0
   649
  The names in cs, if distinct, are used for the innermost parameters;
clasohm@0
   650
   preceding parameters may be renamed to make all params distinct.*)
clasohm@0
   651
fun rename_params_rule (cs, i) state =
clasohm@0
   652
  let val Thm{sign,maxidx,hyps,prop} = state
clasohm@0
   653
      val (tpairs, Bs, Bi, C) = dest_state(state,i)
clasohm@0
   654
      val iparams = map #1 (Logic.strip_params Bi)
clasohm@0
   655
      val short = length iparams - length cs
wenzelm@250
   656
      val newnames =
wenzelm@250
   657
            if short<0 then error"More names than abstractions!"
wenzelm@250
   658
            else variantlist(take (short,iparams), cs) @ cs
clasohm@0
   659
      val freenames = map (#1 o dest_Free) (term_frees prop)
clasohm@0
   660
      val newBi = Logic.list_rename_params (newnames, Bi)
wenzelm@250
   661
  in
clasohm@0
   662
  case findrep cs of
clasohm@0
   663
     c::_ => error ("Bound variables not distinct: " ^ c)
clasohm@0
   664
   | [] => (case cs inter freenames of
clasohm@0
   665
       a::_ => error ("Bound/Free variable clash: " ^ a)
clasohm@0
   666
     | [] => Thm{sign=sign, hyps=hyps, maxidx=maxidx, prop=
wenzelm@250
   667
                    Logic.rule_of(tpairs, Bs@[newBi], C)})
clasohm@0
   668
  end;
clasohm@0
   669
clasohm@0
   670
(*** Preservation of bound variable names ***)
clasohm@0
   671
wenzelm@250
   672
(*Scan a pair of terms; while they are similar,
clasohm@0
   673
  accumulate corresponding bound vars in "al"*)
clasohm@0
   674
fun match_bvs(Abs(x,_,s),Abs(y,_,t), al) = match_bvs(s,t,(x,y)::al)
clasohm@0
   675
  | match_bvs(f$s, g$t, al) = match_bvs(f,g,match_bvs(s,t,al))
clasohm@0
   676
  | match_bvs(_,_,al) = al;
clasohm@0
   677
clasohm@0
   678
(* strip abstractions created by parameters *)
clasohm@0
   679
fun match_bvars((s,t),al) = match_bvs(strip_abs_body s, strip_abs_body t, al);
clasohm@0
   680
clasohm@0
   681
wenzelm@250
   682
(* strip_apply f A(,B) strips off all assumptions/parameters from A
clasohm@0
   683
   introduced by lifting over B, and applies f to remaining part of A*)
clasohm@0
   684
fun strip_apply f =
clasohm@0
   685
  let fun strip(Const("==>",_)$ A1 $ B1,
wenzelm@250
   686
                Const("==>",_)$ _  $ B2) = implies $ A1 $ strip(B1,B2)
wenzelm@250
   687
        | strip((c as Const("all",_)) $ Abs(a,T,t1),
wenzelm@250
   688
                      Const("all",_)  $ Abs(_,_,t2)) = c$Abs(a,T,strip(t1,t2))
wenzelm@250
   689
        | strip(A,_) = f A
clasohm@0
   690
  in strip end;
clasohm@0
   691
clasohm@0
   692
(*Use the alist to rename all bound variables and some unknowns in a term
clasohm@0
   693
  dpairs = current disagreement pairs;  tpairs = permanent ones (flexflex);
clasohm@0
   694
  Preserves unknowns in tpairs and on lhs of dpairs. *)
clasohm@0
   695
fun rename_bvs([],_,_,_) = I
clasohm@0
   696
  | rename_bvs(al,dpairs,tpairs,B) =
wenzelm@250
   697
    let val vars = foldr add_term_vars
wenzelm@250
   698
                        (map fst dpairs @ map fst tpairs @ map snd tpairs, [])
wenzelm@250
   699
        (*unknowns appearing elsewhere be preserved!*)
wenzelm@250
   700
        val vids = map (#1 o #1 o dest_Var) vars;
wenzelm@250
   701
        fun rename(t as Var((x,i),T)) =
wenzelm@250
   702
                (case assoc(al,x) of
wenzelm@250
   703
                   Some(y) => if x mem vids orelse y mem vids then t
wenzelm@250
   704
                              else Var((y,i),T)
wenzelm@250
   705
                 | None=> t)
clasohm@0
   706
          | rename(Abs(x,T,t)) =
wenzelm@250
   707
              Abs(case assoc(al,x) of Some(y) => y | None => x,
wenzelm@250
   708
                  T, rename t)
clasohm@0
   709
          | rename(f$t) = rename f $ rename t
clasohm@0
   710
          | rename(t) = t;
wenzelm@250
   711
        fun strip_ren Ai = strip_apply rename (Ai,B)
clasohm@0
   712
    in strip_ren end;
clasohm@0
   713
clasohm@0
   714
(*Function to rename bounds/unknowns in the argument, lifted over B*)
clasohm@0
   715
fun rename_bvars(dpairs, tpairs, B) =
wenzelm@250
   716
        rename_bvs(foldr match_bvars (dpairs,[]), dpairs, tpairs, B);
clasohm@0
   717
clasohm@0
   718
clasohm@0
   719
(*** RESOLUTION ***)
clasohm@0
   720
clasohm@0
   721
(*strip off pairs of assumptions/parameters in parallel -- they are
clasohm@0
   722
  identical because of lifting*)
wenzelm@250
   723
fun strip_assums2 (Const("==>", _) $ _ $ B1,
wenzelm@250
   724
                   Const("==>", _) $ _ $ B2) = strip_assums2 (B1,B2)
clasohm@0
   725
  | strip_assums2 (Const("all",_)$Abs(a,T,t1),
wenzelm@250
   726
                   Const("all",_)$Abs(_,_,t2)) =
clasohm@0
   727
      let val (B1,B2) = strip_assums2 (t1,t2)
clasohm@0
   728
      in  (Abs(a,T,B1), Abs(a,T,B2))  end
clasohm@0
   729
  | strip_assums2 BB = BB;
clasohm@0
   730
clasohm@0
   731
clasohm@0
   732
(*Composition of object rule r=(A1...Am/B) with proof state s=(B1...Bn/C)
wenzelm@250
   733
  Unifies B with Bi, replacing subgoal i    (1 <= i <= n)
clasohm@0
   734
  If match then forbid instantiations in proof state
clasohm@0
   735
  If lifted then shorten the dpair using strip_assums2.
clasohm@0
   736
  If eres_flg then simultaneously proves A1 by assumption.
wenzelm@250
   737
  nsubgoal is the number of new subgoals (written m above).
clasohm@0
   738
  Curried so that resolution calls dest_state only once.
clasohm@0
   739
*)
clasohm@0
   740
local open Sequence; exception Bicompose
clasohm@0
   741
in
wenzelm@250
   742
fun bicompose_aux match (state, (stpairs, Bs, Bi, C), lifted)
clasohm@0
   743
                        (eres_flg, orule, nsubgoal) =
clasohm@0
   744
 let val Thm{maxidx=smax, hyps=shyps, ...} = state
clasohm@0
   745
     and Thm{maxidx=rmax, hyps=rhyps, prop=rprop,...} = orule;
clasohm@0
   746
     val sign = merge_theories(state,orule);
clasohm@0
   747
     (** Add new theorem with prop = '[| Bs; As |] ==> C' to thq **)
wenzelm@250
   748
     fun addth As ((env as Envir.Envir {maxidx, ...}, tpairs), thq) =
wenzelm@250
   749
       let val normt = Envir.norm_term env;
wenzelm@250
   750
           (*perform minimal copying here by examining env*)
wenzelm@250
   751
           val normp =
wenzelm@250
   752
             if Envir.is_empty env then (tpairs, Bs @ As, C)
wenzelm@250
   753
             else
wenzelm@250
   754
             let val ntps = map (pairself normt) tpairs
wenzelm@250
   755
             in if the (Envir.minidx env) > smax then (*no assignments in state*)
wenzelm@250
   756
                  (ntps, Bs @ map normt As, C)
wenzelm@250
   757
                else if match then raise Bicompose
wenzelm@250
   758
                else (*normalize the new rule fully*)
wenzelm@250
   759
                  (ntps, map normt (Bs @ As), normt C)
wenzelm@250
   760
             end
wenzelm@250
   761
           val th = Thm{sign=sign, hyps=rhyps union shyps, maxidx=maxidx,
wenzelm@250
   762
                        prop= Logic.rule_of normp}
clasohm@0
   763
        in  cons(th, thq)  end  handle Bicompose => thq
clasohm@0
   764
     val (rtpairs,rhorn) = Logic.strip_flexpairs(rprop);
clasohm@0
   765
     val (rAs,B) = Logic.strip_prems(nsubgoal, [], rhorn)
clasohm@0
   766
       handle TERM _ => raise THM("bicompose: rule", 0, [orule,state]);
clasohm@0
   767
     (*Modify assumptions, deleting n-th if n>0 for e-resolution*)
clasohm@0
   768
     fun newAs(As0, n, dpairs, tpairs) =
clasohm@0
   769
       let val As1 = if !Logic.auto_rename orelse not lifted then As0
wenzelm@250
   770
                     else map (rename_bvars(dpairs,tpairs,B)) As0
clasohm@0
   771
       in (map (Logic.flatten_params n) As1)
wenzelm@250
   772
          handle TERM _ =>
wenzelm@250
   773
          raise THM("bicompose: 1st premise", 0, [orule])
clasohm@0
   774
       end;
clasohm@0
   775
     val env = Envir.empty(max[rmax,smax]);
clasohm@0
   776
     val BBi = if lifted then strip_assums2(B,Bi) else (B,Bi);
clasohm@0
   777
     val dpairs = BBi :: (rtpairs@stpairs);
clasohm@0
   778
     (*elim-resolution: try each assumption in turn.  Initially n=1*)
clasohm@0
   779
     fun tryasms (_, _, []) = null
clasohm@0
   780
       | tryasms (As, n, (t,u)::apairs) =
wenzelm@250
   781
          (case pull(Unify.unifiers(sign, env, (t,u)::dpairs))  of
wenzelm@250
   782
               None                   => tryasms (As, n+1, apairs)
wenzelm@250
   783
             | cell as Some((_,tpairs),_) =>
wenzelm@250
   784
                   its_right (addth (newAs(As, n, [BBi,(u,t)], tpairs)))
wenzelm@250
   785
                       (seqof (fn()=> cell),
wenzelm@250
   786
                        seqof (fn()=> pull (tryasms (As, n+1, apairs)))));
clasohm@0
   787
     fun eres [] = raise THM("bicompose: no premises", 0, [orule,state])
clasohm@0
   788
       | eres (A1::As) = tryasms (As, 1, Logic.assum_pairs A1);
clasohm@0
   789
     (*ordinary resolution*)
clasohm@0
   790
     fun res(None) = null
wenzelm@250
   791
       | res(cell as Some((_,tpairs),_)) =
wenzelm@250
   792
             its_right (addth(newAs(rev rAs, 0, [BBi], tpairs)))
wenzelm@250
   793
                       (seqof (fn()=> cell), null)
clasohm@0
   794
 in  if eres_flg then eres(rev rAs)
clasohm@0
   795
     else res(pull(Unify.unifiers(sign, env, dpairs)))
clasohm@0
   796
 end;
clasohm@0
   797
end;  (*open Sequence*)
clasohm@0
   798
clasohm@0
   799
clasohm@0
   800
fun bicompose match arg i state =
clasohm@0
   801
    bicompose_aux match (state, dest_state(state,i), false) arg;
clasohm@0
   802
clasohm@0
   803
(*Quick test whether rule is resolvable with the subgoal with hyps Hs
clasohm@0
   804
  and conclusion B.  If eres_flg then checks 1st premise of rule also*)
clasohm@0
   805
fun could_bires (Hs, B, eres_flg, rule) =
clasohm@0
   806
    let fun could_reshyp (A1::_) = exists (apl(A1,could_unify)) Hs
wenzelm@250
   807
          | could_reshyp [] = false;  (*no premise -- illegal*)
wenzelm@250
   808
    in  could_unify(concl_of rule, B) andalso
wenzelm@250
   809
        (not eres_flg  orelse  could_reshyp (prems_of rule))
clasohm@0
   810
    end;
clasohm@0
   811
clasohm@0
   812
(*Bi-resolution of a state with a list of (flag,rule) pairs.
clasohm@0
   813
  Puts the rule above:  rule/state.  Renames vars in the rules. *)
wenzelm@250
   814
fun biresolution match brules i state =
clasohm@0
   815
    let val lift = lift_rule(state, i);
wenzelm@250
   816
        val (stpairs, Bs, Bi, C) = dest_state(state,i)
wenzelm@250
   817
        val B = Logic.strip_assums_concl Bi;
wenzelm@250
   818
        val Hs = Logic.strip_assums_hyp Bi;
wenzelm@250
   819
        val comp = bicompose_aux match (state, (stpairs, Bs, Bi, C), true);
wenzelm@250
   820
        fun res [] = Sequence.null
wenzelm@250
   821
          | res ((eres_flg, rule)::brules) =
wenzelm@250
   822
              if could_bires (Hs, B, eres_flg, rule)
wenzelm@250
   823
              then Sequence.seqof (*delay processing remainder til needed*)
wenzelm@250
   824
                  (fn()=> Some(comp (eres_flg, lift rule, nprems_of rule),
wenzelm@250
   825
                               res brules))
wenzelm@250
   826
              else res brules
clasohm@0
   827
    in  Sequence.flats (res brules)  end;
clasohm@0
   828
clasohm@0
   829
clasohm@0
   830
(**** THEORIES ****)
clasohm@0
   831
clasohm@0
   832
val pure_thy = Pure{sign = Sign.pure};
clasohm@0
   833
clasohm@0
   834
(*Look up the named axiom in the theory*)
clasohm@0
   835
fun get_axiom thy axname =
clasohm@0
   836
    let fun get (Pure _) = raise Match
wenzelm@250
   837
          | get (Extend{axioms,thy,...}) =
wenzelm@250
   838
             (case Symtab.lookup(axioms,axname) of
wenzelm@250
   839
                  Some th => th
wenzelm@250
   840
                | None => get thy)
wenzelm@250
   841
         | get (Merge{thy1,thy2,...}) =
wenzelm@250
   842
                get thy1  handle Match => get thy2
clasohm@0
   843
    in  get thy
wenzelm@250
   844
        handle Match => raise THEORY("get_axiom: No axiom "^axname, [thy])
clasohm@0
   845
    end;
clasohm@0
   846
clasohm@0
   847
(*Converts Frees to Vars: axioms can be written without question marks*)
clasohm@0
   848
fun prepare_axiom sign sP =
lcp@229
   849
    Logic.varify (term_of (read_cterm sign (sP,propT)));
clasohm@0
   850
clasohm@0
   851
(*Read an axiom for a new theory*)
clasohm@0
   852
fun read_ax sign (a, sP) : string*thm =
clasohm@0
   853
  let val prop = prepare_axiom sign sP
wenzelm@250
   854
  in  (a, Thm{sign=sign, hyps=[], maxidx= maxidx_of_term prop, prop= prop})
clasohm@0
   855
  end
clasohm@0
   856
  handle ERROR =>
wenzelm@250
   857
        error("extend_theory: The error above occurred in axiom " ^ a);
clasohm@0
   858
clasohm@0
   859
fun mk_axioms sign axpairs =
wenzelm@250
   860
        Symtab.st_of_alist(map (read_ax sign) axpairs, Symtab.null)
wenzelm@250
   861
        handle Symtab.DUPLICATE(a) => error("Two axioms named " ^ a);
clasohm@0
   862
clasohm@0
   863
(*Extension of a theory with given classes, types, constants and syntax.
clasohm@0
   864
  Reads the axioms from strings: axpairs have the form (axname, axiom). *)
clasohm@0
   865
fun extend_theory thy thyname ext axpairs =
clasohm@0
   866
  let val sign = Sign.extend (sign_of thy) thyname ext;
clasohm@0
   867
      val axioms= mk_axioms sign axpairs
clasohm@0
   868
  in  Extend{sign=sign, axioms= axioms, thy = thy}  end;
clasohm@0
   869
clasohm@0
   870
(*The union of two theories*)
wenzelm@250
   871
fun merge_theories (thy1, thy2) =
wenzelm@250
   872
  Merge {sign = Sign.merge (sign_of thy1, sign_of thy2),
wenzelm@250
   873
         thy1 = thy1, thy2 = thy2} handle TERM (msg, _) => error msg;
clasohm@0
   874
clasohm@0
   875
clasohm@0
   876
(*** Meta simp sets ***)
clasohm@0
   877
nipkow@288
   878
type rrule = {thm:thm, lhs:term, perm:bool};
nipkow@288
   879
type cong = {thm:thm, lhs:term};
clasohm@0
   880
datatype meta_simpset =
nipkow@288
   881
  Mss of {net:rrule Net.net, congs:(string * cong)list, primes:string,
clasohm@0
   882
          prems: thm list, mk_rews: thm -> thm list};
clasohm@0
   883
clasohm@0
   884
(*A "mss" contains data needed during conversion:
clasohm@0
   885
  net: discrimination net of rewrite rules
clasohm@0
   886
  congs: association list of congruence rules
clasohm@0
   887
  primes: offset for generating unique new names
clasohm@0
   888
          for rewriting under lambda abstractions
clasohm@0
   889
  mk_rews: used when local assumptions are added
clasohm@0
   890
*)
clasohm@0
   891
clasohm@0
   892
val empty_mss = Mss{net= Net.empty, congs= [], primes="", prems= [],
clasohm@0
   893
                    mk_rews = K[]};
clasohm@0
   894
clasohm@0
   895
exception SIMPLIFIER of string * thm;
clasohm@0
   896
lcp@229
   897
fun prtm a sign t = (writeln a; writeln(Sign.string_of_term sign t));
clasohm@0
   898
nipkow@209
   899
val trace_simp = ref false;
nipkow@209
   900
lcp@229
   901
fun trace_term a sign t = if !trace_simp then prtm a sign t else ();
nipkow@209
   902
nipkow@209
   903
fun trace_thm a (Thm{sign,prop,...}) = trace_term a sign prop;
nipkow@209
   904
nipkow@288
   905
fun var_perm(Var _, Var _) = true
nipkow@288
   906
  | var_perm(Abs(_,_,s), Abs(_,_,t)) = var_perm(s,t)
nipkow@288
   907
  | var_perm(t1$t2, u1$u2) = var_perm(t1,u1) andalso var_perm(t2,u2)
nipkow@288
   908
  | var_perm(t,u) = (t=u);
nipkow@288
   909
nipkow@288
   910
clasohm@0
   911
(*simple test for looping rewrite*)
clasohm@0
   912
fun loops sign prems (lhs,rhs) =
clasohm@0
   913
  null(prems) andalso
clasohm@0
   914
  Pattern.eta_matches (#tsig(Sign.rep_sg sign)) (lhs,rhs);
clasohm@0
   915
clasohm@0
   916
fun mk_rrule (thm as Thm{hyps,sign,prop,maxidx,...}) =
clasohm@0
   917
  let val prems = Logic.strip_imp_prems prop
clasohm@0
   918
      val concl = Pattern.eta_contract (Logic.strip_imp_concl prop)
clasohm@0
   919
      val (lhs,rhs) = Logic.dest_equals concl handle TERM _ =>
clasohm@0
   920
                      raise SIMPLIFIER("Rewrite rule not a meta-equality",thm)
nipkow@288
   921
      val perm = var_perm(lhs,rhs) andalso not(lhs=rhs)
nipkow@288
   922
  in if not perm andalso loops sign prems (lhs,rhs)
clasohm@0
   923
     then (prtm "Warning: ignoring looping rewrite rule" sign prop; None)
nipkow@288
   924
     else Some{thm=thm,lhs=lhs,perm=perm}
clasohm@0
   925
  end;
clasohm@0
   926
nipkow@87
   927
local
nipkow@87
   928
 fun eq({thm=Thm{prop=p1,...},...}:rrule,
nipkow@87
   929
        {thm=Thm{prop=p2,...},...}:rrule) = p1 aconv p2
nipkow@87
   930
in
nipkow@87
   931
clasohm@0
   932
fun add_simp(mss as Mss{net,congs,primes,prems,mk_rews},
clasohm@0
   933
             thm as Thm{sign,prop,...}) =
nipkow@87
   934
  case mk_rrule thm of
nipkow@87
   935
    None => mss
nipkow@87
   936
  | Some(rrule as {lhs,...}) =>
nipkow@209
   937
      (trace_thm "Adding rewrite rule:" thm;
nipkow@209
   938
       Mss{net= (Net.insert_term((lhs,rrule),net,eq)
nipkow@209
   939
                 handle Net.INSERT =>
nipkow@87
   940
                  (prtm "Warning: ignoring duplicate rewrite rule" sign prop;
nipkow@87
   941
                   net)),
nipkow@209
   942
           congs=congs, primes=primes, prems=prems,mk_rews=mk_rews});
nipkow@87
   943
nipkow@87
   944
fun del_simp(mss as Mss{net,congs,primes,prems,mk_rews},
nipkow@87
   945
             thm as Thm{sign,prop,...}) =
nipkow@87
   946
  case mk_rrule thm of
nipkow@87
   947
    None => mss
nipkow@87
   948
  | Some(rrule as {lhs,...}) =>
nipkow@87
   949
      Mss{net= (Net.delete_term((lhs,rrule),net,eq)
nipkow@87
   950
                handle Net.INSERT =>
nipkow@87
   951
                 (prtm "Warning: rewrite rule not in simpset" sign prop;
nipkow@87
   952
                  net)),
clasohm@0
   953
             congs=congs, primes=primes, prems=prems,mk_rews=mk_rews}
nipkow@87
   954
nipkow@87
   955
end;
clasohm@0
   956
clasohm@0
   957
val add_simps = foldl add_simp;
nipkow@87
   958
val del_simps = foldl del_simp;
clasohm@0
   959
clasohm@0
   960
fun mss_of thms = add_simps(empty_mss,thms);
clasohm@0
   961
clasohm@0
   962
fun add_cong(Mss{net,congs,primes,prems,mk_rews},thm) =
clasohm@0
   963
  let val (lhs,_) = Logic.dest_equals(concl_of thm) handle TERM _ =>
clasohm@0
   964
                    raise SIMPLIFIER("Congruence not a meta-equality",thm)
clasohm@0
   965
      val lhs = Pattern.eta_contract lhs
clasohm@0
   966
      val (a,_) = dest_Const (head_of lhs) handle TERM _ =>
clasohm@0
   967
                  raise SIMPLIFIER("Congruence must start with a constant",thm)
clasohm@0
   968
  in Mss{net=net, congs=(a,{lhs=lhs,thm=thm})::congs, primes=primes,
clasohm@0
   969
         prems=prems, mk_rews=mk_rews}
clasohm@0
   970
  end;
clasohm@0
   971
clasohm@0
   972
val (op add_congs) = foldl add_cong;
clasohm@0
   973
clasohm@0
   974
fun add_prems(Mss{net,congs,primes,prems,mk_rews},thms) =
clasohm@0
   975
  Mss{net=net, congs=congs, primes=primes, prems=thms@prems, mk_rews=mk_rews};
clasohm@0
   976
clasohm@0
   977
fun prems_of_mss(Mss{prems,...}) = prems;
clasohm@0
   978
clasohm@0
   979
fun set_mk_rews(Mss{net,congs,primes,prems,...},mk_rews) =
clasohm@0
   980
  Mss{net=net, congs=congs, primes=primes, prems=prems, mk_rews=mk_rews};
clasohm@0
   981
fun mk_rews_of_mss(Mss{mk_rews,...}) = mk_rews;
clasohm@0
   982
clasohm@0
   983
wenzelm@250
   984
(*** Meta-level rewriting
clasohm@0
   985
     uses conversions, omitting proofs for efficiency.  See
wenzelm@250
   986
        L C Paulson, A higher-order implementation of rewriting,
wenzelm@250
   987
        Science of Computer Programming 3 (1983), pages 119-149. ***)
clasohm@0
   988
clasohm@0
   989
type prover = meta_simpset -> thm -> thm option;
clasohm@0
   990
type termrec = (Sign.sg * term list) * term;
clasohm@0
   991
type conv = meta_simpset -> termrec -> termrec;
clasohm@0
   992
nipkow@305
   993
datatype order = LESS | EQUAL | GREATER;
nipkow@288
   994
nipkow@305
   995
fun stringord(a,b:string) = if a<b then LESS  else
nipkow@305
   996
                            if a=b then EQUAL else GREATER;
nipkow@305
   997
nipkow@305
   998
fun intord(i,j:int) = if i<j then LESS  else
nipkow@305
   999
                      if i=j then EQUAL else GREATER;
nipkow@288
  1000
nipkow@305
  1001
(* FIXME: "***ABSTRACTION***" is a hack and makes the ordering non-linear *)
nipkow@305
  1002
fun string_of_hd(Const(a,_)) = a
nipkow@305
  1003
  | string_of_hd(Free(a,_))  = a
nipkow@305
  1004
  | string_of_hd(Var(v,_))   = Syntax.string_of_vname v
nipkow@305
  1005
  | string_of_hd(Bound i)    = string_of_int i
nipkow@305
  1006
  | string_of_hd(Abs _)      = "***ABSTRACTION***";
nipkow@288
  1007
nipkow@305
  1008
(* a strict (not reflexive) linear well-founded AC-compatible ordering
nipkow@305
  1009
 * for terms:
nipkow@305
  1010
 * s < t <=> 1. size(s) < size(t) or
nipkow@305
  1011
             2. size(s) = size(t) and s=f(...) and t = g(...) and f<g or
nipkow@305
  1012
             3. size(s) = size(t) and s=f(s1..sn) and t=f(t1..tn) and
nipkow@305
  1013
                (s1..sn) < (t1..tn) (lexicographically)
nipkow@305
  1014
 *)
nipkow@288
  1015
nipkow@288
  1016
(* FIXME: should really take types into account as well.
nipkow@305
  1017
 * Otherwise not linear *)
nipkow@305
  1018
fun termord(t,u) =
nipkow@305
  1019
      (case intord(size_of_term t,size_of_term u) of
nipkow@305
  1020
         EQUAL => let val (f,ts) = strip_comb t and (g,us) = strip_comb u
nipkow@305
  1021
                  in case stringord(string_of_hd f, string_of_hd g) of
nipkow@305
  1022
                       EQUAL => lextermord(ts,us)
nipkow@305
  1023
                     | ord   => ord
nipkow@305
  1024
                  end
nipkow@305
  1025
       | ord => ord)
nipkow@305
  1026
and lextermord(t::ts,u::us) =
nipkow@305
  1027
      (case termord(t,u) of
nipkow@305
  1028
         EQUAL => lextermord(ts,us)
nipkow@305
  1029
       | ord   => ord)
nipkow@305
  1030
  | lextermord([],[]) = EQUAL
nipkow@305
  1031
  | lextermord _ = error("lextermord");
nipkow@288
  1032
nipkow@305
  1033
fun termless tu = (termord tu = LESS);
nipkow@288
  1034
nipkow@208
  1035
fun check_conv(thm as Thm{hyps,prop,...}, prop0) =
nipkow@112
  1036
  let fun err() = (trace_thm "Proved wrong thm (Check subgoaler?)" thm; None)
clasohm@0
  1037
      val (lhs0,_) = Logic.dest_equals(Logic.strip_imp_concl prop0)
clasohm@0
  1038
  in case prop of
clasohm@0
  1039
       Const("==",_) $ lhs $ rhs =>
clasohm@0
  1040
         if (lhs = lhs0) orelse
clasohm@0
  1041
            (lhs aconv (Envir.norm_term (Envir.empty 0) lhs0))
nipkow@208
  1042
         then (trace_thm "SUCCEEDED" thm; Some(hyps,rhs))
clasohm@0
  1043
         else err()
clasohm@0
  1044
     | _ => err()
clasohm@0
  1045
  end;
clasohm@0
  1046
clasohm@0
  1047
(*Conversion to apply the meta simpset to a term*)
nipkow@208
  1048
fun rewritec (prover,signt) (mss as Mss{net,...}) (hypst,t) =
nipkow@225
  1049
  let val t = Pattern.eta_contract t;
nipkow@288
  1050
      fun rew {thm as Thm{sign,hyps,maxidx,prop,...}, lhs, perm} =
wenzelm@250
  1051
        let val unit = if Sign.subsig(sign,signt) then ()
nipkow@208
  1052
                  else (writeln"Warning: rewrite rule from different theory";
nipkow@208
  1053
                        raise Pattern.MATCH)
nipkow@208
  1054
            val insts = Pattern.match (#tsig(Sign.rep_sg signt)) (lhs,t)
clasohm@0
  1055
            val prop' = subst_vars insts prop;
clasohm@0
  1056
            val hyps' = hyps union hypst;
nipkow@208
  1057
            val thm' = Thm{sign=signt, hyps=hyps', prop=prop', maxidx=maxidx}
clasohm@0
  1058
        in if nprems_of thm' = 0
clasohm@0
  1059
           then let val (_,rhs) = Logic.dest_equals prop'
nipkow@288
  1060
                in if perm andalso not(termless(rhs,t)) then None
nipkow@288
  1061
                   else (trace_thm "Rewriting:" thm'; Some(hyps',rhs)) end
clasohm@0
  1062
           else (trace_thm "Trying to rewrite:" thm';
clasohm@0
  1063
                 case prover mss thm' of
clasohm@0
  1064
                   None       => (trace_thm "FAILED" thm'; None)
nipkow@112
  1065
                 | Some(thm2) => check_conv(thm2,prop'))
clasohm@0
  1066
        end
clasohm@0
  1067
nipkow@225
  1068
      fun rews [] = None
nipkow@225
  1069
        | rews (rrule::rrules) =
nipkow@225
  1070
            let val opt = rew rrule handle Pattern.MATCH => None
nipkow@225
  1071
            in case opt of None => rews rrules | some => some end;
clasohm@0
  1072
clasohm@0
  1073
  in case t of
nipkow@208
  1074
       Abs(_,_,body) $ u => Some(hypst,subst_bounds([u], body))
nipkow@225
  1075
     | _                 => rews(Net.match_term net t)
clasohm@0
  1076
  end;
clasohm@0
  1077
clasohm@0
  1078
(*Conversion to apply a congruence rule to a term*)
nipkow@208
  1079
fun congc (prover,signt) {thm=cong,lhs=lhs} (hypst,t) =
clasohm@0
  1080
  let val Thm{sign,hyps,maxidx,prop,...} = cong
nipkow@208
  1081
      val unit = if Sign.subsig(sign,signt) then ()
nipkow@208
  1082
                 else error("Congruence rule from different theory")
nipkow@208
  1083
      val tsig = #tsig(Sign.rep_sg signt)
clasohm@0
  1084
      val insts = Pattern.match tsig (lhs,t) handle Pattern.MATCH =>
clasohm@0
  1085
                  error("Congruence rule did not match")
clasohm@0
  1086
      val prop' = subst_vars insts prop;
nipkow@208
  1087
      val thm' = Thm{sign=signt, hyps=hyps union hypst,
clasohm@0
  1088
                     prop=prop', maxidx=maxidx}
clasohm@0
  1089
      val unit = trace_thm "Applying congruence rule" thm';
nipkow@112
  1090
      fun err() = error("Failed congruence proof!")
clasohm@0
  1091
clasohm@0
  1092
  in case prover thm' of
nipkow@112
  1093
       None => err()
nipkow@112
  1094
     | Some(thm2) => (case check_conv(thm2,prop') of
nipkow@112
  1095
                        None => err() | Some(x) => x)
clasohm@0
  1096
  end;
clasohm@0
  1097
clasohm@0
  1098
nipkow@214
  1099
fun bottomc ((simprem,useprem),prover,sign) =
clasohm@0
  1100
  let fun botc mss trec = let val trec1 = subc mss trec
nipkow@208
  1101
                          in case rewritec (prover,sign) mss trec1 of
clasohm@0
  1102
                               None => trec1
clasohm@0
  1103
                             | Some(trec2) => botc mss trec2
clasohm@0
  1104
                          end
clasohm@0
  1105
clasohm@0
  1106
      and subc (mss as Mss{net,congs,primes,prems,mk_rews})
nipkow@208
  1107
               (trec as (hyps,t)) =
clasohm@0
  1108
        (case t of
clasohm@0
  1109
            Abs(a,T,t) =>
clasohm@0
  1110
              let val v = Free(".subc." ^ primes,T)
clasohm@0
  1111
                  val mss' = Mss{net=net, congs=congs, primes=primes^"'",
clasohm@0
  1112
                                 prems=prems,mk_rews=mk_rews}
nipkow@208
  1113
                  val (hyps',t') = botc mss' (hyps,subst_bounds([v],t))
nipkow@208
  1114
              in  (hyps', Abs(a, T, abstract_over(v,t')))  end
clasohm@0
  1115
          | t$u => (case t of
nipkow@208
  1116
              Const("==>",_)$s  => impc(hyps,s,u,mss)
nipkow@208
  1117
            | Abs(_,_,body)     => subc mss (hyps,subst_bounds([u], body))
clasohm@0
  1118
            | _                 =>
nipkow@208
  1119
                let fun appc() = let val (hyps1,t1) = botc mss (hyps,t)
nipkow@208
  1120
                                     val (hyps2,u1) = botc mss (hyps1,u)
nipkow@208
  1121
                                 in (hyps2,t1$u1) end
clasohm@0
  1122
                    val (h,ts) = strip_comb t
clasohm@0
  1123
                in case h of
clasohm@0
  1124
                     Const(a,_) =>
clasohm@0
  1125
                       (case assoc(congs,a) of
clasohm@0
  1126
                          None => appc()
nipkow@208
  1127
                        | Some(cong) => congc (prover mss,sign) cong trec)
clasohm@0
  1128
                   | _ => appc()
clasohm@0
  1129
                end)
clasohm@0
  1130
          | _ => trec)
clasohm@0
  1131
nipkow@208
  1132
      and impc(hyps,s,u,mss as Mss{mk_rews,...}) =
nipkow@214
  1133
        let val (hyps1,s') = if simprem then botc mss (hyps,s) else (hyps,s)
nipkow@214
  1134
            val mss' =
nipkow@214
  1135
              if not useprem orelse maxidx_of_term s' <> ~1 then mss
nipkow@208
  1136
              else let val thm = Thm{sign=sign,hyps=[s'],prop=s',maxidx= ~1}
nipkow@214
  1137
                   in add_simps(add_prems(mss,[thm]), mk_rews thm) end
nipkow@208
  1138
            val (hyps2,u') = botc mss' (hyps1,u)
nipkow@134
  1139
            val hyps2' = if s' mem hyps1 then hyps2 else hyps2\s'
nipkow@208
  1140
        in (hyps2', Logic.mk_implies(s',u')) end
clasohm@0
  1141
clasohm@0
  1142
  in botc end;
clasohm@0
  1143
clasohm@0
  1144
clasohm@0
  1145
(*** Meta-rewriting: rewrites t to u and returns the theorem t==u ***)
clasohm@0
  1146
(* Parameters:
wenzelm@250
  1147
   mode = (simplify A, use A in simplifying B) when simplifying A ==> B
clasohm@0
  1148
   mss: contains equality theorems of the form [|p1,...|] ==> t==u
clasohm@0
  1149
   prover: how to solve premises in conditional rewrites and congruences
clasohm@0
  1150
*)
clasohm@0
  1151
clasohm@0
  1152
(*** FIXME: check that #primes(mss) does not "occur" in ct alread ***)
nipkow@214
  1153
fun rewrite_cterm mode mss prover ct =
lcp@229
  1154
  let val {sign, t, T, maxidx} = rep_cterm ct;
nipkow@214
  1155
      val (hyps,u) = bottomc (mode,prover,sign) mss ([],t);
clasohm@0
  1156
      val prop = Logic.mk_equals(t,u)
nipkow@208
  1157
  in  Thm{sign= sign, hyps= hyps, maxidx= maxidx_of_term prop, prop= prop}
clasohm@0
  1158
  end
clasohm@0
  1159
clasohm@0
  1160
end;
wenzelm@250
  1161