src/Pure/proofterm.ML
author wenzelm
Fri May 14 19:53:36 2010 +0200 (2010-05-14 ago)
changeset 36883 4ed0d72def50
parent 36882 f33760bb8ca0
child 37216 3165bc303f66
child 37231 e5419ecf92b7
permissions -rw-r--r--
added Proofterm.unconstrain_thm_proof for Thm.unconstrainT -- loosely based on the version by krauss/schropp;
berghofe@11519
     1
(*  Title:      Pure/proofterm.ML
wenzelm@11540
     2
    Author:     Stefan Berghofer, TU Muenchen
berghofe@11519
     3
wenzelm@11540
     4
LF style proof terms.
berghofe@11519
     5
*)
berghofe@11519
     6
berghofe@11615
     7
infix 8 % %% %>;
berghofe@11519
     8
berghofe@11519
     9
signature BASIC_PROOFTERM =
berghofe@11519
    10
sig
wenzelm@32738
    11
  val proofs: int Unsynchronized.ref
berghofe@11519
    12
berghofe@11519
    13
  datatype proof =
wenzelm@28803
    14
     MinProof
wenzelm@28803
    15
   | PBound of int
berghofe@11519
    16
   | Abst of string * typ option * proof
berghofe@11519
    17
   | AbsP of string * term option * proof
wenzelm@28803
    18
   | op % of proof * term option
wenzelm@28803
    19
   | op %% of proof * proof
berghofe@11519
    20
   | Hyp of term
berghofe@11519
    21
   | PAxm of string * term * typ list option
wenzelm@31943
    22
   | OfClass of typ * class
berghofe@11519
    23
   | Oracle of string * term * typ list option
wenzelm@28828
    24
   | Promise of serial * term * typ list
wenzelm@29635
    25
   | PThm of serial * ((string * term * typ list option) * proof_body future)
wenzelm@28803
    26
  and proof_body = PBody of
wenzelm@28803
    27
    {oracles: (string * term) OrdList.T,
wenzelm@29635
    28
     thms: (serial * (string * term * proof_body future)) OrdList.T,
wenzelm@28803
    29
     proof: proof}
berghofe@11519
    30
berghofe@11615
    31
  val %> : proof * term -> proof
berghofe@11519
    32
end;
berghofe@11519
    33
berghofe@11519
    34
signature PROOFTERM =
berghofe@11519
    35
sig
berghofe@11519
    36
  include BASIC_PROOFTERM
berghofe@11519
    37
wenzelm@28815
    38
  type oracle = string * term
wenzelm@29635
    39
  type pthm = serial * (string * term * proof_body future)
wenzelm@32094
    40
  val proof_of: proof_body -> proof
wenzelm@29635
    41
  val join_proof: proof_body future -> proof
wenzelm@30711
    42
  val fold_proof_atoms: bool -> (proof -> 'a -> 'a) -> proof list -> 'a -> 'a
wenzelm@32810
    43
  val fold_body_thms: (string * term * proof_body -> 'a -> 'a) -> proof_body list -> 'a -> 'a
wenzelm@32054
    44
  val join_bodies: proof_body list -> unit
wenzelm@30712
    45
  val status_of: proof_body list -> {failed: bool, oracle: bool, unfinished: bool}
wenzelm@28803
    46
wenzelm@28803
    47
  val oracle_ord: oracle * oracle -> order
wenzelm@28803
    48
  val thm_ord: pthm * pthm -> order
wenzelm@28803
    49
  val merge_oracles: oracle OrdList.T -> oracle OrdList.T -> oracle OrdList.T
wenzelm@28803
    50
  val merge_thms: pthm OrdList.T -> pthm OrdList.T -> pthm OrdList.T
wenzelm@30716
    51
  val all_oracles_of: proof_body -> oracle OrdList.T
wenzelm@30716
    52
  val approximate_proof_body: proof -> proof_body
wenzelm@28803
    53
berghofe@11519
    54
  (** primitive operations **)
wenzelm@28803
    55
  val proof_combt: proof * term list -> proof
wenzelm@28803
    56
  val proof_combt': proof * term option list -> proof
wenzelm@28803
    57
  val proof_combP: proof * proof list -> proof
wenzelm@28803
    58
  val strip_combt: proof -> proof * term option list
wenzelm@28803
    59
  val strip_combP: proof -> proof * proof list
wenzelm@28803
    60
  val strip_thm: proof_body -> proof_body
wenzelm@36620
    61
  val map_proof_terms_same: term Same.operation -> typ Same.operation -> proof Same.operation
wenzelm@36620
    62
  val map_proof_types_same: typ Same.operation -> proof Same.operation
wenzelm@28803
    63
  val map_proof_terms: (term -> term) -> (typ -> typ) -> proof -> proof
wenzelm@36620
    64
  val map_proof_types: (typ -> typ) -> proof -> proof
wenzelm@28803
    65
  val fold_proof_terms: (term -> 'a -> 'a) -> (typ -> 'a -> 'a) -> proof -> 'a -> 'a
wenzelm@28803
    66
  val maxidx_proof: proof -> int -> int
wenzelm@28803
    67
  val size_of_proof: proof -> int
wenzelm@28803
    68
  val change_type: typ list option -> proof -> proof
wenzelm@28803
    69
  val prf_abstract_over: term -> proof -> proof
wenzelm@28803
    70
  val prf_incr_bv: int -> int -> int -> int -> proof -> proof
wenzelm@28803
    71
  val incr_pboundvars: int -> int -> proof -> proof
wenzelm@28803
    72
  val prf_loose_bvar1: proof -> int -> bool
wenzelm@28803
    73
  val prf_loose_Pbvar1: proof -> int -> bool
wenzelm@28803
    74
  val prf_add_loose_bnos: int -> int -> proof -> int list * int list -> int list * int list
wenzelm@28803
    75
  val norm_proof: Envir.env -> proof -> proof
wenzelm@28803
    76
  val norm_proof': Envir.env -> proof -> proof
wenzelm@28803
    77
  val prf_subst_bounds: term list -> proof -> proof
wenzelm@28803
    78
  val prf_subst_pbounds: proof list -> proof -> proof
wenzelm@28803
    79
  val freeze_thaw_prf: proof -> proof * (proof -> proof)
berghofe@11519
    80
berghofe@11519
    81
  (** proof terms for specific inference rules **)
wenzelm@28803
    82
  val implies_intr_proof: term -> proof -> proof
wenzelm@28803
    83
  val forall_intr_proof: term -> string -> proof -> proof
wenzelm@28803
    84
  val varify_proof: term -> (string * sort) list -> proof -> proof
wenzelm@36619
    85
  val legacy_freezeT: term -> proof -> proof
wenzelm@28803
    86
  val rotate_proof: term list -> term -> int -> proof -> proof
wenzelm@36742
    87
  val permute_prems_proof: term list -> int -> int -> proof -> proof
wenzelm@19908
    88
  val generalize: string list * string list -> int -> proof -> proof
wenzelm@28803
    89
  val instantiate: ((indexname * sort) * typ) list * ((indexname * typ) * term) list
wenzelm@16880
    90
    -> proof -> proof
wenzelm@28803
    91
  val lift_proof: term -> int -> term -> proof -> proof
wenzelm@32027
    92
  val incr_indexes: int -> proof -> proof
wenzelm@28803
    93
  val assumption_proof: term list -> term -> int -> proof -> proof
wenzelm@28803
    94
  val bicompose_proof: bool -> term list -> term list -> term list -> term option ->
berghofe@23296
    95
    int -> int -> proof -> proof -> proof
wenzelm@28803
    96
  val equality_axms: (string * term) list
wenzelm@28803
    97
  val reflexive_axm: proof
wenzelm@28803
    98
  val symmetric_axm: proof
wenzelm@28803
    99
  val transitive_axm: proof
wenzelm@28803
   100
  val equal_intr_axm: proof
wenzelm@28803
   101
  val equal_elim_axm: proof
wenzelm@28803
   102
  val abstract_rule_axm: proof
wenzelm@28803
   103
  val combination_axm: proof
wenzelm@28803
   104
  val reflexive: proof
wenzelm@28803
   105
  val symmetric: proof -> proof
wenzelm@28803
   106
  val transitive: term -> typ -> proof -> proof -> proof
wenzelm@28803
   107
  val abstract_rule: term -> string -> proof -> proof
wenzelm@28803
   108
  val combination: term -> term -> term -> term -> typ -> proof -> proof -> proof
wenzelm@28803
   109
  val equal_intr: term -> term -> proof -> proof -> proof
wenzelm@28803
   110
  val equal_elim: term -> term -> proof -> proof -> proof
wenzelm@36621
   111
  val strip_shyps_proof: Sorts.algebra -> (typ * sort) list -> (typ * sort) list ->
wenzelm@36621
   112
    sort list -> proof -> proof
wenzelm@36740
   113
  val classrel_proof: theory -> class * class -> proof
wenzelm@36740
   114
  val arity_proof: theory -> string * sort list * class -> proof
wenzelm@36741
   115
  val of_sort_proof: theory -> (typ * class -> proof) -> typ * sort -> proof list
wenzelm@36740
   116
  val install_axclass_proofs:
wenzelm@36740
   117
   {classrel_proof: theory -> class * class -> proof,
wenzelm@36740
   118
    arity_proof: theory -> string * sort list * class -> proof} -> unit
wenzelm@28803
   119
  val axm_proof: string -> term -> proof
wenzelm@30716
   120
  val oracle_proof: string -> term -> oracle * proof
berghofe@11519
   121
berghofe@11519
   122
  (** rewriting on proof terms **)
wenzelm@28803
   123
  val add_prf_rrule: proof * proof -> theory -> theory
wenzelm@33722
   124
  val add_prf_rproc: (typ list -> proof -> (proof * proof) option) -> theory -> theory
wenzelm@33722
   125
  val no_skel: proof
wenzelm@33722
   126
  val normal_skel: proof
wenzelm@28803
   127
  val rewrite_proof: theory -> (proof * proof) list *
wenzelm@33722
   128
    (typ list -> proof -> (proof * proof) option) list -> proof -> proof
wenzelm@28803
   129
  val rewrite_proof_notypes: (proof * proof) list *
wenzelm@33722
   130
    (typ list -> proof -> (proof * proof) option) list -> proof -> proof
wenzelm@28803
   131
  val rew_proof: theory -> proof -> proof
wenzelm@36877
   132
wenzelm@36877
   133
  val promise_proof: theory -> serial -> term -> proof
wenzelm@36877
   134
  val fulfill_norm_proof: theory -> (serial * proof_body) list -> proof_body -> proof_body
wenzelm@36882
   135
  val unconstrain_thm_proofs: bool Unsynchronized.ref
wenzelm@36882
   136
  val thm_proof: theory -> string -> sort list -> term list -> term ->
wenzelm@36877
   137
    (serial * proof_body future) list -> proof_body -> pthm * proof
wenzelm@36883
   138
  val unconstrain_thm_proof: theory -> sort list -> term ->
wenzelm@36883
   139
    (serial * proof_body future) list -> proof_body -> pthm * proof
wenzelm@36877
   140
  val get_name: term list -> term -> proof -> string
wenzelm@36877
   141
  val get_name_unconstrained: sort list -> term list -> term -> proof -> string
wenzelm@36877
   142
  val guess_name: proof -> string
berghofe@11519
   143
end
berghofe@11519
   144
berghofe@11519
   145
structure Proofterm : PROOFTERM =
berghofe@11519
   146
struct
berghofe@11519
   147
wenzelm@28803
   148
(***** datatype proof *****)
wenzelm@28803
   149
berghofe@11519
   150
datatype proof =
wenzelm@28803
   151
   MinProof
wenzelm@28803
   152
 | PBound of int
berghofe@11519
   153
 | Abst of string * typ option * proof
berghofe@11519
   154
 | AbsP of string * term option * proof
wenzelm@12497
   155
 | op % of proof * term option
wenzelm@12497
   156
 | op %% of proof * proof
berghofe@11519
   157
 | Hyp of term
berghofe@11519
   158
 | PAxm of string * term * typ list option
wenzelm@31943
   159
 | OfClass of typ * class
berghofe@11519
   160
 | Oracle of string * term * typ list option
wenzelm@28828
   161
 | Promise of serial * term * typ list
wenzelm@29635
   162
 | PThm of serial * ((string * term * typ list option) * proof_body future)
wenzelm@28803
   163
and proof_body = PBody of
wenzelm@28803
   164
  {oracles: (string * term) OrdList.T,
wenzelm@29635
   165
   thms: (serial * (string * term * proof_body future)) OrdList.T,
wenzelm@28803
   166
   proof: proof};
berghofe@11519
   167
wenzelm@28815
   168
type oracle = string * term;
wenzelm@29635
   169
type pthm = serial * (string * term * proof_body future);
wenzelm@28815
   170
wenzelm@28803
   171
fun proof_of (PBody {proof, ...}) = proof;
wenzelm@32094
   172
val join_proof = Future.join #> proof_of;
berghofe@17017
   173
berghofe@17017
   174
wenzelm@28803
   175
(***** proof atoms *****)
wenzelm@28803
   176
wenzelm@28803
   177
fun fold_proof_atoms all f =
wenzelm@28803
   178
  let
wenzelm@28803
   179
    fun app (Abst (_, _, prf)) = app prf
wenzelm@28803
   180
      | app (AbsP (_, _, prf)) = app prf
wenzelm@28803
   181
      | app (prf % _) = app prf
wenzelm@28803
   182
      | app (prf1 %% prf2) = app prf1 #> app prf2
wenzelm@28803
   183
      | app (prf as PThm (i, (_, body))) = (fn (x, seen) =>
wenzelm@28803
   184
          if Inttab.defined seen i then (x, seen)
wenzelm@28803
   185
          else
wenzelm@28815
   186
            let val (x', seen') =
wenzelm@29635
   187
              (if all then app (join_proof body) else I) (x, Inttab.update (i, ()) seen)
wenzelm@28815
   188
            in (f prf x', seen') end)
wenzelm@28803
   189
      | app prf = (fn (x, seen) => (f prf x, seen));
wenzelm@28803
   190
  in fn prfs => fn x => #1 (fold app prfs (x, Inttab.empty)) end;
berghofe@19357
   191
wenzelm@30711
   192
fun fold_body_thms f =
wenzelm@30711
   193
  let
wenzelm@32726
   194
    fun app (PBody {thms, ...}) =
wenzelm@32094
   195
     (Future.join_results (map (#3 o #2) thms);
wenzelm@32094
   196
      thms |> fold (fn (i, (name, prop, body)) => fn (x, seen) =>
wenzelm@32726
   197
        if Inttab.defined seen i then (x, seen)
wenzelm@32094
   198
        else
wenzelm@32094
   199
          let
wenzelm@32094
   200
            val body' = Future.join body;
wenzelm@32726
   201
            val (x', seen') = app body' (x, Inttab.update (i, ()) seen);
wenzelm@32810
   202
          in (f (name, prop, body') x', seen') end));
wenzelm@32726
   203
  in fn bodies => fn x => #1 (fold app bodies (x, Inttab.empty)) end;
wenzelm@30711
   204
wenzelm@32054
   205
fun join_bodies bodies = fold_body_thms (fn _ => fn () => ()) bodies ();
wenzelm@32054
   206
wenzelm@30712
   207
fun status_of bodies =
wenzelm@30711
   208
  let
wenzelm@30711
   209
    fun status (PBody {oracles, thms, ...}) x =
wenzelm@30711
   210
      let
wenzelm@30711
   211
        val ((oracle, unfinished, failed), seen) =
wenzelm@30711
   212
          (thms, x) |-> fold (fn (i, (_, _, body)) => fn (st, seen) =>
wenzelm@30711
   213
            if Inttab.defined seen i then (st, seen)
wenzelm@30711
   214
            else
wenzelm@30711
   215
              let val seen' = Inttab.update (i, ()) seen in
wenzelm@30711
   216
                (case Future.peek body of
wenzelm@30711
   217
                  SOME (Exn.Result body') => status body' (st, seen')
wenzelm@30711
   218
                | SOME (Exn.Exn _) =>
wenzelm@30711
   219
                    let val (oracle, unfinished, _) = st
wenzelm@30711
   220
                    in ((oracle, unfinished, true), seen') end
wenzelm@30711
   221
                | NONE =>
wenzelm@30711
   222
                    let val (oracle, _, failed) = st
wenzelm@30711
   223
                    in ((oracle, true, failed), seen') end)
wenzelm@30711
   224
              end);
wenzelm@30711
   225
      in ((oracle orelse not (null oracles), unfinished, failed), seen) end;
wenzelm@32057
   226
    val (oracle, unfinished, failed) =
wenzelm@32057
   227
      #1 (fold status bodies ((false, false, false), Inttab.empty));
wenzelm@30711
   228
  in {oracle = oracle, unfinished = unfinished, failed = failed} end;
wenzelm@30711
   229
wenzelm@28803
   230
wenzelm@28815
   231
(* proof body *)
wenzelm@28803
   232
wenzelm@35408
   233
val oracle_ord = prod_ord fast_string_ord Term_Ord.fast_term_ord;
wenzelm@28803
   234
fun thm_ord ((i, _): pthm, (j, _)) = int_ord (j, i);
wenzelm@28803
   235
wenzelm@30716
   236
val merge_oracles = OrdList.union oracle_ord;
wenzelm@30716
   237
val merge_thms = OrdList.union thm_ord;
wenzelm@30716
   238
wenzelm@30716
   239
val all_oracles_of =
wenzelm@30716
   240
  let
wenzelm@32057
   241
    fun collect (PBody {oracles, thms, ...}) =
wenzelm@32094
   242
     (Future.join_results (map (#3 o #2) thms);
wenzelm@32057
   243
      thms |> fold (fn (i, (_, _, body)) => fn (x, seen) =>
wenzelm@32057
   244
        if Inttab.defined seen i then (x, seen)
wenzelm@32057
   245
        else
wenzelm@32057
   246
          let
wenzelm@32057
   247
            val body' = Future.join body;
wenzelm@32057
   248
            val (x', seen') = collect body' (x, Inttab.update (i, ()) seen);
wenzelm@32094
   249
          in (merge_oracles oracles x', seen') end));
wenzelm@30716
   250
  in fn body => #1 (collect body ([], Inttab.empty)) end;
wenzelm@30716
   251
wenzelm@30716
   252
fun approximate_proof_body prf =
wenzelm@28803
   253
  let
wenzelm@28803
   254
    val (oracles, thms) = fold_proof_atoms false
wenzelm@28803
   255
      (fn Oracle (s, prop, _) => apfst (cons (s, prop))
wenzelm@28815
   256
        | PThm (i, ((name, prop, _), body)) => apsnd (cons (i, (name, prop, body)))
wenzelm@28803
   257
        | _ => I) [prf] ([], []);
wenzelm@30716
   258
  in
wenzelm@30716
   259
    PBody
wenzelm@30716
   260
     {oracles = OrdList.make oracle_ord oracles,
wenzelm@30716
   261
      thms = OrdList.make thm_ord thms,
wenzelm@30716
   262
      proof = prf}
wenzelm@30716
   263
  end;
berghofe@11519
   264
wenzelm@28803
   265
wenzelm@28803
   266
(***** proof objects with different levels of detail *****)
berghofe@11519
   267
skalberg@15531
   268
fun (prf %> t) = prf % SOME t;
berghofe@11519
   269
skalberg@15570
   270
val proof_combt = Library.foldl (op %>);
skalberg@15570
   271
val proof_combt' = Library.foldl (op %);
skalberg@15570
   272
val proof_combP = Library.foldl (op %%);
berghofe@11519
   273
wenzelm@21646
   274
fun strip_combt prf =
berghofe@11615
   275
    let fun stripc (prf % t, ts) = stripc (prf, t::ts)
wenzelm@21646
   276
          | stripc  x =  x
berghofe@11519
   277
    in  stripc (prf, [])  end;
berghofe@11519
   278
wenzelm@21646
   279
fun strip_combP prf =
berghofe@11615
   280
    let fun stripc (prf %% prf', prfs) = stripc (prf, prf'::prfs)
berghofe@11519
   281
          | stripc  x =  x
berghofe@11519
   282
    in  stripc (prf, [])  end;
berghofe@11519
   283
wenzelm@28803
   284
fun strip_thm (body as PBody {proof, ...}) =
wenzelm@28803
   285
  (case strip_combt (fst (strip_combP proof)) of
wenzelm@29635
   286
    (PThm (_, (_, body')), _) => Future.join body'
wenzelm@28803
   287
  | _ => body);
berghofe@11519
   288
wenzelm@23178
   289
val mk_Abst = fold_rev (fn (s, T:typ) => fn prf => Abst (s, NONE, prf));
skalberg@15531
   290
fun mk_AbsP (i, prf) = funpow i (fn prf => AbsP ("H", NONE, prf)) prf;
berghofe@11519
   291
wenzelm@36620
   292
fun map_proof_same term typ ofclass =
wenzelm@20000
   293
  let
wenzelm@32024
   294
    val typs = Same.map typ;
wenzelm@20000
   295
wenzelm@32024
   296
    fun proof (Abst (s, T, prf)) =
wenzelm@32024
   297
          (Abst (s, Same.map_option typ T, Same.commit proof prf)
wenzelm@32024
   298
            handle Same.SAME => Abst (s, T, proof prf))
wenzelm@32024
   299
      | proof (AbsP (s, t, prf)) =
wenzelm@32024
   300
          (AbsP (s, Same.map_option term t, Same.commit proof prf)
wenzelm@32024
   301
            handle Same.SAME => AbsP (s, t, proof prf))
wenzelm@32024
   302
      | proof (prf % t) =
wenzelm@32024
   303
          (proof prf % Same.commit (Same.map_option term) t
wenzelm@32024
   304
            handle Same.SAME => prf % Same.map_option term t)
wenzelm@32024
   305
      | proof (prf1 %% prf2) =
wenzelm@32024
   306
          (proof prf1 %% Same.commit proof prf2
wenzelm@32024
   307
            handle Same.SAME => prf1 %% proof prf2)
wenzelm@32024
   308
      | proof (PAxm (a, prop, SOME Ts)) = PAxm (a, prop, SOME (typs Ts))
wenzelm@36620
   309
      | proof (OfClass T_c) = ofclass T_c
wenzelm@32024
   310
      | proof (Oracle (a, prop, SOME Ts)) = Oracle (a, prop, SOME (typs Ts))
wenzelm@32024
   311
      | proof (Promise (i, prop, Ts)) = Promise (i, prop, typs Ts)
wenzelm@32057
   312
      | proof (PThm (i, ((a, prop, SOME Ts), body))) =
wenzelm@32057
   313
          PThm (i, ((a, prop, SOME (typs Ts)), body))
wenzelm@32024
   314
      | proof _ = raise Same.SAME;
wenzelm@36620
   315
  in proof end;
wenzelm@36620
   316
wenzelm@36620
   317
fun map_proof_terms_same term typ = map_proof_same term typ (fn (T, c) => OfClass (typ T, c));
wenzelm@36620
   318
fun map_proof_types_same typ = map_proof_terms_same (Term_Subst.map_types_same typ) typ;
wenzelm@20000
   319
haftmann@22662
   320
fun same eq f x =
berghofe@11715
   321
  let val x' = f x
wenzelm@32019
   322
  in if eq (x, x') then raise Same.SAME else x' end;
berghofe@11715
   323
wenzelm@36620
   324
fun map_proof_terms f g = Same.commit (map_proof_terms_same (same (op =) f) (same (op =) g));
wenzelm@36620
   325
fun map_proof_types f = Same.commit (map_proof_types_same (same (op =) f));
berghofe@11519
   326
wenzelm@20147
   327
fun fold_proof_terms f g (Abst (_, SOME T, prf)) = g T #> fold_proof_terms f g prf
wenzelm@20147
   328
  | fold_proof_terms f g (Abst (_, NONE, prf)) = fold_proof_terms f g prf
wenzelm@20147
   329
  | fold_proof_terms f g (AbsP (_, SOME t, prf)) = f t #> fold_proof_terms f g prf
wenzelm@20147
   330
  | fold_proof_terms f g (AbsP (_, NONE, prf)) = fold_proof_terms f g prf
wenzelm@20147
   331
  | fold_proof_terms f g (prf % SOME t) = fold_proof_terms f g prf #> f t
wenzelm@20147
   332
  | fold_proof_terms f g (prf % NONE) = fold_proof_terms f g prf
wenzelm@20147
   333
  | fold_proof_terms f g (prf1 %% prf2) =
wenzelm@20147
   334
      fold_proof_terms f g prf1 #> fold_proof_terms f g prf2
wenzelm@20159
   335
  | fold_proof_terms _ g (PAxm (_, _, SOME Ts)) = fold g Ts
wenzelm@31943
   336
  | fold_proof_terms _ g (OfClass (T, _)) = g T
wenzelm@28828
   337
  | fold_proof_terms _ g (Oracle (_, _, SOME Ts)) = fold g Ts
wenzelm@28828
   338
  | fold_proof_terms _ g (Promise (_, _, Ts)) = fold g Ts
wenzelm@28803
   339
  | fold_proof_terms _ g (PThm (_, ((_, _, SOME Ts), _))) = fold g Ts
wenzelm@20147
   340
  | fold_proof_terms _ _ _ = I;
berghofe@11519
   341
wenzelm@20300
   342
fun maxidx_proof prf = fold_proof_terms Term.maxidx_term Term.maxidx_typ prf;
berghofe@12868
   343
berghofe@13744
   344
fun size_of_proof (Abst (_, _, prf)) = 1 + size_of_proof prf
berghofe@13749
   345
  | size_of_proof (AbsP (_, t, prf)) = 1 + size_of_proof prf
wenzelm@28803
   346
  | size_of_proof (prf % _) = 1 + size_of_proof prf
berghofe@13744
   347
  | size_of_proof (prf1 %% prf2) = size_of_proof prf1 + size_of_proof prf2
berghofe@13744
   348
  | size_of_proof _ = 1;
berghofe@13744
   349
wenzelm@28803
   350
fun change_type opTs (PAxm (name, prop, _)) = PAxm (name, prop, opTs)
wenzelm@31943
   351
  | change_type (SOME [T]) (OfClass (_, c)) = OfClass (T, c)
berghofe@12907
   352
  | change_type opTs (Oracle (name, prop, _)) = Oracle (name, prop, opTs)
wenzelm@36879
   353
  | change_type opTs (Promise _) = raise Fail "change_type: unexpected promise"
wenzelm@32057
   354
  | change_type opTs (PThm (i, ((name, prop, _), body))) =
wenzelm@32057
   355
      PThm (i, ((name, prop, opTs), body))
berghofe@12907
   356
  | change_type _ prf = prf;
berghofe@12907
   357
berghofe@11519
   358
berghofe@11519
   359
(***** utilities *****)
berghofe@11519
   360
berghofe@11519
   361
fun strip_abs (_::Ts) (Abs (_, _, t)) = strip_abs Ts t
berghofe@11519
   362
  | strip_abs _ t = t;
berghofe@11519
   363
skalberg@15570
   364
fun mk_abs Ts t = Library.foldl (fn (t', T) => Abs ("", T, t')) (t, Ts);
berghofe@11519
   365
berghofe@11519
   366
wenzelm@21646
   367
(*Abstraction of a proof term over its occurrences of v,
berghofe@11519
   368
    which must contain no loose bound variables.
berghofe@11519
   369
  The resulting proof term is ready to become the body of an Abst.*)
berghofe@11519
   370
berghofe@11519
   371
fun prf_abstract_over v =
berghofe@11519
   372
  let
berghofe@11715
   373
    fun abst' lev u = if v aconv u then Bound lev else
berghofe@11715
   374
      (case u of
berghofe@11715
   375
         Abs (a, T, t) => Abs (a, T, abst' (lev + 1) t)
wenzelm@32019
   376
       | f $ t => (abst' lev f $ absth' lev t handle Same.SAME => f $ abst' lev t)
wenzelm@32019
   377
       | _ => raise Same.SAME)
wenzelm@32019
   378
    and absth' lev t = (abst' lev t handle Same.SAME => t);
berghofe@11519
   379
berghofe@11715
   380
    fun abst lev (AbsP (a, t, prf)) =
wenzelm@32024
   381
          (AbsP (a, Same.map_option (abst' lev) t, absth lev prf)
wenzelm@32019
   382
           handle Same.SAME => AbsP (a, t, abst lev prf))
berghofe@11715
   383
      | abst lev (Abst (a, T, prf)) = Abst (a, T, abst (lev + 1) prf)
berghofe@11715
   384
      | abst lev (prf1 %% prf2) = (abst lev prf1 %% absth lev prf2
wenzelm@32019
   385
          handle Same.SAME => prf1 %% abst lev prf2)
skalberg@15570
   386
      | abst lev (prf % t) = (abst lev prf % Option.map (absth' lev) t
wenzelm@32024
   387
          handle Same.SAME => prf % Same.map_option (abst' lev) t)
wenzelm@32019
   388
      | abst _ _ = raise Same.SAME
wenzelm@32024
   389
    and absth lev prf = (abst lev prf handle Same.SAME => prf);
berghofe@11519
   390
berghofe@11715
   391
  in absth 0 end;
berghofe@11519
   392
berghofe@11519
   393
berghofe@11519
   394
(*increments a proof term's non-local bound variables
berghofe@11519
   395
  required when moving a proof term within abstractions
berghofe@11519
   396
     inc is  increment for bound variables
berghofe@11519
   397
     lev is  level at which a bound variable is considered 'loose'*)
berghofe@11519
   398
berghofe@11519
   399
fun incr_bv' inct tlev t = incr_bv (inct, tlev, t);
berghofe@11519
   400
berghofe@11715
   401
fun prf_incr_bv' incP inct Plev tlev (PBound i) =
wenzelm@32019
   402
      if i >= Plev then PBound (i+incP) else raise Same.SAME
berghofe@11715
   403
  | prf_incr_bv' incP inct Plev tlev (AbsP (a, t, body)) =
wenzelm@32024
   404
      (AbsP (a, Same.map_option (same (op =) (incr_bv' inct tlev)) t,
wenzelm@32019
   405
         prf_incr_bv incP inct (Plev+1) tlev body) handle Same.SAME =>
berghofe@11715
   406
           AbsP (a, t, prf_incr_bv' incP inct (Plev+1) tlev body))
berghofe@11715
   407
  | prf_incr_bv' incP inct Plev tlev (Abst (a, T, body)) =
berghofe@11715
   408
      Abst (a, T, prf_incr_bv' incP inct Plev (tlev+1) body)
wenzelm@21646
   409
  | prf_incr_bv' incP inct Plev tlev (prf %% prf') =
berghofe@11715
   410
      (prf_incr_bv' incP inct Plev tlev prf %% prf_incr_bv incP inct Plev tlev prf'
wenzelm@32019
   411
       handle Same.SAME => prf %% prf_incr_bv' incP inct Plev tlev prf')
wenzelm@21646
   412
  | prf_incr_bv' incP inct Plev tlev (prf % t) =
skalberg@15570
   413
      (prf_incr_bv' incP inct Plev tlev prf % Option.map (incr_bv' inct tlev) t
wenzelm@32024
   414
       handle Same.SAME => prf % Same.map_option (same (op =) (incr_bv' inct tlev)) t)
wenzelm@32019
   415
  | prf_incr_bv' _ _ _ _ _ = raise Same.SAME
berghofe@11715
   416
and prf_incr_bv incP inct Plev tlev prf =
wenzelm@32019
   417
      (prf_incr_bv' incP inct Plev tlev prf handle Same.SAME => prf);
berghofe@11519
   418
berghofe@11519
   419
fun incr_pboundvars  0 0 prf = prf
berghofe@11519
   420
  | incr_pboundvars incP inct prf = prf_incr_bv incP inct 0 0 prf;
berghofe@11519
   421
berghofe@11519
   422
berghofe@11615
   423
fun prf_loose_bvar1 (prf1 %% prf2) k = prf_loose_bvar1 prf1 k orelse prf_loose_bvar1 prf2 k
skalberg@15531
   424
  | prf_loose_bvar1 (prf % SOME t) k = prf_loose_bvar1 prf k orelse loose_bvar1 (t, k)
skalberg@15531
   425
  | prf_loose_bvar1 (_ % NONE) _ = true
skalberg@15531
   426
  | prf_loose_bvar1 (AbsP (_, SOME t, prf)) k = loose_bvar1 (t, k) orelse prf_loose_bvar1 prf k
skalberg@15531
   427
  | prf_loose_bvar1 (AbsP (_, NONE, _)) k = true
berghofe@11519
   428
  | prf_loose_bvar1 (Abst (_, _, prf)) k = prf_loose_bvar1 prf (k+1)
berghofe@11519
   429
  | prf_loose_bvar1 _ _ = false;
berghofe@11519
   430
berghofe@11519
   431
fun prf_loose_Pbvar1 (PBound i) k = i = k
berghofe@11615
   432
  | prf_loose_Pbvar1 (prf1 %% prf2) k = prf_loose_Pbvar1 prf1 k orelse prf_loose_Pbvar1 prf2 k
berghofe@11615
   433
  | prf_loose_Pbvar1 (prf % _) k = prf_loose_Pbvar1 prf k
berghofe@11519
   434
  | prf_loose_Pbvar1 (AbsP (_, _, prf)) k = prf_loose_Pbvar1 prf (k+1)
berghofe@11519
   435
  | prf_loose_Pbvar1 (Abst (_, _, prf)) k = prf_loose_Pbvar1 prf k
berghofe@11519
   436
  | prf_loose_Pbvar1 _ _ = false;
berghofe@11519
   437
berghofe@12279
   438
fun prf_add_loose_bnos plev tlev (PBound i) (is, js) =
wenzelm@17492
   439
      if i < plev then (is, js) else (insert (op =) (i-plev) is, js)
berghofe@12279
   440
  | prf_add_loose_bnos plev tlev (prf1 %% prf2) p =
berghofe@12279
   441
      prf_add_loose_bnos plev tlev prf2
berghofe@12279
   442
        (prf_add_loose_bnos plev tlev prf1 p)
berghofe@12279
   443
  | prf_add_loose_bnos plev tlev (prf % opt) (is, js) =
berghofe@12279
   444
      prf_add_loose_bnos plev tlev prf (case opt of
wenzelm@17492
   445
          NONE => (is, insert (op =) ~1 js)
skalberg@15531
   446
        | SOME t => (is, add_loose_bnos (t, tlev, js)))
berghofe@12279
   447
  | prf_add_loose_bnos plev tlev (AbsP (_, opt, prf)) (is, js) =
berghofe@12279
   448
      prf_add_loose_bnos (plev+1) tlev prf (case opt of
wenzelm@17492
   449
          NONE => (is, insert (op =) ~1 js)
skalberg@15531
   450
        | SOME t => (is, add_loose_bnos (t, tlev, js)))
berghofe@12279
   451
  | prf_add_loose_bnos plev tlev (Abst (_, _, prf)) p =
berghofe@12279
   452
      prf_add_loose_bnos plev (tlev+1) prf p
berghofe@12279
   453
  | prf_add_loose_bnos _ _ _ _ = ([], []);
berghofe@12279
   454
berghofe@11519
   455
berghofe@11519
   456
(**** substitutions ****)
berghofe@11519
   457
wenzelm@31977
   458
fun del_conflicting_tvars envT T = Term_Subst.instantiateT
wenzelm@19482
   459
  (map_filter (fn ixnS as (_, S) =>
haftmann@26328
   460
     (Type.lookup envT ixnS; NONE) handle TYPE _ =>
wenzelm@29270
   461
        SOME (ixnS, TFree ("'dummy", S))) (OldTerm.typ_tvars T)) T;
berghofe@18316
   462
wenzelm@31977
   463
fun del_conflicting_vars env t = Term_Subst.instantiate
wenzelm@19482
   464
  (map_filter (fn ixnS as (_, S) =>
wenzelm@32019
   465
     (Type.lookup (Envir.type_env env) ixnS; NONE) handle TYPE _ =>
wenzelm@29270
   466
        SOME (ixnS, TFree ("'dummy", S))) (OldTerm.term_tvars t),
wenzelm@19482
   467
   map_filter (fn Var (ixnT as (_, T)) =>
berghofe@18316
   468
     (Envir.lookup (env, ixnT); NONE) handle TYPE _ =>
wenzelm@29265
   469
        SOME (ixnT, Free ("dummy", T))) (OldTerm.term_vars t)) t;
berghofe@18316
   470
berghofe@11519
   471
fun norm_proof env =
berghofe@11519
   472
  let
wenzelm@32019
   473
    val envT = Envir.type_env env;
berghofe@18316
   474
    fun msg s = warning ("type conflict in norm_proof:\n" ^ s);
berghofe@18316
   475
    fun htype f t = f env t handle TYPE (s, _, _) =>
berghofe@18316
   476
      (msg s; f env (del_conflicting_vars env t));
berghofe@18316
   477
    fun htypeT f T = f envT T handle TYPE (s, _, _) =>
berghofe@18316
   478
      (msg s; f envT (del_conflicting_tvars envT T));
berghofe@18316
   479
    fun htypeTs f Ts = f envT Ts handle TYPE (s, _, _) =>
berghofe@18316
   480
      (msg s; f envT (map (del_conflicting_tvars envT) Ts));
wenzelm@32024
   481
wenzelm@32019
   482
    fun norm (Abst (s, T, prf)) =
wenzelm@32024
   483
          (Abst (s, Same.map_option (htypeT Envir.norm_type_same) T, Same.commit norm prf)
wenzelm@32019
   484
            handle Same.SAME => Abst (s, T, norm prf))
wenzelm@32019
   485
      | norm (AbsP (s, t, prf)) =
wenzelm@32024
   486
          (AbsP (s, Same.map_option (htype Envir.norm_term_same) t, Same.commit norm prf)
wenzelm@32019
   487
            handle Same.SAME => AbsP (s, t, norm prf))
wenzelm@32019
   488
      | norm (prf % t) =
wenzelm@32019
   489
          (norm prf % Option.map (htype Envir.norm_term) t
wenzelm@32024
   490
            handle Same.SAME => prf % Same.map_option (htype Envir.norm_term_same) t)
wenzelm@32019
   491
      | norm (prf1 %% prf2) =
wenzelm@32019
   492
          (norm prf1 %% Same.commit norm prf2
wenzelm@32019
   493
            handle Same.SAME => prf1 %% norm prf2)
wenzelm@32019
   494
      | norm (PAxm (s, prop, Ts)) =
wenzelm@32024
   495
          PAxm (s, prop, Same.map_option (htypeTs Envir.norm_types_same) Ts)
wenzelm@32019
   496
      | norm (OfClass (T, c)) =
wenzelm@32019
   497
          OfClass (htypeT Envir.norm_type_same T, c)
wenzelm@32019
   498
      | norm (Oracle (s, prop, Ts)) =
wenzelm@32024
   499
          Oracle (s, prop, Same.map_option (htypeTs Envir.norm_types_same) Ts)
wenzelm@32019
   500
      | norm (Promise (i, prop, Ts)) =
wenzelm@32019
   501
          Promise (i, prop, htypeTs Envir.norm_types_same Ts)
wenzelm@28803
   502
      | norm (PThm (i, ((s, t, Ts), body))) =
wenzelm@32024
   503
          PThm (i, ((s, t, Same.map_option (htypeTs Envir.norm_types_same) Ts), body))
wenzelm@32019
   504
      | norm _ = raise Same.SAME;
wenzelm@32019
   505
  in Same.commit norm end;
berghofe@11519
   506
wenzelm@28803
   507
berghofe@11519
   508
(***** Remove some types in proof term (to save space) *****)
berghofe@11519
   509
berghofe@11519
   510
fun remove_types (Abs (s, _, t)) = Abs (s, dummyT, remove_types t)
berghofe@11519
   511
  | remove_types (t $ u) = remove_types t $ remove_types u
berghofe@11519
   512
  | remove_types (Const (s, _)) = Const (s, dummyT)
berghofe@11519
   513
  | remove_types t = t;
berghofe@11519
   514
wenzelm@32032
   515
fun remove_types_env (Envir.Envir {maxidx, tenv, tyenv}) =
wenzelm@32032
   516
  Envir.Envir {maxidx = maxidx, tenv = Vartab.map (apsnd remove_types) tenv, tyenv = tyenv};
berghofe@11519
   517
berghofe@11519
   518
fun norm_proof' env prf = norm_proof (remove_types_env env) prf;
berghofe@11519
   519
wenzelm@28803
   520
berghofe@11519
   521
(**** substitution of bound variables ****)
berghofe@11519
   522
berghofe@11519
   523
fun prf_subst_bounds args prf =
berghofe@11519
   524
  let
berghofe@11519
   525
    val n = length args;
berghofe@11519
   526
    fun subst' lev (Bound i) =
wenzelm@32019
   527
         (if i<lev then raise Same.SAME    (*var is locally bound*)
wenzelm@30146
   528
          else  incr_boundvars lev (nth args (i-lev))
wenzelm@30146
   529
                  handle Subscript => Bound (i-n))  (*loose: change it*)
berghofe@11519
   530
      | subst' lev (Abs (a, T, body)) = Abs (a, T,  subst' (lev+1) body)
berghofe@11519
   531
      | subst' lev (f $ t) = (subst' lev f $ substh' lev t
wenzelm@32019
   532
          handle Same.SAME => f $ subst' lev t)
wenzelm@32019
   533
      | subst' _ _ = raise Same.SAME
wenzelm@32019
   534
    and substh' lev t = (subst' lev t handle Same.SAME => t);
berghofe@11519
   535
wenzelm@32057
   536
    fun subst lev (AbsP (a, t, body)) =
wenzelm@32057
   537
        (AbsP (a, Same.map_option (subst' lev) t, substh lev body)
wenzelm@32019
   538
          handle Same.SAME => AbsP (a, t, subst lev body))
berghofe@11519
   539
      | subst lev (Abst (a, T, body)) = Abst (a, T, subst (lev+1) body)
berghofe@11615
   540
      | subst lev (prf %% prf') = (subst lev prf %% substh lev prf'
wenzelm@32019
   541
          handle Same.SAME => prf %% subst lev prf')
skalberg@15570
   542
      | subst lev (prf % t) = (subst lev prf % Option.map (substh' lev) t
wenzelm@32024
   543
          handle Same.SAME => prf % Same.map_option (subst' lev) t)
wenzelm@32019
   544
      | subst _ _ = raise Same.SAME
wenzelm@32024
   545
    and substh lev prf = (subst lev prf handle Same.SAME => prf);
berghofe@11519
   546
  in case args of [] => prf | _ => substh 0 prf end;
berghofe@11519
   547
berghofe@11519
   548
fun prf_subst_pbounds args prf =
berghofe@11519
   549
  let
berghofe@11519
   550
    val n = length args;
berghofe@11519
   551
    fun subst (PBound i) Plev tlev =
wenzelm@32019
   552
         (if i < Plev then raise Same.SAME    (*var is locally bound*)
wenzelm@30146
   553
          else incr_pboundvars Plev tlev (nth args (i-Plev))
berghofe@11519
   554
                 handle Subscript => PBound (i-n)  (*loose: change it*))
berghofe@11519
   555
      | subst (AbsP (a, t, body)) Plev tlev = AbsP (a, t, subst body (Plev+1) tlev)
berghofe@11519
   556
      | subst (Abst (a, T, body)) Plev tlev = Abst (a, T, subst body Plev (tlev+1))
berghofe@11615
   557
      | subst (prf %% prf') Plev tlev = (subst prf Plev tlev %% substh prf' Plev tlev
wenzelm@32019
   558
          handle Same.SAME => prf %% subst prf' Plev tlev)
berghofe@11615
   559
      | subst (prf % t) Plev tlev = subst prf Plev tlev % t
wenzelm@32019
   560
      | subst  prf _ _ = raise Same.SAME
wenzelm@32019
   561
    and substh prf Plev tlev = (subst prf Plev tlev handle Same.SAME => prf)
berghofe@11519
   562
  in case args of [] => prf | _ => substh prf 0 0 end;
berghofe@11519
   563
berghofe@11519
   564
berghofe@11519
   565
(**** Freezing and thawing of variables in proof terms ****)
berghofe@11519
   566
berghofe@11519
   567
fun frzT names =
haftmann@17325
   568
  map_type_tvar (fn (ixn, xs) => TFree ((the o AList.lookup (op =) names) ixn, xs));
berghofe@11519
   569
berghofe@11519
   570
fun thawT names =
haftmann@17325
   571
  map_type_tfree (fn (s, xs) => case AList.lookup (op =) names s of
skalberg@15531
   572
      NONE => TFree (s, xs)
skalberg@15531
   573
    | SOME ixn => TVar (ixn, xs));
berghofe@11519
   574
berghofe@11519
   575
fun freeze names names' (t $ u) =
berghofe@11519
   576
      freeze names names' t $ freeze names names' u
berghofe@11519
   577
  | freeze names names' (Abs (s, T, t)) =
berghofe@11519
   578
      Abs (s, frzT names' T, freeze names names' t)
berghofe@11519
   579
  | freeze names names' (Const (s, T)) = Const (s, frzT names' T)
berghofe@11519
   580
  | freeze names names' (Free (s, T)) = Free (s, frzT names' T)
berghofe@11519
   581
  | freeze names names' (Var (ixn, T)) =
haftmann@17325
   582
      Free ((the o AList.lookup (op =) names) ixn, frzT names' T)
berghofe@11519
   583
  | freeze names names' t = t;
berghofe@11519
   584
berghofe@11519
   585
fun thaw names names' (t $ u) =
berghofe@11519
   586
      thaw names names' t $ thaw names names' u
berghofe@11519
   587
  | thaw names names' (Abs (s, T, t)) =
berghofe@11519
   588
      Abs (s, thawT names' T, thaw names names' t)
berghofe@11519
   589
  | thaw names names' (Const (s, T)) = Const (s, thawT names' T)
wenzelm@21646
   590
  | thaw names names' (Free (s, T)) =
berghofe@11519
   591
      let val T' = thawT names' T
haftmann@17325
   592
      in case AList.lookup (op =) names s of
skalberg@15531
   593
          NONE => Free (s, T')
skalberg@15531
   594
        | SOME ixn => Var (ixn, T')
berghofe@11519
   595
      end
berghofe@11519
   596
  | thaw names names' (Var (ixn, T)) = Var (ixn, thawT names' T)
berghofe@11519
   597
  | thaw names names' t = t;
berghofe@11519
   598
berghofe@11519
   599
fun freeze_thaw_prf prf =
berghofe@11519
   600
  let
berghofe@11519
   601
    val (fs, Tfs, vs, Tvs) = fold_proof_terms
wenzelm@20147
   602
      (fn t => fn (fs, Tfs, vs, Tvs) =>
wenzelm@29261
   603
         (Term.add_free_names t fs, Term.add_tfree_names t Tfs,
wenzelm@29261
   604
          Term.add_var_names t vs, Term.add_tvar_names t Tvs))
wenzelm@20147
   605
      (fn T => fn (fs, Tfs, vs, Tvs) =>
wenzelm@29261
   606
         (fs, Term.add_tfree_namesT T Tfs,
wenzelm@29261
   607
          vs, Term.add_tvar_namesT T Tvs))
wenzelm@20147
   608
      prf ([], [], [], []);
wenzelm@29261
   609
    val names = vs ~~ Name.variant_list fs (map fst vs);
wenzelm@20071
   610
    val names' = Tvs ~~ Name.variant_list Tfs (map fst Tvs);
berghofe@11519
   611
    val rnames = map swap names;
berghofe@11519
   612
    val rnames' = map swap names';
berghofe@11519
   613
  in
berghofe@11519
   614
    (map_proof_terms (freeze names names') (frzT names') prf,
berghofe@11519
   615
     map_proof_terms (thaw rnames rnames') (thawT rnames'))
berghofe@11519
   616
  end;
berghofe@11519
   617
berghofe@11519
   618
berghofe@11519
   619
(***** implication introduction *****)
berghofe@11519
   620
berghofe@11519
   621
fun implies_intr_proof h prf =
berghofe@11519
   622
  let
wenzelm@32019
   623
    fun abshyp i (Hyp t) = if h aconv t then PBound i else raise Same.SAME
berghofe@11519
   624
      | abshyp i (Abst (s, T, prf)) = Abst (s, T, abshyp i prf)
wenzelm@32024
   625
      | abshyp i (AbsP (s, t, prf)) = AbsP (s, t, abshyp (i + 1) prf)
berghofe@11615
   626
      | abshyp i (prf % t) = abshyp i prf % t
wenzelm@32024
   627
      | abshyp i (prf1 %% prf2) =
wenzelm@32024
   628
          (abshyp i prf1 %% abshyph i prf2
wenzelm@32024
   629
            handle Same.SAME => prf1 %% abshyp i prf2)
wenzelm@32019
   630
      | abshyp _ _ = raise Same.SAME
wenzelm@32024
   631
    and abshyph i prf = (abshyp i prf handle Same.SAME => prf);
berghofe@11519
   632
  in
skalberg@15531
   633
    AbsP ("H", NONE (*h*), abshyph 0 prf)
berghofe@11519
   634
  end;
berghofe@11519
   635
berghofe@11519
   636
berghofe@11519
   637
(***** forall introduction *****)
berghofe@11519
   638
skalberg@15531
   639
fun forall_intr_proof x a prf = Abst (a, NONE, prf_abstract_over x prf);
berghofe@11519
   640
berghofe@11519
   641
berghofe@11519
   642
(***** varify *****)
berghofe@11519
   643
berghofe@11519
   644
fun varify_proof t fixed prf =
berghofe@11519
   645
  let
wenzelm@19304
   646
    val fs = Term.fold_types (Term.fold_atyps
wenzelm@19304
   647
      (fn TFree v => if member (op =) fixed v then I else insert (op =) v | _ => I)) t [];
wenzelm@29261
   648
    val used = Name.context
wenzelm@29261
   649
      |> fold_types (fold_atyps (fn TVar ((a, _), _) => Name.declare a | _ => I)) t;
wenzelm@32024
   650
    val fmap = fs ~~ #1 (Name.variants (map fst fs) used);
berghofe@11519
   651
    fun thaw (f as (a, S)) =
haftmann@17314
   652
      (case AList.lookup (op =) fmap f of
skalberg@15531
   653
        NONE => TFree f
skalberg@15531
   654
      | SOME b => TVar ((b, 0), S));
wenzelm@28803
   655
  in map_proof_terms (map_types (map_type_tfree thaw)) (map_type_tfree thaw) prf end;
berghofe@11519
   656
berghofe@11519
   657
berghofe@11519
   658
local
berghofe@11519
   659
berghofe@11519
   660
fun new_name (ix, (pairs,used)) =
wenzelm@20071
   661
  let val v = Name.variant used (string_of_indexname ix)
berghofe@11519
   662
  in  ((ix, v) :: pairs, v :: used)  end;
berghofe@11519
   663
haftmann@17325
   664
fun freeze_one alist (ix, sort) = (case AList.lookup (op =) alist ix of
skalberg@15531
   665
    NONE => TVar (ix, sort)
skalberg@15531
   666
  | SOME name => TFree (name, sort));
berghofe@11519
   667
berghofe@11519
   668
in
berghofe@11519
   669
wenzelm@36619
   670
fun legacy_freezeT t prf =
berghofe@11519
   671
  let
wenzelm@29270
   672
    val used = OldTerm.it_term_types OldTerm.add_typ_tfree_names (t, [])
wenzelm@29270
   673
    and tvars = map #1 (OldTerm.it_term_types OldTerm.add_typ_tvars (t, []));
wenzelm@23178
   674
    val (alist, _) = List.foldr new_name ([], used) tvars;
berghofe@11519
   675
  in
berghofe@11519
   676
    (case alist of
berghofe@11519
   677
      [] => prf (*nothing to do!*)
berghofe@11519
   678
    | _ =>
berghofe@11519
   679
      let val frzT = map_type_tvar (freeze_one alist)
wenzelm@20548
   680
      in map_proof_terms (map_types frzT) frzT prf end)
berghofe@11519
   681
  end;
berghofe@11519
   682
berghofe@11519
   683
end;
berghofe@11519
   684
berghofe@11519
   685
berghofe@11519
   686
(***** rotate assumptions *****)
berghofe@11519
   687
berghofe@11519
   688
fun rotate_proof Bs Bi m prf =
berghofe@11519
   689
  let
berghofe@11519
   690
    val params = Term.strip_all_vars Bi;
berghofe@11519
   691
    val asms = Logic.strip_imp_prems (Term.strip_all_body Bi);
berghofe@11519
   692
    val i = length asms;
berghofe@11519
   693
    val j = length Bs;
berghofe@11519
   694
  in
berghofe@11519
   695
    mk_AbsP (j+1, proof_combP (prf, map PBound
wenzelm@23178
   696
      (j downto 1) @ [mk_Abst params (mk_AbsP (i,
berghofe@11519
   697
        proof_combP (proof_combt (PBound i, map Bound ((length params - 1) downto 0)),
wenzelm@23178
   698
          map PBound (((i-m-1) downto 0) @ ((i-1) downto (i-m))))))]))
berghofe@11519
   699
  end;
berghofe@11519
   700
berghofe@11519
   701
berghofe@11519
   702
(***** permute premises *****)
berghofe@11519
   703
wenzelm@36742
   704
fun permute_prems_proof prems j k prf =
berghofe@11519
   705
  let val n = length prems
berghofe@11519
   706
  in mk_AbsP (n, proof_combP (prf,
berghofe@11519
   707
    map PBound ((n-1 downto n-j) @ (k-1 downto 0) @ (n-j-1 downto k))))
berghofe@11519
   708
  end;
berghofe@11519
   709
berghofe@11519
   710
wenzelm@19908
   711
(***** generalization *****)
wenzelm@19908
   712
wenzelm@20000
   713
fun generalize (tfrees, frees) idx =
wenzelm@36620
   714
  Same.commit (map_proof_terms_same
wenzelm@36620
   715
    (Term_Subst.generalize_same (tfrees, frees) idx)
wenzelm@36620
   716
    (Term_Subst.generalizeT_same tfrees idx));
wenzelm@19908
   717
wenzelm@19908
   718
berghofe@11519
   719
(***** instantiation *****)
berghofe@11519
   720
wenzelm@20000
   721
fun instantiate (instT, inst) =
wenzelm@36620
   722
  Same.commit (map_proof_terms_same
wenzelm@36620
   723
    (Term_Subst.instantiate_same (instT, map (apsnd remove_types) inst))
wenzelm@36620
   724
    (Term_Subst.instantiateT_same instT));
berghofe@11519
   725
berghofe@11519
   726
berghofe@11519
   727
(***** lifting *****)
berghofe@11519
   728
berghofe@11519
   729
fun lift_proof Bi inc prop prf =
berghofe@11519
   730
  let
wenzelm@32024
   731
    fun lift'' Us Ts t =
wenzelm@32024
   732
      strip_abs Ts (Logic.incr_indexes (Us, inc) (mk_abs Ts t));
berghofe@11519
   733
berghofe@11715
   734
    fun lift' Us Ts (Abst (s, T, prf)) =
wenzelm@32024
   735
          (Abst (s, Same.map_option (Logic.incr_tvar_same inc) T, lifth' Us (dummyT::Ts) prf)
wenzelm@32019
   736
           handle Same.SAME => Abst (s, T, lift' Us (dummyT::Ts) prf))
berghofe@11715
   737
      | lift' Us Ts (AbsP (s, t, prf)) =
wenzelm@32024
   738
          (AbsP (s, Same.map_option (same (op =) (lift'' Us Ts)) t, lifth' Us Ts prf)
wenzelm@32019
   739
           handle Same.SAME => AbsP (s, t, lift' Us Ts prf))
skalberg@15570
   740
      | lift' Us Ts (prf % t) = (lift' Us Ts prf % Option.map (lift'' Us Ts) t
wenzelm@32024
   741
          handle Same.SAME => prf % Same.map_option (same (op =) (lift'' Us Ts)) t)
berghofe@11715
   742
      | lift' Us Ts (prf1 %% prf2) = (lift' Us Ts prf1 %% lifth' Us Ts prf2
wenzelm@32019
   743
          handle Same.SAME => prf1 %% lift' Us Ts prf2)
berghofe@11715
   744
      | lift' _ _ (PAxm (s, prop, Ts)) =
wenzelm@32024
   745
          PAxm (s, prop, (Same.map_option o Same.map) (Logic.incr_tvar_same inc) Ts)
wenzelm@31943
   746
      | lift' _ _ (OfClass (T, c)) =
wenzelm@32024
   747
          OfClass (Logic.incr_tvar_same inc T, c)
wenzelm@28828
   748
      | lift' _ _ (Oracle (s, prop, Ts)) =
wenzelm@32024
   749
          Oracle (s, prop, (Same.map_option o Same.map) (Logic.incr_tvar_same inc) Ts)
wenzelm@28828
   750
      | lift' _ _ (Promise (i, prop, Ts)) =
wenzelm@32024
   751
          Promise (i, prop, Same.map (Logic.incr_tvar_same inc) Ts)
wenzelm@28803
   752
      | lift' _ _ (PThm (i, ((s, prop, Ts), body))) =
wenzelm@32024
   753
          PThm (i, ((s, prop, (Same.map_option o Same.map) (Logic.incr_tvar inc) Ts), body))
wenzelm@32019
   754
      | lift' _ _ _ = raise Same.SAME
wenzelm@32019
   755
    and lifth' Us Ts prf = (lift' Us Ts prf handle Same.SAME => prf);
berghofe@11519
   756
wenzelm@18030
   757
    val ps = map (Logic.lift_all inc Bi) (Logic.strip_imp_prems prop);
berghofe@11519
   758
    val k = length ps;
berghofe@11519
   759
wenzelm@23178
   760
    fun mk_app b (i, j, prf) =
berghofe@11615
   761
          if b then (i-1, j, prf %% PBound i) else (i, j-1, prf %> Bound j);
berghofe@11519
   762
berghofe@11519
   763
    fun lift Us bs i j (Const ("==>", _) $ A $ B) =
wenzelm@20147
   764
            AbsP ("H", NONE (*A*), lift Us (true::bs) (i+1) j B)
wenzelm@21646
   765
      | lift Us bs i j (Const ("all", _) $ Abs (a, T, t)) =
wenzelm@20147
   766
            Abst (a, NONE (*T*), lift (T::Us) (false::bs) i (j+1) t)
berghofe@11715
   767
      | lift Us bs i j _ = proof_combP (lifth' (rev Us) [] prf,
wenzelm@23178
   768
            map (fn k => (#3 (fold_rev mk_app bs (i-1, j-1, PBound k))))
berghofe@11519
   769
              (i + k - 1 downto i));
berghofe@11519
   770
  in
berghofe@11519
   771
    mk_AbsP (k, lift [] [] 0 0 Bi)
berghofe@11519
   772
  end;
berghofe@11519
   773
wenzelm@32027
   774
fun incr_indexes i =
wenzelm@36620
   775
  Same.commit (map_proof_terms_same
wenzelm@36620
   776
    (Logic.incr_indexes_same ([], i)) (Logic.incr_tvar_same i));
wenzelm@32027
   777
berghofe@11519
   778
berghofe@11519
   779
(***** proof by assumption *****)
berghofe@11519
   780
berghofe@23296
   781
fun mk_asm_prf t i m =
berghofe@23296
   782
  let
berghofe@23296
   783
    fun imp_prf _ i 0 = PBound i
berghofe@23296
   784
      | imp_prf (Const ("==>", _) $ A $ B) i m = AbsP ("H", NONE (*A*), imp_prf B (i+1) (m-1))
berghofe@23296
   785
      | imp_prf _ i _ = PBound i;
berghofe@23296
   786
    fun all_prf (Const ("all", _) $ Abs (a, T, t)) = Abst (a, NONE (*T*), all_prf t)
berghofe@23296
   787
      | all_prf t = imp_prf t (~i) m
berghofe@23296
   788
  in all_prf t end;
berghofe@11519
   789
berghofe@11519
   790
fun assumption_proof Bs Bi n prf =
berghofe@11519
   791
  mk_AbsP (length Bs, proof_combP (prf,
berghofe@23296
   792
    map PBound (length Bs - 1 downto 0) @ [mk_asm_prf Bi n ~1]));
berghofe@11519
   793
berghofe@11519
   794
berghofe@11519
   795
(***** Composition of object rule with proof state *****)
berghofe@11519
   796
berghofe@11519
   797
fun flatten_params_proof i j n (Const ("==>", _) $ A $ B, k) =
skalberg@15531
   798
      AbsP ("H", NONE (*A*), flatten_params_proof (i+1) j n (B, k))
berghofe@11519
   799
  | flatten_params_proof i j n (Const ("all", _) $ Abs (a, T, t), k) =
skalberg@15531
   800
      Abst (a, NONE (*T*), flatten_params_proof i (j+1) n (t, k))
berghofe@11519
   801
  | flatten_params_proof i j n (_, k) = proof_combP (proof_combt (PBound (k+i),
wenzelm@19304
   802
      map Bound (j-1 downto 0)), map PBound (remove (op =) (i-n) (i-1 downto 0)));
berghofe@11519
   803
berghofe@23296
   804
fun bicompose_proof flatten Bs oldAs newAs A n m rprf sprf =
berghofe@11519
   805
  let
berghofe@11519
   806
    val la = length newAs;
berghofe@11519
   807
    val lb = length Bs;
berghofe@11519
   808
  in
berghofe@11519
   809
    mk_AbsP (lb+la, proof_combP (sprf,
berghofe@11615
   810
      map PBound (lb + la - 1 downto la)) %%
berghofe@23296
   811
        proof_combP (rprf, (if n>0 then [mk_asm_prf (the A) n m] else []) @
wenzelm@18485
   812
          map (if flatten then flatten_params_proof 0 0 n else PBound o snd)
wenzelm@18485
   813
            (oldAs ~~ (la - 1 downto 0))))
berghofe@11519
   814
  end;
berghofe@11519
   815
berghofe@11519
   816
berghofe@11519
   817
(***** axioms for equality *****)
berghofe@11519
   818
wenzelm@14854
   819
val aT = TFree ("'a", []);
wenzelm@14854
   820
val bT = TFree ("'b", []);
berghofe@11519
   821
val x = Free ("x", aT);
berghofe@11519
   822
val y = Free ("y", aT);
berghofe@11519
   823
val z = Free ("z", aT);
berghofe@11519
   824
val A = Free ("A", propT);
berghofe@11519
   825
val B = Free ("B", propT);
berghofe@11519
   826
val f = Free ("f", aT --> bT);
berghofe@11519
   827
val g = Free ("g", aT --> bT);
berghofe@11519
   828
berghofe@11519
   829
val equality_axms =
wenzelm@35851
   830
 [("reflexive", Logic.mk_equals (x, x)),
wenzelm@35851
   831
  ("symmetric", Logic.mk_implies (Logic.mk_equals (x, y), Logic.mk_equals (y, x))),
wenzelm@35851
   832
  ("transitive",
wenzelm@35851
   833
    Logic.list_implies ([Logic.mk_equals (x, y), Logic.mk_equals (y, z)], Logic.mk_equals (x, z))),
wenzelm@35851
   834
  ("equal_intr",
wenzelm@35851
   835
    Logic.list_implies ([Logic.mk_implies (A, B), Logic.mk_implies (B, A)], Logic.mk_equals (A, B))),
wenzelm@35851
   836
  ("equal_elim", Logic.list_implies ([Logic.mk_equals (A, B), A], B)),
wenzelm@35851
   837
  ("abstract_rule",
wenzelm@35851
   838
    Logic.mk_implies
wenzelm@35851
   839
      (Logic.all x
wenzelm@35851
   840
        (Logic.mk_equals (f $ x, g $ x)), Logic.mk_equals (lambda x (f $ x), lambda x (g $ x)))),
wenzelm@35851
   841
  ("combination", Logic.list_implies
wenzelm@35851
   842
    ([Logic.mk_equals (f, g), Logic.mk_equals (x, y)], Logic.mk_equals (f $ x, g $ y)))];
berghofe@11519
   843
berghofe@11519
   844
val [reflexive_axm, symmetric_axm, transitive_axm, equal_intr_axm,
berghofe@11519
   845
  equal_elim_axm, abstract_rule_axm, combination_axm] =
wenzelm@35851
   846
    map (fn (s, t) => PAxm ("Pure." ^ s, Logic.varify_global t, NONE)) equality_axms;
berghofe@11519
   847
skalberg@15531
   848
val reflexive = reflexive_axm % NONE;
berghofe@11519
   849
wenzelm@26424
   850
fun symmetric (prf as PAxm ("Pure.reflexive", _, _) % _) = prf
skalberg@15531
   851
  | symmetric prf = symmetric_axm % NONE % NONE %% prf;
berghofe@11519
   852
wenzelm@26424
   853
fun transitive _ _ (PAxm ("Pure.reflexive", _, _) % _) prf2 = prf2
wenzelm@26424
   854
  | transitive _ _ prf1 (PAxm ("Pure.reflexive", _, _) % _) = prf1
berghofe@11519
   855
  | transitive u (Type ("prop", [])) prf1 prf2 =
skalberg@15531
   856
      transitive_axm % NONE % SOME (remove_types u) % NONE %% prf1 %% prf2
berghofe@11519
   857
  | transitive u T prf1 prf2 =
skalberg@15531
   858
      transitive_axm % NONE % NONE % NONE %% prf1 %% prf2;
berghofe@11519
   859
berghofe@11519
   860
fun abstract_rule x a prf =
skalberg@15531
   861
  abstract_rule_axm % NONE % NONE %% forall_intr_proof x a prf;
berghofe@11519
   862
wenzelm@26424
   863
fun check_comb (PAxm ("Pure.combination", _, _) % f % g % _ % _ %% prf %% _) =
wenzelm@19502
   864
      is_some f orelse check_comb prf
wenzelm@26424
   865
  | check_comb (PAxm ("Pure.transitive", _, _) % _ % _ % _ %% prf1 %% prf2) =
berghofe@11519
   866
      check_comb prf1 andalso check_comb prf2
wenzelm@26424
   867
  | check_comb (PAxm ("Pure.symmetric", _, _) % _ % _ %% prf) = check_comb prf
berghofe@11519
   868
  | check_comb _ = false;
berghofe@11519
   869
berghofe@11519
   870
fun combination f g t u (Type (_, [T, U])) prf1 prf2 =
berghofe@11519
   871
  let
berghofe@11519
   872
    val f = Envir.beta_norm f;
berghofe@11519
   873
    val g = Envir.beta_norm g;
berghofe@11519
   874
    val prf =  if check_comb prf1 then
skalberg@15531
   875
        combination_axm % NONE % NONE
berghofe@11519
   876
      else (case prf1 of
wenzelm@26424
   877
          PAxm ("Pure.reflexive", _, _) % _ =>
skalberg@15531
   878
            combination_axm %> remove_types f % NONE
berghofe@11615
   879
        | _ => combination_axm %> remove_types f %> remove_types g)
berghofe@11519
   880
  in
berghofe@11519
   881
    (case T of
berghofe@11615
   882
       Type ("fun", _) => prf %
berghofe@11519
   883
         (case head_of f of
skalberg@15531
   884
            Abs _ => SOME (remove_types t)
skalberg@15531
   885
          | Var _ => SOME (remove_types t)
skalberg@15531
   886
          | _ => NONE) %
berghofe@11519
   887
         (case head_of g of
skalberg@15531
   888
            Abs _ => SOME (remove_types u)
skalberg@15531
   889
          | Var _ => SOME (remove_types u)
skalberg@15531
   890
          | _ => NONE) %% prf1 %% prf2
skalberg@15531
   891
     | _ => prf % NONE % NONE %% prf1 %% prf2)
berghofe@11519
   892
  end;
berghofe@11519
   893
berghofe@11519
   894
fun equal_intr A B prf1 prf2 =
berghofe@11615
   895
  equal_intr_axm %> remove_types A %> remove_types B %% prf1 %% prf2;
berghofe@11519
   896
berghofe@11519
   897
fun equal_elim A B prf1 prf2 =
berghofe@11615
   898
  equal_elim_axm %> remove_types A %> remove_types B %% prf1 %% prf2;
berghofe@11519
   899
berghofe@11519
   900
wenzelm@36740
   901
(**** type classes ****)
wenzelm@36621
   902
wenzelm@36621
   903
fun strip_shyps_proof algebra present witnessed extra_sorts prf =
wenzelm@36621
   904
  let
wenzelm@36621
   905
    fun get S2 (T, S1) = if Sorts.sort_le algebra (S1, S2) then SOME T else NONE;
wenzelm@36732
   906
    val extra = map (fn S => (TFree ("'dummy", S), S)) extra_sorts;
wenzelm@36621
   907
    val replacements = present @ extra @ witnessed;
wenzelm@36621
   908
    fun replace T =
wenzelm@36621
   909
      if exists (fn (T', _) => T' = T) present then raise Same.SAME
wenzelm@36621
   910
      else
wenzelm@36621
   911
        (case get_first (get (Type.sort_of_atyp T)) replacements of
wenzelm@36621
   912
          SOME T' => T'
wenzelm@36621
   913
        | NONE => raise Fail "strip_shyps_proof: bad type variable in proof term");
wenzelm@36621
   914
  in Same.commit (map_proof_types_same (Term_Subst.map_atypsT_same replace)) prf end;
wenzelm@36621
   915
wenzelm@36621
   916
wenzelm@36740
   917
local
wenzelm@36740
   918
wenzelm@36740
   919
type axclass_proofs =
wenzelm@36740
   920
 {classrel_proof: theory -> class * class -> proof,
wenzelm@36740
   921
  arity_proof: theory -> string * sort list * class -> proof};
wenzelm@36740
   922
wenzelm@36740
   923
val axclass_proofs: axclass_proofs Single_Assignment.var =
wenzelm@36740
   924
  Single_Assignment.var "Proofterm.axclass_proofs";
wenzelm@36740
   925
wenzelm@36740
   926
fun axclass_proof which thy x =
wenzelm@36740
   927
  (case Single_Assignment.peek axclass_proofs of
wenzelm@36740
   928
    NONE => raise Fail "Axclass proof operations not installed"
wenzelm@36740
   929
  | SOME prfs => which prfs thy x);
wenzelm@36740
   930
wenzelm@36740
   931
in
wenzelm@36740
   932
wenzelm@36740
   933
val classrel_proof = axclass_proof #classrel_proof;
wenzelm@36740
   934
val arity_proof = axclass_proof #arity_proof;
wenzelm@36740
   935
wenzelm@36740
   936
fun install_axclass_proofs prfs = Single_Assignment.assign axclass_proofs prfs;
wenzelm@36740
   937
wenzelm@36740
   938
end;
wenzelm@36740
   939
wenzelm@36740
   940
wenzelm@36741
   941
local
wenzelm@36741
   942
wenzelm@36741
   943
fun canonical_instance typs =
wenzelm@36741
   944
  let
wenzelm@36741
   945
    val names = Name.invents Name.context Name.aT (length typs);
wenzelm@36741
   946
    val instT = map2 (fn a => fn T => (((a, 0), []), Type.strip_sorts T)) names typs;
wenzelm@36741
   947
  in instantiate (instT, []) end;
wenzelm@36741
   948
wenzelm@36741
   949
in
wenzelm@36741
   950
wenzelm@36741
   951
fun of_sort_proof thy hyps =
wenzelm@36741
   952
  Sorts.of_sort_derivation (Sign.classes_of thy)
wenzelm@36741
   953
   {class_relation = fn typ => fn (prf, c1) => fn c2 =>
wenzelm@36741
   954
      if c1 = c2 then prf
wenzelm@36741
   955
      else canonical_instance [typ] (classrel_proof thy (c1, c2)) %% prf,
wenzelm@36741
   956
    type_constructor = fn (a, typs) => fn dom => fn c =>
wenzelm@36741
   957
      let val Ss = map (map snd) dom and prfs = maps (map fst) dom
wenzelm@36741
   958
      in proof_combP (canonical_instance typs (arity_proof thy (a, Ss, c)), prfs) end,
wenzelm@36741
   959
    type_variable = fn typ => map (fn c => (hyps (typ, c), c)) (Type.sort_of_atyp typ)};
wenzelm@36741
   960
wenzelm@36741
   961
end;
wenzelm@36741
   962
wenzelm@36741
   963
berghofe@11519
   964
(***** axioms and theorems *****)
berghofe@11519
   965
wenzelm@32738
   966
val proofs = Unsynchronized.ref 2;
wenzelm@28803
   967
berghofe@28812
   968
fun vars_of t = map Var (rev (Term.add_vars t []));
berghofe@28812
   969
fun frees_of t = map Free (rev (Term.add_frees t []));
berghofe@11519
   970
berghofe@11519
   971
fun test_args _ [] = true
berghofe@11519
   972
  | test_args is (Bound i :: ts) =
wenzelm@17492
   973
      not (member (op =) is i) andalso test_args (i :: is) ts
berghofe@11519
   974
  | test_args _ _ = false;
berghofe@11519
   975
berghofe@11519
   976
fun is_fun (Type ("fun", _)) = true
berghofe@11519
   977
  | is_fun (TVar _) = true
berghofe@11519
   978
  | is_fun _ = false;
berghofe@11519
   979
berghofe@11519
   980
fun add_funvars Ts (vs, t) =
berghofe@11519
   981
  if is_fun (fastype_of1 (Ts, t)) then
haftmann@33042
   982
    union (op =) vs (map_filter (fn Var (ixn, T) =>
haftmann@33037
   983
      if is_fun T then SOME ixn else NONE | _ => NONE) (vars_of t))
berghofe@11519
   984
  else vs;
berghofe@11519
   985
berghofe@11519
   986
fun add_npvars q p Ts (vs, Const ("==>", _) $ t $ u) =
berghofe@11519
   987
      add_npvars q p Ts (add_npvars q (not p) Ts (vs, t), u)
berghofe@11519
   988
  | add_npvars q p Ts (vs, Const ("all", Type (_, [Type (_, [T, _]), _])) $ t) =
berghofe@11519
   989
      add_npvars q p Ts (vs, if p andalso q then betapply (t, Var (("",0), T)) else t)
berghofe@12041
   990
  | add_npvars q p Ts (vs, Abs (_, T, t)) = add_npvars q p (T::Ts) (vs, t)
berghofe@12041
   991
  | add_npvars _ _ Ts (vs, t) = add_npvars' Ts (vs, t)
berghofe@12041
   992
and add_npvars' Ts (vs, t) = (case strip_comb t of
berghofe@11519
   993
    (Var (ixn, _), ts) => if test_args [] ts then vs
haftmann@17314
   994
      else Library.foldl (add_npvars' Ts)
haftmann@17314
   995
        (AList.update (op =) (ixn,
haftmann@17314
   996
          Library.foldl (add_funvars Ts) ((these ooo AList.lookup) (op =) vs ixn, ts)) vs, ts)
skalberg@15570
   997
  | (Abs (_, T, u), ts) => Library.foldl (add_npvars' (T::Ts)) (vs, u :: ts)
skalberg@15570
   998
  | (_, ts) => Library.foldl (add_npvars' Ts) (vs, ts));
berghofe@11519
   999
haftmann@33042
  1000
fun prop_vars (Const ("==>", _) $ P $ Q) = union (op =) (prop_vars P) (prop_vars Q)
berghofe@11519
  1001
  | prop_vars (Const ("all", _) $ Abs (_, _, t)) = prop_vars t
berghofe@11519
  1002
  | prop_vars t = (case strip_comb t of
berghofe@11519
  1003
      (Var (ixn, _), _) => [ixn] | _ => []);
berghofe@11519
  1004
berghofe@11519
  1005
fun is_proj t =
berghofe@11519
  1006
  let
berghofe@11519
  1007
    fun is_p i t = (case strip_comb t of
berghofe@11519
  1008
        (Bound j, []) => false
berghofe@11519
  1009
      | (Bound j, ts) => j >= i orelse exists (is_p i) ts
berghofe@11519
  1010
      | (Abs (_, _, u), _) => is_p (i+1) u
berghofe@11519
  1011
      | (_, ts) => exists (is_p i) ts)
berghofe@11519
  1012
  in (case strip_abs_body t of
berghofe@11519
  1013
        Bound _ => true
berghofe@11519
  1014
      | t' => is_p 0 t')
berghofe@11519
  1015
  end;
berghofe@11519
  1016
wenzelm@21646
  1017
fun needed_vars prop =
haftmann@33042
  1018
  union (op =) (Library.foldl (uncurry (union (op =)))
haftmann@33042
  1019
    ([], map (uncurry (insert (op =))) (add_npvars true true [] ([], prop))))
haftmann@33042
  1020
  (prop_vars prop);
berghofe@11519
  1021
berghofe@11519
  1022
fun gen_axm_proof c name prop =
berghofe@11519
  1023
  let
berghofe@11519
  1024
    val nvs = needed_vars prop;
berghofe@11519
  1025
    val args = map (fn (v as Var (ixn, _)) =>
wenzelm@17492
  1026
        if member (op =) nvs ixn then SOME v else NONE) (vars_of prop) @
berghofe@28812
  1027
      map SOME (frees_of prop);
berghofe@11519
  1028
  in
skalberg@15531
  1029
    proof_combt' (c (name, prop, NONE), args)
berghofe@11519
  1030
  end;
berghofe@11519
  1031
berghofe@11519
  1032
val axm_proof = gen_axm_proof PAxm;
berghofe@17017
  1033
berghofe@17017
  1034
val dummy = Const (Term.dummy_patternN, dummyT);
berghofe@17017
  1035
berghofe@17017
  1036
fun oracle_proof name prop =
wenzelm@30716
  1037
  if ! proofs = 0 then ((name, dummy), Oracle (name, dummy, NONE))
wenzelm@30716
  1038
  else ((name, prop), gen_axm_proof Oracle name prop);
berghofe@11519
  1039
wenzelm@32785
  1040
val shrink_proof =
wenzelm@17492
  1041
  let
wenzelm@17492
  1042
    fun shrink ls lev (prf as Abst (a, T, body)) =
wenzelm@17492
  1043
          let val (b, is, ch, body') = shrink ls (lev+1) body
wenzelm@26631
  1044
          in (b, is, ch, if ch then Abst (a, T, body') else prf) end
wenzelm@17492
  1045
      | shrink ls lev (prf as AbsP (a, t, body)) =
wenzelm@17492
  1046
          let val (b, is, ch, body') = shrink (lev::ls) lev body
wenzelm@19482
  1047
          in (b orelse member (op =) is 0, map_filter (fn 0 => NONE | i => SOME (i-1)) is,
wenzelm@26631
  1048
            ch, if ch then AbsP (a, t, body') else prf)
wenzelm@17492
  1049
          end
wenzelm@17492
  1050
      | shrink ls lev prf =
wenzelm@17492
  1051
          let val (is, ch, _, prf') = shrink' ls lev [] [] prf
wenzelm@17492
  1052
          in (false, is, ch, prf') end
wenzelm@17492
  1053
    and shrink' ls lev ts prfs (prf as prf1 %% prf2) =
wenzelm@17492
  1054
          let
wenzelm@17492
  1055
            val p as (_, is', ch', prf') = shrink ls lev prf2;
wenzelm@17492
  1056
            val (is, ch, ts', prf'') = shrink' ls lev ts (p::prfs) prf1
haftmann@33042
  1057
          in (union (op =) is is', ch orelse ch', ts',
wenzelm@17492
  1058
              if ch orelse ch' then prf'' %% prf' else prf)
wenzelm@17492
  1059
          end
wenzelm@17492
  1060
      | shrink' ls lev ts prfs (prf as prf1 % t) =
wenzelm@17492
  1061
          let val (is, ch, (ch', t')::ts', prf') = shrink' ls lev (t::ts) prfs prf1
wenzelm@17492
  1062
          in (is, ch orelse ch', ts',
wenzelm@26631
  1063
              if ch orelse ch' then prf' % t' else prf) end
wenzelm@17492
  1064
      | shrink' ls lev ts prfs (prf as PBound i) =
wenzelm@30146
  1065
          (if exists (fn SOME (Bound j) => lev-j <= nth ls i | _ => true) ts
haftmann@18928
  1066
             orelse has_duplicates (op =)
haftmann@18928
  1067
               (Library.foldl (fn (js, SOME (Bound j)) => j :: js | (js, _) => js) ([], ts))
wenzelm@17492
  1068
             orelse exists #1 prfs then [i] else [], false, map (pair false) ts, prf)
wenzelm@31903
  1069
      | shrink' ls lev ts prfs (prf as Hyp _) = ([], false, map (pair false) ts, prf)
wenzelm@31903
  1070
      | shrink' ls lev ts prfs (prf as MinProof) = ([], false, map (pair false) ts, prf)
wenzelm@31943
  1071
      | shrink' ls lev ts prfs (prf as OfClass _) = ([], false, map (pair false) ts, prf)
wenzelm@17492
  1072
      | shrink' ls lev ts prfs prf =
wenzelm@17492
  1073
          let
wenzelm@28803
  1074
            val prop =
wenzelm@28803
  1075
              (case prf of
wenzelm@28803
  1076
                PAxm (_, prop, _) => prop
wenzelm@28803
  1077
              | Oracle (_, prop, _) => prop
wenzelm@28803
  1078
              | Promise (_, prop, _) => prop
wenzelm@28803
  1079
              | PThm (_, ((_, prop, _), _)) => prop
wenzelm@36879
  1080
              | _ => raise Fail "shrink: proof not in normal form");
wenzelm@17492
  1081
            val vs = vars_of prop;
wenzelm@19012
  1082
            val (ts', ts'') = chop (length vs) ts;
haftmann@33957
  1083
            val insts = take (length ts') (map (fst o dest_Var) vs) ~~ ts';
wenzelm@17492
  1084
            val nvs = Library.foldl (fn (ixns', (ixn, ixns)) =>
wenzelm@17492
  1085
              insert (op =) ixn (case AList.lookup (op =) insts ixn of
haftmann@33042
  1086
                  SOME (SOME t) => if is_proj t then union (op =) ixns ixns' else ixns'
haftmann@33042
  1087
                | _ => union (op =) ixns ixns'))
wenzelm@17492
  1088
                  (needed prop ts'' prfs, add_npvars false true [] ([], prop));
wenzelm@17492
  1089
            val insts' = map
wenzelm@17492
  1090
              (fn (ixn, x as SOME _) => if member (op =) nvs ixn then (false, x) else (true, NONE)
wenzelm@17492
  1091
                | (_, x) => (false, x)) insts
wenzelm@17492
  1092
          in ([], false, insts' @ map (pair false) ts'', prf) end
wenzelm@17492
  1093
    and needed (Const ("==>", _) $ t $ u) ts ((b, _, _, _)::prfs) =
haftmann@33042
  1094
          union (op =) (if b then map (fst o dest_Var) (vars_of t) else []) (needed u ts prfs)
wenzelm@17492
  1095
      | needed (Var (ixn, _)) (_::_) _ = [ixn]
wenzelm@17492
  1096
      | needed _ _ _ = [];
wenzelm@17492
  1097
  in shrink end;
berghofe@11519
  1098
berghofe@11519
  1099
berghofe@11519
  1100
(**** Simple first order matching functions for terms and proofs ****)
berghofe@11519
  1101
berghofe@11519
  1102
exception PMatch;
berghofe@11519
  1103
berghofe@11519
  1104
(** see pattern.ML **)
berghofe@11519
  1105
wenzelm@33317
  1106
fun flt (i: int) = filter (fn n => n < i);
berghofe@12279
  1107
berghofe@12279
  1108
fun fomatch Ts tymatch j =
berghofe@11519
  1109
  let
berghofe@11519
  1110
    fun mtch (instsp as (tyinsts, insts)) = fn
berghofe@11519
  1111
        (Var (ixn, T), t)  =>
berghofe@12279
  1112
          if j>0 andalso not (null (flt j (loose_bnos t)))
berghofe@12279
  1113
          then raise PMatch
berghofe@12279
  1114
          else (tymatch (tyinsts, fn () => (T, fastype_of1 (Ts, t))),
berghofe@12279
  1115
            (ixn, t) :: insts)
berghofe@11519
  1116
      | (Free (a, T), Free (b, U)) =>
wenzelm@20147
  1117
          if a=b then (tymatch (tyinsts, K (T, U)), insts) else raise PMatch
berghofe@11519
  1118
      | (Const (a, T), Const (b, U))  =>
wenzelm@20147
  1119
          if a=b then (tymatch (tyinsts, K (T, U)), insts) else raise PMatch
berghofe@11519
  1120
      | (f $ t, g $ u) => mtch (mtch instsp (f, g)) (t, u)
berghofe@12279
  1121
      | (Bound i, Bound j) => if i=j then instsp else raise PMatch
berghofe@11519
  1122
      | _ => raise PMatch
berghofe@11519
  1123
  in mtch end;
berghofe@11519
  1124
berghofe@12279
  1125
fun match_proof Ts tymatch =
berghofe@11519
  1126
  let
skalberg@15531
  1127
    fun optmatch _ inst (NONE, _) = inst
skalberg@15531
  1128
      | optmatch _ _ (SOME _, NONE) = raise PMatch
skalberg@15531
  1129
      | optmatch mtch inst (SOME x, SOME y) = mtch inst (x, y)
berghofe@12279
  1130
berghofe@12279
  1131
    fun matcht Ts j (pinst, tinst) (t, u) =
berghofe@12279
  1132
      (pinst, fomatch Ts tymatch j tinst (t, Envir.beta_norm u));
berghofe@12279
  1133
    fun matchT (pinst, (tyinsts, insts)) p =
berghofe@12279
  1134
      (pinst, (tymatch (tyinsts, K p), insts));
skalberg@15570
  1135
    fun matchTs inst (Ts, Us) = Library.foldl (uncurry matchT) (inst, Ts ~~ Us);
berghofe@12279
  1136
berghofe@12279
  1137
    fun mtch Ts i j (pinst, tinst) (Hyp (Var (ixn, _)), prf) =
berghofe@12279
  1138
          if i = 0 andalso j = 0 then ((ixn, prf) :: pinst, tinst)
berghofe@12279
  1139
          else (case apfst (flt i) (apsnd (flt j)
berghofe@12279
  1140
                  (prf_add_loose_bnos 0 0 prf ([], []))) of
berghofe@12279
  1141
              ([], []) => ((ixn, incr_pboundvars (~i) (~j) prf) :: pinst, tinst)
berghofe@12279
  1142
            | ([], _) => if j = 0 then
berghofe@12279
  1143
                   ((ixn, incr_pboundvars (~i) (~j) prf) :: pinst, tinst)
berghofe@12279
  1144
                 else raise PMatch
berghofe@12279
  1145
            | _ => raise PMatch)
berghofe@12279
  1146
      | mtch Ts i j inst (prf1 % opt1, prf2 % opt2) =
berghofe@12279
  1147
          optmatch (matcht Ts j) (mtch Ts i j inst (prf1, prf2)) (opt1, opt2)
berghofe@12279
  1148
      | mtch Ts i j inst (prf1 %% prf2, prf1' %% prf2') =
berghofe@12279
  1149
          mtch Ts i j (mtch Ts i j inst (prf1, prf1')) (prf2, prf2')
berghofe@12279
  1150
      | mtch Ts i j inst (Abst (_, opT, prf1), Abst (_, opU, prf2)) =
wenzelm@18485
  1151
          mtch (the_default dummyT opU :: Ts) i (j+1)
berghofe@12279
  1152
            (optmatch matchT inst (opT, opU)) (prf1, prf2)
berghofe@12279
  1153
      | mtch Ts i j inst (prf1, Abst (_, opU, prf2)) =
wenzelm@18485
  1154
          mtch (the_default dummyT opU :: Ts) i (j+1) inst
berghofe@12279
  1155
            (incr_pboundvars 0 1 prf1 %> Bound 0, prf2)
berghofe@12279
  1156
      | mtch Ts i j inst (AbsP (_, opt, prf1), AbsP (_, opu, prf2)) =
berghofe@12279
  1157
          mtch Ts (i+1) j (optmatch (matcht Ts j) inst (opt, opu)) (prf1, prf2)
berghofe@12279
  1158
      | mtch Ts i j inst (prf1, AbsP (_, _, prf2)) =
berghofe@12279
  1159
          mtch Ts (i+1) j inst (incr_pboundvars 1 0 prf1 %% PBound 0, prf2)
wenzelm@28803
  1160
      | mtch Ts i j inst (PAxm (s1, _, opTs), PAxm (s2, _, opUs)) =
wenzelm@28803
  1161
          if s1 = s2 then optmatch matchTs inst (opTs, opUs)
wenzelm@28803
  1162
          else raise PMatch
wenzelm@31943
  1163
      | mtch Ts i j inst (OfClass (T1, c1), OfClass (T2, c2)) =
wenzelm@31903
  1164
          if c1 = c2 then matchT inst (T1, T2)
wenzelm@31903
  1165
          else raise PMatch
wenzelm@28803
  1166
      | mtch Ts i j inst (PThm (_, ((name1, prop1, opTs), _)), PThm (_, ((name2, prop2, opUs), _))) =
wenzelm@28803
  1167
          if name1 = name2 andalso prop1 = prop2 then
berghofe@12279
  1168
            optmatch matchTs inst (opTs, opUs)
berghofe@11519
  1169
          else raise PMatch
berghofe@12279
  1170
      | mtch _ _ _ inst (PBound i, PBound j) = if i = j then inst else raise PMatch
berghofe@12279
  1171
      | mtch _ _ _ _ _ = raise PMatch
berghofe@12279
  1172
  in mtch Ts 0 0 end;
berghofe@11519
  1173
berghofe@11519
  1174
fun prf_subst (pinst, (tyinsts, insts)) =
berghofe@11519
  1175
  let
wenzelm@32049
  1176
    val substT = Envir.subst_type_same tyinsts;
wenzelm@32049
  1177
    val substTs = Same.map substT;
berghofe@11519
  1178
wenzelm@32049
  1179
    fun subst' lev (Var (xi, _)) =
wenzelm@32049
  1180
        (case AList.lookup (op =) insts xi of
wenzelm@32049
  1181
          NONE => raise Same.SAME
skalberg@15531
  1182
        | SOME u => incr_boundvars lev u)
wenzelm@32049
  1183
      | subst' _ (Const (s, T)) = Const (s, substT T)
wenzelm@32049
  1184
      | subst' _ (Free (s, T)) = Free (s, substT T)
wenzelm@32049
  1185
      | subst' lev (Abs (a, T, body)) =
wenzelm@32049
  1186
          (Abs (a, substT T, Same.commit (subst' (lev + 1)) body)
wenzelm@32049
  1187
            handle Same.SAME => Abs (a, T, subst' (lev + 1) body))
wenzelm@32049
  1188
      | subst' lev (f $ t) =
wenzelm@32049
  1189
          (subst' lev f $ Same.commit (subst' lev) t
wenzelm@32049
  1190
            handle Same.SAME => f $ subst' lev t)
wenzelm@32049
  1191
      | subst' _ _ = raise Same.SAME;
berghofe@11519
  1192
berghofe@11519
  1193
    fun subst plev tlev (AbsP (a, t, body)) =
wenzelm@32049
  1194
          (AbsP (a, Same.map_option (subst' tlev) t, Same.commit (subst (plev + 1) tlev) body)
wenzelm@32049
  1195
            handle Same.SAME => AbsP (a, t, subst (plev + 1) tlev body))
berghofe@11519
  1196
      | subst plev tlev (Abst (a, T, body)) =
wenzelm@32049
  1197
          (Abst (a, Same.map_option substT T, Same.commit (subst plev (tlev + 1)) body)
wenzelm@32049
  1198
            handle Same.SAME => Abst (a, T, subst plev (tlev + 1) body))
wenzelm@32049
  1199
      | subst plev tlev (prf %% prf') =
wenzelm@32049
  1200
          (subst plev tlev prf %% Same.commit (subst plev tlev) prf'
wenzelm@32049
  1201
            handle Same.SAME => prf %% subst plev tlev prf')
wenzelm@32049
  1202
      | subst plev tlev (prf % t) =
wenzelm@32049
  1203
          (subst plev tlev prf % Same.commit (Same.map_option (subst' tlev)) t
wenzelm@32049
  1204
            handle Same.SAME => prf % Same.map_option (subst' tlev) t)
wenzelm@32049
  1205
      | subst plev tlev (Hyp (Var (xi, _))) =
wenzelm@32049
  1206
          (case AList.lookup (op =) pinst xi of
wenzelm@32049
  1207
            NONE => raise Same.SAME
wenzelm@32049
  1208
          | SOME prf' => incr_pboundvars plev tlev prf')
wenzelm@32049
  1209
      | subst _ _ (PAxm (id, prop, Ts)) = PAxm (id, prop, Same.map_option substTs Ts)
wenzelm@31943
  1210
      | subst _ _ (OfClass (T, c)) = OfClass (substT T, c)
wenzelm@32049
  1211
      | subst _ _ (Oracle (id, prop, Ts)) = Oracle (id, prop, Same.map_option substTs Ts)
wenzelm@32049
  1212
      | subst _ _ (Promise (i, prop, Ts)) = Promise (i, prop, substTs Ts)
wenzelm@28803
  1213
      | subst _ _ (PThm (i, ((id, prop, Ts), body))) =
wenzelm@32049
  1214
          PThm (i, ((id, prop, Same.map_option substTs Ts), body))
wenzelm@32049
  1215
      | subst _ _ _ = raise Same.SAME;
wenzelm@32049
  1216
  in fn t => subst 0 0 t handle Same.SAME => t end;
berghofe@11519
  1217
wenzelm@21646
  1218
(*A fast unification filter: true unless the two terms cannot be unified.
berghofe@12871
  1219
  Terms must be NORMAL.  Treats all Vars as distinct. *)
berghofe@12871
  1220
fun could_unify prf1 prf2 =
berghofe@12871
  1221
  let
berghofe@12871
  1222
    fun matchrands (prf1 %% prf2) (prf1' %% prf2') =
berghofe@12871
  1223
          could_unify prf2 prf2' andalso matchrands prf1 prf1'
skalberg@15531
  1224
      | matchrands (prf % SOME t) (prf' % SOME t') =
berghofe@12871
  1225
          Term.could_unify (t, t') andalso matchrands prf prf'
berghofe@12871
  1226
      | matchrands (prf % _) (prf' % _) = matchrands prf prf'
berghofe@12871
  1227
      | matchrands _ _ = true
berghofe@12871
  1228
berghofe@12871
  1229
    fun head_of (prf %% _) = head_of prf
berghofe@12871
  1230
      | head_of (prf % _) = head_of prf
berghofe@12871
  1231
      | head_of prf = prf
berghofe@12871
  1232
berghofe@12871
  1233
  in case (head_of prf1, head_of prf2) of
berghofe@12871
  1234
        (_, Hyp (Var _)) => true
berghofe@12871
  1235
      | (Hyp (Var _), _) => true
wenzelm@28803
  1236
      | (PAxm (a, _, _), PAxm (b, _, _)) => a = b andalso matchrands prf1 prf2
wenzelm@31943
  1237
      | (OfClass (_, c), OfClass (_, d)) => c = d andalso matchrands prf1 prf2
wenzelm@28803
  1238
      | (PThm (_, ((a, propa, _), _)), PThm (_, ((b, propb, _), _))) =>
berghofe@12871
  1239
          a = b andalso propa = propb andalso matchrands prf1 prf2
wenzelm@28803
  1240
      | (PBound i, PBound j) => i = j andalso matchrands prf1 prf2
berghofe@12871
  1241
      | (AbsP _, _) =>  true   (*because of possible eta equality*)
berghofe@12871
  1242
      | (Abst _, _) =>  true
berghofe@12871
  1243
      | (_, AbsP _) =>  true
berghofe@12871
  1244
      | (_, Abst _) =>  true
berghofe@12871
  1245
      | _ => false
berghofe@12871
  1246
  end;
berghofe@12871
  1247
wenzelm@28329
  1248
berghofe@11519
  1249
(**** rewriting on proof terms ****)
berghofe@11519
  1250
wenzelm@33722
  1251
val no_skel = PBound 0;
wenzelm@33722
  1252
val normal_skel = Hyp (Var ((Name.uu, 0), propT));
berghofe@13102
  1253
berghofe@12279
  1254
fun rewrite_prf tymatch (rules, procs) prf =
berghofe@11519
  1255
  let
wenzelm@33722
  1256
    fun rew _ (Abst (_, _, body) % SOME t) = SOME (prf_subst_bounds [t] body, no_skel)
wenzelm@33722
  1257
      | rew _ (AbsP (_, _, body) %% prf) = SOME (prf_subst_pbounds [prf] body, no_skel)
wenzelm@33722
  1258
      | rew Ts prf =
wenzelm@33722
  1259
          (case get_first (fn r => r Ts prf) procs of
wenzelm@33722
  1260
            NONE => get_first (fn (prf1, prf2) => SOME (prf_subst
wenzelm@33722
  1261
              (match_proof Ts tymatch ([], (Vartab.empty, [])) (prf1, prf)) prf2, prf2)
wenzelm@33722
  1262
                 handle PMatch => NONE) (filter (could_unify prf o fst) rules)
wenzelm@33722
  1263
          | some => some);
berghofe@11519
  1264
berghofe@11615
  1265
    fun rew0 Ts (prf as AbsP (_, _, prf' %% PBound 0)) =
berghofe@11519
  1266
          if prf_loose_Pbvar1 prf' 0 then rew Ts prf
berghofe@11519
  1267
          else
berghofe@11519
  1268
            let val prf'' = incr_pboundvars (~1) 0 prf'
wenzelm@33722
  1269
            in SOME (the_default (prf'', no_skel) (rew Ts prf'')) end
skalberg@15531
  1270
      | rew0 Ts (prf as Abst (_, _, prf' % SOME (Bound 0))) =
berghofe@11519
  1271
          if prf_loose_bvar1 prf' 0 then rew Ts prf
berghofe@11519
  1272
          else
berghofe@11519
  1273
            let val prf'' = incr_pboundvars 0 (~1) prf'
wenzelm@33722
  1274
            in SOME (the_default (prf'', no_skel) (rew Ts prf'')) end
berghofe@11519
  1275
      | rew0 Ts prf = rew Ts prf;
berghofe@11519
  1276
skalberg@15531
  1277
    fun rew1 _ (Hyp (Var _)) _ = NONE
berghofe@13102
  1278
      | rew1 Ts skel prf = (case rew2 Ts skel prf of
skalberg@15531
  1279
          SOME prf1 => (case rew0 Ts prf1 of
wenzelm@19502
  1280
              SOME (prf2, skel') => SOME (the_default prf2 (rew1 Ts skel' prf2))
skalberg@15531
  1281
            | NONE => SOME prf1)
skalberg@15531
  1282
        | NONE => (case rew0 Ts prf of
wenzelm@19502
  1283
              SOME (prf1, skel') => SOME (the_default prf1 (rew1 Ts skel' prf1))
skalberg@15531
  1284
            | NONE => NONE))
berghofe@11519
  1285
skalberg@15531
  1286
    and rew2 Ts skel (prf % SOME t) = (case prf of
berghofe@11519
  1287
            Abst (_, _, body) =>
berghofe@11519
  1288
              let val prf' = prf_subst_bounds [t] body
wenzelm@33722
  1289
              in SOME (the_default prf' (rew2 Ts no_skel prf')) end
wenzelm@33722
  1290
          | _ => (case rew1 Ts (case skel of skel' % _ => skel' | _ => no_skel) prf of
skalberg@15531
  1291
              SOME prf' => SOME (prf' % SOME t)
skalberg@15531
  1292
            | NONE => NONE))
skalberg@15570
  1293
      | rew2 Ts skel (prf % NONE) = Option.map (fn prf' => prf' % NONE)
wenzelm@33722
  1294
          (rew1 Ts (case skel of skel' % _ => skel' | _ => no_skel) prf)
berghofe@13102
  1295
      | rew2 Ts skel (prf1 %% prf2) = (case prf1 of
berghofe@11519
  1296
            AbsP (_, _, body) =>
berghofe@11519
  1297
              let val prf' = prf_subst_pbounds [prf2] body
wenzelm@33722
  1298
              in SOME (the_default prf' (rew2 Ts no_skel prf')) end
berghofe@13102
  1299
          | _ =>
berghofe@13102
  1300
            let val (skel1, skel2) = (case skel of
berghofe@13102
  1301
                skel1 %% skel2 => (skel1, skel2)
wenzelm@33722
  1302
              | _ => (no_skel, no_skel))
berghofe@13102
  1303
            in case rew1 Ts skel1 prf1 of
skalberg@15531
  1304
                SOME prf1' => (case rew1 Ts skel2 prf2 of
skalberg@15531
  1305
                    SOME prf2' => SOME (prf1' %% prf2')
skalberg@15531
  1306
                  | NONE => SOME (prf1' %% prf2))
skalberg@15531
  1307
              | NONE => (case rew1 Ts skel2 prf2 of
skalberg@15531
  1308
                    SOME prf2' => SOME (prf1 %% prf2')
skalberg@15531
  1309
                  | NONE => NONE)
berghofe@13102
  1310
            end)
wenzelm@19502
  1311
      | rew2 Ts skel (Abst (s, T, prf)) = (case rew1 (the_default dummyT T :: Ts)
wenzelm@33722
  1312
              (case skel of Abst (_, _, skel') => skel' | _ => no_skel) prf of
skalberg@15531
  1313
            SOME prf' => SOME (Abst (s, T, prf'))
skalberg@15531
  1314
          | NONE => NONE)
berghofe@13102
  1315
      | rew2 Ts skel (AbsP (s, t, prf)) = (case rew1 Ts
wenzelm@33722
  1316
              (case skel of AbsP (_, _, skel') => skel' | _ => no_skel) prf of
skalberg@15531
  1317
            SOME prf' => SOME (AbsP (s, t, prf'))
skalberg@15531
  1318
          | NONE => NONE)
wenzelm@32049
  1319
      | rew2 _ _ _ = NONE;
berghofe@11519
  1320
wenzelm@33722
  1321
  in the_default prf (rew1 [] no_skel prf) end;
berghofe@11519
  1322
wenzelm@17203
  1323
fun rewrite_proof thy = rewrite_prf (fn (tyenv, f) =>
wenzelm@17203
  1324
  Sign.typ_match thy (f ()) tyenv handle Type.TYPE_MATCH => raise PMatch);
berghofe@11519
  1325
berghofe@11715
  1326
fun rewrite_proof_notypes rews = rewrite_prf fst rews;
berghofe@11615
  1327
wenzelm@16940
  1328
berghofe@11519
  1329
(**** theory data ****)
berghofe@11519
  1330
wenzelm@33522
  1331
structure ProofData = Theory_Data
wenzelm@22846
  1332
(
wenzelm@33722
  1333
  type T =
wenzelm@33722
  1334
    (stamp * (proof * proof)) list *
wenzelm@33722
  1335
    (stamp * (typ list -> proof -> (proof * proof) option)) list;
berghofe@11519
  1336
berghofe@12233
  1337
  val empty = ([], []);
wenzelm@16458
  1338
  val extend = I;
wenzelm@33522
  1339
  fun merge ((rules1, procs1), (rules2, procs2)) : T =
wenzelm@28803
  1340
    (AList.merge (op =) (K true) (rules1, rules2),
haftmann@22662
  1341
      AList.merge (op =) (K true) (procs1, procs2));
wenzelm@22846
  1342
);
berghofe@11519
  1343
wenzelm@28803
  1344
fun get_data thy = let val (rules, procs) = ProofData.get thy in (map #2 rules, map #2 procs) end;
wenzelm@28803
  1345
fun rew_proof thy = rewrite_prf fst (get_data thy);
berghofe@23780
  1346
wenzelm@28803
  1347
fun add_prf_rrule r = (ProofData.map o apfst) (cons (stamp (), r));
wenzelm@28803
  1348
fun add_prf_rproc p = (ProofData.map o apsnd) (cons (stamp (), p));
wenzelm@28803
  1349
wenzelm@28803
  1350
wenzelm@28828
  1351
(***** promises *****)
berghofe@11519
  1352
wenzelm@28828
  1353
fun promise_proof thy i prop =
wenzelm@28828
  1354
  let
wenzelm@28828
  1355
    val _ = prop |> Term.exists_subterm (fn t =>
wenzelm@28828
  1356
      (Term.is_Free t orelse Term.is_Var t) andalso
wenzelm@36879
  1357
        raise Fail ("promise_proof: illegal variable " ^ Syntax.string_of_term_global thy t));
wenzelm@28828
  1358
    val _ = prop |> Term.exists_type (Term.exists_subtype
wenzelm@36879
  1359
      (fn TFree (a, _) => raise Fail ("promise_proof: illegal type variable " ^ quote a)
wenzelm@28828
  1360
        | _ => false));
wenzelm@28828
  1361
  in Promise (i, prop, map TVar (Term.add_tvars prop [])) end;
wenzelm@28828
  1362
wenzelm@33722
  1363
fun fulfill_norm_proof thy ps body0 =
wenzelm@33722
  1364
  let
wenzelm@33722
  1365
    val PBody {oracles = oracles0, thms = thms0, proof = proof0} = body0;
wenzelm@33722
  1366
    val oracles = fold (fn (_, PBody {oracles, ...}) => merge_oracles oracles) ps oracles0;
wenzelm@33722
  1367
    val thms = fold (fn (_, PBody {thms, ...}) => merge_thms thms) ps thms0;
wenzelm@33722
  1368
    val proofs = fold (fn (i, PBody {proof, ...}) => Inttab.update (i, proof)) ps Inttab.empty;
wenzelm@28875
  1369
wenzelm@33722
  1370
    fun fill (Promise (i, prop, Ts)) =
wenzelm@33722
  1371
          (case Inttab.lookup proofs i of
wenzelm@33722
  1372
            NONE => NONE
wenzelm@33722
  1373
          | SOME prf => SOME (instantiate (Term.add_tvars prop [] ~~ Ts, []) prf, normal_skel))
wenzelm@33722
  1374
      | fill _ = NONE;
wenzelm@33722
  1375
    val (rules, procs) = get_data thy;
wenzelm@33722
  1376
    val proof = rewrite_prf fst (rules, K fill :: procs) proof0;
wenzelm@33722
  1377
  in PBody {oracles = oracles, thms = thms, proof = proof} end;
wenzelm@28828
  1378
wenzelm@36882
  1379
fun fulfill_proof_future _ [] postproc body = Future.value (postproc body)
wenzelm@36882
  1380
  | fulfill_proof_future thy promises postproc body =
wenzelm@29642
  1381
      Future.fork_deps (map snd promises) (fn () =>
wenzelm@36882
  1382
        postproc (fulfill_norm_proof thy (map (apsnd Future.join) promises) body));
wenzelm@29642
  1383
wenzelm@28828
  1384
wenzelm@36878
  1385
(***** abstraction over sort constraints *****)
wenzelm@36878
  1386
wenzelm@36882
  1387
fun unconstrainT_prf thy (atyp_map, constraints) =
wenzelm@36878
  1388
  let
wenzelm@36878
  1389
    fun hyp_map hyp =
wenzelm@36878
  1390
      (case AList.lookup (op =) constraints hyp of
wenzelm@36878
  1391
        SOME t => Hyp t
wenzelm@36882
  1392
      | NONE => raise Fail "unconstrainT_prf: missing constraint");
wenzelm@36878
  1393
wenzelm@36882
  1394
    val typ = Term_Subst.map_atypsT_same (Type.strip_sorts o atyp_map);
wenzelm@36878
  1395
    fun ofclass (ty, c) =
wenzelm@36878
  1396
      let val ty' = Term.map_atyps atyp_map ty;
wenzelm@36878
  1397
      in the_single (of_sort_proof thy hyp_map (ty', [c])) end;
wenzelm@36878
  1398
  in
wenzelm@36878
  1399
    Same.commit (map_proof_same (Term_Subst.map_types_same typ) typ ofclass)
wenzelm@36878
  1400
    #> fold_rev (implies_intr_proof o snd) constraints
wenzelm@36878
  1401
  end;
wenzelm@36878
  1402
wenzelm@36882
  1403
fun unconstrainT_body thy constrs (PBody {oracles, thms, proof}) =
wenzelm@36878
  1404
  PBody
wenzelm@36883
  1405
   {oracles = oracles,  (* FIXME merge (!), unconstrain (!?!) *)
wenzelm@36883
  1406
    thms = thms,  (* FIXME merge (!) *)
wenzelm@36882
  1407
    proof = unconstrainT_prf thy constrs proof};
wenzelm@36878
  1408
wenzelm@36878
  1409
wenzelm@28828
  1410
(***** theorems *****)
berghofe@11519
  1411
wenzelm@36883
  1412
fun prepare_thm_proof do_unconstrain thy name shyps hyps concl promises body =
berghofe@11519
  1413
  let
wenzelm@28803
  1414
    val PBody {oracles = oracles0, thms = thms0, proof = prf} = body;
wenzelm@32810
  1415
    val prop = Logic.list_implies (hyps, concl);
berghofe@11519
  1416
    val nvs = needed_vars prop;
berghofe@11519
  1417
    val args = map (fn (v as Var (ixn, _)) =>
wenzelm@17492
  1418
        if member (op =) nvs ixn then SOME v else NONE) (vars_of prop) @
berghofe@28812
  1419
      map SOME (frees_of prop);
wenzelm@28803
  1420
wenzelm@36883
  1421
    val (postproc, ofclasses, prop1, args1) =
wenzelm@36883
  1422
      if do_unconstrain then
wenzelm@36882
  1423
        let
wenzelm@36882
  1424
          val ((atyp_map, constraints), prop1) = Logic.unconstrainT shyps prop;
wenzelm@36882
  1425
          val postproc = unconstrainT_body thy (atyp_map, constraints);
wenzelm@36883
  1426
          val args1 =
wenzelm@36883
  1427
            (map o Option.map o Term.map_types o Term.map_atyps)
wenzelm@36883
  1428
              (Type.strip_sorts o atyp_map) args;
wenzelm@36883
  1429
        in (postproc, map (OfClass o fst) constraints, prop1, args1) end
wenzelm@36883
  1430
      else (I, [], prop, args);
wenzelm@36882
  1431
    val argsP = ofclasses @ map Hyp hyps;
wenzelm@36882
  1432
wenzelm@28803
  1433
    val proof0 =
wenzelm@28876
  1434
      if ! proofs = 2 then
wenzelm@32785
  1435
        #4 (shrink_proof [] 0 (rew_proof thy (fold_rev implies_intr_proof hyps prf)))
wenzelm@28876
  1436
      else MinProof;
wenzelm@29642
  1437
    val body0 = PBody {oracles = oracles0, thms = thms0, proof = proof0};
wenzelm@28803
  1438
wenzelm@36882
  1439
    fun new_prf () = (serial (), fulfill_proof_future thy promises postproc body0);
wenzelm@36880
  1440
    val (i, body') =
wenzelm@28803
  1441
      (case strip_combt (fst (strip_combP prf)) of
wenzelm@28803
  1442
        (PThm (i, ((old_name, prop', NONE), body')), args') =>
wenzelm@36882
  1443
          if (old_name = "" orelse old_name = name) andalso prop1 = prop' andalso args = args'
wenzelm@36880
  1444
          then (i, body')
wenzelm@28803
  1445
          else new_prf ()
wenzelm@28815
  1446
      | _ => new_prf ());
wenzelm@36882
  1447
    val head = PThm (i, ((name, prop1, NONE), body'));
wenzelm@36883
  1448
  in ((i, (name, prop1, body')), head, args, argsP, args1) end;
wenzelm@36883
  1449
wenzelm@36883
  1450
val unconstrain_thm_proofs = Unsynchronized.ref false;
wenzelm@36883
  1451
wenzelm@36883
  1452
fun thm_proof thy name shyps hyps concl promises body =
wenzelm@36883
  1453
  let val (pthm, head, args, argsP, _) =
wenzelm@36883
  1454
    prepare_thm_proof (! unconstrain_thm_proofs) thy name shyps hyps concl promises body
wenzelm@36883
  1455
  in (pthm, proof_combP (proof_combt' (head, args), argsP)) end;
wenzelm@36883
  1456
wenzelm@36883
  1457
fun unconstrain_thm_proof thy shyps concl promises body =
wenzelm@36883
  1458
  let
wenzelm@36883
  1459
    val (pthm, head, _, _, args) =
wenzelm@36883
  1460
      prepare_thm_proof true thy "" shyps [] concl promises body
wenzelm@36883
  1461
  in (pthm, proof_combt' (head, args)) end;
wenzelm@36883
  1462
berghofe@11519
  1463
wenzelm@21646
  1464
fun get_name hyps prop prf =
wenzelm@12923
  1465
  let val prop = Logic.list_implies (hyps, prop) in
wenzelm@12923
  1466
    (case strip_combt (fst (strip_combP prf)) of
wenzelm@32183
  1467
      (PThm (_, ((name, prop', _), _)), _) => if prop = prop' then name else ""
wenzelm@21646
  1468
    | _ => "")
wenzelm@12923
  1469
  end;
berghofe@11519
  1470
wenzelm@36877
  1471
fun get_name_unconstrained shyps hyps prop prf =
wenzelm@36877
  1472
  let val (_, prop) = Logic.unconstrainT shyps (Logic.list_implies (hyps, prop)) in
wenzelm@36877
  1473
    (case strip_combt (fst (strip_combP prf)) of
wenzelm@36877
  1474
      (PThm (_, ((name, prop', _), _)), _) => if prop = prop' then name else ""
wenzelm@36877
  1475
    | _ => "")
wenzelm@36877
  1476
  end;
wenzelm@36877
  1477
wenzelm@36877
  1478
fun guess_name (PThm (_, ((name, _, _), _))) = name
wenzelm@36877
  1479
  | guess_name (prf %% Hyp _) = guess_name prf
wenzelm@36877
  1480
  | guess_name (prf %% OfClass _) = guess_name prf
wenzelm@36877
  1481
  | guess_name (prf % NONE) = guess_name prf
wenzelm@36877
  1482
  | guess_name (prf % SOME (Var _)) = guess_name prf
wenzelm@36877
  1483
  | guess_name _ = "";
wenzelm@36877
  1484
berghofe@11519
  1485
end;
berghofe@11519
  1486
wenzelm@32094
  1487
structure Basic_Proofterm : BASIC_PROOFTERM = Proofterm;
wenzelm@32094
  1488
open Basic_Proofterm;