src/Pure/proofterm.ML
author kleing
Mon Jun 21 10:25:57 2004 +0200 (2004-06-21)
changeset 14981 e73f8140af78
parent 14854 61bdf2ae4dc5
child 15030 1be2cce95318
permissions -rw-r--r--
Merged in license change from Isabelle2004
     1 (*  Title:      Pure/proofterm.ML
     2     ID:         $Id$
     3     Author:     Stefan Berghofer, TU Muenchen
     4 
     5 LF style proof terms.
     6 *)
     7 
     8 infix 8 % %% %>;
     9 
    10 signature BASIC_PROOFTERM =
    11 sig
    12   val proofs: int ref
    13 
    14   datatype proof =
    15      PBound of int
    16    | Abst of string * typ option * proof
    17    | AbsP of string * term option * proof
    18    | % of proof * term option
    19    | %% of proof * proof
    20    | Hyp of term
    21    | PThm of (string * (string * string list) list) * proof * term * typ list option
    22    | PAxm of string * term * typ list option
    23    | Oracle of string * term * typ list option
    24    | MinProof of proof list;
    25 
    26   val %> : proof * term -> proof
    27 end;
    28 
    29 signature PROOFTERM =
    30 sig
    31   include BASIC_PROOFTERM
    32 
    33   val infer_derivs : (proof -> proof -> proof) -> bool * proof -> bool * proof -> bool * proof
    34   val infer_derivs' : (proof -> proof) -> (bool * proof -> bool * proof)
    35 
    36   (** primitive operations **)
    37   val proof_combt : proof * term list -> proof
    38   val proof_combt' : proof * term option list -> proof
    39   val proof_combP : proof * proof list -> proof
    40   val strip_combt : proof -> proof * term option list
    41   val strip_combP : proof -> proof * proof list
    42   val strip_thm : proof -> proof
    43   val map_proof_terms : (term -> term) -> (typ -> typ) -> proof -> proof
    44   val fold_proof_terms : (term * 'a -> 'a) -> (typ * 'a -> 'a) -> 'a * proof -> 'a
    45   val add_prf_names : string list * proof -> string list
    46   val add_prf_tfree_names : string list * proof -> string list
    47   val add_prf_tvar_ixns : indexname list * proof -> indexname list
    48   val maxidx_of_proof : proof -> int
    49   val size_of_proof : proof -> int
    50   val change_type : typ list option -> proof -> proof
    51   val prf_abstract_over : term -> proof -> proof
    52   val prf_incr_bv : int -> int -> int -> int -> proof -> proof
    53   val incr_pboundvars : int -> int -> proof -> proof
    54   val prf_loose_bvar1 : proof -> int -> bool
    55   val prf_loose_Pbvar1 : proof -> int -> bool
    56   val prf_add_loose_bnos : int -> int -> proof ->
    57     int list * int list -> int list * int list
    58   val norm_proof : Envir.env -> proof -> proof
    59   val norm_proof' : Envir.env -> proof -> proof
    60   val prf_subst_bounds : term list -> proof -> proof
    61   val prf_subst_pbounds : proof list -> proof -> proof
    62   val freeze_thaw_prf : proof -> proof * (proof -> proof)
    63 
    64   val thms_of_proof : (term * proof) list Symtab.table -> proof ->
    65     (term * proof) list Symtab.table
    66   val axms_of_proof : proof Symtab.table -> proof -> proof Symtab.table
    67   val oracles_of_proof : proof list -> proof -> proof list
    68 
    69   (** proof terms for specific inference rules **)
    70   val implies_intr_proof : term -> proof -> proof
    71   val forall_intr_proof : term -> string -> proof -> proof
    72   val varify_proof : term -> string list -> proof -> proof
    73   val freezeT : term -> proof -> proof
    74   val rotate_proof : term list -> term -> int -> proof -> proof
    75   val permute_prems_prf : term list -> int -> int -> proof -> proof
    76   val instantiate : (indexname * typ) list -> (term * term) list -> proof -> proof
    77   val lift_proof : term -> int -> term -> proof -> proof
    78   val assumption_proof : term list -> term -> int -> proof -> proof
    79   val bicompose_proof : term list -> term list -> term list -> term option ->
    80     int -> proof -> proof -> proof
    81   val equality_axms : (string * term) list
    82   val reflexive_axm : proof
    83   val symmetric_axm : proof
    84   val transitive_axm : proof
    85   val equal_intr_axm : proof
    86   val equal_elim_axm : proof
    87   val abstract_rule_axm : proof
    88   val combination_axm : proof
    89   val reflexive : proof
    90   val symmetric : proof -> proof
    91   val transitive : term -> typ -> proof -> proof -> proof
    92   val abstract_rule : term -> string -> proof -> proof
    93   val combination : term -> term -> term -> term -> typ -> proof -> proof -> proof
    94   val equal_intr : term -> term -> proof -> proof -> proof
    95   val equal_elim : term -> term -> proof -> proof -> proof
    96   val axm_proof : string -> term -> proof
    97   val oracle_proof : string -> term -> proof
    98   val thm_proof : Sign.sg -> string * (string * string list) list ->
    99     term list -> term -> proof -> proof
   100   val get_name_tags : term list -> term -> proof -> string * (string * string list) list
   101 
   102   (** rewriting on proof terms **)
   103   val add_prf_rrules : (proof * proof) list -> theory -> theory
   104   val add_prf_rprocs : (string * (Term.typ list -> proof -> proof option)) list ->
   105     theory -> theory
   106   val rewrite_proof : Type.tsig -> (proof * proof) list *
   107     (string * (typ list -> proof -> proof option)) list -> proof -> proof
   108   val rewrite_proof_notypes : (proof * proof) list *
   109     (string * (typ list -> proof -> proof option)) list -> proof -> proof
   110   val init : theory -> theory
   111   
   112 end
   113 
   114 structure Proofterm : PROOFTERM =
   115 struct
   116 
   117 open Envir;
   118 
   119 datatype proof =
   120    PBound of int
   121  | Abst of string * typ option * proof
   122  | AbsP of string * term option * proof
   123  | op % of proof * term option
   124  | op %% of proof * proof
   125  | Hyp of term
   126  | PThm of (string * (string * string list) list) * proof * term * typ list option
   127  | PAxm of string * term * typ list option
   128  | Oracle of string * term * typ list option
   129  | MinProof of proof list;
   130 
   131 fun oracles_of_proof prfs prf =
   132   let
   133     fun oras_of (tabs, Abst (_, _, prf)) = oras_of (tabs, prf)
   134       | oras_of (tabs, AbsP (_, _, prf)) = oras_of (tabs, prf)
   135       | oras_of (tabs, prf % _) = oras_of (tabs, prf)
   136       | oras_of (tabs, prf1 %% prf2) = oras_of (oras_of (tabs, prf1), prf2)
   137       | oras_of (tabs as (thms, oras), PThm ((name, _), prf, prop, _)) =
   138           (case Symtab.lookup (thms, name) of
   139              None => oras_of ((Symtab.update ((name, [prop]), thms), oras), prf)
   140            | Some ps => if prop mem ps then tabs else
   141                oras_of ((Symtab.update ((name, prop::ps), thms), oras), prf))
   142       | oras_of ((thms, oras), prf as Oracle _) = (thms, prf ins oras)
   143       | oras_of (tabs, MinProof prfs) = foldl oras_of (tabs, prfs)
   144       | oras_of (tabs, _) = tabs
   145   in
   146     snd (oras_of ((Symtab.empty, prfs), prf))
   147   end;
   148 
   149 fun thms_of_proof tab (Abst (_, _, prf)) = thms_of_proof tab prf
   150   | thms_of_proof tab (AbsP (_, _, prf)) = thms_of_proof tab prf
   151   | thms_of_proof tab (prf1 %% prf2) = thms_of_proof (thms_of_proof tab prf1) prf2
   152   | thms_of_proof tab (prf % _) = thms_of_proof tab prf
   153   | thms_of_proof tab (prf' as PThm ((s, _), prf, prop, _)) =
   154       (case Symtab.lookup (tab, s) of
   155          None => thms_of_proof (Symtab.update ((s, [(prop, prf')]), tab)) prf
   156        | Some ps => if exists (equal prop o fst) ps then tab else
   157            thms_of_proof (Symtab.update ((s, (prop, prf')::ps), tab)) prf)
   158   | thms_of_proof tab (MinProof prfs) = foldl (uncurry thms_of_proof) (tab, prfs)
   159   | thms_of_proof tab _ = tab;
   160 
   161 fun axms_of_proof tab (Abst (_, _, prf)) = axms_of_proof tab prf
   162   | axms_of_proof tab (AbsP (_, _, prf)) = axms_of_proof tab prf
   163   | axms_of_proof tab (prf1 %% prf2) = axms_of_proof (axms_of_proof tab prf1) prf2
   164   | axms_of_proof tab (prf % _) = axms_of_proof tab prf
   165   | axms_of_proof tab (prf as PAxm (s, _, _)) = Symtab.update ((s, prf), tab)
   166   | axms_of_proof tab (MinProof prfs) = foldl (uncurry axms_of_proof) (tab, prfs)
   167   | axms_of_proof tab _ = tab;
   168 
   169 (** collect all theorems, axioms and oracles **)
   170 
   171 fun mk_min_proof (prfs, Abst (_, _, prf)) = mk_min_proof (prfs, prf)
   172   | mk_min_proof (prfs, AbsP (_, _, prf)) = mk_min_proof (prfs, prf)
   173   | mk_min_proof (prfs, prf % _) = mk_min_proof (prfs, prf)
   174   | mk_min_proof (prfs, prf1 %% prf2) = mk_min_proof (mk_min_proof (prfs, prf1), prf2)
   175   | mk_min_proof (prfs, prf as PThm _) = prf ins prfs
   176   | mk_min_proof (prfs, prf as PAxm _) = prf ins prfs
   177   | mk_min_proof (prfs, prf as Oracle _) = prf ins prfs
   178   | mk_min_proof (prfs, MinProof prfs') = prfs union prfs'
   179   | mk_min_proof (prfs, _) = prfs;
   180 
   181 (** proof objects with different levels of detail **)
   182 
   183 val proofs = ref 2;
   184 
   185 fun err_illegal_level i =
   186   error ("Illegal level of detail for proof objects: " ^ string_of_int i);
   187 
   188 fun if_ora b = if b then oracles_of_proof else K;
   189 
   190 fun infer_derivs f (ora1, prf1) (ora2, prf2) =
   191   (ora1 orelse ora2, 
   192    case !proofs of
   193      2 => f prf1 prf2
   194    | 1 => MinProof (mk_min_proof (mk_min_proof ([], prf1), prf2))
   195    | 0 => MinProof (if_ora ora2 (if_ora ora1 [] prf1) prf2)
   196    | i => err_illegal_level i);
   197 
   198 fun infer_derivs' f (ora, prf) =
   199   (ora,
   200    case !proofs of
   201      2 => f prf
   202    | 1 => MinProof (mk_min_proof ([], prf))
   203    | 0 => MinProof (if_ora ora [] prf)
   204    | i => err_illegal_level i);
   205 
   206 fun (prf %> t) = prf % Some t;
   207 
   208 val proof_combt = foldl (op %>);
   209 val proof_combt' = foldl (op %);
   210 val proof_combP = foldl (op %%);
   211 
   212 fun strip_combt prf = 
   213     let fun stripc (prf % t, ts) = stripc (prf, t::ts)
   214           | stripc  x =  x 
   215     in  stripc (prf, [])  end;
   216 
   217 fun strip_combP prf = 
   218     let fun stripc (prf %% prf', prfs) = stripc (prf, prf'::prfs)
   219           | stripc  x =  x
   220     in  stripc (prf, [])  end;
   221 
   222 fun strip_thm prf = (case strip_combt (fst (strip_combP prf)) of
   223       (PThm (_, prf', _, _), _) => prf'
   224     | _ => prf);
   225 
   226 val mk_Abst = foldr (fn ((s, T:typ), prf) => Abst (s, None, prf));
   227 fun mk_AbsP (i, prf) = funpow i (fn prf => AbsP ("H", None, prf)) prf;
   228 
   229 fun apsome' f None = raise SAME
   230   | apsome' f (Some x) = Some (f x);
   231 
   232 fun same f x =
   233   let val x' = f x
   234   in if x = x' then raise SAME else x' end;
   235 
   236 fun map_proof_terms f g =
   237   let
   238     fun mapp (Abst (s, T, prf)) = (Abst (s, apsome' (same g) T, mapph prf)
   239           handle SAME => Abst (s, T, mapp prf))
   240       | mapp (AbsP (s, t, prf)) = (AbsP (s, apsome' (same f) t, mapph prf)
   241           handle SAME => AbsP (s, t, mapp prf))
   242       | mapp (prf % t) = (mapp prf % apsome f t
   243           handle SAME => prf % apsome' (same f) t)
   244       | mapp (prf1 %% prf2) = (mapp prf1 %% mapph prf2
   245           handle SAME => prf1 %% mapp prf2)
   246       | mapp (PThm (a, prf, prop, Some Ts)) =
   247           PThm (a, prf, prop, Some (same (map g) Ts))
   248       | mapp (PAxm (a, prop, Some Ts)) =
   249           PAxm (a, prop, Some (same (map g) Ts))
   250       | mapp _ = raise SAME
   251     and mapph prf = (mapp prf handle SAME => prf)
   252 
   253   in mapph end;
   254 
   255 fun fold_proof_terms f g (a, Abst (_, Some T, prf)) = fold_proof_terms f g (g (T, a), prf)
   256   | fold_proof_terms f g (a, Abst (_, None, prf)) = fold_proof_terms f g (a, prf)
   257   | fold_proof_terms f g (a, AbsP (_, Some t, prf)) = fold_proof_terms f g (f (t, a), prf)
   258   | fold_proof_terms f g (a, AbsP (_, None, prf)) = fold_proof_terms f g (a, prf)
   259   | fold_proof_terms f g (a, prf % Some t) = f (t, fold_proof_terms f g (a, prf))
   260   | fold_proof_terms f g (a, prf % None) = fold_proof_terms f g (a, prf)
   261   | fold_proof_terms f g (a, prf1 %% prf2) = fold_proof_terms f g
   262       (fold_proof_terms f g (a, prf1), prf2)
   263   | fold_proof_terms _ g (a, PThm (_, _, _, Some Ts)) = foldr g (Ts, a)
   264   | fold_proof_terms _ g (a, PAxm (_, prop, Some Ts)) = foldr g (Ts, a)
   265   | fold_proof_terms _ _ (a, _) = a;
   266 
   267 val add_prf_names = fold_proof_terms add_term_names ((uncurry K) o swap);
   268 val add_prf_tfree_names = fold_proof_terms add_term_tfree_names add_typ_tfree_names;
   269 val add_prf_tvar_ixns = fold_proof_terms add_term_tvar_ixns (add_typ_ixns o swap);
   270 
   271 fun maxidx_of_proof prf = fold_proof_terms
   272   (Int.max o apfst maxidx_of_term) (Int.max o apfst maxidx_of_typ) (~1, prf); 
   273 
   274 fun size_of_proof (Abst (_, _, prf)) = 1 + size_of_proof prf
   275   | size_of_proof (AbsP (_, t, prf)) = 1 + size_of_proof prf
   276   | size_of_proof (prf1 %% prf2) = size_of_proof prf1 + size_of_proof prf2
   277   | size_of_proof (prf % _) = 1 + size_of_proof prf
   278   | size_of_proof _ = 1;
   279 
   280 fun change_type opTs (PThm (name, prf, prop, _)) = PThm (name, prf, prop, opTs)
   281   | change_type opTs (PAxm (name, prop, _)) = PAxm (name, prop, opTs)
   282   | change_type opTs (Oracle (name, prop, _)) = Oracle (name, prop, opTs)
   283   | change_type _ prf = prf;
   284 
   285 
   286 (***** utilities *****)
   287 
   288 fun strip_abs (_::Ts) (Abs (_, _, t)) = strip_abs Ts t
   289   | strip_abs _ t = t;
   290 
   291 fun mk_abs Ts t = foldl (fn (t', T) => Abs ("", T, t')) (t, Ts);
   292 
   293 
   294 (*Abstraction of a proof term over its occurrences of v, 
   295     which must contain no loose bound variables.
   296   The resulting proof term is ready to become the body of an Abst.*)
   297 
   298 fun prf_abstract_over v =
   299   let
   300     fun abst' lev u = if v aconv u then Bound lev else
   301       (case u of
   302          Abs (a, T, t) => Abs (a, T, abst' (lev + 1) t)
   303        | f $ t => (abst' lev f $ absth' lev t handle SAME => f $ abst' lev t)
   304        | _ => raise SAME)
   305     and absth' lev t = (abst' lev t handle SAME => t);
   306 
   307     fun abst lev (AbsP (a, t, prf)) =
   308           (AbsP (a, apsome' (abst' lev) t, absth lev prf)
   309            handle SAME => AbsP (a, t, abst lev prf))
   310       | abst lev (Abst (a, T, prf)) = Abst (a, T, abst (lev + 1) prf)
   311       | abst lev (prf1 %% prf2) = (abst lev prf1 %% absth lev prf2
   312           handle SAME => prf1 %% abst lev prf2)
   313       | abst lev (prf % t) = (abst lev prf % apsome (absth' lev) t
   314           handle SAME => prf % apsome' (abst' lev) t)
   315       | abst _ _ = raise SAME
   316     and absth lev prf = (abst lev prf handle SAME => prf)
   317 
   318   in absth 0 end;
   319 
   320 
   321 (*increments a proof term's non-local bound variables
   322   required when moving a proof term within abstractions
   323      inc is  increment for bound variables
   324      lev is  level at which a bound variable is considered 'loose'*)
   325 
   326 fun incr_bv' inct tlev t = incr_bv (inct, tlev, t);
   327 
   328 fun prf_incr_bv' incP inct Plev tlev (PBound i) =
   329       if i >= Plev then PBound (i+incP) else raise SAME 
   330   | prf_incr_bv' incP inct Plev tlev (AbsP (a, t, body)) =
   331       (AbsP (a, apsome' (same (incr_bv' inct tlev)) t,
   332          prf_incr_bv incP inct (Plev+1) tlev body) handle SAME =>
   333            AbsP (a, t, prf_incr_bv' incP inct (Plev+1) tlev body))
   334   | prf_incr_bv' incP inct Plev tlev (Abst (a, T, body)) =
   335       Abst (a, T, prf_incr_bv' incP inct Plev (tlev+1) body)
   336   | prf_incr_bv' incP inct Plev tlev (prf %% prf') = 
   337       (prf_incr_bv' incP inct Plev tlev prf %% prf_incr_bv incP inct Plev tlev prf'
   338        handle SAME => prf %% prf_incr_bv' incP inct Plev tlev prf')
   339   | prf_incr_bv' incP inct Plev tlev (prf % t) = 
   340       (prf_incr_bv' incP inct Plev tlev prf % apsome (incr_bv' inct tlev) t
   341        handle SAME => prf % apsome' (same (incr_bv' inct tlev)) t)
   342   | prf_incr_bv' _ _ _ _ _ = raise SAME
   343 and prf_incr_bv incP inct Plev tlev prf =
   344       (prf_incr_bv' incP inct Plev tlev prf handle SAME => prf);
   345 
   346 fun incr_pboundvars  0 0 prf = prf
   347   | incr_pboundvars incP inct prf = prf_incr_bv incP inct 0 0 prf;
   348 
   349 
   350 fun prf_loose_bvar1 (prf1 %% prf2) k = prf_loose_bvar1 prf1 k orelse prf_loose_bvar1 prf2 k
   351   | prf_loose_bvar1 (prf % Some t) k = prf_loose_bvar1 prf k orelse loose_bvar1 (t, k)
   352   | prf_loose_bvar1 (_ % None) _ = true
   353   | prf_loose_bvar1 (AbsP (_, Some t, prf)) k = loose_bvar1 (t, k) orelse prf_loose_bvar1 prf k
   354   | prf_loose_bvar1 (AbsP (_, None, _)) k = true
   355   | prf_loose_bvar1 (Abst (_, _, prf)) k = prf_loose_bvar1 prf (k+1)
   356   | prf_loose_bvar1 _ _ = false;
   357 
   358 fun prf_loose_Pbvar1 (PBound i) k = i = k
   359   | prf_loose_Pbvar1 (prf1 %% prf2) k = prf_loose_Pbvar1 prf1 k orelse prf_loose_Pbvar1 prf2 k
   360   | prf_loose_Pbvar1 (prf % _) k = prf_loose_Pbvar1 prf k
   361   | prf_loose_Pbvar1 (AbsP (_, _, prf)) k = prf_loose_Pbvar1 prf (k+1)
   362   | prf_loose_Pbvar1 (Abst (_, _, prf)) k = prf_loose_Pbvar1 prf k
   363   | prf_loose_Pbvar1 _ _ = false;
   364 
   365 fun prf_add_loose_bnos plev tlev (PBound i) (is, js) =
   366       if i < plev then (is, js) else ((i-plev) ins is, js)
   367   | prf_add_loose_bnos plev tlev (prf1 %% prf2) p =
   368       prf_add_loose_bnos plev tlev prf2
   369         (prf_add_loose_bnos plev tlev prf1 p)
   370   | prf_add_loose_bnos plev tlev (prf % opt) (is, js) =
   371       prf_add_loose_bnos plev tlev prf (case opt of
   372           None => (is, ~1 ins js)
   373         | Some t => (is, add_loose_bnos (t, tlev, js)))
   374   | prf_add_loose_bnos plev tlev (AbsP (_, opt, prf)) (is, js) =
   375       prf_add_loose_bnos (plev+1) tlev prf (case opt of
   376           None => (is, ~1 ins js)
   377         | Some t => (is, add_loose_bnos (t, tlev, js)))
   378   | prf_add_loose_bnos plev tlev (Abst (_, _, prf)) p =
   379       prf_add_loose_bnos plev (tlev+1) prf p
   380   | prf_add_loose_bnos _ _ _ _ = ([], []);
   381 
   382 
   383 (**** substitutions ****)
   384 
   385 fun norm_proof env =
   386   let
   387     val envT = type_env env;
   388     fun norm (Abst (s, T, prf)) = (Abst (s, apsome' (norm_type_same envT) T, normh prf)
   389           handle SAME => Abst (s, T, norm prf))
   390       | norm (AbsP (s, t, prf)) = (AbsP (s, apsome' (norm_term_same env) t, normh prf)
   391           handle SAME => AbsP (s, t, norm prf))
   392       | norm (prf % t) = (norm prf % apsome (norm_term env) t
   393           handle SAME => prf % apsome' (norm_term_same env) t)
   394       | norm (prf1 %% prf2) = (norm prf1 %% normh prf2
   395           handle SAME => prf1 %% norm prf2)
   396       | norm (PThm (s, prf, t, Ts)) = PThm (s, prf, t, apsome' (norm_types_same envT) Ts)
   397       | norm (PAxm (s, prop, Ts)) = PAxm (s, prop, apsome' (norm_types_same envT) Ts)
   398       | norm _ = raise SAME
   399     and normh prf = (norm prf handle SAME => prf);
   400   in normh end;
   401 
   402 (***** Remove some types in proof term (to save space) *****)
   403 
   404 fun remove_types (Abs (s, _, t)) = Abs (s, dummyT, remove_types t)
   405   | remove_types (t $ u) = remove_types t $ remove_types u
   406   | remove_types (Const (s, _)) = Const (s, dummyT)
   407   | remove_types t = t;
   408 
   409 fun remove_types_env (Envir.Envir {iTs, asol, maxidx}) =
   410   Envir.Envir {iTs = iTs, asol = Vartab.map remove_types asol, maxidx = maxidx};
   411 
   412 fun norm_proof' env prf = norm_proof (remove_types_env env) prf;
   413 
   414 (**** substitution of bound variables ****)
   415 
   416 fun prf_subst_bounds args prf =
   417   let
   418     val n = length args;
   419     fun subst' lev (Bound i) =
   420          (if i<lev then raise SAME    (*var is locally bound*)
   421           else  incr_boundvars lev (List.nth (args, i-lev))
   422                   handle Subscript => Bound (i-n)  (*loose: change it*))
   423       | subst' lev (Abs (a, T, body)) = Abs (a, T,  subst' (lev+1) body)
   424       | subst' lev (f $ t) = (subst' lev f $ substh' lev t
   425           handle SAME => f $ subst' lev t)
   426       | subst' _ _ = raise SAME
   427     and substh' lev t = (subst' lev t handle SAME => t);
   428 
   429     fun subst lev (AbsP (a, t, body)) = (AbsP (a, apsome' (subst' lev) t, substh lev body)
   430           handle SAME => AbsP (a, t, subst lev body))
   431       | subst lev (Abst (a, T, body)) = Abst (a, T, subst (lev+1) body)
   432       | subst lev (prf %% prf') = (subst lev prf %% substh lev prf'
   433           handle SAME => prf %% subst lev prf')
   434       | subst lev (prf % t) = (subst lev prf % apsome (substh' lev) t
   435           handle SAME => prf % apsome' (subst' lev) t)
   436       | subst _ _ = raise SAME
   437     and substh lev prf = (subst lev prf handle SAME => prf)
   438   in case args of [] => prf | _ => substh 0 prf end;
   439 
   440 fun prf_subst_pbounds args prf =
   441   let
   442     val n = length args;
   443     fun subst (PBound i) Plev tlev =
   444  	 (if i < Plev then raise SAME    (*var is locally bound*)
   445           else incr_pboundvars Plev tlev (List.nth (args, i-Plev))
   446                  handle Subscript => PBound (i-n)  (*loose: change it*))
   447       | subst (AbsP (a, t, body)) Plev tlev = AbsP (a, t, subst body (Plev+1) tlev)
   448       | subst (Abst (a, T, body)) Plev tlev = Abst (a, T, subst body Plev (tlev+1))
   449       | subst (prf %% prf') Plev tlev = (subst prf Plev tlev %% substh prf' Plev tlev
   450           handle SAME => prf %% subst prf' Plev tlev)
   451       | subst (prf % t) Plev tlev = subst prf Plev tlev % t
   452       | subst  prf _ _ = raise SAME
   453     and substh prf Plev tlev = (subst prf Plev tlev handle SAME => prf)
   454   in case args of [] => prf | _ => substh prf 0 0 end;
   455 
   456 
   457 (**** Freezing and thawing of variables in proof terms ****)
   458 
   459 fun frzT names =
   460   map_type_tvar (fn (ixn, xs) => TFree (the (assoc (names, ixn)), xs));
   461 
   462 fun thawT names =
   463   map_type_tfree (fn (s, xs) => case assoc (names, s) of
   464       None => TFree (s, xs)
   465     | Some ixn => TVar (ixn, xs));
   466 
   467 fun freeze names names' (t $ u) =
   468       freeze names names' t $ freeze names names' u
   469   | freeze names names' (Abs (s, T, t)) =
   470       Abs (s, frzT names' T, freeze names names' t)
   471   | freeze names names' (Const (s, T)) = Const (s, frzT names' T)
   472   | freeze names names' (Free (s, T)) = Free (s, frzT names' T)
   473   | freeze names names' (Var (ixn, T)) =
   474       Free (the (assoc (names, ixn)), frzT names' T)
   475   | freeze names names' t = t;
   476 
   477 fun thaw names names' (t $ u) =
   478       thaw names names' t $ thaw names names' u
   479   | thaw names names' (Abs (s, T, t)) =
   480       Abs (s, thawT names' T, thaw names names' t)
   481   | thaw names names' (Const (s, T)) = Const (s, thawT names' T)
   482   | thaw names names' (Free (s, T)) = 
   483       let val T' = thawT names' T
   484       in case assoc (names, s) of
   485           None => Free (s, T')
   486         | Some ixn => Var (ixn, T')
   487       end
   488   | thaw names names' (Var (ixn, T)) = Var (ixn, thawT names' T)
   489   | thaw names names' t = t;
   490 
   491 fun freeze_thaw_prf prf =
   492   let
   493     val (fs, Tfs, vs, Tvs) = fold_proof_terms
   494       (fn (t, (fs, Tfs, vs, Tvs)) =>
   495          (add_term_frees (t, fs), add_term_tfree_names (t, Tfs),
   496           add_term_vars (t, vs), add_term_tvar_ixns (t, Tvs)))
   497       (fn (T, (fs, Tfs, vs, Tvs)) =>
   498          (fs, add_typ_tfree_names (T, Tfs),
   499           vs, add_typ_ixns (Tvs, T)))
   500             (([], [], [], []), prf);
   501     val fs' = map (fst o dest_Free) fs;
   502     val vs' = map (fst o dest_Var) vs;
   503     val names = vs' ~~ variantlist (map fst vs', fs');
   504     val names' = Tvs ~~ variantlist (map fst Tvs, Tfs);
   505     val rnames = map swap names;
   506     val rnames' = map swap names';
   507   in
   508     (map_proof_terms (freeze names names') (frzT names') prf,
   509      map_proof_terms (thaw rnames rnames') (thawT rnames'))
   510   end;
   511 
   512 
   513 (***** implication introduction *****)
   514 
   515 fun implies_intr_proof h prf =
   516   let
   517     fun abshyp i (Hyp t) = if h aconv t then PBound i else raise SAME
   518       | abshyp i (Abst (s, T, prf)) = Abst (s, T, abshyp i prf)
   519       | abshyp i (AbsP (s, t, prf)) = AbsP (s, t, abshyp (i+1) prf)
   520       | abshyp i (prf % t) = abshyp i prf % t
   521       | abshyp i (prf1 %% prf2) = (abshyp i prf1 %% abshyph i prf2
   522           handle SAME => prf1 %% abshyp i prf2)
   523       | abshyp _ _ = raise SAME
   524     and abshyph i prf = (abshyp i prf handle SAME => prf)
   525   in
   526     AbsP ("H", None (*h*), abshyph 0 prf)
   527   end;
   528 
   529 
   530 (***** forall introduction *****)
   531 
   532 fun forall_intr_proof x a prf = Abst (a, None, prf_abstract_over x prf);
   533 
   534 
   535 (***** varify *****)
   536 
   537 fun varify_proof t fixed prf =
   538   let
   539     val fs = add_term_tfree_names (t, []) \\ fixed;
   540     val ixns = add_term_tvar_ixns (t, []);
   541     val fmap = fs ~~ variantlist (fs, map #1 ixns)
   542     fun thaw (f as (a, S)) =
   543       (case assoc (fmap, a) of
   544         None => TFree f
   545       | Some b => TVar ((b, 0), S));
   546   in map_proof_terms (map_term_types (map_type_tfree thaw)) (map_type_tfree thaw) prf
   547   end;
   548 
   549 
   550 local
   551 
   552 fun new_name (ix, (pairs,used)) =
   553   let val v = variant used (string_of_indexname ix)
   554   in  ((ix, v) :: pairs, v :: used)  end;
   555 
   556 fun freeze_one alist (ix, sort) = (case assoc (alist, ix) of
   557     None => TVar (ix, sort)
   558   | Some name => TFree (name, sort));
   559 
   560 in
   561 
   562 fun freezeT t prf =
   563   let
   564     val used = it_term_types add_typ_tfree_names (t, [])
   565     and tvars = map #1 (it_term_types add_typ_tvars (t, []));
   566     val (alist, _) = foldr new_name (tvars, ([], used));
   567   in
   568     (case alist of
   569       [] => prf (*nothing to do!*)
   570     | _ =>
   571       let val frzT = map_type_tvar (freeze_one alist)
   572       in map_proof_terms (map_term_types frzT) frzT prf end)
   573   end;
   574 
   575 end;
   576 
   577 
   578 (***** rotate assumptions *****)
   579 
   580 fun rotate_proof Bs Bi m prf =
   581   let
   582     val params = Term.strip_all_vars Bi;
   583     val asms = Logic.strip_imp_prems (Term.strip_all_body Bi);
   584     val i = length asms;
   585     val j = length Bs;
   586   in
   587     mk_AbsP (j+1, proof_combP (prf, map PBound
   588       (j downto 1) @ [mk_Abst (params, mk_AbsP (i,
   589         proof_combP (proof_combt (PBound i, map Bound ((length params - 1) downto 0)),
   590           map PBound (((i-m-1) downto 0) @ ((i-1) downto (i-m))))))]))
   591   end;
   592 
   593 
   594 (***** permute premises *****)
   595 
   596 fun permute_prems_prf prems j k prf =
   597   let val n = length prems
   598   in mk_AbsP (n, proof_combP (prf,
   599     map PBound ((n-1 downto n-j) @ (k-1 downto 0) @ (n-j-1 downto k))))
   600   end;
   601 
   602 
   603 (***** instantiation *****)
   604 
   605 fun instantiate vTs tpairs =
   606   map_proof_terms (subst_atomic (map (apsnd remove_types) tpairs) o
   607     subst_TVars vTs) (typ_subst_TVars vTs);
   608 
   609 
   610 (***** lifting *****)
   611 
   612 fun lift_proof Bi inc prop prf =
   613   let
   614     val (_, lift_all) = Logic.lift_fns (Bi, inc);
   615 
   616     fun lift'' Us Ts t = strip_abs Ts (Logic.incr_indexes (Us, inc) (mk_abs Ts t));
   617 
   618     fun lift' Us Ts (Abst (s, T, prf)) =
   619           (Abst (s, apsome' (same (incr_tvar inc)) T, lifth' Us (dummyT::Ts) prf)
   620            handle SAME => Abst (s, T, lift' Us (dummyT::Ts) prf))
   621       | lift' Us Ts (AbsP (s, t, prf)) =
   622           (AbsP (s, apsome' (same (lift'' Us Ts)) t, lifth' Us Ts prf)
   623            handle SAME => AbsP (s, t, lift' Us Ts prf))
   624       | lift' Us Ts (prf % t) = (lift' Us Ts prf % apsome (lift'' Us Ts) t
   625           handle SAME => prf % apsome' (same (lift'' Us Ts)) t)
   626       | lift' Us Ts (prf1 %% prf2) = (lift' Us Ts prf1 %% lifth' Us Ts prf2
   627           handle SAME => prf1 %% lift' Us Ts prf2)
   628       | lift' _ _ (PThm (s, prf, prop, Ts)) =
   629           PThm (s, prf, prop, apsome' (same (map (incr_tvar inc))) Ts)
   630       | lift' _ _ (PAxm (s, prop, Ts)) =
   631           PAxm (s, prop, apsome' (same (map (incr_tvar inc))) Ts)
   632       | lift' _ _ _ = raise SAME
   633     and lifth' Us Ts prf = (lift' Us Ts prf handle SAME => prf);
   634 
   635     val ps = map lift_all (Logic.strip_imp_prems prop);
   636     val k = length ps;
   637 
   638     fun mk_app (b, (i, j, prf)) = 
   639           if b then (i-1, j, prf %% PBound i) else (i, j-1, prf %> Bound j);
   640 
   641     fun lift Us bs i j (Const ("==>", _) $ A $ B) =
   642 	    AbsP ("H", None (*A*), lift Us (true::bs) (i+1) j B)
   643       | lift Us bs i j (Const ("all", _) $ Abs (a, T, t)) = 
   644 	    Abst (a, None (*T*), lift (T::Us) (false::bs) i (j+1) t)
   645       | lift Us bs i j _ = proof_combP (lifth' (rev Us) [] prf,
   646             map (fn k => (#3 (foldr mk_app (bs, (i-1, j-1, PBound k)))))
   647               (i + k - 1 downto i));
   648   in
   649     mk_AbsP (k, lift [] [] 0 0 Bi)
   650   end;
   651 
   652 
   653 (***** proof by assumption *****)
   654 
   655 fun mk_asm_prf (Const ("==>", _) $ A $ B) i = AbsP ("H", None (*A*), mk_asm_prf B (i+1))
   656   | mk_asm_prf (Const ("all", _) $ Abs (a, T, t)) i = Abst (a, None (*T*), mk_asm_prf t i)
   657   | mk_asm_prf _ i = PBound i;
   658 
   659 fun assumption_proof Bs Bi n prf =
   660   mk_AbsP (length Bs, proof_combP (prf,
   661     map PBound (length Bs - 1 downto 0) @ [mk_asm_prf Bi (~n)]));
   662 
   663 
   664 (***** Composition of object rule with proof state *****)
   665 
   666 fun flatten_params_proof i j n (Const ("==>", _) $ A $ B, k) =
   667       AbsP ("H", None (*A*), flatten_params_proof (i+1) j n (B, k))
   668   | flatten_params_proof i j n (Const ("all", _) $ Abs (a, T, t), k) =
   669       Abst (a, None (*T*), flatten_params_proof i (j+1) n (t, k))
   670   | flatten_params_proof i j n (_, k) = proof_combP (proof_combt (PBound (k+i),
   671       map Bound (j-1 downto 0)), map PBound (i-1 downto 0 \ i-n));
   672 
   673 fun bicompose_proof Bs oldAs newAs A n rprf sprf =
   674   let
   675     val la = length newAs;
   676     val lb = length Bs;
   677   in
   678     mk_AbsP (lb+la, proof_combP (sprf,
   679       map PBound (lb + la - 1 downto la)) %%
   680         proof_combP (rprf, (if n>0 then [mk_asm_prf (the A) (~n)] else []) @
   681           map (flatten_params_proof 0 0 n) (oldAs ~~ (la - 1 downto 0))))
   682   end;
   683 
   684 
   685 (***** axioms for equality *****)
   686 
   687 val aT = TFree ("'a", []);
   688 val bT = TFree ("'b", []);
   689 val x = Free ("x", aT);
   690 val y = Free ("y", aT);
   691 val z = Free ("z", aT);
   692 val A = Free ("A", propT);
   693 val B = Free ("B", propT);
   694 val f = Free ("f", aT --> bT);
   695 val g = Free ("g", aT --> bT);
   696 
   697 local open Logic in
   698 
   699 val equality_axms =
   700   [("reflexive", mk_equals (x, x)),
   701    ("symmetric", mk_implies (mk_equals (x, y), mk_equals (y, x))),
   702    ("transitive", list_implies ([mk_equals (x, y), mk_equals (y, z)], mk_equals (x, z))),
   703    ("equal_intr", list_implies ([mk_implies (A, B), mk_implies (B, A)], mk_equals (A, B))),
   704    ("equal_elim", list_implies ([mk_equals (A, B), A], B)),
   705    ("abstract_rule", Logic.mk_implies
   706       (all aT $ Abs ("x", aT, equals bT $ (f $ Bound 0) $ (g $ Bound 0)),
   707        equals (aT --> bT) $
   708          Abs ("x", aT, f $ Bound 0) $ Abs ("x", aT, g $ Bound 0))),
   709    ("combination", Logic.list_implies
   710       ([Logic.mk_equals (f, g), Logic.mk_equals (x, y)],
   711        Logic.mk_equals (f $ x, g $ y)))];
   712 
   713 val [reflexive_axm, symmetric_axm, transitive_axm, equal_intr_axm,
   714   equal_elim_axm, abstract_rule_axm, combination_axm] =
   715     map (fn (s, t) => PAxm ("ProtoPure." ^ s, varify t, None)) equality_axms;
   716 
   717 end;
   718 
   719 val reflexive = reflexive_axm % None;
   720 
   721 fun symmetric (prf as PAxm ("ProtoPure.reflexive", _, _) % _) = prf
   722   | symmetric prf = symmetric_axm % None % None %% prf;
   723 
   724 fun transitive _ _ (PAxm ("ProtoPure.reflexive", _, _) % _) prf2 = prf2
   725   | transitive _ _ prf1 (PAxm ("ProtoPure.reflexive", _, _) % _) = prf1
   726   | transitive u (Type ("prop", [])) prf1 prf2 =
   727       transitive_axm % None % Some (remove_types u) % None %% prf1 %% prf2
   728   | transitive u T prf1 prf2 =
   729       transitive_axm % None % None % None %% prf1 %% prf2;
   730 
   731 fun abstract_rule x a prf =
   732   abstract_rule_axm % None % None %% forall_intr_proof x a prf;
   733 
   734 fun check_comb (PAxm ("ProtoPure.combination", _, _) % f % g % _ % _ %% prf %% _) =
   735       is_some f orelse check_comb prf
   736   | check_comb (PAxm ("ProtoPure.transitive", _, _) % _ % _ % _ %% prf1 %% prf2) =
   737       check_comb prf1 andalso check_comb prf2
   738   | check_comb (PAxm ("ProtoPure.symmetric", _, _) % _ % _ %% prf) = check_comb prf
   739   | check_comb _ = false;
   740 
   741 fun combination f g t u (Type (_, [T, U])) prf1 prf2 =
   742   let
   743     val f = Envir.beta_norm f;
   744     val g = Envir.beta_norm g;
   745     val prf =  if check_comb prf1 then
   746         combination_axm % None % None
   747       else (case prf1 of
   748           PAxm ("ProtoPure.reflexive", _, _) % _ =>
   749             combination_axm %> remove_types f % None
   750         | _ => combination_axm %> remove_types f %> remove_types g)
   751   in
   752     (case T of
   753        Type ("fun", _) => prf %
   754          (case head_of f of
   755             Abs _ => Some (remove_types t)
   756           | Var _ => Some (remove_types t)
   757           | _ => None) %
   758          (case head_of g of
   759             Abs _ => Some (remove_types u)
   760           | Var _ => Some (remove_types u)
   761           | _ => None) %% prf1 %% prf2
   762      | _ => prf % None % None %% prf1 %% prf2)
   763   end;
   764 
   765 fun equal_intr A B prf1 prf2 =
   766   equal_intr_axm %> remove_types A %> remove_types B %% prf1 %% prf2;
   767 
   768 fun equal_elim A B prf1 prf2 =
   769   equal_elim_axm %> remove_types A %> remove_types B %% prf1 %% prf2;
   770 
   771 
   772 (***** axioms and theorems *****)
   773 
   774 fun vars_of t = rev (foldl_aterms
   775   (fn (vs, v as Var _) => v ins vs | (vs, _) => vs) ([], t));
   776 
   777 fun test_args _ [] = true
   778   | test_args is (Bound i :: ts) =
   779       not (i mem is) andalso test_args (i :: is) ts
   780   | test_args _ _ = false;
   781 
   782 fun is_fun (Type ("fun", _)) = true
   783   | is_fun (TVar _) = true
   784   | is_fun _ = false;
   785 
   786 fun add_funvars Ts (vs, t) =
   787   if is_fun (fastype_of1 (Ts, t)) then
   788     vs union mapfilter (fn Var (ixn, T) =>
   789       if is_fun T then Some ixn else None | _ => None) (vars_of t)
   790   else vs;
   791 
   792 fun add_npvars q p Ts (vs, Const ("==>", _) $ t $ u) =
   793       add_npvars q p Ts (add_npvars q (not p) Ts (vs, t), u)
   794   | add_npvars q p Ts (vs, Const ("all", Type (_, [Type (_, [T, _]), _])) $ t) =
   795       add_npvars q p Ts (vs, if p andalso q then betapply (t, Var (("",0), T)) else t)
   796   | add_npvars q p Ts (vs, Abs (_, T, t)) = add_npvars q p (T::Ts) (vs, t)
   797   | add_npvars _ _ Ts (vs, t) = add_npvars' Ts (vs, t)
   798 and add_npvars' Ts (vs, t) = (case strip_comb t of
   799     (Var (ixn, _), ts) => if test_args [] ts then vs
   800       else foldl (add_npvars' Ts) (overwrite (vs,
   801         (ixn, foldl (add_funvars Ts) (if_none (assoc (vs, ixn)) [], ts))), ts)
   802   | (Abs (_, T, u), ts) => foldl (add_npvars' (T::Ts)) (vs, u :: ts)
   803   | (_, ts) => foldl (add_npvars' Ts) (vs, ts));
   804 
   805 fun prop_vars (Const ("==>", _) $ P $ Q) = prop_vars P union prop_vars Q
   806   | prop_vars (Const ("all", _) $ Abs (_, _, t)) = prop_vars t
   807   | prop_vars t = (case strip_comb t of
   808       (Var (ixn, _), _) => [ixn] | _ => []);
   809 
   810 fun is_proj t =
   811   let
   812     fun is_p i t = (case strip_comb t of
   813         (Bound j, []) => false
   814       | (Bound j, ts) => j >= i orelse exists (is_p i) ts
   815       | (Abs (_, _, u), _) => is_p (i+1) u
   816       | (_, ts) => exists (is_p i) ts)
   817   in (case strip_abs_body t of
   818         Bound _ => true
   819       | t' => is_p 0 t')
   820   end;
   821 
   822 fun needed_vars prop = 
   823   foldl op union ([], map op ins (add_npvars true true [] ([], prop))) union
   824   prop_vars prop;
   825 
   826 fun gen_axm_proof c name prop =
   827   let
   828     val nvs = needed_vars prop;
   829     val args = map (fn (v as Var (ixn, _)) =>
   830         if ixn mem nvs then Some v else None) (vars_of prop) @
   831       map Some (sort (make_ord atless) (term_frees prop));
   832   in
   833     proof_combt' (c (name, prop, None), args)
   834   end;
   835 
   836 val axm_proof = gen_axm_proof PAxm;
   837 val oracle_proof = gen_axm_proof Oracle;
   838 
   839 fun shrink ls lev (prf as Abst (a, T, body)) =
   840       let val (b, is, ch, body') = shrink ls (lev+1) body
   841       in (b, is, ch, if ch then Abst (a, T, body') else prf) end
   842   | shrink ls lev (prf as AbsP (a, t, body)) =
   843       let val (b, is, ch, body') = shrink (lev::ls) lev body
   844       in (b orelse 0 mem is, mapfilter (fn 0 => None | i => Some (i-1)) is,
   845         ch, if ch then AbsP (a, t, body') else prf)
   846       end
   847   | shrink ls lev prf =
   848       let val (is, ch, _, prf') = shrink' ls lev [] [] prf
   849       in (false, is, ch, prf') end
   850 and shrink' ls lev ts prfs (prf as prf1 %% prf2) =
   851       let
   852         val p as (_, is', ch', prf') = shrink ls lev prf2;
   853         val (is, ch, ts', prf'') = shrink' ls lev ts (p::prfs) prf1
   854       in (is union is', ch orelse ch', ts',
   855           if ch orelse ch' then prf'' %% prf' else prf)
   856       end
   857   | shrink' ls lev ts prfs (prf as prf1 % t) =
   858       let val (is, ch, (ch', t')::ts', prf') = shrink' ls lev (t::ts) prfs prf1
   859       in (is, ch orelse ch', ts', if ch orelse ch' then prf' % t' else prf) end
   860   | shrink' ls lev ts prfs (prf as PBound i) =
   861       (if exists (fn Some (Bound j) => lev-j <= nth_elem (i, ls) | _ => true) ts
   862          orelse not (null (duplicates
   863            (foldl (fn (js, Some (Bound j)) => j :: js | (js, _) => js) ([], ts))))
   864          orelse exists #1 prfs then [i] else [], false, map (pair false) ts, prf)
   865   | shrink' ls lev ts prfs (prf as Hyp _) = ([], false, map (pair false) ts, prf)
   866   | shrink' ls lev ts prfs (prf as MinProof _) =
   867       ([], false, map (pair false) ts, prf)
   868   | shrink' ls lev ts prfs prf =
   869       let
   870         val prop = (case prf of PThm (_, _, prop, _) => prop | PAxm (_, prop, _) => prop
   871           | Oracle (_, prop, _) => prop | _ => error "shrink: proof not in normal form");
   872         val vs = vars_of prop;
   873         val (ts', ts'') = splitAt (length vs, ts)
   874         val insts = take (length ts', map (fst o dest_Var) vs) ~~ ts';
   875         val nvs = foldl (fn (ixns', (ixn, ixns)) =>
   876           ixn ins (case assoc (insts, ixn) of
   877               Some (Some t) => if is_proj t then ixns union ixns' else ixns'
   878             | _ => ixns union ixns'))
   879               (needed prop ts'' prfs, add_npvars false true [] ([], prop));
   880         val insts' = map
   881           (fn (ixn, x as Some _) => if ixn mem nvs then (false, x) else (true, None)
   882             | (_, x) => (false, x)) insts
   883       in ([], false, insts' @ map (pair false) ts'', prf) end
   884 and needed (Const ("==>", _) $ t $ u) ts ((b, _, _, _)::prfs) =
   885       (if b then map (fst o dest_Var) (vars_of t) else []) union needed u ts prfs
   886   | needed (Var (ixn, _)) (_::_) _ = [ixn]
   887   | needed _ _ _ = [];
   888 
   889 
   890 (**** Simple first order matching functions for terms and proofs ****)
   891 
   892 exception PMatch;
   893 
   894 (** see pattern.ML **)
   895 
   896 fun flt (i: int) = filter (fn n => n < i);
   897 
   898 fun fomatch Ts tymatch j =
   899   let
   900     fun mtch (instsp as (tyinsts, insts)) = fn
   901         (Var (ixn, T), t)  =>
   902           if j>0 andalso not (null (flt j (loose_bnos t)))
   903           then raise PMatch
   904           else (tymatch (tyinsts, fn () => (T, fastype_of1 (Ts, t))),
   905             (ixn, t) :: insts)
   906       | (Free (a, T), Free (b, U)) =>
   907 	  if a=b then (tymatch (tyinsts, K (T, U)), insts) else raise PMatch
   908       | (Const (a, T), Const (b, U))  =>
   909 	  if a=b then (tymatch (tyinsts, K (T, U)), insts) else raise PMatch
   910       | (f $ t, g $ u) => mtch (mtch instsp (f, g)) (t, u)
   911       | (Bound i, Bound j) => if i=j then instsp else raise PMatch
   912       | _ => raise PMatch
   913   in mtch end;
   914 
   915 fun match_proof Ts tymatch =
   916   let
   917     fun optmatch _ inst (None, _) = inst
   918       | optmatch _ _ (Some _, None) = raise PMatch
   919       | optmatch mtch inst (Some x, Some y) = mtch inst (x, y)
   920 
   921     fun matcht Ts j (pinst, tinst) (t, u) =
   922       (pinst, fomatch Ts tymatch j tinst (t, Envir.beta_norm u));
   923     fun matchT (pinst, (tyinsts, insts)) p =
   924       (pinst, (tymatch (tyinsts, K p), insts));
   925     fun matchTs inst (Ts, Us) = foldl (uncurry matchT) (inst, Ts ~~ Us);
   926 
   927     fun mtch Ts i j (pinst, tinst) (Hyp (Var (ixn, _)), prf) =
   928           if i = 0 andalso j = 0 then ((ixn, prf) :: pinst, tinst)
   929           else (case apfst (flt i) (apsnd (flt j)
   930                   (prf_add_loose_bnos 0 0 prf ([], []))) of
   931               ([], []) => ((ixn, incr_pboundvars (~i) (~j) prf) :: pinst, tinst)
   932             | ([], _) => if j = 0 then
   933                    ((ixn, incr_pboundvars (~i) (~j) prf) :: pinst, tinst)
   934                  else raise PMatch
   935             | _ => raise PMatch)
   936       | mtch Ts i j inst (prf1 % opt1, prf2 % opt2) =
   937           optmatch (matcht Ts j) (mtch Ts i j inst (prf1, prf2)) (opt1, opt2)
   938       | mtch Ts i j inst (prf1 %% prf2, prf1' %% prf2') =
   939           mtch Ts i j (mtch Ts i j inst (prf1, prf1')) (prf2, prf2')
   940       | mtch Ts i j inst (Abst (_, opT, prf1), Abst (_, opU, prf2)) =
   941           mtch (if_none opU dummyT :: Ts) i (j+1)
   942             (optmatch matchT inst (opT, opU)) (prf1, prf2)
   943       | mtch Ts i j inst (prf1, Abst (_, opU, prf2)) =
   944           mtch (if_none opU dummyT :: Ts) i (j+1) inst
   945             (incr_pboundvars 0 1 prf1 %> Bound 0, prf2)
   946       | mtch Ts i j inst (AbsP (_, opt, prf1), AbsP (_, opu, prf2)) =
   947           mtch Ts (i+1) j (optmatch (matcht Ts j) inst (opt, opu)) (prf1, prf2)
   948       | mtch Ts i j inst (prf1, AbsP (_, _, prf2)) =
   949           mtch Ts (i+1) j inst (incr_pboundvars 1 0 prf1 %% PBound 0, prf2)
   950       | mtch Ts i j inst (PThm ((name1, _), _, prop1, opTs),
   951             PThm ((name2, _), _, prop2, opUs)) =
   952           if name1=name2 andalso prop1=prop2 then
   953             optmatch matchTs inst (opTs, opUs)
   954           else raise PMatch
   955       | mtch Ts i j inst (PAxm (s1, _, opTs), PAxm (s2, _, opUs)) =
   956           if s1=s2 then optmatch matchTs inst (opTs, opUs)
   957           else raise PMatch
   958       | mtch _ _ _ inst (PBound i, PBound j) = if i = j then inst else raise PMatch
   959       | mtch _ _ _ _ _ = raise PMatch
   960   in mtch Ts 0 0 end;
   961 
   962 fun prf_subst (pinst, (tyinsts, insts)) =
   963   let
   964     val substT = typ_subst_TVars_Vartab tyinsts;
   965 
   966     fun subst' lev (t as Var (ixn, _)) = (case assoc (insts, ixn) of
   967           None => t
   968         | Some u => incr_boundvars lev u)
   969       | subst' lev (Const (s, T)) = Const (s, substT T)
   970       | subst' lev (Free (s, T)) = Free (s, substT T)
   971       | subst' lev (Abs (a, T, body)) = Abs (a, substT T, subst' (lev+1) body)
   972       | subst' lev (f $ t) = subst' lev f $ subst' lev t
   973       | subst' _ t = t;
   974 
   975     fun subst plev tlev (AbsP (a, t, body)) =
   976           AbsP (a, apsome (subst' tlev) t, subst (plev+1) tlev body)
   977       | subst plev tlev (Abst (a, T, body)) =
   978           Abst (a, apsome substT T, subst plev (tlev+1) body)
   979       | subst plev tlev (prf %% prf') = subst plev tlev prf %% subst plev tlev prf'
   980       | subst plev tlev (prf % t) = subst plev tlev prf % apsome (subst' tlev) t
   981       | subst plev tlev (prf as Hyp (Var (ixn, _))) = (case assoc (pinst, ixn) of
   982           None => prf
   983         | Some prf' => incr_pboundvars plev tlev prf')
   984       | subst _ _ (PThm (id, prf, prop, Ts)) =
   985           PThm (id, prf, prop, apsome (map substT) Ts)
   986       | subst _ _ (PAxm (id, prop, Ts)) =
   987           PAxm (id, prop, apsome (map substT) Ts)
   988       | subst _ _ t = t
   989   in subst 0 0 end;
   990 
   991 (*A fast unification filter: true unless the two terms cannot be unified. 
   992   Terms must be NORMAL.  Treats all Vars as distinct. *)
   993 fun could_unify prf1 prf2 =
   994   let
   995     fun matchrands (prf1 %% prf2) (prf1' %% prf2') =
   996           could_unify prf2 prf2' andalso matchrands prf1 prf1'
   997       | matchrands (prf % Some t) (prf' % Some t') =
   998           Term.could_unify (t, t') andalso matchrands prf prf'
   999       | matchrands (prf % _) (prf' % _) = matchrands prf prf'
  1000       | matchrands _ _ = true
  1001 
  1002     fun head_of (prf %% _) = head_of prf
  1003       | head_of (prf % _) = head_of prf
  1004       | head_of prf = prf
  1005 
  1006   in case (head_of prf1, head_of prf2) of
  1007         (_, Hyp (Var _)) => true
  1008       | (Hyp (Var _), _) => true
  1009       | (PThm ((a, _), _, propa, _), PThm ((b, _), _, propb, _)) =>
  1010           a = b andalso propa = propb andalso matchrands prf1 prf2
  1011       | (PAxm (a, _, _), PAxm (b, _, _)) => a = b andalso matchrands prf1 prf2
  1012       | (PBound i, PBound j) =>  i = j andalso matchrands prf1 prf2
  1013       | (AbsP _, _) =>  true   (*because of possible eta equality*)
  1014       | (Abst _, _) =>  true
  1015       | (_, AbsP _) =>  true
  1016       | (_, Abst _) =>  true
  1017       | _ => false
  1018   end;
  1019 
  1020 (**** rewriting on proof terms ****)
  1021 
  1022 val skel0 = PBound 0;
  1023 
  1024 fun rewrite_prf tymatch (rules, procs) prf =
  1025   let
  1026     fun rew _ (Abst (_, _, body) % Some t) = Some (prf_subst_bounds [t] body, skel0)
  1027       | rew _ (AbsP (_, _, body) %% prf) = Some (prf_subst_pbounds [prf] body, skel0)
  1028       | rew Ts prf = (case get_first (fn (_, r) => r Ts prf) procs of
  1029           Some prf' => Some (prf', skel0)
  1030         | None => get_first (fn (prf1, prf2) => Some (prf_subst
  1031             (match_proof Ts tymatch ([], (Vartab.empty, [])) (prf1, prf)) prf2, prf2)
  1032                handle PMatch => None) (filter (could_unify prf o fst) rules));
  1033 
  1034     fun rew0 Ts (prf as AbsP (_, _, prf' %% PBound 0)) =
  1035           if prf_loose_Pbvar1 prf' 0 then rew Ts prf
  1036           else
  1037             let val prf'' = incr_pboundvars (~1) 0 prf'
  1038             in Some (if_none (rew Ts prf'') (prf'', skel0)) end
  1039       | rew0 Ts (prf as Abst (_, _, prf' % Some (Bound 0))) =
  1040           if prf_loose_bvar1 prf' 0 then rew Ts prf
  1041           else
  1042             let val prf'' = incr_pboundvars 0 (~1) prf'
  1043             in Some (if_none (rew Ts prf'') (prf'', skel0)) end
  1044       | rew0 Ts prf = rew Ts prf;
  1045 
  1046     fun rew1 _ (Hyp (Var _)) _ = None
  1047       | rew1 Ts skel prf = (case rew2 Ts skel prf of
  1048           Some prf1 => (case rew0 Ts prf1 of
  1049               Some (prf2, skel') => Some (if_none (rew1 Ts skel' prf2) prf2)
  1050             | None => Some prf1)
  1051         | None => (case rew0 Ts prf of
  1052               Some (prf1, skel') => Some (if_none (rew1 Ts skel' prf1) prf1)
  1053             | None => None))
  1054 
  1055     and rew2 Ts skel (prf % Some t) = (case prf of
  1056             Abst (_, _, body) =>
  1057               let val prf' = prf_subst_bounds [t] body
  1058               in Some (if_none (rew2 Ts skel0 prf') prf') end
  1059           | _ => (case rew1 Ts (case skel of skel' % _ => skel' | _ => skel0) prf of
  1060               Some prf' => Some (prf' % Some t)
  1061             | None => None))
  1062       | rew2 Ts skel (prf % None) = apsome (fn prf' => prf' % None)
  1063           (rew1 Ts (case skel of skel' % _ => skel' | _ => skel0) prf)
  1064       | rew2 Ts skel (prf1 %% prf2) = (case prf1 of
  1065             AbsP (_, _, body) =>
  1066               let val prf' = prf_subst_pbounds [prf2] body
  1067               in Some (if_none (rew2 Ts skel0 prf') prf') end
  1068           | _ =>
  1069             let val (skel1, skel2) = (case skel of
  1070                 skel1 %% skel2 => (skel1, skel2)
  1071               | _ => (skel0, skel0))
  1072             in case rew1 Ts skel1 prf1 of
  1073                 Some prf1' => (case rew1 Ts skel2 prf2 of
  1074                     Some prf2' => Some (prf1' %% prf2')
  1075                   | None => Some (prf1' %% prf2))
  1076               | None => (case rew1 Ts skel2 prf2 of
  1077                     Some prf2' => Some (prf1 %% prf2')
  1078                   | None => None)
  1079             end)
  1080       | rew2 Ts skel (Abst (s, T, prf)) = (case rew1 (if_none T dummyT :: Ts)
  1081               (case skel of Abst (_, _, skel') => skel' | _ => skel0) prf of
  1082             Some prf' => Some (Abst (s, T, prf'))
  1083           | None => None)
  1084       | rew2 Ts skel (AbsP (s, t, prf)) = (case rew1 Ts
  1085               (case skel of AbsP (_, _, skel') => skel' | _ => skel0) prf of
  1086             Some prf' => Some (AbsP (s, t, prf'))
  1087           | None => None)
  1088       | rew2 _ _ _ = None
  1089 
  1090   in if_none (rew1 [] skel0 prf) prf end;
  1091 
  1092 fun rewrite_proof tsig = rewrite_prf (fn (tab, f) =>
  1093   Type.typ_match tsig (tab, f ()) handle Type.TYPE_MATCH => raise PMatch);
  1094 
  1095 fun rewrite_proof_notypes rews = rewrite_prf fst rews;
  1096 
  1097 (**** theory data ****)
  1098 
  1099 (* data kind 'Pure/proof' *)
  1100 
  1101 structure ProofArgs =
  1102 struct
  1103   val name = "Pure/proof";
  1104   type T = ((proof * proof) list *
  1105     (string * (typ list -> proof -> proof option)) list);
  1106 
  1107   val empty = ([], []);
  1108   val copy = I;
  1109   val prep_ext = I;
  1110   fun merge ((rules1, procs1), (rules2, procs2)) =
  1111     (merge_lists rules1 rules2, merge_alists procs1 procs2);
  1112   fun print _ _ = ();
  1113 end;
  1114 
  1115 structure ProofData = TheoryDataFun(ProofArgs);
  1116 
  1117 val init = ProofData.init;
  1118 
  1119 fun add_prf_rrules rs thy =
  1120   let val r = ProofData.get thy
  1121   in ProofData.put (rs @ fst r, snd r) thy end;
  1122 
  1123 fun add_prf_rprocs ps thy =
  1124   let val r = ProofData.get thy
  1125   in ProofData.put (fst r, ps @ snd r) thy end;
  1126 
  1127 fun thm_proof sign (name, tags) hyps prop prf =
  1128   let
  1129     val prop = Logic.list_implies (hyps, prop);
  1130     val nvs = needed_vars prop;
  1131     val args = map (fn (v as Var (ixn, _)) =>
  1132         if ixn mem nvs then Some v else None) (vars_of prop) @
  1133       map Some (sort (make_ord atless) (term_frees prop));
  1134     val opt_prf = if ! proofs = 2 then
  1135         #4 (shrink [] 0 (rewrite_prf fst (ProofData.get_sg sign)
  1136           (foldr (uncurry implies_intr_proof) (hyps, prf))))
  1137       else MinProof (mk_min_proof ([], prf));
  1138     val head = (case strip_combt (fst (strip_combP prf)) of
  1139         (PThm ((old_name, _), prf', prop', None), args') =>
  1140           if (old_name="" orelse old_name=name) andalso
  1141              prop = prop' andalso args = args' then
  1142             PThm ((name, tags), prf', prop, None)
  1143           else
  1144             PThm ((name, tags), opt_prf, prop, None)
  1145       | _ => PThm ((name, tags), opt_prf, prop, None))
  1146   in
  1147     proof_combP (proof_combt' (head, args), map Hyp hyps)
  1148   end;
  1149 
  1150 fun get_name_tags hyps prop prf =
  1151   let val prop = Logic.list_implies (hyps, prop) in
  1152     (case strip_combt (fst (strip_combP prf)) of
  1153       (PThm ((name, tags), _, prop', _), _) =>
  1154         if prop=prop' then (name, tags) else ("", [])
  1155     | (PAxm (name, prop', _), _) =>
  1156         if prop=prop' then (name, []) else ("", [])
  1157     | _ => ("", []))
  1158   end;
  1159 
  1160 end;
  1161 
  1162 structure BasicProofterm : BASIC_PROOFTERM = Proofterm;
  1163 open BasicProofterm;