src/Pure/proofterm.ML
author wenzelm
Fri Dec 14 11:52:54 2001 +0100 (2001-12-14)
changeset 12498 3b0091bf06e8
parent 12497 ec6ba9e6eef3
child 12868 cdf338ef5fad
permissions -rw-r--r--
changed Thm.varifyT';
     1 (*  Title:      Pure/proofterm.ML
     2     ID:         $Id$
     3     Author:     Stefan Berghofer, TU Muenchen
     4     License:    GPL (GNU GENERAL PUBLIC LICENSE)
     5 
     6 LF style proof terms.
     7 *)
     8 
     9 infix 8 % %% %>;
    10 
    11 signature BASIC_PROOFTERM =
    12 sig
    13   val proofs: int ref
    14 
    15   datatype proof =
    16      PBound of int
    17    | Abst of string * typ option * proof
    18    | AbsP of string * term option * proof
    19    | op % of proof * term option
    20    | op %% of proof * proof
    21    | Hyp of term
    22    | PThm of (string * (string * string list) list) * proof * term * typ list option
    23    | PAxm of string * term * typ list option
    24    | Oracle of string * term * typ list option
    25    | MinProof of proof list;
    26 
    27   val %> : proof * term -> proof
    28 end;
    29 
    30 signature PROOFTERM =
    31 sig
    32   include BASIC_PROOFTERM
    33 
    34   val infer_derivs : (proof -> proof -> proof) -> bool * proof -> bool * proof -> bool * proof
    35   val infer_derivs' : (proof -> proof) -> (bool * proof -> bool * proof)
    36 
    37   (** primitive operations **)
    38   val proof_combt : proof * term list -> proof
    39   val proof_combt' : proof * term option list -> proof
    40   val proof_combP : proof * proof list -> proof
    41   val strip_combt : proof -> proof * term option list
    42   val strip_combP : proof -> proof * proof list
    43   val strip_thm : proof -> proof
    44   val map_proof_terms : (term -> term) -> (typ -> typ) -> proof -> proof
    45   val fold_proof_terms : (term * 'a -> 'a) -> (typ * 'a -> 'a) -> 'a * proof -> 'a
    46   val add_prf_names : string list * proof -> string list
    47   val add_prf_tfree_names : string list * proof -> string list
    48   val add_prf_tvar_ixns : indexname list * proof -> indexname list
    49   val prf_abstract_over : term -> proof -> proof
    50   val prf_incr_bv : int -> int -> int -> int -> proof -> proof
    51   val incr_pboundvars : int -> int -> proof -> proof
    52   val prf_loose_bvar1 : proof -> int -> bool
    53   val prf_loose_Pbvar1 : proof -> int -> bool
    54   val prf_add_loose_bnos : int -> int -> proof ->
    55     int list * int list -> int list * int list
    56   val norm_proof : Envir.env -> proof -> proof
    57   val norm_proof' : Envir.env -> proof -> proof
    58   val prf_subst_bounds : term list -> proof -> proof
    59   val prf_subst_pbounds : proof list -> proof -> proof
    60   val freeze_thaw_prf : proof -> proof * (proof -> proof)
    61 
    62   val thms_of_proof : (term * proof) list Symtab.table -> proof ->
    63     (term * proof) list Symtab.table
    64   val axms_of_proof : proof Symtab.table -> proof -> proof Symtab.table
    65   val oracles_of_proof : proof list -> proof -> proof list
    66 
    67   (** proof terms for specific inference rules **)
    68   val implies_intr_proof : term -> proof -> proof
    69   val forall_intr_proof : term -> string -> proof -> proof
    70   val varify_proof : term -> string list -> proof -> proof
    71   val freezeT : term -> proof -> proof
    72   val rotate_proof : term list -> term -> int -> proof -> proof
    73   val permute_prems_prf : term list -> int -> int -> proof -> proof
    74   val instantiate : (indexname * typ) list -> (term * term) list -> proof -> proof
    75   val lift_proof : term -> int -> term -> proof -> proof
    76   val assumption_proof : term list -> term -> int -> proof -> proof
    77   val bicompose_proof : term list -> term list -> term list -> term option ->
    78     int -> proof -> proof -> proof
    79   val equality_axms : (string * term) list
    80   val reflexive_axm : proof
    81   val symmetric_axm : proof
    82   val transitive_axm : proof
    83   val equal_intr_axm : proof
    84   val equal_elim_axm : proof
    85   val abstract_rule_axm : proof
    86   val combination_axm : proof
    87   val reflexive : proof
    88   val symmetric : proof -> proof
    89   val transitive : term -> typ -> proof -> proof -> proof
    90   val abstract_rule : term -> string -> proof -> proof
    91   val combination : term -> term -> term -> term -> typ -> proof -> proof -> proof
    92   val equal_intr : term -> term -> proof -> proof -> proof
    93   val equal_elim : term -> term -> proof -> proof -> proof
    94   val axm_proof : string -> term -> proof
    95   val oracle_proof : string -> term -> proof
    96   val thm_proof : Sign.sg -> string * (string * string list) list ->
    97     term list -> term -> proof -> proof
    98   val get_name_tags : term -> proof -> string * (string * string list) list
    99 
   100   (** rewriting on proof terms **)
   101   val add_prf_rrules : (proof * proof) list -> theory -> theory
   102   val add_prf_rprocs : (string * (Term.typ list -> proof -> proof option)) list ->
   103     theory -> theory
   104   val rewrite_proof : Type.type_sig -> (proof * proof) list *
   105     (string * (typ list -> proof -> proof option)) list -> proof -> proof
   106   val rewrite_proof_notypes : (proof * proof) list *
   107     (string * (typ list -> proof -> proof option)) list -> proof -> proof
   108   val init : theory -> theory
   109   
   110 end
   111 
   112 structure Proofterm : PROOFTERM =
   113 struct
   114 
   115 open Envir;
   116 
   117 datatype proof =
   118    PBound of int
   119  | Abst of string * typ option * proof
   120  | AbsP of string * term option * proof
   121  | op % of proof * term option
   122  | op %% of proof * proof
   123  | Hyp of term
   124  | PThm of (string * (string * string list) list) * proof * term * typ list option
   125  | PAxm of string * term * typ list option
   126  | Oracle of string * term * typ list option
   127  | MinProof of proof list;
   128 
   129 fun oracles_of_proof prfs prf =
   130   let
   131     fun oras_of (tabs, Abst (_, _, prf)) = oras_of (tabs, prf)
   132       | oras_of (tabs, AbsP (_, _, prf)) = oras_of (tabs, prf)
   133       | oras_of (tabs, prf % _) = oras_of (tabs, prf)
   134       | oras_of (tabs, prf1 %% prf2) = oras_of (oras_of (tabs, prf1), prf2)
   135       | oras_of (tabs as (thms, oras), PThm ((name, _), prf, prop, _)) =
   136           (case Symtab.lookup (thms, name) of
   137              None => oras_of ((Symtab.update ((name, [prop]), thms), oras), prf)
   138            | Some ps => if prop mem ps then tabs else
   139                oras_of ((Symtab.update ((name, prop::ps), thms), oras), prf))
   140       | oras_of ((thms, oras), prf as Oracle _) = (thms, prf ins oras)
   141       | oras_of (tabs, MinProof prfs) = foldl oras_of (tabs, prfs)
   142       | oras_of (tabs, _) = tabs
   143   in
   144     snd (oras_of ((Symtab.empty, prfs), prf))
   145   end;
   146 
   147 fun thms_of_proof tab (Abst (_, _, prf)) = thms_of_proof tab prf
   148   | thms_of_proof tab (AbsP (_, _, prf)) = thms_of_proof tab prf
   149   | thms_of_proof tab (prf1 %% prf2) = thms_of_proof (thms_of_proof tab prf1) prf2
   150   | thms_of_proof tab (prf % _) = thms_of_proof tab prf
   151   | thms_of_proof tab (prf' as PThm ((s, _), prf, prop, _)) =
   152       (case Symtab.lookup (tab, s) of
   153          None => thms_of_proof (Symtab.update ((s, [(prop, prf')]), tab)) prf
   154        | Some ps => if exists (equal prop o fst) ps then tab else
   155            thms_of_proof (Symtab.update ((s, (prop, prf')::ps), tab)) prf)
   156   | thms_of_proof tab _ = tab;
   157 
   158 fun axms_of_proof tab (Abst (_, _, prf)) = axms_of_proof tab prf
   159   | axms_of_proof tab (AbsP (_, _, prf)) = axms_of_proof tab prf
   160   | axms_of_proof tab (prf1 %% prf2) = axms_of_proof (axms_of_proof tab prf1) prf2
   161   | axms_of_proof tab (prf % _) = axms_of_proof tab prf
   162   | axms_of_proof tab (prf as PAxm (s, _, _)) = Symtab.update ((s, prf), tab)
   163   | axms_of_proof tab _ = tab;
   164 
   165 (** collect all theorems, axioms and oracles **)
   166 
   167 fun mk_min_proof (prfs, Abst (_, _, prf)) = mk_min_proof (prfs, prf)
   168   | mk_min_proof (prfs, AbsP (_, _, prf)) = mk_min_proof (prfs, prf)
   169   | mk_min_proof (prfs, prf % _) = mk_min_proof (prfs, prf)
   170   | mk_min_proof (prfs, prf1 %% prf2) = mk_min_proof (mk_min_proof (prfs, prf1), prf2)
   171   | mk_min_proof (prfs, prf as PThm _) = prf ins prfs
   172   | mk_min_proof (prfs, prf as PAxm _) = prf ins prfs
   173   | mk_min_proof (prfs, prf as Oracle _) = prf ins prfs
   174   | mk_min_proof (prfs, MinProof prfs') = prfs union prfs'
   175   | mk_min_proof (prfs, _) = prfs;
   176 
   177 (** proof objects with different levels of detail **)
   178 
   179 val proofs = ref 2;
   180 
   181 fun err_illegal_level i =
   182   error ("Illegal level of detail for proof objects: " ^ string_of_int i);
   183 
   184 fun if_ora b = if b then oracles_of_proof else K;
   185 
   186 fun infer_derivs f (ora1, prf1) (ora2, prf2) =
   187   (ora1 orelse ora2, 
   188    case !proofs of
   189      2 => f prf1 prf2
   190    | 1 => MinProof (mk_min_proof (mk_min_proof ([], prf1), prf2))
   191    | 0 => MinProof (if_ora ora2 (if_ora ora1 [] prf1) prf2)
   192    | i => err_illegal_level i);
   193 
   194 fun infer_derivs' f (ora, prf) =
   195   (ora,
   196    case !proofs of
   197      2 => f prf
   198    | 1 => MinProof (mk_min_proof ([], prf))
   199    | 0 => MinProof (if_ora ora [] prf)
   200    | i => err_illegal_level i);
   201 
   202 fun (prf %> t) = prf % Some t;
   203 
   204 val proof_combt = foldl (op %>);
   205 val proof_combt' = foldl (op %);
   206 val proof_combP = foldl (op %%);
   207 
   208 fun strip_combt prf = 
   209     let fun stripc (prf % t, ts) = stripc (prf, t::ts)
   210           | stripc  x =  x 
   211     in  stripc (prf, [])  end;
   212 
   213 fun strip_combP prf = 
   214     let fun stripc (prf %% prf', prfs) = stripc (prf, prf'::prfs)
   215           | stripc  x =  x
   216     in  stripc (prf, [])  end;
   217 
   218 fun strip_thm prf = (case strip_combt (fst (strip_combP prf)) of
   219       (PThm (_, prf', _, _), _) => prf'
   220     | _ => prf);
   221 
   222 val mk_Abst = foldr (fn ((s, T:typ), prf) => Abst (s, None, prf));
   223 fun mk_AbsP (i, prf) = funpow i (fn prf => AbsP ("H", None, prf)) prf;
   224 
   225 fun apsome' f None = raise SAME
   226   | apsome' f (Some x) = Some (f x);
   227 
   228 fun same f x =
   229   let val x' = f x
   230   in if x = x' then raise SAME else x' end;
   231 
   232 fun map_proof_terms f g =
   233   let
   234     fun mapp (Abst (s, T, prf)) = (Abst (s, apsome' (same g) T, mapph prf)
   235           handle SAME => Abst (s, T, mapp prf))
   236       | mapp (AbsP (s, t, prf)) = (AbsP (s, apsome' (same f) t, mapph prf)
   237           handle SAME => AbsP (s, t, mapp prf))
   238       | mapp (prf % t) = (mapp prf % apsome f t
   239           handle SAME => prf % apsome' (same f) t)
   240       | mapp (prf1 %% prf2) = (mapp prf1 %% mapph prf2
   241           handle SAME => prf1 %% mapp prf2)
   242       | mapp (PThm (a, prf, prop, Some Ts)) =
   243           PThm (a, prf, prop, Some (same (map g) Ts))
   244       | mapp (PAxm (a, prop, Some Ts)) =
   245           PAxm (a, prop, Some (same (map g) Ts))
   246       | mapp _ = raise SAME
   247     and mapph prf = (mapp prf handle SAME => prf)
   248 
   249   in mapph end;
   250 
   251 fun fold_proof_terms f g (a, Abst (_, Some T, prf)) = fold_proof_terms f g (g (T, a), prf)
   252   | fold_proof_terms f g (a, Abst (_, None, prf)) = fold_proof_terms f g (a, prf)
   253   | fold_proof_terms f g (a, AbsP (_, Some t, prf)) = fold_proof_terms f g (f (t, a), prf)
   254   | fold_proof_terms f g (a, AbsP (_, None, prf)) = fold_proof_terms f g (a, prf)
   255   | fold_proof_terms f g (a, prf % Some t) = f (t, fold_proof_terms f g (a, prf))
   256   | fold_proof_terms f g (a, prf % None) = fold_proof_terms f g (a, prf)
   257   | fold_proof_terms f g (a, prf1 %% prf2) = fold_proof_terms f g
   258       (fold_proof_terms f g (a, prf1), prf2)
   259   | fold_proof_terms _ g (a, PThm (_, _, _, Some Ts)) = foldr g (Ts, a)
   260   | fold_proof_terms _ g (a, PAxm (_, prop, Some Ts)) = foldr g (Ts, a)
   261   | fold_proof_terms _ _ (a, _) = a;
   262 
   263 val add_prf_names = fold_proof_terms add_term_names ((uncurry K) o swap);
   264 val add_prf_tfree_names = fold_proof_terms add_term_tfree_names add_typ_tfree_names;
   265 val add_prf_tvar_ixns = fold_proof_terms add_term_tvar_ixns (add_typ_ixns o swap);
   266 
   267 
   268 (***** utilities *****)
   269 
   270 fun strip_abs (_::Ts) (Abs (_, _, t)) = strip_abs Ts t
   271   | strip_abs _ t = t;
   272 
   273 fun mk_abs Ts t = foldl (fn (t', T) => Abs ("", T, t')) (t, Ts);
   274 
   275 
   276 (*Abstraction of a proof term over its occurrences of v, 
   277     which must contain no loose bound variables.
   278   The resulting proof term is ready to become the body of an Abst.*)
   279 
   280 fun prf_abstract_over v =
   281   let
   282     fun abst' lev u = if v aconv u then Bound lev else
   283       (case u of
   284          Abs (a, T, t) => Abs (a, T, abst' (lev + 1) t)
   285        | f $ t => (abst' lev f $ absth' lev t handle SAME => f $ abst' lev t)
   286        | _ => raise SAME)
   287     and absth' lev t = (abst' lev t handle SAME => t);
   288 
   289     fun abst lev (AbsP (a, t, prf)) =
   290           (AbsP (a, apsome' (abst' lev) t, absth lev prf)
   291            handle SAME => AbsP (a, t, abst lev prf))
   292       | abst lev (Abst (a, T, prf)) = Abst (a, T, abst (lev + 1) prf)
   293       | abst lev (prf1 %% prf2) = (abst lev prf1 %% absth lev prf2
   294           handle SAME => prf1 %% abst lev prf2)
   295       | abst lev (prf % t) = (abst lev prf % apsome (absth' lev) t
   296           handle SAME => prf % apsome' (abst' lev) t)
   297       | abst _ _ = raise SAME
   298     and absth lev prf = (abst lev prf handle SAME => prf)
   299 
   300   in absth 0 end;
   301 
   302 
   303 (*increments a proof term's non-local bound variables
   304   required when moving a proof term within abstractions
   305      inc is  increment for bound variables
   306      lev is  level at which a bound variable is considered 'loose'*)
   307 
   308 fun incr_bv' inct tlev t = incr_bv (inct, tlev, t);
   309 
   310 fun prf_incr_bv' incP inct Plev tlev (PBound i) =
   311       if i >= Plev then PBound (i+incP) else raise SAME 
   312   | prf_incr_bv' incP inct Plev tlev (AbsP (a, t, body)) =
   313       (AbsP (a, apsome' (same (incr_bv' inct tlev)) t,
   314          prf_incr_bv incP inct (Plev+1) tlev body) handle SAME =>
   315            AbsP (a, t, prf_incr_bv' incP inct (Plev+1) tlev body))
   316   | prf_incr_bv' incP inct Plev tlev (Abst (a, T, body)) =
   317       Abst (a, T, prf_incr_bv' incP inct Plev (tlev+1) body)
   318   | prf_incr_bv' incP inct Plev tlev (prf %% prf') = 
   319       (prf_incr_bv' incP inct Plev tlev prf %% prf_incr_bv incP inct Plev tlev prf'
   320        handle SAME => prf %% prf_incr_bv' incP inct Plev tlev prf')
   321   | prf_incr_bv' incP inct Plev tlev (prf % t) = 
   322       (prf_incr_bv' incP inct Plev tlev prf % apsome (incr_bv' inct tlev) t
   323        handle SAME => prf % apsome' (same (incr_bv' inct tlev)) t)
   324   | prf_incr_bv' _ _ _ _ _ = raise SAME
   325 and prf_incr_bv incP inct Plev tlev prf =
   326       (prf_incr_bv' incP inct Plev tlev prf handle SAME => prf);
   327 
   328 fun incr_pboundvars  0 0 prf = prf
   329   | incr_pboundvars incP inct prf = prf_incr_bv incP inct 0 0 prf;
   330 
   331 
   332 fun prf_loose_bvar1 (prf1 %% prf2) k = prf_loose_bvar1 prf1 k orelse prf_loose_bvar1 prf2 k
   333   | prf_loose_bvar1 (prf % Some t) k = prf_loose_bvar1 prf k orelse loose_bvar1 (t, k)
   334   | prf_loose_bvar1 (_ % None) _ = true
   335   | prf_loose_bvar1 (AbsP (_, Some t, prf)) k = loose_bvar1 (t, k) orelse prf_loose_bvar1 prf k
   336   | prf_loose_bvar1 (AbsP (_, None, _)) k = true
   337   | prf_loose_bvar1 (Abst (_, _, prf)) k = prf_loose_bvar1 prf (k+1)
   338   | prf_loose_bvar1 _ _ = false;
   339 
   340 fun prf_loose_Pbvar1 (PBound i) k = i = k
   341   | prf_loose_Pbvar1 (prf1 %% prf2) k = prf_loose_Pbvar1 prf1 k orelse prf_loose_Pbvar1 prf2 k
   342   | prf_loose_Pbvar1 (prf % _) k = prf_loose_Pbvar1 prf k
   343   | prf_loose_Pbvar1 (AbsP (_, _, prf)) k = prf_loose_Pbvar1 prf (k+1)
   344   | prf_loose_Pbvar1 (Abst (_, _, prf)) k = prf_loose_Pbvar1 prf k
   345   | prf_loose_Pbvar1 _ _ = false;
   346 
   347 fun prf_add_loose_bnos plev tlev (PBound i) (is, js) =
   348       if i < plev then (is, js) else ((i-plev) ins is, js)
   349   | prf_add_loose_bnos plev tlev (prf1 %% prf2) p =
   350       prf_add_loose_bnos plev tlev prf2
   351         (prf_add_loose_bnos plev tlev prf1 p)
   352   | prf_add_loose_bnos plev tlev (prf % opt) (is, js) =
   353       prf_add_loose_bnos plev tlev prf (case opt of
   354           None => (is, ~1 ins js)
   355         | Some t => (is, add_loose_bnos (t, tlev, js)))
   356   | prf_add_loose_bnos plev tlev (AbsP (_, opt, prf)) (is, js) =
   357       prf_add_loose_bnos (plev+1) tlev prf (case opt of
   358           None => (is, ~1 ins js)
   359         | Some t => (is, add_loose_bnos (t, tlev, js)))
   360   | prf_add_loose_bnos plev tlev (Abst (_, _, prf)) p =
   361       prf_add_loose_bnos plev (tlev+1) prf p
   362   | prf_add_loose_bnos _ _ _ _ = ([], []);
   363 
   364 
   365 (**** substitutions ****)
   366 
   367 fun norm_proof env =
   368   let
   369     val envT = type_env env;
   370     fun norm (Abst (s, T, prf)) = (Abst (s, apsome' (norm_type_same envT) T, normh prf)
   371           handle SAME => Abst (s, T, norm prf))
   372       | norm (AbsP (s, t, prf)) = (AbsP (s, apsome' (norm_term_same env) t, normh prf)
   373           handle SAME => AbsP (s, t, norm prf))
   374       | norm (prf % t) = (norm prf % apsome (norm_term env) t
   375           handle SAME => prf % apsome' (norm_term_same env) t)
   376       | norm (prf1 %% prf2) = (norm prf1 %% normh prf2
   377           handle SAME => prf1 %% norm prf2)
   378       | norm (PThm (s, prf, t, Ts)) = PThm (s, prf, t, apsome' (norm_types_same envT) Ts)
   379       | norm (PAxm (s, prop, Ts)) = PAxm (s, prop, apsome' (norm_types_same envT) Ts)
   380       | norm _ = raise SAME
   381     and normh prf = (norm prf handle SAME => prf);
   382   in normh end;
   383 
   384 (***** Remove some types in proof term (to save space) *****)
   385 
   386 fun remove_types (Abs (s, _, t)) = Abs (s, dummyT, remove_types t)
   387   | remove_types (t $ u) = remove_types t $ remove_types u
   388   | remove_types (Const (s, _)) = Const (s, dummyT)
   389   | remove_types t = t;
   390 
   391 fun remove_types_env (Envir.Envir {iTs, asol, maxidx}) =
   392   Envir.Envir {iTs = iTs, asol = Vartab.map remove_types asol, maxidx = maxidx};
   393 
   394 fun norm_proof' env prf = norm_proof (remove_types_env env) prf;
   395 
   396 (**** substitution of bound variables ****)
   397 
   398 fun prf_subst_bounds args prf =
   399   let
   400     val n = length args;
   401     fun subst' lev (Bound i) =
   402          (if i<lev then raise SAME    (*var is locally bound*)
   403           else  incr_boundvars lev (List.nth (args, i-lev))
   404                   handle Subscript => Bound (i-n)  (*loose: change it*))
   405       | subst' lev (Abs (a, T, body)) = Abs (a, T,  subst' (lev+1) body)
   406       | subst' lev (f $ t) = (subst' lev f $ substh' lev t
   407           handle SAME => f $ subst' lev t)
   408       | subst' _ _ = raise SAME
   409     and substh' lev t = (subst' lev t handle SAME => t);
   410 
   411     fun subst lev (AbsP (a, t, body)) = (AbsP (a, apsome' (subst' lev) t, substh lev body)
   412           handle SAME => AbsP (a, t, subst lev body))
   413       | subst lev (Abst (a, T, body)) = Abst (a, T, subst (lev+1) body)
   414       | subst lev (prf %% prf') = (subst lev prf %% substh lev prf'
   415           handle SAME => prf %% subst lev prf')
   416       | subst lev (prf % t) = (subst lev prf % apsome (substh' lev) t
   417           handle SAME => prf % apsome' (subst' lev) t)
   418       | subst _ _ = raise SAME
   419     and substh lev prf = (subst lev prf handle SAME => prf)
   420   in case args of [] => prf | _ => substh 0 prf end;
   421 
   422 fun prf_subst_pbounds args prf =
   423   let
   424     val n = length args;
   425     fun subst (PBound i) Plev tlev =
   426  	 (if i < Plev then raise SAME    (*var is locally bound*)
   427           else incr_pboundvars Plev tlev (List.nth (args, i-Plev))
   428                  handle Subscript => PBound (i-n)  (*loose: change it*))
   429       | subst (AbsP (a, t, body)) Plev tlev = AbsP (a, t, subst body (Plev+1) tlev)
   430       | subst (Abst (a, T, body)) Plev tlev = Abst (a, T, subst body Plev (tlev+1))
   431       | subst (prf %% prf') Plev tlev = (subst prf Plev tlev %% substh prf' Plev tlev
   432           handle SAME => prf %% subst prf' Plev tlev)
   433       | subst (prf % t) Plev tlev = subst prf Plev tlev % t
   434       | subst  prf _ _ = raise SAME
   435     and substh prf Plev tlev = (subst prf Plev tlev handle SAME => prf)
   436   in case args of [] => prf | _ => substh prf 0 0 end;
   437 
   438 
   439 (**** Freezing and thawing of variables in proof terms ****)
   440 
   441 fun frzT names =
   442   map_type_tvar (fn (ixn, xs) => TFree (the (assoc (names, ixn)), xs));
   443 
   444 fun thawT names =
   445   map_type_tfree (fn (s, xs) => case assoc (names, s) of
   446       None => TFree (s, xs)
   447     | Some ixn => TVar (ixn, xs));
   448 
   449 fun freeze names names' (t $ u) =
   450       freeze names names' t $ freeze names names' u
   451   | freeze names names' (Abs (s, T, t)) =
   452       Abs (s, frzT names' T, freeze names names' t)
   453   | freeze names names' (Const (s, T)) = Const (s, frzT names' T)
   454   | freeze names names' (Free (s, T)) = Free (s, frzT names' T)
   455   | freeze names names' (Var (ixn, T)) =
   456       Free (the (assoc (names, ixn)), frzT names' T)
   457   | freeze names names' t = t;
   458 
   459 fun thaw names names' (t $ u) =
   460       thaw names names' t $ thaw names names' u
   461   | thaw names names' (Abs (s, T, t)) =
   462       Abs (s, thawT names' T, thaw names names' t)
   463   | thaw names names' (Const (s, T)) = Const (s, thawT names' T)
   464   | thaw names names' (Free (s, T)) = 
   465       let val T' = thawT names' T
   466       in case assoc (names, s) of
   467           None => Free (s, T')
   468         | Some ixn => Var (ixn, T')
   469       end
   470   | thaw names names' (Var (ixn, T)) = Var (ixn, thawT names' T)
   471   | thaw names names' t = t;
   472 
   473 fun freeze_thaw_prf prf =
   474   let
   475     val (fs, Tfs, vs, Tvs) = fold_proof_terms
   476       (fn (t, (fs, Tfs, vs, Tvs)) =>
   477          (add_term_frees (t, fs), add_term_tfree_names (t, Tfs),
   478           add_term_vars (t, vs), add_term_tvar_ixns (t, Tvs)))
   479       (fn (T, (fs, Tfs, vs, Tvs)) =>
   480          (fs, add_typ_tfree_names (T, Tfs),
   481           vs, add_typ_ixns (Tvs, T)))
   482             (([], [], [], []), prf);
   483     val fs' = map (fst o dest_Free) fs;
   484     val vs' = map (fst o dest_Var) vs;
   485     val names = vs' ~~ variantlist (map fst vs', fs');
   486     val names' = Tvs ~~ variantlist (map fst Tvs, Tfs);
   487     val rnames = map swap names;
   488     val rnames' = map swap names';
   489   in
   490     (map_proof_terms (freeze names names') (frzT names') prf,
   491      map_proof_terms (thaw rnames rnames') (thawT rnames'))
   492   end;
   493 
   494 
   495 (***** implication introduction *****)
   496 
   497 fun implies_intr_proof h prf =
   498   let
   499     fun abshyp i (Hyp t) = if h aconv t then PBound i else raise SAME
   500       | abshyp i (Abst (s, T, prf)) = Abst (s, T, abshyp i prf)
   501       | abshyp i (AbsP (s, t, prf)) = AbsP (s, t, abshyp (i+1) prf)
   502       | abshyp i (prf % t) = abshyp i prf % t
   503       | abshyp i (prf1 %% prf2) = (abshyp i prf1 %% abshyph i prf2
   504           handle SAME => prf1 %% abshyp i prf2)
   505       | abshyp _ _ = raise SAME
   506     and abshyph i prf = (abshyp i prf handle SAME => prf)
   507   in
   508     AbsP ("H", None (*h*), abshyph 0 prf)
   509   end;
   510 
   511 
   512 (***** forall introduction *****)
   513 
   514 fun forall_intr_proof x a prf = Abst (a, None, prf_abstract_over x prf);
   515 
   516 
   517 (***** varify *****)
   518 
   519 fun varify_proof t fixed prf =
   520   let
   521     val fs = add_term_tfree_names (t, []) \\ fixed;
   522     val ixns = add_term_tvar_ixns (t, []);
   523     val fmap = fs ~~ variantlist (fs, map #1 ixns)
   524     fun thaw (f as (a, S)) =
   525       (case assoc (fmap, a) of
   526         None => TFree f
   527       | Some b => TVar ((b, 0), S));
   528   in map_proof_terms (map_term_types (map_type_tfree thaw)) (map_type_tfree thaw) prf
   529   end;
   530 
   531 
   532 local
   533 
   534 fun new_name (ix, (pairs,used)) =
   535   let val v = variant used (string_of_indexname ix)
   536   in  ((ix, v) :: pairs, v :: used)  end;
   537 
   538 fun freeze_one alist (ix, sort) = (case assoc (alist, ix) of
   539     None => TVar (ix, sort)
   540   | Some name => TFree (name, sort));
   541 
   542 in
   543 
   544 fun freezeT t prf =
   545   let
   546     val used = it_term_types add_typ_tfree_names (t, [])
   547     and tvars = map #1 (it_term_types add_typ_tvars (t, []));
   548     val (alist, _) = foldr new_name (tvars, ([], used));
   549   in
   550     (case alist of
   551       [] => prf (*nothing to do!*)
   552     | _ =>
   553       let val frzT = map_type_tvar (freeze_one alist)
   554       in map_proof_terms (map_term_types frzT) frzT prf end)
   555   end;
   556 
   557 end;
   558 
   559 
   560 (***** rotate assumptions *****)
   561 
   562 fun rotate_proof Bs Bi m prf =
   563   let
   564     val params = Term.strip_all_vars Bi;
   565     val asms = Logic.strip_imp_prems (Term.strip_all_body Bi);
   566     val i = length asms;
   567     val j = length Bs;
   568   in
   569     mk_AbsP (j+1, proof_combP (prf, map PBound
   570       (j downto 1) @ [mk_Abst (params, mk_AbsP (i,
   571         proof_combP (proof_combt (PBound i, map Bound ((length params - 1) downto 0)),
   572           map PBound (((i-m-1) downto 0) @ ((i-1) downto (i-m))))))]))
   573   end;
   574 
   575 
   576 (***** permute premises *****)
   577 
   578 fun permute_prems_prf prems j k prf =
   579   let val n = length prems
   580   in mk_AbsP (n, proof_combP (prf,
   581     map PBound ((n-1 downto n-j) @ (k-1 downto 0) @ (n-j-1 downto k))))
   582   end;
   583 
   584 
   585 (***** instantiation *****)
   586 
   587 fun instantiate vTs tpairs =
   588   map_proof_terms (subst_atomic (map (apsnd remove_types) tpairs) o
   589     subst_TVars vTs) (typ_subst_TVars vTs);
   590 
   591 
   592 (***** lifting *****)
   593 
   594 fun lift_proof Bi inc prop prf =
   595   let
   596     val (_, lift_all) = Logic.lift_fns (Bi, inc);
   597 
   598     fun lift'' Us Ts t = strip_abs Ts (Logic.incr_indexes (Us, inc) (mk_abs Ts t));
   599 
   600     fun lift' Us Ts (Abst (s, T, prf)) =
   601           (Abst (s, apsome' (same (incr_tvar inc)) T, lifth' Us (dummyT::Ts) prf)
   602            handle SAME => Abst (s, T, lift' Us (dummyT::Ts) prf))
   603       | lift' Us Ts (AbsP (s, t, prf)) =
   604           (AbsP (s, apsome' (same (lift'' Us Ts)) t, lifth' Us Ts prf)
   605            handle SAME => AbsP (s, t, lift' Us Ts prf))
   606       | lift' Us Ts (prf % t) = (lift' Us Ts prf % apsome (lift'' Us Ts) t
   607           handle SAME => prf % apsome' (same (lift'' Us Ts)) t)
   608       | lift' Us Ts (prf1 %% prf2) = (lift' Us Ts prf1 %% lifth' Us Ts prf2
   609           handle SAME => prf1 %% lift' Us Ts prf2)
   610       | lift' _ _ (PThm (s, prf, prop, Ts)) =
   611           PThm (s, prf, prop, apsome' (same (map (incr_tvar inc))) Ts)
   612       | lift' _ _ (PAxm (s, prop, Ts)) =
   613           PAxm (s, prop, apsome' (same (map (incr_tvar inc))) Ts)
   614       | lift' _ _ _ = raise SAME
   615     and lifth' Us Ts prf = (lift' Us Ts prf handle SAME => prf);
   616 
   617     val ps = map lift_all (Logic.strip_imp_prems (snd (Logic.strip_flexpairs prop)));
   618     val k = length ps;
   619 
   620     fun mk_app (b, (i, j, prf)) = 
   621           if b then (i-1, j, prf %% PBound i) else (i, j-1, prf %> Bound j);
   622 
   623     fun lift Us bs i j (Const ("==>", _) $ A $ B) =
   624 	    AbsP ("H", None (*A*), lift Us (true::bs) (i+1) j B)
   625       | lift Us bs i j (Const ("all", _) $ Abs (a, T, t)) = 
   626 	    Abst (a, None (*T*), lift (T::Us) (false::bs) i (j+1) t)
   627       | lift Us bs i j _ = proof_combP (lifth' (rev Us) [] prf,
   628             map (fn k => (#3 (foldr mk_app (bs, (i-1, j-1, PBound k)))))
   629               (i + k - 1 downto i));
   630   in
   631     mk_AbsP (k, lift [] [] 0 0 Bi)
   632   end;
   633 
   634 
   635 (***** proof by assumption *****)
   636 
   637 fun mk_asm_prf (Const ("==>", _) $ A $ B) i = AbsP ("H", None (*A*), mk_asm_prf B (i+1))
   638   | mk_asm_prf (Const ("all", _) $ Abs (a, T, t)) i = Abst (a, None (*T*), mk_asm_prf t i)
   639   | mk_asm_prf _ i = PBound i;
   640 
   641 fun assumption_proof Bs Bi n prf =
   642   mk_AbsP (length Bs, proof_combP (prf,
   643     map PBound (length Bs - 1 downto 0) @ [mk_asm_prf Bi (~n)]));
   644 
   645 
   646 (***** Composition of object rule with proof state *****)
   647 
   648 fun flatten_params_proof i j n (Const ("==>", _) $ A $ B, k) =
   649       AbsP ("H", None (*A*), flatten_params_proof (i+1) j n (B, k))
   650   | flatten_params_proof i j n (Const ("all", _) $ Abs (a, T, t), k) =
   651       Abst (a, None (*T*), flatten_params_proof i (j+1) n (t, k))
   652   | flatten_params_proof i j n (_, k) = proof_combP (proof_combt (PBound (k+i),
   653       map Bound (j-1 downto 0)), map PBound (i-1 downto 0 \ i-n));
   654 
   655 fun bicompose_proof Bs oldAs newAs A n rprf sprf =
   656   let
   657     val la = length newAs;
   658     val lb = length Bs;
   659   in
   660     mk_AbsP (lb+la, proof_combP (sprf,
   661       map PBound (lb + la - 1 downto la)) %%
   662         proof_combP (rprf, (if n>0 then [mk_asm_prf (the A) (~n)] else []) @
   663           map (flatten_params_proof 0 0 n) (oldAs ~~ (la - 1 downto 0))))
   664   end;
   665 
   666 
   667 (***** axioms for equality *****)
   668 
   669 val aT = TFree ("'a", ["logic"]);
   670 val bT = TFree ("'b", ["logic"]);
   671 val x = Free ("x", aT);
   672 val y = Free ("y", aT);
   673 val z = Free ("z", aT);
   674 val A = Free ("A", propT);
   675 val B = Free ("B", propT);
   676 val f = Free ("f", aT --> bT);
   677 val g = Free ("g", aT --> bT);
   678 
   679 local open Logic in
   680 
   681 val equality_axms =
   682   [("reflexive", mk_equals (x, x)),
   683    ("symmetric", mk_implies (mk_equals (x, y), mk_equals (y, x))),
   684    ("transitive", list_implies ([mk_equals (x, y), mk_equals (y, z)], mk_equals (x, z))),
   685    ("equal_intr", list_implies ([mk_implies (A, B), mk_implies (B, A)], mk_equals (A, B))),
   686    ("equal_elim", list_implies ([mk_equals (A, B), A], B)),
   687    ("abstract_rule", Logic.mk_implies
   688       (all aT $ Abs ("x", aT, equals bT $ (f $ Bound 0) $ (g $ Bound 0)),
   689        equals (aT --> bT) $
   690          Abs ("x", aT, f $ Bound 0) $ Abs ("x", aT, g $ Bound 0))),
   691    ("combination", Logic.list_implies
   692       ([Logic.mk_equals (f, g), Logic.mk_equals (x, y)],
   693        Logic.mk_equals (f $ x, g $ y)))];
   694 
   695 val [reflexive_axm, symmetric_axm, transitive_axm, equal_intr_axm,
   696   equal_elim_axm, abstract_rule_axm, combination_axm] =
   697     map (fn (s, t) => PAxm ("ProtoPure." ^ s, varify t, None)) equality_axms;
   698 
   699 end;
   700 
   701 val reflexive = reflexive_axm % None;
   702 
   703 fun symmetric (prf as PAxm ("ProtoPure.reflexive", _, _) % _) = prf
   704   | symmetric prf = symmetric_axm % None % None %% prf;
   705 
   706 fun transitive _ _ (PAxm ("ProtoPure.reflexive", _, _) % _) prf2 = prf2
   707   | transitive _ _ prf1 (PAxm ("ProtoPure.reflexive", _, _) % _) = prf1
   708   | transitive u (Type ("prop", [])) prf1 prf2 =
   709       transitive_axm % None % Some (remove_types u) % None %% prf1 %% prf2
   710   | transitive u T prf1 prf2 =
   711       transitive_axm % None % None % None %% prf1 %% prf2;
   712 
   713 fun abstract_rule x a prf =
   714   abstract_rule_axm % None % None %% forall_intr_proof x a prf;
   715 
   716 fun check_comb (PAxm ("ProtoPure.combination", _, _) % f % g % _ % _ %% prf %% _) =
   717       is_some f orelse check_comb prf
   718   | check_comb (PAxm ("ProtoPure.transitive", _, _) % _ % _ % _ %% prf1 %% prf2) =
   719       check_comb prf1 andalso check_comb prf2
   720   | check_comb (PAxm ("ProtoPure.symmetric", _, _) % _ % _ %% prf) = check_comb prf
   721   | check_comb _ = false;
   722 
   723 fun combination f g t u (Type (_, [T, U])) prf1 prf2 =
   724   let
   725     val f = Envir.beta_norm f;
   726     val g = Envir.beta_norm g;
   727     val prf =  if check_comb prf1 then
   728         combination_axm % None % None
   729       else (case prf1 of
   730           PAxm ("ProtoPure.reflexive", _, _) % _ =>
   731             combination_axm %> remove_types f % None
   732         | _ => combination_axm %> remove_types f %> remove_types g)
   733   in
   734     (case T of
   735        Type ("fun", _) => prf %
   736          (case head_of f of
   737             Abs _ => Some (remove_types t)
   738           | Var _ => Some (remove_types t)
   739           | _ => None) %
   740          (case head_of g of
   741             Abs _ => Some (remove_types u)
   742           | Var _ => Some (remove_types u)
   743           | _ => None) %% prf1 %% prf2
   744      | _ => prf % None % None %% prf1 %% prf2)
   745   end;
   746 
   747 fun equal_intr A B prf1 prf2 =
   748   equal_intr_axm %> remove_types A %> remove_types B %% prf1 %% prf2;
   749 
   750 fun equal_elim A B prf1 prf2 =
   751   equal_elim_axm %> remove_types A %> remove_types B %% prf1 %% prf2;
   752 
   753 
   754 (***** axioms and theorems *****)
   755 
   756 fun vars_of t = rev (foldl_aterms
   757   (fn (vs, v as Var _) => v ins vs | (vs, _) => vs) ([], t));
   758 
   759 fun test_args _ [] = true
   760   | test_args is (Bound i :: ts) =
   761       not (i mem is) andalso test_args (i :: is) ts
   762   | test_args _ _ = false;
   763 
   764 fun is_fun (Type ("fun", _)) = true
   765   | is_fun (TVar _) = true
   766   | is_fun _ = false;
   767 
   768 fun add_funvars Ts (vs, t) =
   769   if is_fun (fastype_of1 (Ts, t)) then
   770     vs union mapfilter (fn Var (ixn, T) =>
   771       if is_fun T then Some ixn else None | _ => None) (vars_of t)
   772   else vs;
   773 
   774 fun add_npvars q p Ts (vs, Const ("==>", _) $ t $ u) =
   775       add_npvars q p Ts (add_npvars q (not p) Ts (vs, t), u)
   776   | add_npvars q p Ts (vs, Const ("all", Type (_, [Type (_, [T, _]), _])) $ t) =
   777       add_npvars q p Ts (vs, if p andalso q then betapply (t, Var (("",0), T)) else t)
   778   | add_npvars q p Ts (vs, Abs (_, T, t)) = add_npvars q p (T::Ts) (vs, t)
   779   | add_npvars _ _ Ts (vs, t) = add_npvars' Ts (vs, t)
   780 and add_npvars' Ts (vs, t) = (case strip_comb t of
   781     (Var (ixn, _), ts) => if test_args [] ts then vs
   782       else foldl (add_npvars' Ts) (overwrite (vs,
   783         (ixn, foldl (add_funvars Ts) (if_none (assoc (vs, ixn)) [], ts))), ts)
   784   | (Abs (_, T, u), ts) => foldl (add_npvars' (T::Ts)) (vs, u :: ts)
   785   | (_, ts) => foldl (add_npvars' Ts) (vs, ts));
   786 
   787 fun prop_vars (Const ("==>", _) $ P $ Q) = prop_vars P union prop_vars Q
   788   | prop_vars (Const ("all", _) $ Abs (_, _, t)) = prop_vars t
   789   | prop_vars t = (case strip_comb t of
   790       (Var (ixn, _), _) => [ixn] | _ => []);
   791 
   792 fun is_proj t =
   793   let
   794     fun is_p i t = (case strip_comb t of
   795         (Bound j, []) => false
   796       | (Bound j, ts) => j >= i orelse exists (is_p i) ts
   797       | (Abs (_, _, u), _) => is_p (i+1) u
   798       | (_, ts) => exists (is_p i) ts)
   799   in (case strip_abs_body t of
   800         Bound _ => true
   801       | t' => is_p 0 t')
   802   end;
   803 
   804 fun needed_vars prop = 
   805   foldl op union ([], map op ins (add_npvars true true [] ([], prop))) union
   806   prop_vars prop;
   807 
   808 fun gen_axm_proof c name prop =
   809   let
   810     val nvs = needed_vars prop;
   811     val args = map (fn (v as Var (ixn, _)) =>
   812         if ixn mem nvs then Some v else None) (vars_of prop) @
   813       map Some (sort (make_ord atless) (term_frees prop));
   814   in
   815     proof_combt' (c (name, prop, None), args)
   816   end;
   817 
   818 val axm_proof = gen_axm_proof PAxm;
   819 val oracle_proof = gen_axm_proof Oracle;
   820 
   821 fun shrink ls lev (prf as Abst (a, T, body)) =
   822       let val (b, is, ch, body') = shrink ls (lev+1) body
   823       in (b, is, ch, if ch then Abst (a, T, body') else prf) end
   824   | shrink ls lev (prf as AbsP (a, t, body)) =
   825       let val (b, is, ch, body') = shrink (lev::ls) lev body
   826       in (b orelse 0 mem is, mapfilter (fn 0 => None | i => Some (i-1)) is,
   827         ch, if ch then AbsP (a, t, body') else prf)
   828       end
   829   | shrink ls lev prf =
   830       let val (is, ch, _, prf') = shrink' ls lev [] [] prf
   831       in (false, is, ch, prf') end
   832 and shrink' ls lev ts prfs (prf as prf1 %% prf2) =
   833       let
   834         val p as (_, is', ch', prf') = shrink ls lev prf2;
   835         val (is, ch, ts', prf'') = shrink' ls lev ts (p::prfs) prf1
   836       in (is union is', ch orelse ch', ts',
   837           if ch orelse ch' then prf'' %% prf' else prf)
   838       end
   839   | shrink' ls lev ts prfs (prf as prf1 % t) =
   840       let val (is, ch, (ch', t')::ts', prf') = shrink' ls lev (t::ts) prfs prf1
   841       in (is, ch orelse ch', ts', if ch orelse ch' then prf' % t' else prf) end
   842   | shrink' ls lev ts prfs (prf as PBound i) =
   843       (if exists (fn Some (Bound j) => lev-j <= nth_elem (i, ls) | _ => true) ts
   844          orelse not (null (duplicates
   845            (foldl (fn (js, Some (Bound j)) => j :: js | (js, _) => js) ([], ts))))
   846          orelse exists #1 prfs then [i] else [], false, map (pair false) ts, prf)
   847   | shrink' ls lev ts prfs (prf as Hyp _) = ([], false, map (pair false) ts, prf)
   848   | shrink' ls lev ts prfs (prf as MinProof _) =
   849       ([], false, map (pair false) ts, prf)
   850   | shrink' ls lev ts prfs prf =
   851       let
   852         val prop = (case prf of PThm (_, _, prop, _) => prop | PAxm (_, prop, _) => prop
   853           | Oracle (_, prop, _) => prop | _ => error "shrink: proof not in normal form");
   854         val vs = vars_of prop;
   855         val ts' = take (length vs, ts)
   856         val ts'' = drop (length vs, ts)
   857         val insts = take (length ts', map (fst o dest_Var) vs) ~~ ts';
   858         val nvs = foldl (fn (ixns', (ixn, ixns)) =>
   859           ixn ins (case assoc (insts, ixn) of
   860               Some (Some t) => if is_proj t then ixns union ixns' else ixns'
   861             | _ => ixns union ixns'))
   862               (needed prop ts'' prfs, add_npvars false true [] ([], prop));
   863         val insts' = map
   864           (fn (ixn, x as Some _) => if ixn mem nvs then (false, x) else (true, None)
   865             | (_, x) => (false, x)) insts
   866       in ([], false, insts' @ map (pair false) ts'', prf) end
   867 and needed (Const ("==>", _) $ t $ u) ts ((b, _, _, _)::prfs) =
   868       (if b then map (fst o dest_Var) (vars_of t) else []) union needed u ts prfs
   869   | needed (Var (ixn, _)) (_::_) _ = [ixn]
   870   | needed _ _ _ = [];
   871 
   872 
   873 (**** Simple first order matching functions for terms and proofs ****)
   874 
   875 exception PMatch;
   876 
   877 (** see pattern.ML **)
   878 
   879 fun flt i = filter (fn n => n < i);
   880 
   881 fun fomatch Ts tymatch j =
   882   let
   883     fun mtch (instsp as (tyinsts, insts)) = fn
   884         (Var (ixn, T), t)  =>
   885           if j>0 andalso not (null (flt j (loose_bnos t)))
   886           then raise PMatch
   887           else (tymatch (tyinsts, fn () => (T, fastype_of1 (Ts, t))),
   888             (ixn, t) :: insts)
   889       | (Free (a, T), Free (b, U)) =>
   890 	  if a=b then (tymatch (tyinsts, K (T, U)), insts) else raise PMatch
   891       | (Const (a, T), Const (b, U))  =>
   892 	  if a=b then (tymatch (tyinsts, K (T, U)), insts) else raise PMatch
   893       | (f $ t, g $ u) => mtch (mtch instsp (f, g)) (t, u)
   894       | (Bound i, Bound j) => if i=j then instsp else raise PMatch
   895       | _ => raise PMatch
   896   in mtch end;
   897 
   898 fun match_proof Ts tymatch =
   899   let
   900     fun optmatch _ inst (None, _) = inst
   901       | optmatch _ _ (Some _, None) = raise PMatch
   902       | optmatch mtch inst (Some x, Some y) = mtch inst (x, y)
   903 
   904     fun matcht Ts j (pinst, tinst) (t, u) =
   905       (pinst, fomatch Ts tymatch j tinst (t, Envir.beta_norm u));
   906     fun matchT (pinst, (tyinsts, insts)) p =
   907       (pinst, (tymatch (tyinsts, K p), insts));
   908     fun matchTs inst (Ts, Us) = foldl (uncurry matchT) (inst, Ts ~~ Us);
   909 
   910     fun mtch Ts i j (pinst, tinst) (Hyp (Var (ixn, _)), prf) =
   911           if i = 0 andalso j = 0 then ((ixn, prf) :: pinst, tinst)
   912           else (case apfst (flt i) (apsnd (flt j)
   913                   (prf_add_loose_bnos 0 0 prf ([], []))) of
   914               ([], []) => ((ixn, incr_pboundvars (~i) (~j) prf) :: pinst, tinst)
   915             | ([], _) => if j = 0 then
   916                    ((ixn, incr_pboundvars (~i) (~j) prf) :: pinst, tinst)
   917                  else raise PMatch
   918             | _ => raise PMatch)
   919       | mtch Ts i j inst (prf1 % opt1, prf2 % opt2) =
   920           optmatch (matcht Ts j) (mtch Ts i j inst (prf1, prf2)) (opt1, opt2)
   921       | mtch Ts i j inst (prf1 %% prf2, prf1' %% prf2') =
   922           mtch Ts i j (mtch Ts i j inst (prf1, prf1')) (prf2, prf2')
   923       | mtch Ts i j inst (Abst (_, opT, prf1), Abst (_, opU, prf2)) =
   924           mtch (if_none opU dummyT :: Ts) i (j+1)
   925             (optmatch matchT inst (opT, opU)) (prf1, prf2)
   926       | mtch Ts i j inst (prf1, Abst (_, opU, prf2)) =
   927           mtch (if_none opU dummyT :: Ts) i (j+1) inst
   928             (incr_pboundvars 0 1 prf1 %> Bound 0, prf2)
   929       | mtch Ts i j inst (AbsP (_, opt, prf1), AbsP (_, opu, prf2)) =
   930           mtch Ts (i+1) j (optmatch (matcht Ts j) inst (opt, opu)) (prf1, prf2)
   931       | mtch Ts i j inst (prf1, AbsP (_, _, prf2)) =
   932           mtch Ts (i+1) j inst (incr_pboundvars 1 0 prf1 %% PBound 0, prf2)
   933       | mtch Ts i j inst (PThm ((name1, _), _, prop1, opTs),
   934             PThm ((name2, _), _, prop2, opUs)) =
   935           if name1=name2 andalso prop1=prop2 then
   936             optmatch matchTs inst (opTs, opUs)
   937           else raise PMatch
   938       | mtch Ts i j inst (PAxm (s1, _, opTs), PAxm (s2, _, opUs)) =
   939           if s1=s2 then optmatch matchTs inst (opTs, opUs)
   940           else raise PMatch
   941       | mtch _ _ _ inst (PBound i, PBound j) = if i = j then inst else raise PMatch
   942       | mtch _ _ _ _ _ = raise PMatch
   943   in mtch Ts 0 0 end;
   944 
   945 fun prf_subst (pinst, (tyinsts, insts)) =
   946   let
   947     val substT = typ_subst_TVars_Vartab tyinsts;
   948 
   949     fun subst' lev (t as Var (ixn, _)) = (case assoc (insts, ixn) of
   950           None => t
   951         | Some u => incr_boundvars lev u)
   952       | subst' lev (Const (s, T)) = Const (s, substT T)
   953       | subst' lev (Free (s, T)) = Free (s, substT T)
   954       | subst' lev (Abs (a, T, body)) = Abs (a, substT T, subst' (lev+1) body)
   955       | subst' lev (f $ t) = subst' lev f $ subst' lev t
   956       | subst' _ t = t;
   957 
   958     fun subst plev tlev (AbsP (a, t, body)) =
   959           AbsP (a, apsome (subst' tlev) t, subst (plev+1) tlev body)
   960       | subst plev tlev (Abst (a, T, body)) =
   961           Abst (a, apsome substT T, subst plev (tlev+1) body)
   962       | subst plev tlev (prf %% prf') = subst plev tlev prf %% subst plev tlev prf'
   963       | subst plev tlev (prf % t) = subst plev tlev prf % apsome (subst' tlev) t
   964       | subst plev tlev (prf as Hyp (Var (ixn, _))) = (case assoc (pinst, ixn) of
   965           None => prf
   966         | Some prf' => incr_pboundvars plev tlev prf')
   967       | subst _ _ (PThm (id, prf, prop, Ts)) =
   968           PThm (id, prf, prop, apsome (map substT) Ts)
   969       | subst _ _ (PAxm (id, prop, Ts)) =
   970           PAxm (id, prop, apsome (map substT) Ts)
   971       | subst _ _ t = t
   972   in subst 0 0 end;
   973 
   974 (**** rewriting on proof terms ****)
   975 
   976 fun rewrite_prf tymatch (rules, procs) prf =
   977   let
   978     fun rew _ (Abst (_, _, body) % Some t) = Some (prf_subst_bounds [t] body)
   979       | rew _ (AbsP (_, _, body) %% prf) = Some (prf_subst_pbounds [prf] body)
   980       | rew Ts prf = (case get_first (fn (_, r) => r Ts prf) procs of
   981           Some prf' => Some prf'
   982         | None => get_first (fn (prf1, prf2) => Some (prf_subst
   983             (match_proof Ts tymatch ([], (Vartab.empty, [])) (prf1, prf)) prf2)
   984                handle PMatch => None) rules);
   985 
   986     fun rew0 Ts (prf as AbsP (_, _, prf' %% PBound 0)) =
   987           if prf_loose_Pbvar1 prf' 0 then rew Ts prf
   988           else
   989             let val prf'' = incr_pboundvars (~1) 0 prf'
   990             in Some (if_none (rew Ts prf'') prf'') end
   991       | rew0 Ts (prf as Abst (_, _, prf' % Some (Bound 0))) =
   992           if prf_loose_bvar1 prf' 0 then rew Ts prf
   993           else
   994             let val prf'' = incr_pboundvars 0 (~1) prf'
   995             in Some (if_none (rew Ts prf'') prf'') end
   996       | rew0 Ts prf = rew Ts prf;
   997 
   998     fun rew1 Ts prf = (case rew2 Ts prf of
   999           Some prf1 => (case rew0 Ts prf1 of
  1000               Some prf2 => Some (if_none (rew1 Ts prf2) prf2)
  1001             | None => Some prf1)
  1002         | None => (case rew0 Ts prf of
  1003               Some prf1 => Some (if_none (rew1 Ts prf1) prf1)
  1004             | None => None))
  1005 
  1006     and rew2 Ts (prf % Some t) = (case prf of
  1007             Abst (_, _, body) =>
  1008               let val prf' = prf_subst_bounds [t] body
  1009               in Some (if_none (rew2 Ts prf') prf') end
  1010           | _ => (case rew1 Ts prf of
  1011               Some prf' => Some (prf' % Some t)
  1012             | None => None))
  1013       | rew2 Ts (prf % None) = apsome (fn prf' => prf' % None) (rew1 Ts prf)
  1014       | rew2 Ts (prf1 %% prf2) = (case prf1 of
  1015             AbsP (_, _, body) =>
  1016               let val prf' = prf_subst_pbounds [prf2] body
  1017               in Some (if_none (rew2 Ts prf') prf') end
  1018           | _ => (case rew1 Ts prf1 of
  1019               Some prf1' => (case rew1 Ts prf2 of
  1020                   Some prf2' => Some (prf1' %% prf2')
  1021                 | None => Some (prf1' %% prf2))
  1022             | None => (case rew1 Ts prf2 of
  1023                   Some prf2' => Some (prf1 %% prf2')
  1024                 | None => None)))
  1025       | rew2 Ts (Abst (s, T, prf)) = (case rew1 (if_none T dummyT :: Ts) prf of
  1026             Some prf' => Some (Abst (s, T, prf'))
  1027           | None => None)
  1028       | rew2 Ts (AbsP (s, t, prf)) = (case rew1 Ts prf of
  1029             Some prf' => Some (AbsP (s, t, prf'))
  1030           | None => None)
  1031       | rew2 _ _ = None
  1032 
  1033   in if_none (rew1 [] prf) prf end;
  1034 
  1035 fun rewrite_proof tsig = rewrite_prf (fn (tab, f) =>
  1036   Type.typ_match tsig (tab, f ()) handle Type.TYPE_MATCH => raise PMatch);
  1037 
  1038 fun rewrite_proof_notypes rews = rewrite_prf fst rews;
  1039 
  1040 (**** theory data ****)
  1041 
  1042 (* data kind 'Pure/proof' *)
  1043 
  1044 structure ProofArgs =
  1045 struct
  1046   val name = "Pure/proof";
  1047   type T = ((proof * proof) list *
  1048     (string * (typ list -> proof -> proof option)) list);
  1049 
  1050   val empty = ([], []);
  1051   val copy = I;
  1052   val prep_ext = I;
  1053   fun merge ((rules1, procs1), (rules2, procs2)) =
  1054     (merge_lists rules1 rules2, merge_alists procs1 procs2);
  1055   fun print _ _ = ();
  1056 end;
  1057 
  1058 structure ProofData = TheoryDataFun(ProofArgs);
  1059 
  1060 val init = ProofData.init;
  1061 
  1062 fun add_prf_rrules rs thy =
  1063   let val r = ProofData.get thy
  1064   in ProofData.put (rs @ fst r, snd r) thy end;
  1065 
  1066 fun add_prf_rprocs ps thy =
  1067   let val r = ProofData.get thy
  1068   in ProofData.put (fst r, ps @ snd r) thy end;
  1069 
  1070 fun thm_proof sign (name, tags) hyps prop prf =
  1071   let
  1072     val hyps' = gen_distinct op aconv hyps;
  1073     val prop = Logic.list_implies (hyps', prop);
  1074     val nvs = needed_vars prop;
  1075     val args = map (fn (v as Var (ixn, _)) =>
  1076         if ixn mem nvs then Some v else None) (vars_of prop) @
  1077       map Some (sort (make_ord atless) (term_frees prop));
  1078     val opt_prf = if ! proofs = 2 then
  1079         #4 (shrink [] 0 (rewrite_prf fst (ProofData.get_sg sign)
  1080           (foldr (uncurry implies_intr_proof) (hyps', prf))))
  1081       else MinProof (mk_min_proof ([], prf));
  1082     val head = (case strip_combt (fst (strip_combP prf)) of
  1083         (PThm ((old_name, _), prf', prop', None), args') =>
  1084           if (old_name="" orelse old_name=name) andalso
  1085              prop = prop' andalso args = args' then
  1086             PThm ((name, tags), prf', prop, None)
  1087           else
  1088             PThm ((name, tags), opt_prf, prop, None)
  1089       | _ => PThm ((name, tags), opt_prf, prop, None))
  1090   in
  1091     proof_combP (proof_combt' (head, args), map Hyp hyps')
  1092   end;
  1093 
  1094 fun get_name_tags prop prf = (case strip_combt (fst (strip_combP prf)) of
  1095       (PThm ((name, tags), _, prop', _), _) =>
  1096         if prop=prop' then (name, tags) else ("", [])
  1097     | (PAxm (name, prop', _), _) =>
  1098         if prop=prop' then (name, []) else ("", [])
  1099     | _ => ("", []));
  1100 
  1101 end;
  1102 
  1103 structure BasicProofterm : BASIC_PROOFTERM = Proofterm;
  1104 open BasicProofterm;