src/Pure/proofterm.ML
author wenzelm
Sat May 08 15:24:59 2010 +0200 (2010-05-08 ago)
changeset 36740 6248aa22c694
parent 36732 9c2ee10809b2
child 36741 d65ed9d7275e
permissions -rw-r--r--
back-patching of axclass proofs;
     1 (*  Title:      Pure/proofterm.ML
     2     Author:     Stefan Berghofer, TU Muenchen
     3 
     4 LF style proof terms.
     5 *)
     6 
     7 infix 8 % %% %>;
     8 
     9 signature BASIC_PROOFTERM =
    10 sig
    11   val proofs: int Unsynchronized.ref
    12 
    13   datatype proof =
    14      MinProof
    15    | PBound of int
    16    | Abst of string * typ option * proof
    17    | AbsP of string * term option * proof
    18    | op % of proof * term option
    19    | op %% of proof * proof
    20    | Hyp of term
    21    | PAxm of string * term * typ list option
    22    | OfClass of typ * class
    23    | Oracle of string * term * typ list option
    24    | Promise of serial * term * typ list
    25    | PThm of serial * ((string * term * typ list option) * proof_body future)
    26   and proof_body = PBody of
    27     {oracles: (string * term) OrdList.T,
    28      thms: (serial * (string * term * proof_body future)) OrdList.T,
    29      proof: proof}
    30 
    31   val %> : proof * term -> proof
    32 end;
    33 
    34 signature PROOFTERM =
    35 sig
    36   include BASIC_PROOFTERM
    37 
    38   type oracle = string * term
    39   type pthm = serial * (string * term * proof_body future)
    40   val proof_of: proof_body -> proof
    41   val join_proof: proof_body future -> proof
    42   val fold_proof_atoms: bool -> (proof -> 'a -> 'a) -> proof list -> 'a -> 'a
    43   val fold_body_thms: (string * term * proof_body -> 'a -> 'a) -> proof_body list -> 'a -> 'a
    44   val join_bodies: proof_body list -> unit
    45   val status_of: proof_body list -> {failed: bool, oracle: bool, unfinished: bool}
    46 
    47   val oracle_ord: oracle * oracle -> order
    48   val thm_ord: pthm * pthm -> order
    49   val merge_oracles: oracle OrdList.T -> oracle OrdList.T -> oracle OrdList.T
    50   val merge_thms: pthm OrdList.T -> pthm OrdList.T -> pthm OrdList.T
    51   val all_oracles_of: proof_body -> oracle OrdList.T
    52   val approximate_proof_body: proof -> proof_body
    53 
    54   (** primitive operations **)
    55   val proof_combt: proof * term list -> proof
    56   val proof_combt': proof * term option list -> proof
    57   val proof_combP: proof * proof list -> proof
    58   val strip_combt: proof -> proof * term option list
    59   val strip_combP: proof -> proof * proof list
    60   val strip_thm: proof_body -> proof_body
    61   val map_proof_terms_same: term Same.operation -> typ Same.operation -> proof Same.operation
    62   val map_proof_types_same: typ Same.operation -> proof Same.operation
    63   val map_proof_terms: (term -> term) -> (typ -> typ) -> proof -> proof
    64   val map_proof_types: (typ -> typ) -> proof -> proof
    65   val fold_proof_terms: (term -> 'a -> 'a) -> (typ -> 'a -> 'a) -> proof -> 'a -> 'a
    66   val maxidx_proof: proof -> int -> int
    67   val size_of_proof: proof -> int
    68   val change_type: typ list option -> proof -> proof
    69   val prf_abstract_over: term -> proof -> proof
    70   val prf_incr_bv: int -> int -> int -> int -> proof -> proof
    71   val incr_pboundvars: int -> int -> proof -> proof
    72   val prf_loose_bvar1: proof -> int -> bool
    73   val prf_loose_Pbvar1: proof -> int -> bool
    74   val prf_add_loose_bnos: int -> int -> proof -> int list * int list -> int list * int list
    75   val norm_proof: Envir.env -> proof -> proof
    76   val norm_proof': Envir.env -> proof -> proof
    77   val prf_subst_bounds: term list -> proof -> proof
    78   val prf_subst_pbounds: proof list -> proof -> proof
    79   val freeze_thaw_prf: proof -> proof * (proof -> proof)
    80 
    81   (** proof terms for specific inference rules **)
    82   val implies_intr_proof: term -> proof -> proof
    83   val forall_intr_proof: term -> string -> proof -> proof
    84   val varify_proof: term -> (string * sort) list -> proof -> proof
    85   val legacy_freezeT: term -> proof -> proof
    86   val rotate_proof: term list -> term -> int -> proof -> proof
    87   val permute_prems_prf: term list -> int -> int -> proof -> proof
    88   val generalize: string list * string list -> int -> proof -> proof
    89   val instantiate: ((indexname * sort) * typ) list * ((indexname * typ) * term) list
    90     -> proof -> proof
    91   val lift_proof: term -> int -> term -> proof -> proof
    92   val incr_indexes: int -> proof -> proof
    93   val assumption_proof: term list -> term -> int -> proof -> proof
    94   val bicompose_proof: bool -> term list -> term list -> term list -> term option ->
    95     int -> int -> proof -> proof -> proof
    96   val equality_axms: (string * term) list
    97   val reflexive_axm: proof
    98   val symmetric_axm: proof
    99   val transitive_axm: proof
   100   val equal_intr_axm: proof
   101   val equal_elim_axm: proof
   102   val abstract_rule_axm: proof
   103   val combination_axm: proof
   104   val reflexive: proof
   105   val symmetric: proof -> proof
   106   val transitive: term -> typ -> proof -> proof -> proof
   107   val abstract_rule: term -> string -> proof -> proof
   108   val combination: term -> term -> term -> term -> typ -> proof -> proof -> proof
   109   val equal_intr: term -> term -> proof -> proof -> proof
   110   val equal_elim: term -> term -> proof -> proof -> proof
   111   val strip_shyps_proof: Sorts.algebra -> (typ * sort) list -> (typ * sort) list ->
   112     sort list -> proof -> proof
   113   val classrel_proof: theory -> class * class -> proof
   114   val arity_proof: theory -> string * sort list * class -> proof
   115   val install_axclass_proofs:
   116    {classrel_proof: theory -> class * class -> proof,
   117     arity_proof: theory -> string * sort list * class -> proof} -> unit
   118   val axm_proof: string -> term -> proof
   119   val oracle_proof: string -> term -> oracle * proof
   120   val promise_proof: theory -> serial -> term -> proof
   121   val fulfill_norm_proof: theory -> (serial * proof_body) list -> proof_body -> proof_body
   122   val thm_proof: theory -> string -> term list -> term ->
   123     (serial * proof_body future) list -> proof_body -> pthm * proof
   124   val get_name: term list -> term -> proof -> string
   125 
   126   (** rewriting on proof terms **)
   127   val add_prf_rrule: proof * proof -> theory -> theory
   128   val add_prf_rproc: (typ list -> proof -> (proof * proof) option) -> theory -> theory
   129   val no_skel: proof
   130   val normal_skel: proof
   131   val rewrite_proof: theory -> (proof * proof) list *
   132     (typ list -> proof -> (proof * proof) option) list -> proof -> proof
   133   val rewrite_proof_notypes: (proof * proof) list *
   134     (typ list -> proof -> (proof * proof) option) list -> proof -> proof
   135   val rew_proof: theory -> proof -> proof
   136 end
   137 
   138 structure Proofterm : PROOFTERM =
   139 struct
   140 
   141 (***** datatype proof *****)
   142 
   143 datatype proof =
   144    MinProof
   145  | PBound of int
   146  | Abst of string * typ option * proof
   147  | AbsP of string * term option * proof
   148  | op % of proof * term option
   149  | op %% of proof * proof
   150  | Hyp of term
   151  | PAxm of string * term * typ list option
   152  | OfClass of typ * class
   153  | Oracle of string * term * typ list option
   154  | Promise of serial * term * typ list
   155  | PThm of serial * ((string * term * typ list option) * proof_body future)
   156 and proof_body = PBody of
   157   {oracles: (string * term) OrdList.T,
   158    thms: (serial * (string * term * proof_body future)) OrdList.T,
   159    proof: proof};
   160 
   161 type oracle = string * term;
   162 type pthm = serial * (string * term * proof_body future);
   163 
   164 fun proof_of (PBody {proof, ...}) = proof;
   165 val join_proof = Future.join #> proof_of;
   166 
   167 
   168 (***** proof atoms *****)
   169 
   170 fun fold_proof_atoms all f =
   171   let
   172     fun app (Abst (_, _, prf)) = app prf
   173       | app (AbsP (_, _, prf)) = app prf
   174       | app (prf % _) = app prf
   175       | app (prf1 %% prf2) = app prf1 #> app prf2
   176       | app (prf as PThm (i, (_, body))) = (fn (x, seen) =>
   177           if Inttab.defined seen i then (x, seen)
   178           else
   179             let val (x', seen') =
   180               (if all then app (join_proof body) else I) (x, Inttab.update (i, ()) seen)
   181             in (f prf x', seen') end)
   182       | app prf = (fn (x, seen) => (f prf x, seen));
   183   in fn prfs => fn x => #1 (fold app prfs (x, Inttab.empty)) end;
   184 
   185 fun fold_body_thms f =
   186   let
   187     fun app (PBody {thms, ...}) =
   188      (Future.join_results (map (#3 o #2) thms);
   189       thms |> fold (fn (i, (name, prop, body)) => fn (x, seen) =>
   190         if Inttab.defined seen i then (x, seen)
   191         else
   192           let
   193             val body' = Future.join body;
   194             val (x', seen') = app body' (x, Inttab.update (i, ()) seen);
   195           in (f (name, prop, body') x', seen') end));
   196   in fn bodies => fn x => #1 (fold app bodies (x, Inttab.empty)) end;
   197 
   198 fun join_bodies bodies = fold_body_thms (fn _ => fn () => ()) bodies ();
   199 
   200 fun status_of bodies =
   201   let
   202     fun status (PBody {oracles, thms, ...}) x =
   203       let
   204         val ((oracle, unfinished, failed), seen) =
   205           (thms, x) |-> fold (fn (i, (_, _, body)) => fn (st, seen) =>
   206             if Inttab.defined seen i then (st, seen)
   207             else
   208               let val seen' = Inttab.update (i, ()) seen in
   209                 (case Future.peek body of
   210                   SOME (Exn.Result body') => status body' (st, seen')
   211                 | SOME (Exn.Exn _) =>
   212                     let val (oracle, unfinished, _) = st
   213                     in ((oracle, unfinished, true), seen') end
   214                 | NONE =>
   215                     let val (oracle, _, failed) = st
   216                     in ((oracle, true, failed), seen') end)
   217               end);
   218       in ((oracle orelse not (null oracles), unfinished, failed), seen) end;
   219     val (oracle, unfinished, failed) =
   220       #1 (fold status bodies ((false, false, false), Inttab.empty));
   221   in {oracle = oracle, unfinished = unfinished, failed = failed} end;
   222 
   223 
   224 (* proof body *)
   225 
   226 val oracle_ord = prod_ord fast_string_ord Term_Ord.fast_term_ord;
   227 fun thm_ord ((i, _): pthm, (j, _)) = int_ord (j, i);
   228 
   229 val merge_oracles = OrdList.union oracle_ord;
   230 val merge_thms = OrdList.union thm_ord;
   231 
   232 val all_oracles_of =
   233   let
   234     fun collect (PBody {oracles, thms, ...}) =
   235      (Future.join_results (map (#3 o #2) thms);
   236       thms |> fold (fn (i, (_, _, body)) => fn (x, seen) =>
   237         if Inttab.defined seen i then (x, seen)
   238         else
   239           let
   240             val body' = Future.join body;
   241             val (x', seen') = collect body' (x, Inttab.update (i, ()) seen);
   242           in (merge_oracles oracles x', seen') end));
   243   in fn body => #1 (collect body ([], Inttab.empty)) end;
   244 
   245 fun approximate_proof_body prf =
   246   let
   247     val (oracles, thms) = fold_proof_atoms false
   248       (fn Oracle (s, prop, _) => apfst (cons (s, prop))
   249         | PThm (i, ((name, prop, _), body)) => apsnd (cons (i, (name, prop, body)))
   250         | _ => I) [prf] ([], []);
   251   in
   252     PBody
   253      {oracles = OrdList.make oracle_ord oracles,
   254       thms = OrdList.make thm_ord thms,
   255       proof = prf}
   256   end;
   257 
   258 
   259 (***** proof objects with different levels of detail *****)
   260 
   261 fun (prf %> t) = prf % SOME t;
   262 
   263 val proof_combt = Library.foldl (op %>);
   264 val proof_combt' = Library.foldl (op %);
   265 val proof_combP = Library.foldl (op %%);
   266 
   267 fun strip_combt prf =
   268     let fun stripc (prf % t, ts) = stripc (prf, t::ts)
   269           | stripc  x =  x
   270     in  stripc (prf, [])  end;
   271 
   272 fun strip_combP prf =
   273     let fun stripc (prf %% prf', prfs) = stripc (prf, prf'::prfs)
   274           | stripc  x =  x
   275     in  stripc (prf, [])  end;
   276 
   277 fun strip_thm (body as PBody {proof, ...}) =
   278   (case strip_combt (fst (strip_combP proof)) of
   279     (PThm (_, (_, body')), _) => Future.join body'
   280   | _ => body);
   281 
   282 val mk_Abst = fold_rev (fn (s, T:typ) => fn prf => Abst (s, NONE, prf));
   283 fun mk_AbsP (i, prf) = funpow i (fn prf => AbsP ("H", NONE, prf)) prf;
   284 
   285 fun map_proof_same term typ ofclass =
   286   let
   287     val typs = Same.map typ;
   288 
   289     fun proof (Abst (s, T, prf)) =
   290           (Abst (s, Same.map_option typ T, Same.commit proof prf)
   291             handle Same.SAME => Abst (s, T, proof prf))
   292       | proof (AbsP (s, t, prf)) =
   293           (AbsP (s, Same.map_option term t, Same.commit proof prf)
   294             handle Same.SAME => AbsP (s, t, proof prf))
   295       | proof (prf % t) =
   296           (proof prf % Same.commit (Same.map_option term) t
   297             handle Same.SAME => prf % Same.map_option term t)
   298       | proof (prf1 %% prf2) =
   299           (proof prf1 %% Same.commit proof prf2
   300             handle Same.SAME => prf1 %% proof prf2)
   301       | proof (PAxm (a, prop, SOME Ts)) = PAxm (a, prop, SOME (typs Ts))
   302       | proof (OfClass T_c) = ofclass T_c
   303       | proof (Oracle (a, prop, SOME Ts)) = Oracle (a, prop, SOME (typs Ts))
   304       | proof (Promise (i, prop, Ts)) = Promise (i, prop, typs Ts)
   305       | proof (PThm (i, ((a, prop, SOME Ts), body))) =
   306           PThm (i, ((a, prop, SOME (typs Ts)), body))
   307       | proof _ = raise Same.SAME;
   308   in proof end;
   309 
   310 fun map_proof_terms_same term typ = map_proof_same term typ (fn (T, c) => OfClass (typ T, c));
   311 fun map_proof_types_same typ = map_proof_terms_same (Term_Subst.map_types_same typ) typ;
   312 
   313 fun same eq f x =
   314   let val x' = f x
   315   in if eq (x, x') then raise Same.SAME else x' end;
   316 
   317 fun map_proof_terms f g = Same.commit (map_proof_terms_same (same (op =) f) (same (op =) g));
   318 fun map_proof_types f = Same.commit (map_proof_types_same (same (op =) f));
   319 
   320 fun fold_proof_terms f g (Abst (_, SOME T, prf)) = g T #> fold_proof_terms f g prf
   321   | fold_proof_terms f g (Abst (_, NONE, prf)) = fold_proof_terms f g prf
   322   | fold_proof_terms f g (AbsP (_, SOME t, prf)) = f t #> fold_proof_terms f g prf
   323   | fold_proof_terms f g (AbsP (_, NONE, prf)) = fold_proof_terms f g prf
   324   | fold_proof_terms f g (prf % SOME t) = fold_proof_terms f g prf #> f t
   325   | fold_proof_terms f g (prf % NONE) = fold_proof_terms f g prf
   326   | fold_proof_terms f g (prf1 %% prf2) =
   327       fold_proof_terms f g prf1 #> fold_proof_terms f g prf2
   328   | fold_proof_terms _ g (PAxm (_, _, SOME Ts)) = fold g Ts
   329   | fold_proof_terms _ g (OfClass (T, _)) = g T
   330   | fold_proof_terms _ g (Oracle (_, _, SOME Ts)) = fold g Ts
   331   | fold_proof_terms _ g (Promise (_, _, Ts)) = fold g Ts
   332   | fold_proof_terms _ g (PThm (_, ((_, _, SOME Ts), _))) = fold g Ts
   333   | fold_proof_terms _ _ _ = I;
   334 
   335 fun maxidx_proof prf = fold_proof_terms Term.maxidx_term Term.maxidx_typ prf;
   336 
   337 fun size_of_proof (Abst (_, _, prf)) = 1 + size_of_proof prf
   338   | size_of_proof (AbsP (_, t, prf)) = 1 + size_of_proof prf
   339   | size_of_proof (prf % _) = 1 + size_of_proof prf
   340   | size_of_proof (prf1 %% prf2) = size_of_proof prf1 + size_of_proof prf2
   341   | size_of_proof _ = 1;
   342 
   343 fun change_type opTs (PAxm (name, prop, _)) = PAxm (name, prop, opTs)
   344   | change_type (SOME [T]) (OfClass (_, c)) = OfClass (T, c)
   345   | change_type opTs (Oracle (name, prop, _)) = Oracle (name, prop, opTs)
   346   | change_type opTs (Promise _) = error "change_type: unexpected promise"
   347   | change_type opTs (PThm (i, ((name, prop, _), body))) =
   348       PThm (i, ((name, prop, opTs), body))
   349   | change_type _ prf = prf;
   350 
   351 
   352 (***** utilities *****)
   353 
   354 fun strip_abs (_::Ts) (Abs (_, _, t)) = strip_abs Ts t
   355   | strip_abs _ t = t;
   356 
   357 fun mk_abs Ts t = Library.foldl (fn (t', T) => Abs ("", T, t')) (t, Ts);
   358 
   359 
   360 (*Abstraction of a proof term over its occurrences of v,
   361     which must contain no loose bound variables.
   362   The resulting proof term is ready to become the body of an Abst.*)
   363 
   364 fun prf_abstract_over v =
   365   let
   366     fun abst' lev u = if v aconv u then Bound lev else
   367       (case u of
   368          Abs (a, T, t) => Abs (a, T, abst' (lev + 1) t)
   369        | f $ t => (abst' lev f $ absth' lev t handle Same.SAME => f $ abst' lev t)
   370        | _ => raise Same.SAME)
   371     and absth' lev t = (abst' lev t handle Same.SAME => t);
   372 
   373     fun abst lev (AbsP (a, t, prf)) =
   374           (AbsP (a, Same.map_option (abst' lev) t, absth lev prf)
   375            handle Same.SAME => AbsP (a, t, abst lev prf))
   376       | abst lev (Abst (a, T, prf)) = Abst (a, T, abst (lev + 1) prf)
   377       | abst lev (prf1 %% prf2) = (abst lev prf1 %% absth lev prf2
   378           handle Same.SAME => prf1 %% abst lev prf2)
   379       | abst lev (prf % t) = (abst lev prf % Option.map (absth' lev) t
   380           handle Same.SAME => prf % Same.map_option (abst' lev) t)
   381       | abst _ _ = raise Same.SAME
   382     and absth lev prf = (abst lev prf handle Same.SAME => prf);
   383 
   384   in absth 0 end;
   385 
   386 
   387 (*increments a proof term's non-local bound variables
   388   required when moving a proof term within abstractions
   389      inc is  increment for bound variables
   390      lev is  level at which a bound variable is considered 'loose'*)
   391 
   392 fun incr_bv' inct tlev t = incr_bv (inct, tlev, t);
   393 
   394 fun prf_incr_bv' incP inct Plev tlev (PBound i) =
   395       if i >= Plev then PBound (i+incP) else raise Same.SAME
   396   | prf_incr_bv' incP inct Plev tlev (AbsP (a, t, body)) =
   397       (AbsP (a, Same.map_option (same (op =) (incr_bv' inct tlev)) t,
   398          prf_incr_bv incP inct (Plev+1) tlev body) handle Same.SAME =>
   399            AbsP (a, t, prf_incr_bv' incP inct (Plev+1) tlev body))
   400   | prf_incr_bv' incP inct Plev tlev (Abst (a, T, body)) =
   401       Abst (a, T, prf_incr_bv' incP inct Plev (tlev+1) body)
   402   | prf_incr_bv' incP inct Plev tlev (prf %% prf') =
   403       (prf_incr_bv' incP inct Plev tlev prf %% prf_incr_bv incP inct Plev tlev prf'
   404        handle Same.SAME => prf %% prf_incr_bv' incP inct Plev tlev prf')
   405   | prf_incr_bv' incP inct Plev tlev (prf % t) =
   406       (prf_incr_bv' incP inct Plev tlev prf % Option.map (incr_bv' inct tlev) t
   407        handle Same.SAME => prf % Same.map_option (same (op =) (incr_bv' inct tlev)) t)
   408   | prf_incr_bv' _ _ _ _ _ = raise Same.SAME
   409 and prf_incr_bv incP inct Plev tlev prf =
   410       (prf_incr_bv' incP inct Plev tlev prf handle Same.SAME => prf);
   411 
   412 fun incr_pboundvars  0 0 prf = prf
   413   | incr_pboundvars incP inct prf = prf_incr_bv incP inct 0 0 prf;
   414 
   415 
   416 fun prf_loose_bvar1 (prf1 %% prf2) k = prf_loose_bvar1 prf1 k orelse prf_loose_bvar1 prf2 k
   417   | prf_loose_bvar1 (prf % SOME t) k = prf_loose_bvar1 prf k orelse loose_bvar1 (t, k)
   418   | prf_loose_bvar1 (_ % NONE) _ = true
   419   | prf_loose_bvar1 (AbsP (_, SOME t, prf)) k = loose_bvar1 (t, k) orelse prf_loose_bvar1 prf k
   420   | prf_loose_bvar1 (AbsP (_, NONE, _)) k = true
   421   | prf_loose_bvar1 (Abst (_, _, prf)) k = prf_loose_bvar1 prf (k+1)
   422   | prf_loose_bvar1 _ _ = false;
   423 
   424 fun prf_loose_Pbvar1 (PBound i) k = i = k
   425   | prf_loose_Pbvar1 (prf1 %% prf2) k = prf_loose_Pbvar1 prf1 k orelse prf_loose_Pbvar1 prf2 k
   426   | prf_loose_Pbvar1 (prf % _) k = prf_loose_Pbvar1 prf k
   427   | prf_loose_Pbvar1 (AbsP (_, _, prf)) k = prf_loose_Pbvar1 prf (k+1)
   428   | prf_loose_Pbvar1 (Abst (_, _, prf)) k = prf_loose_Pbvar1 prf k
   429   | prf_loose_Pbvar1 _ _ = false;
   430 
   431 fun prf_add_loose_bnos plev tlev (PBound i) (is, js) =
   432       if i < plev then (is, js) else (insert (op =) (i-plev) is, js)
   433   | prf_add_loose_bnos plev tlev (prf1 %% prf2) p =
   434       prf_add_loose_bnos plev tlev prf2
   435         (prf_add_loose_bnos plev tlev prf1 p)
   436   | prf_add_loose_bnos plev tlev (prf % opt) (is, js) =
   437       prf_add_loose_bnos plev tlev prf (case opt of
   438           NONE => (is, insert (op =) ~1 js)
   439         | SOME t => (is, add_loose_bnos (t, tlev, js)))
   440   | prf_add_loose_bnos plev tlev (AbsP (_, opt, prf)) (is, js) =
   441       prf_add_loose_bnos (plev+1) tlev prf (case opt of
   442           NONE => (is, insert (op =) ~1 js)
   443         | SOME t => (is, add_loose_bnos (t, tlev, js)))
   444   | prf_add_loose_bnos plev tlev (Abst (_, _, prf)) p =
   445       prf_add_loose_bnos plev (tlev+1) prf p
   446   | prf_add_loose_bnos _ _ _ _ = ([], []);
   447 
   448 
   449 (**** substitutions ****)
   450 
   451 fun del_conflicting_tvars envT T = Term_Subst.instantiateT
   452   (map_filter (fn ixnS as (_, S) =>
   453      (Type.lookup envT ixnS; NONE) handle TYPE _ =>
   454         SOME (ixnS, TFree ("'dummy", S))) (OldTerm.typ_tvars T)) T;
   455 
   456 fun del_conflicting_vars env t = Term_Subst.instantiate
   457   (map_filter (fn ixnS as (_, S) =>
   458      (Type.lookup (Envir.type_env env) ixnS; NONE) handle TYPE _ =>
   459         SOME (ixnS, TFree ("'dummy", S))) (OldTerm.term_tvars t),
   460    map_filter (fn Var (ixnT as (_, T)) =>
   461      (Envir.lookup (env, ixnT); NONE) handle TYPE _ =>
   462         SOME (ixnT, Free ("dummy", T))) (OldTerm.term_vars t)) t;
   463 
   464 fun norm_proof env =
   465   let
   466     val envT = Envir.type_env env;
   467     fun msg s = warning ("type conflict in norm_proof:\n" ^ s);
   468     fun htype f t = f env t handle TYPE (s, _, _) =>
   469       (msg s; f env (del_conflicting_vars env t));
   470     fun htypeT f T = f envT T handle TYPE (s, _, _) =>
   471       (msg s; f envT (del_conflicting_tvars envT T));
   472     fun htypeTs f Ts = f envT Ts handle TYPE (s, _, _) =>
   473       (msg s; f envT (map (del_conflicting_tvars envT) Ts));
   474 
   475     fun norm (Abst (s, T, prf)) =
   476           (Abst (s, Same.map_option (htypeT Envir.norm_type_same) T, Same.commit norm prf)
   477             handle Same.SAME => Abst (s, T, norm prf))
   478       | norm (AbsP (s, t, prf)) =
   479           (AbsP (s, Same.map_option (htype Envir.norm_term_same) t, Same.commit norm prf)
   480             handle Same.SAME => AbsP (s, t, norm prf))
   481       | norm (prf % t) =
   482           (norm prf % Option.map (htype Envir.norm_term) t
   483             handle Same.SAME => prf % Same.map_option (htype Envir.norm_term_same) t)
   484       | norm (prf1 %% prf2) =
   485           (norm prf1 %% Same.commit norm prf2
   486             handle Same.SAME => prf1 %% norm prf2)
   487       | norm (PAxm (s, prop, Ts)) =
   488           PAxm (s, prop, Same.map_option (htypeTs Envir.norm_types_same) Ts)
   489       | norm (OfClass (T, c)) =
   490           OfClass (htypeT Envir.norm_type_same T, c)
   491       | norm (Oracle (s, prop, Ts)) =
   492           Oracle (s, prop, Same.map_option (htypeTs Envir.norm_types_same) Ts)
   493       | norm (Promise (i, prop, Ts)) =
   494           Promise (i, prop, htypeTs Envir.norm_types_same Ts)
   495       | norm (PThm (i, ((s, t, Ts), body))) =
   496           PThm (i, ((s, t, Same.map_option (htypeTs Envir.norm_types_same) Ts), body))
   497       | norm _ = raise Same.SAME;
   498   in Same.commit norm end;
   499 
   500 
   501 (***** Remove some types in proof term (to save space) *****)
   502 
   503 fun remove_types (Abs (s, _, t)) = Abs (s, dummyT, remove_types t)
   504   | remove_types (t $ u) = remove_types t $ remove_types u
   505   | remove_types (Const (s, _)) = Const (s, dummyT)
   506   | remove_types t = t;
   507 
   508 fun remove_types_env (Envir.Envir {maxidx, tenv, tyenv}) =
   509   Envir.Envir {maxidx = maxidx, tenv = Vartab.map (apsnd remove_types) tenv, tyenv = tyenv};
   510 
   511 fun norm_proof' env prf = norm_proof (remove_types_env env) prf;
   512 
   513 
   514 (**** substitution of bound variables ****)
   515 
   516 fun prf_subst_bounds args prf =
   517   let
   518     val n = length args;
   519     fun subst' lev (Bound i) =
   520          (if i<lev then raise Same.SAME    (*var is locally bound*)
   521           else  incr_boundvars lev (nth args (i-lev))
   522                   handle Subscript => Bound (i-n))  (*loose: change it*)
   523       | subst' lev (Abs (a, T, body)) = Abs (a, T,  subst' (lev+1) body)
   524       | subst' lev (f $ t) = (subst' lev f $ substh' lev t
   525           handle Same.SAME => f $ subst' lev t)
   526       | subst' _ _ = raise Same.SAME
   527     and substh' lev t = (subst' lev t handle Same.SAME => t);
   528 
   529     fun subst lev (AbsP (a, t, body)) =
   530         (AbsP (a, Same.map_option (subst' lev) t, substh lev body)
   531           handle Same.SAME => AbsP (a, t, subst lev body))
   532       | subst lev (Abst (a, T, body)) = Abst (a, T, subst (lev+1) body)
   533       | subst lev (prf %% prf') = (subst lev prf %% substh lev prf'
   534           handle Same.SAME => prf %% subst lev prf')
   535       | subst lev (prf % t) = (subst lev prf % Option.map (substh' lev) t
   536           handle Same.SAME => prf % Same.map_option (subst' lev) t)
   537       | subst _ _ = raise Same.SAME
   538     and substh lev prf = (subst lev prf handle Same.SAME => prf);
   539   in case args of [] => prf | _ => substh 0 prf end;
   540 
   541 fun prf_subst_pbounds args prf =
   542   let
   543     val n = length args;
   544     fun subst (PBound i) Plev tlev =
   545          (if i < Plev then raise Same.SAME    (*var is locally bound*)
   546           else incr_pboundvars Plev tlev (nth args (i-Plev))
   547                  handle Subscript => PBound (i-n)  (*loose: change it*))
   548       | subst (AbsP (a, t, body)) Plev tlev = AbsP (a, t, subst body (Plev+1) tlev)
   549       | subst (Abst (a, T, body)) Plev tlev = Abst (a, T, subst body Plev (tlev+1))
   550       | subst (prf %% prf') Plev tlev = (subst prf Plev tlev %% substh prf' Plev tlev
   551           handle Same.SAME => prf %% subst prf' Plev tlev)
   552       | subst (prf % t) Plev tlev = subst prf Plev tlev % t
   553       | subst  prf _ _ = raise Same.SAME
   554     and substh prf Plev tlev = (subst prf Plev tlev handle Same.SAME => prf)
   555   in case args of [] => prf | _ => substh prf 0 0 end;
   556 
   557 
   558 (**** Freezing and thawing of variables in proof terms ****)
   559 
   560 fun frzT names =
   561   map_type_tvar (fn (ixn, xs) => TFree ((the o AList.lookup (op =) names) ixn, xs));
   562 
   563 fun thawT names =
   564   map_type_tfree (fn (s, xs) => case AList.lookup (op =) names s of
   565       NONE => TFree (s, xs)
   566     | SOME ixn => TVar (ixn, xs));
   567 
   568 fun freeze names names' (t $ u) =
   569       freeze names names' t $ freeze names names' u
   570   | freeze names names' (Abs (s, T, t)) =
   571       Abs (s, frzT names' T, freeze names names' t)
   572   | freeze names names' (Const (s, T)) = Const (s, frzT names' T)
   573   | freeze names names' (Free (s, T)) = Free (s, frzT names' T)
   574   | freeze names names' (Var (ixn, T)) =
   575       Free ((the o AList.lookup (op =) names) ixn, frzT names' T)
   576   | freeze names names' t = t;
   577 
   578 fun thaw names names' (t $ u) =
   579       thaw names names' t $ thaw names names' u
   580   | thaw names names' (Abs (s, T, t)) =
   581       Abs (s, thawT names' T, thaw names names' t)
   582   | thaw names names' (Const (s, T)) = Const (s, thawT names' T)
   583   | thaw names names' (Free (s, T)) =
   584       let val T' = thawT names' T
   585       in case AList.lookup (op =) names s of
   586           NONE => Free (s, T')
   587         | SOME ixn => Var (ixn, T')
   588       end
   589   | thaw names names' (Var (ixn, T)) = Var (ixn, thawT names' T)
   590   | thaw names names' t = t;
   591 
   592 fun freeze_thaw_prf prf =
   593   let
   594     val (fs, Tfs, vs, Tvs) = fold_proof_terms
   595       (fn t => fn (fs, Tfs, vs, Tvs) =>
   596          (Term.add_free_names t fs, Term.add_tfree_names t Tfs,
   597           Term.add_var_names t vs, Term.add_tvar_names t Tvs))
   598       (fn T => fn (fs, Tfs, vs, Tvs) =>
   599          (fs, Term.add_tfree_namesT T Tfs,
   600           vs, Term.add_tvar_namesT T Tvs))
   601       prf ([], [], [], []);
   602     val names = vs ~~ Name.variant_list fs (map fst vs);
   603     val names' = Tvs ~~ Name.variant_list Tfs (map fst Tvs);
   604     val rnames = map swap names;
   605     val rnames' = map swap names';
   606   in
   607     (map_proof_terms (freeze names names') (frzT names') prf,
   608      map_proof_terms (thaw rnames rnames') (thawT rnames'))
   609   end;
   610 
   611 
   612 (***** implication introduction *****)
   613 
   614 fun implies_intr_proof h prf =
   615   let
   616     fun abshyp i (Hyp t) = if h aconv t then PBound i else raise Same.SAME
   617       | abshyp i (Abst (s, T, prf)) = Abst (s, T, abshyp i prf)
   618       | abshyp i (AbsP (s, t, prf)) = AbsP (s, t, abshyp (i + 1) prf)
   619       | abshyp i (prf % t) = abshyp i prf % t
   620       | abshyp i (prf1 %% prf2) =
   621           (abshyp i prf1 %% abshyph i prf2
   622             handle Same.SAME => prf1 %% abshyp i prf2)
   623       | abshyp _ _ = raise Same.SAME
   624     and abshyph i prf = (abshyp i prf handle Same.SAME => prf);
   625   in
   626     AbsP ("H", NONE (*h*), abshyph 0 prf)
   627   end;
   628 
   629 
   630 (***** forall introduction *****)
   631 
   632 fun forall_intr_proof x a prf = Abst (a, NONE, prf_abstract_over x prf);
   633 
   634 
   635 (***** varify *****)
   636 
   637 fun varify_proof t fixed prf =
   638   let
   639     val fs = Term.fold_types (Term.fold_atyps
   640       (fn TFree v => if member (op =) fixed v then I else insert (op =) v | _ => I)) t [];
   641     val used = Name.context
   642       |> fold_types (fold_atyps (fn TVar ((a, _), _) => Name.declare a | _ => I)) t;
   643     val fmap = fs ~~ #1 (Name.variants (map fst fs) used);
   644     fun thaw (f as (a, S)) =
   645       (case AList.lookup (op =) fmap f of
   646         NONE => TFree f
   647       | SOME b => TVar ((b, 0), S));
   648   in map_proof_terms (map_types (map_type_tfree thaw)) (map_type_tfree thaw) prf end;
   649 
   650 
   651 local
   652 
   653 fun new_name (ix, (pairs,used)) =
   654   let val v = Name.variant used (string_of_indexname ix)
   655   in  ((ix, v) :: pairs, v :: used)  end;
   656 
   657 fun freeze_one alist (ix, sort) = (case AList.lookup (op =) alist ix of
   658     NONE => TVar (ix, sort)
   659   | SOME name => TFree (name, sort));
   660 
   661 in
   662 
   663 fun legacy_freezeT t prf =
   664   let
   665     val used = OldTerm.it_term_types OldTerm.add_typ_tfree_names (t, [])
   666     and tvars = map #1 (OldTerm.it_term_types OldTerm.add_typ_tvars (t, []));
   667     val (alist, _) = List.foldr new_name ([], used) tvars;
   668   in
   669     (case alist of
   670       [] => prf (*nothing to do!*)
   671     | _ =>
   672       let val frzT = map_type_tvar (freeze_one alist)
   673       in map_proof_terms (map_types frzT) frzT prf end)
   674   end;
   675 
   676 end;
   677 
   678 
   679 (***** rotate assumptions *****)
   680 
   681 fun rotate_proof Bs Bi m prf =
   682   let
   683     val params = Term.strip_all_vars Bi;
   684     val asms = Logic.strip_imp_prems (Term.strip_all_body Bi);
   685     val i = length asms;
   686     val j = length Bs;
   687   in
   688     mk_AbsP (j+1, proof_combP (prf, map PBound
   689       (j downto 1) @ [mk_Abst params (mk_AbsP (i,
   690         proof_combP (proof_combt (PBound i, map Bound ((length params - 1) downto 0)),
   691           map PBound (((i-m-1) downto 0) @ ((i-1) downto (i-m))))))]))
   692   end;
   693 
   694 
   695 (***** permute premises *****)
   696 
   697 fun permute_prems_prf prems j k prf =
   698   let val n = length prems
   699   in mk_AbsP (n, proof_combP (prf,
   700     map PBound ((n-1 downto n-j) @ (k-1 downto 0) @ (n-j-1 downto k))))
   701   end;
   702 
   703 
   704 (***** generalization *****)
   705 
   706 fun generalize (tfrees, frees) idx =
   707   Same.commit (map_proof_terms_same
   708     (Term_Subst.generalize_same (tfrees, frees) idx)
   709     (Term_Subst.generalizeT_same tfrees idx));
   710 
   711 
   712 (***** instantiation *****)
   713 
   714 fun instantiate (instT, inst) =
   715   Same.commit (map_proof_terms_same
   716     (Term_Subst.instantiate_same (instT, map (apsnd remove_types) inst))
   717     (Term_Subst.instantiateT_same instT));
   718 
   719 
   720 (***** lifting *****)
   721 
   722 fun lift_proof Bi inc prop prf =
   723   let
   724     fun lift'' Us Ts t =
   725       strip_abs Ts (Logic.incr_indexes (Us, inc) (mk_abs Ts t));
   726 
   727     fun lift' Us Ts (Abst (s, T, prf)) =
   728           (Abst (s, Same.map_option (Logic.incr_tvar_same inc) T, lifth' Us (dummyT::Ts) prf)
   729            handle Same.SAME => Abst (s, T, lift' Us (dummyT::Ts) prf))
   730       | lift' Us Ts (AbsP (s, t, prf)) =
   731           (AbsP (s, Same.map_option (same (op =) (lift'' Us Ts)) t, lifth' Us Ts prf)
   732            handle Same.SAME => AbsP (s, t, lift' Us Ts prf))
   733       | lift' Us Ts (prf % t) = (lift' Us Ts prf % Option.map (lift'' Us Ts) t
   734           handle Same.SAME => prf % Same.map_option (same (op =) (lift'' Us Ts)) t)
   735       | lift' Us Ts (prf1 %% prf2) = (lift' Us Ts prf1 %% lifth' Us Ts prf2
   736           handle Same.SAME => prf1 %% lift' Us Ts prf2)
   737       | lift' _ _ (PAxm (s, prop, Ts)) =
   738           PAxm (s, prop, (Same.map_option o Same.map) (Logic.incr_tvar_same inc) Ts)
   739       | lift' _ _ (OfClass (T, c)) =
   740           OfClass (Logic.incr_tvar_same inc T, c)
   741       | lift' _ _ (Oracle (s, prop, Ts)) =
   742           Oracle (s, prop, (Same.map_option o Same.map) (Logic.incr_tvar_same inc) Ts)
   743       | lift' _ _ (Promise (i, prop, Ts)) =
   744           Promise (i, prop, Same.map (Logic.incr_tvar_same inc) Ts)
   745       | lift' _ _ (PThm (i, ((s, prop, Ts), body))) =
   746           PThm (i, ((s, prop, (Same.map_option o Same.map) (Logic.incr_tvar inc) Ts), body))
   747       | lift' _ _ _ = raise Same.SAME
   748     and lifth' Us Ts prf = (lift' Us Ts prf handle Same.SAME => prf);
   749 
   750     val ps = map (Logic.lift_all inc Bi) (Logic.strip_imp_prems prop);
   751     val k = length ps;
   752 
   753     fun mk_app b (i, j, prf) =
   754           if b then (i-1, j, prf %% PBound i) else (i, j-1, prf %> Bound j);
   755 
   756     fun lift Us bs i j (Const ("==>", _) $ A $ B) =
   757             AbsP ("H", NONE (*A*), lift Us (true::bs) (i+1) j B)
   758       | lift Us bs i j (Const ("all", _) $ Abs (a, T, t)) =
   759             Abst (a, NONE (*T*), lift (T::Us) (false::bs) i (j+1) t)
   760       | lift Us bs i j _ = proof_combP (lifth' (rev Us) [] prf,
   761             map (fn k => (#3 (fold_rev mk_app bs (i-1, j-1, PBound k))))
   762               (i + k - 1 downto i));
   763   in
   764     mk_AbsP (k, lift [] [] 0 0 Bi)
   765   end;
   766 
   767 fun incr_indexes i =
   768   Same.commit (map_proof_terms_same
   769     (Logic.incr_indexes_same ([], i)) (Logic.incr_tvar_same i));
   770 
   771 
   772 (***** proof by assumption *****)
   773 
   774 fun mk_asm_prf t i m =
   775   let
   776     fun imp_prf _ i 0 = PBound i
   777       | imp_prf (Const ("==>", _) $ A $ B) i m = AbsP ("H", NONE (*A*), imp_prf B (i+1) (m-1))
   778       | imp_prf _ i _ = PBound i;
   779     fun all_prf (Const ("all", _) $ Abs (a, T, t)) = Abst (a, NONE (*T*), all_prf t)
   780       | all_prf t = imp_prf t (~i) m
   781   in all_prf t end;
   782 
   783 fun assumption_proof Bs Bi n prf =
   784   mk_AbsP (length Bs, proof_combP (prf,
   785     map PBound (length Bs - 1 downto 0) @ [mk_asm_prf Bi n ~1]));
   786 
   787 
   788 (***** Composition of object rule with proof state *****)
   789 
   790 fun flatten_params_proof i j n (Const ("==>", _) $ A $ B, k) =
   791       AbsP ("H", NONE (*A*), flatten_params_proof (i+1) j n (B, k))
   792   | flatten_params_proof i j n (Const ("all", _) $ Abs (a, T, t), k) =
   793       Abst (a, NONE (*T*), flatten_params_proof i (j+1) n (t, k))
   794   | flatten_params_proof i j n (_, k) = proof_combP (proof_combt (PBound (k+i),
   795       map Bound (j-1 downto 0)), map PBound (remove (op =) (i-n) (i-1 downto 0)));
   796 
   797 fun bicompose_proof flatten Bs oldAs newAs A n m rprf sprf =
   798   let
   799     val la = length newAs;
   800     val lb = length Bs;
   801   in
   802     mk_AbsP (lb+la, proof_combP (sprf,
   803       map PBound (lb + la - 1 downto la)) %%
   804         proof_combP (rprf, (if n>0 then [mk_asm_prf (the A) n m] else []) @
   805           map (if flatten then flatten_params_proof 0 0 n else PBound o snd)
   806             (oldAs ~~ (la - 1 downto 0))))
   807   end;
   808 
   809 
   810 (***** axioms for equality *****)
   811 
   812 val aT = TFree ("'a", []);
   813 val bT = TFree ("'b", []);
   814 val x = Free ("x", aT);
   815 val y = Free ("y", aT);
   816 val z = Free ("z", aT);
   817 val A = Free ("A", propT);
   818 val B = Free ("B", propT);
   819 val f = Free ("f", aT --> bT);
   820 val g = Free ("g", aT --> bT);
   821 
   822 val equality_axms =
   823  [("reflexive", Logic.mk_equals (x, x)),
   824   ("symmetric", Logic.mk_implies (Logic.mk_equals (x, y), Logic.mk_equals (y, x))),
   825   ("transitive",
   826     Logic.list_implies ([Logic.mk_equals (x, y), Logic.mk_equals (y, z)], Logic.mk_equals (x, z))),
   827   ("equal_intr",
   828     Logic.list_implies ([Logic.mk_implies (A, B), Logic.mk_implies (B, A)], Logic.mk_equals (A, B))),
   829   ("equal_elim", Logic.list_implies ([Logic.mk_equals (A, B), A], B)),
   830   ("abstract_rule",
   831     Logic.mk_implies
   832       (Logic.all x
   833         (Logic.mk_equals (f $ x, g $ x)), Logic.mk_equals (lambda x (f $ x), lambda x (g $ x)))),
   834   ("combination", Logic.list_implies
   835     ([Logic.mk_equals (f, g), Logic.mk_equals (x, y)], Logic.mk_equals (f $ x, g $ y)))];
   836 
   837 val [reflexive_axm, symmetric_axm, transitive_axm, equal_intr_axm,
   838   equal_elim_axm, abstract_rule_axm, combination_axm] =
   839     map (fn (s, t) => PAxm ("Pure." ^ s, Logic.varify_global t, NONE)) equality_axms;
   840 
   841 val reflexive = reflexive_axm % NONE;
   842 
   843 fun symmetric (prf as PAxm ("Pure.reflexive", _, _) % _) = prf
   844   | symmetric prf = symmetric_axm % NONE % NONE %% prf;
   845 
   846 fun transitive _ _ (PAxm ("Pure.reflexive", _, _) % _) prf2 = prf2
   847   | transitive _ _ prf1 (PAxm ("Pure.reflexive", _, _) % _) = prf1
   848   | transitive u (Type ("prop", [])) prf1 prf2 =
   849       transitive_axm % NONE % SOME (remove_types u) % NONE %% prf1 %% prf2
   850   | transitive u T prf1 prf2 =
   851       transitive_axm % NONE % NONE % NONE %% prf1 %% prf2;
   852 
   853 fun abstract_rule x a prf =
   854   abstract_rule_axm % NONE % NONE %% forall_intr_proof x a prf;
   855 
   856 fun check_comb (PAxm ("Pure.combination", _, _) % f % g % _ % _ %% prf %% _) =
   857       is_some f orelse check_comb prf
   858   | check_comb (PAxm ("Pure.transitive", _, _) % _ % _ % _ %% prf1 %% prf2) =
   859       check_comb prf1 andalso check_comb prf2
   860   | check_comb (PAxm ("Pure.symmetric", _, _) % _ % _ %% prf) = check_comb prf
   861   | check_comb _ = false;
   862 
   863 fun combination f g t u (Type (_, [T, U])) prf1 prf2 =
   864   let
   865     val f = Envir.beta_norm f;
   866     val g = Envir.beta_norm g;
   867     val prf =  if check_comb prf1 then
   868         combination_axm % NONE % NONE
   869       else (case prf1 of
   870           PAxm ("Pure.reflexive", _, _) % _ =>
   871             combination_axm %> remove_types f % NONE
   872         | _ => combination_axm %> remove_types f %> remove_types g)
   873   in
   874     (case T of
   875        Type ("fun", _) => prf %
   876          (case head_of f of
   877             Abs _ => SOME (remove_types t)
   878           | Var _ => SOME (remove_types t)
   879           | _ => NONE) %
   880          (case head_of g of
   881             Abs _ => SOME (remove_types u)
   882           | Var _ => SOME (remove_types u)
   883           | _ => NONE) %% prf1 %% prf2
   884      | _ => prf % NONE % NONE %% prf1 %% prf2)
   885   end;
   886 
   887 fun equal_intr A B prf1 prf2 =
   888   equal_intr_axm %> remove_types A %> remove_types B %% prf1 %% prf2;
   889 
   890 fun equal_elim A B prf1 prf2 =
   891   equal_elim_axm %> remove_types A %> remove_types B %% prf1 %% prf2;
   892 
   893 
   894 (**** type classes ****)
   895 
   896 fun strip_shyps_proof algebra present witnessed extra_sorts prf =
   897   let
   898     fun get S2 (T, S1) = if Sorts.sort_le algebra (S1, S2) then SOME T else NONE;
   899     val extra = map (fn S => (TFree ("'dummy", S), S)) extra_sorts;
   900     val replacements = present @ extra @ witnessed;
   901     fun replace T =
   902       if exists (fn (T', _) => T' = T) present then raise Same.SAME
   903       else
   904         (case get_first (get (Type.sort_of_atyp T)) replacements of
   905           SOME T' => T'
   906         | NONE => raise Fail "strip_shyps_proof: bad type variable in proof term");
   907   in Same.commit (map_proof_types_same (Term_Subst.map_atypsT_same replace)) prf end;
   908 
   909 
   910 local
   911 
   912 type axclass_proofs =
   913  {classrel_proof: theory -> class * class -> proof,
   914   arity_proof: theory -> string * sort list * class -> proof};
   915 
   916 val axclass_proofs: axclass_proofs Single_Assignment.var =
   917   Single_Assignment.var "Proofterm.axclass_proofs";
   918 
   919 fun axclass_proof which thy x =
   920   (case Single_Assignment.peek axclass_proofs of
   921     NONE => raise Fail "Axclass proof operations not installed"
   922   | SOME prfs => which prfs thy x);
   923 
   924 in
   925 
   926 val classrel_proof = axclass_proof #classrel_proof;
   927 val arity_proof = axclass_proof #arity_proof;
   928 
   929 fun install_axclass_proofs prfs = Single_Assignment.assign axclass_proofs prfs;
   930 
   931 end;
   932 
   933 
   934 (***** axioms and theorems *****)
   935 
   936 val proofs = Unsynchronized.ref 2;
   937 
   938 fun vars_of t = map Var (rev (Term.add_vars t []));
   939 fun frees_of t = map Free (rev (Term.add_frees t []));
   940 
   941 fun test_args _ [] = true
   942   | test_args is (Bound i :: ts) =
   943       not (member (op =) is i) andalso test_args (i :: is) ts
   944   | test_args _ _ = false;
   945 
   946 fun is_fun (Type ("fun", _)) = true
   947   | is_fun (TVar _) = true
   948   | is_fun _ = false;
   949 
   950 fun add_funvars Ts (vs, t) =
   951   if is_fun (fastype_of1 (Ts, t)) then
   952     union (op =) vs (map_filter (fn Var (ixn, T) =>
   953       if is_fun T then SOME ixn else NONE | _ => NONE) (vars_of t))
   954   else vs;
   955 
   956 fun add_npvars q p Ts (vs, Const ("==>", _) $ t $ u) =
   957       add_npvars q p Ts (add_npvars q (not p) Ts (vs, t), u)
   958   | add_npvars q p Ts (vs, Const ("all", Type (_, [Type (_, [T, _]), _])) $ t) =
   959       add_npvars q p Ts (vs, if p andalso q then betapply (t, Var (("",0), T)) else t)
   960   | add_npvars q p Ts (vs, Abs (_, T, t)) = add_npvars q p (T::Ts) (vs, t)
   961   | add_npvars _ _ Ts (vs, t) = add_npvars' Ts (vs, t)
   962 and add_npvars' Ts (vs, t) = (case strip_comb t of
   963     (Var (ixn, _), ts) => if test_args [] ts then vs
   964       else Library.foldl (add_npvars' Ts)
   965         (AList.update (op =) (ixn,
   966           Library.foldl (add_funvars Ts) ((these ooo AList.lookup) (op =) vs ixn, ts)) vs, ts)
   967   | (Abs (_, T, u), ts) => Library.foldl (add_npvars' (T::Ts)) (vs, u :: ts)
   968   | (_, ts) => Library.foldl (add_npvars' Ts) (vs, ts));
   969 
   970 fun prop_vars (Const ("==>", _) $ P $ Q) = union (op =) (prop_vars P) (prop_vars Q)
   971   | prop_vars (Const ("all", _) $ Abs (_, _, t)) = prop_vars t
   972   | prop_vars t = (case strip_comb t of
   973       (Var (ixn, _), _) => [ixn] | _ => []);
   974 
   975 fun is_proj t =
   976   let
   977     fun is_p i t = (case strip_comb t of
   978         (Bound j, []) => false
   979       | (Bound j, ts) => j >= i orelse exists (is_p i) ts
   980       | (Abs (_, _, u), _) => is_p (i+1) u
   981       | (_, ts) => exists (is_p i) ts)
   982   in (case strip_abs_body t of
   983         Bound _ => true
   984       | t' => is_p 0 t')
   985   end;
   986 
   987 fun needed_vars prop =
   988   union (op =) (Library.foldl (uncurry (union (op =)))
   989     ([], map (uncurry (insert (op =))) (add_npvars true true [] ([], prop))))
   990   (prop_vars prop);
   991 
   992 fun gen_axm_proof c name prop =
   993   let
   994     val nvs = needed_vars prop;
   995     val args = map (fn (v as Var (ixn, _)) =>
   996         if member (op =) nvs ixn then SOME v else NONE) (vars_of prop) @
   997       map SOME (frees_of prop);
   998   in
   999     proof_combt' (c (name, prop, NONE), args)
  1000   end;
  1001 
  1002 val axm_proof = gen_axm_proof PAxm;
  1003 
  1004 val dummy = Const (Term.dummy_patternN, dummyT);
  1005 
  1006 fun oracle_proof name prop =
  1007   if ! proofs = 0 then ((name, dummy), Oracle (name, dummy, NONE))
  1008   else ((name, prop), gen_axm_proof Oracle name prop);
  1009 
  1010 val shrink_proof =
  1011   let
  1012     fun shrink ls lev (prf as Abst (a, T, body)) =
  1013           let val (b, is, ch, body') = shrink ls (lev+1) body
  1014           in (b, is, ch, if ch then Abst (a, T, body') else prf) end
  1015       | shrink ls lev (prf as AbsP (a, t, body)) =
  1016           let val (b, is, ch, body') = shrink (lev::ls) lev body
  1017           in (b orelse member (op =) is 0, map_filter (fn 0 => NONE | i => SOME (i-1)) is,
  1018             ch, if ch then AbsP (a, t, body') else prf)
  1019           end
  1020       | shrink ls lev prf =
  1021           let val (is, ch, _, prf') = shrink' ls lev [] [] prf
  1022           in (false, is, ch, prf') end
  1023     and shrink' ls lev ts prfs (prf as prf1 %% prf2) =
  1024           let
  1025             val p as (_, is', ch', prf') = shrink ls lev prf2;
  1026             val (is, ch, ts', prf'') = shrink' ls lev ts (p::prfs) prf1
  1027           in (union (op =) is is', ch orelse ch', ts',
  1028               if ch orelse ch' then prf'' %% prf' else prf)
  1029           end
  1030       | shrink' ls lev ts prfs (prf as prf1 % t) =
  1031           let val (is, ch, (ch', t')::ts', prf') = shrink' ls lev (t::ts) prfs prf1
  1032           in (is, ch orelse ch', ts',
  1033               if ch orelse ch' then prf' % t' else prf) end
  1034       | shrink' ls lev ts prfs (prf as PBound i) =
  1035           (if exists (fn SOME (Bound j) => lev-j <= nth ls i | _ => true) ts
  1036              orelse has_duplicates (op =)
  1037                (Library.foldl (fn (js, SOME (Bound j)) => j :: js | (js, _) => js) ([], ts))
  1038              orelse exists #1 prfs then [i] else [], false, map (pair false) ts, prf)
  1039       | shrink' ls lev ts prfs (prf as Hyp _) = ([], false, map (pair false) ts, prf)
  1040       | shrink' ls lev ts prfs (prf as MinProof) = ([], false, map (pair false) ts, prf)
  1041       | shrink' ls lev ts prfs (prf as OfClass _) = ([], false, map (pair false) ts, prf)
  1042       | shrink' ls lev ts prfs prf =
  1043           let
  1044             val prop =
  1045               (case prf of
  1046                 PAxm (_, prop, _) => prop
  1047               | Oracle (_, prop, _) => prop
  1048               | Promise (_, prop, _) => prop
  1049               | PThm (_, ((_, prop, _), _)) => prop
  1050               | _ => error "shrink: proof not in normal form");
  1051             val vs = vars_of prop;
  1052             val (ts', ts'') = chop (length vs) ts;
  1053             val insts = take (length ts') (map (fst o dest_Var) vs) ~~ ts';
  1054             val nvs = Library.foldl (fn (ixns', (ixn, ixns)) =>
  1055               insert (op =) ixn (case AList.lookup (op =) insts ixn of
  1056                   SOME (SOME t) => if is_proj t then union (op =) ixns ixns' else ixns'
  1057                 | _ => union (op =) ixns ixns'))
  1058                   (needed prop ts'' prfs, add_npvars false true [] ([], prop));
  1059             val insts' = map
  1060               (fn (ixn, x as SOME _) => if member (op =) nvs ixn then (false, x) else (true, NONE)
  1061                 | (_, x) => (false, x)) insts
  1062           in ([], false, insts' @ map (pair false) ts'', prf) end
  1063     and needed (Const ("==>", _) $ t $ u) ts ((b, _, _, _)::prfs) =
  1064           union (op =) (if b then map (fst o dest_Var) (vars_of t) else []) (needed u ts prfs)
  1065       | needed (Var (ixn, _)) (_::_) _ = [ixn]
  1066       | needed _ _ _ = [];
  1067   in shrink end;
  1068 
  1069 
  1070 (**** Simple first order matching functions for terms and proofs ****)
  1071 
  1072 exception PMatch;
  1073 
  1074 (** see pattern.ML **)
  1075 
  1076 fun flt (i: int) = filter (fn n => n < i);
  1077 
  1078 fun fomatch Ts tymatch j =
  1079   let
  1080     fun mtch (instsp as (tyinsts, insts)) = fn
  1081         (Var (ixn, T), t)  =>
  1082           if j>0 andalso not (null (flt j (loose_bnos t)))
  1083           then raise PMatch
  1084           else (tymatch (tyinsts, fn () => (T, fastype_of1 (Ts, t))),
  1085             (ixn, t) :: insts)
  1086       | (Free (a, T), Free (b, U)) =>
  1087           if a=b then (tymatch (tyinsts, K (T, U)), insts) else raise PMatch
  1088       | (Const (a, T), Const (b, U))  =>
  1089           if a=b then (tymatch (tyinsts, K (T, U)), insts) else raise PMatch
  1090       | (f $ t, g $ u) => mtch (mtch instsp (f, g)) (t, u)
  1091       | (Bound i, Bound j) => if i=j then instsp else raise PMatch
  1092       | _ => raise PMatch
  1093   in mtch end;
  1094 
  1095 fun match_proof Ts tymatch =
  1096   let
  1097     fun optmatch _ inst (NONE, _) = inst
  1098       | optmatch _ _ (SOME _, NONE) = raise PMatch
  1099       | optmatch mtch inst (SOME x, SOME y) = mtch inst (x, y)
  1100 
  1101     fun matcht Ts j (pinst, tinst) (t, u) =
  1102       (pinst, fomatch Ts tymatch j tinst (t, Envir.beta_norm u));
  1103     fun matchT (pinst, (tyinsts, insts)) p =
  1104       (pinst, (tymatch (tyinsts, K p), insts));
  1105     fun matchTs inst (Ts, Us) = Library.foldl (uncurry matchT) (inst, Ts ~~ Us);
  1106 
  1107     fun mtch Ts i j (pinst, tinst) (Hyp (Var (ixn, _)), prf) =
  1108           if i = 0 andalso j = 0 then ((ixn, prf) :: pinst, tinst)
  1109           else (case apfst (flt i) (apsnd (flt j)
  1110                   (prf_add_loose_bnos 0 0 prf ([], []))) of
  1111               ([], []) => ((ixn, incr_pboundvars (~i) (~j) prf) :: pinst, tinst)
  1112             | ([], _) => if j = 0 then
  1113                    ((ixn, incr_pboundvars (~i) (~j) prf) :: pinst, tinst)
  1114                  else raise PMatch
  1115             | _ => raise PMatch)
  1116       | mtch Ts i j inst (prf1 % opt1, prf2 % opt2) =
  1117           optmatch (matcht Ts j) (mtch Ts i j inst (prf1, prf2)) (opt1, opt2)
  1118       | mtch Ts i j inst (prf1 %% prf2, prf1' %% prf2') =
  1119           mtch Ts i j (mtch Ts i j inst (prf1, prf1')) (prf2, prf2')
  1120       | mtch Ts i j inst (Abst (_, opT, prf1), Abst (_, opU, prf2)) =
  1121           mtch (the_default dummyT opU :: Ts) i (j+1)
  1122             (optmatch matchT inst (opT, opU)) (prf1, prf2)
  1123       | mtch Ts i j inst (prf1, Abst (_, opU, prf2)) =
  1124           mtch (the_default dummyT opU :: Ts) i (j+1) inst
  1125             (incr_pboundvars 0 1 prf1 %> Bound 0, prf2)
  1126       | mtch Ts i j inst (AbsP (_, opt, prf1), AbsP (_, opu, prf2)) =
  1127           mtch Ts (i+1) j (optmatch (matcht Ts j) inst (opt, opu)) (prf1, prf2)
  1128       | mtch Ts i j inst (prf1, AbsP (_, _, prf2)) =
  1129           mtch Ts (i+1) j inst (incr_pboundvars 1 0 prf1 %% PBound 0, prf2)
  1130       | mtch Ts i j inst (PAxm (s1, _, opTs), PAxm (s2, _, opUs)) =
  1131           if s1 = s2 then optmatch matchTs inst (opTs, opUs)
  1132           else raise PMatch
  1133       | mtch Ts i j inst (OfClass (T1, c1), OfClass (T2, c2)) =
  1134           if c1 = c2 then matchT inst (T1, T2)
  1135           else raise PMatch
  1136       | mtch Ts i j inst (PThm (_, ((name1, prop1, opTs), _)), PThm (_, ((name2, prop2, opUs), _))) =
  1137           if name1 = name2 andalso prop1 = prop2 then
  1138             optmatch matchTs inst (opTs, opUs)
  1139           else raise PMatch
  1140       | mtch _ _ _ inst (PBound i, PBound j) = if i = j then inst else raise PMatch
  1141       | mtch _ _ _ _ _ = raise PMatch
  1142   in mtch Ts 0 0 end;
  1143 
  1144 fun prf_subst (pinst, (tyinsts, insts)) =
  1145   let
  1146     val substT = Envir.subst_type_same tyinsts;
  1147     val substTs = Same.map substT;
  1148 
  1149     fun subst' lev (Var (xi, _)) =
  1150         (case AList.lookup (op =) insts xi of
  1151           NONE => raise Same.SAME
  1152         | SOME u => incr_boundvars lev u)
  1153       | subst' _ (Const (s, T)) = Const (s, substT T)
  1154       | subst' _ (Free (s, T)) = Free (s, substT T)
  1155       | subst' lev (Abs (a, T, body)) =
  1156           (Abs (a, substT T, Same.commit (subst' (lev + 1)) body)
  1157             handle Same.SAME => Abs (a, T, subst' (lev + 1) body))
  1158       | subst' lev (f $ t) =
  1159           (subst' lev f $ Same.commit (subst' lev) t
  1160             handle Same.SAME => f $ subst' lev t)
  1161       | subst' _ _ = raise Same.SAME;
  1162 
  1163     fun subst plev tlev (AbsP (a, t, body)) =
  1164           (AbsP (a, Same.map_option (subst' tlev) t, Same.commit (subst (plev + 1) tlev) body)
  1165             handle Same.SAME => AbsP (a, t, subst (plev + 1) tlev body))
  1166       | subst plev tlev (Abst (a, T, body)) =
  1167           (Abst (a, Same.map_option substT T, Same.commit (subst plev (tlev + 1)) body)
  1168             handle Same.SAME => Abst (a, T, subst plev (tlev + 1) body))
  1169       | subst plev tlev (prf %% prf') =
  1170           (subst plev tlev prf %% Same.commit (subst plev tlev) prf'
  1171             handle Same.SAME => prf %% subst plev tlev prf')
  1172       | subst plev tlev (prf % t) =
  1173           (subst plev tlev prf % Same.commit (Same.map_option (subst' tlev)) t
  1174             handle Same.SAME => prf % Same.map_option (subst' tlev) t)
  1175       | subst plev tlev (Hyp (Var (xi, _))) =
  1176           (case AList.lookup (op =) pinst xi of
  1177             NONE => raise Same.SAME
  1178           | SOME prf' => incr_pboundvars plev tlev prf')
  1179       | subst _ _ (PAxm (id, prop, Ts)) = PAxm (id, prop, Same.map_option substTs Ts)
  1180       | subst _ _ (OfClass (T, c)) = OfClass (substT T, c)
  1181       | subst _ _ (Oracle (id, prop, Ts)) = Oracle (id, prop, Same.map_option substTs Ts)
  1182       | subst _ _ (Promise (i, prop, Ts)) = Promise (i, prop, substTs Ts)
  1183       | subst _ _ (PThm (i, ((id, prop, Ts), body))) =
  1184           PThm (i, ((id, prop, Same.map_option substTs Ts), body))
  1185       | subst _ _ _ = raise Same.SAME;
  1186   in fn t => subst 0 0 t handle Same.SAME => t end;
  1187 
  1188 (*A fast unification filter: true unless the two terms cannot be unified.
  1189   Terms must be NORMAL.  Treats all Vars as distinct. *)
  1190 fun could_unify prf1 prf2 =
  1191   let
  1192     fun matchrands (prf1 %% prf2) (prf1' %% prf2') =
  1193           could_unify prf2 prf2' andalso matchrands prf1 prf1'
  1194       | matchrands (prf % SOME t) (prf' % SOME t') =
  1195           Term.could_unify (t, t') andalso matchrands prf prf'
  1196       | matchrands (prf % _) (prf' % _) = matchrands prf prf'
  1197       | matchrands _ _ = true
  1198 
  1199     fun head_of (prf %% _) = head_of prf
  1200       | head_of (prf % _) = head_of prf
  1201       | head_of prf = prf
  1202 
  1203   in case (head_of prf1, head_of prf2) of
  1204         (_, Hyp (Var _)) => true
  1205       | (Hyp (Var _), _) => true
  1206       | (PAxm (a, _, _), PAxm (b, _, _)) => a = b andalso matchrands prf1 prf2
  1207       | (OfClass (_, c), OfClass (_, d)) => c = d andalso matchrands prf1 prf2
  1208       | (PThm (_, ((a, propa, _), _)), PThm (_, ((b, propb, _), _))) =>
  1209           a = b andalso propa = propb andalso matchrands prf1 prf2
  1210       | (PBound i, PBound j) => i = j andalso matchrands prf1 prf2
  1211       | (AbsP _, _) =>  true   (*because of possible eta equality*)
  1212       | (Abst _, _) =>  true
  1213       | (_, AbsP _) =>  true
  1214       | (_, Abst _) =>  true
  1215       | _ => false
  1216   end;
  1217 
  1218 
  1219 (**** rewriting on proof terms ****)
  1220 
  1221 val no_skel = PBound 0;
  1222 val normal_skel = Hyp (Var ((Name.uu, 0), propT));
  1223 
  1224 fun rewrite_prf tymatch (rules, procs) prf =
  1225   let
  1226     fun rew _ (Abst (_, _, body) % SOME t) = SOME (prf_subst_bounds [t] body, no_skel)
  1227       | rew _ (AbsP (_, _, body) %% prf) = SOME (prf_subst_pbounds [prf] body, no_skel)
  1228       | rew Ts prf =
  1229           (case get_first (fn r => r Ts prf) procs of
  1230             NONE => get_first (fn (prf1, prf2) => SOME (prf_subst
  1231               (match_proof Ts tymatch ([], (Vartab.empty, [])) (prf1, prf)) prf2, prf2)
  1232                  handle PMatch => NONE) (filter (could_unify prf o fst) rules)
  1233           | some => some);
  1234 
  1235     fun rew0 Ts (prf as AbsP (_, _, prf' %% PBound 0)) =
  1236           if prf_loose_Pbvar1 prf' 0 then rew Ts prf
  1237           else
  1238             let val prf'' = incr_pboundvars (~1) 0 prf'
  1239             in SOME (the_default (prf'', no_skel) (rew Ts prf'')) end
  1240       | rew0 Ts (prf as Abst (_, _, prf' % SOME (Bound 0))) =
  1241           if prf_loose_bvar1 prf' 0 then rew Ts prf
  1242           else
  1243             let val prf'' = incr_pboundvars 0 (~1) prf'
  1244             in SOME (the_default (prf'', no_skel) (rew Ts prf'')) end
  1245       | rew0 Ts prf = rew Ts prf;
  1246 
  1247     fun rew1 _ (Hyp (Var _)) _ = NONE
  1248       | rew1 Ts skel prf = (case rew2 Ts skel prf of
  1249           SOME prf1 => (case rew0 Ts prf1 of
  1250               SOME (prf2, skel') => SOME (the_default prf2 (rew1 Ts skel' prf2))
  1251             | NONE => SOME prf1)
  1252         | NONE => (case rew0 Ts prf of
  1253               SOME (prf1, skel') => SOME (the_default prf1 (rew1 Ts skel' prf1))
  1254             | NONE => NONE))
  1255 
  1256     and rew2 Ts skel (prf % SOME t) = (case prf of
  1257             Abst (_, _, body) =>
  1258               let val prf' = prf_subst_bounds [t] body
  1259               in SOME (the_default prf' (rew2 Ts no_skel prf')) end
  1260           | _ => (case rew1 Ts (case skel of skel' % _ => skel' | _ => no_skel) prf of
  1261               SOME prf' => SOME (prf' % SOME t)
  1262             | NONE => NONE))
  1263       | rew2 Ts skel (prf % NONE) = Option.map (fn prf' => prf' % NONE)
  1264           (rew1 Ts (case skel of skel' % _ => skel' | _ => no_skel) prf)
  1265       | rew2 Ts skel (prf1 %% prf2) = (case prf1 of
  1266             AbsP (_, _, body) =>
  1267               let val prf' = prf_subst_pbounds [prf2] body
  1268               in SOME (the_default prf' (rew2 Ts no_skel prf')) end
  1269           | _ =>
  1270             let val (skel1, skel2) = (case skel of
  1271                 skel1 %% skel2 => (skel1, skel2)
  1272               | _ => (no_skel, no_skel))
  1273             in case rew1 Ts skel1 prf1 of
  1274                 SOME prf1' => (case rew1 Ts skel2 prf2 of
  1275                     SOME prf2' => SOME (prf1' %% prf2')
  1276                   | NONE => SOME (prf1' %% prf2))
  1277               | NONE => (case rew1 Ts skel2 prf2 of
  1278                     SOME prf2' => SOME (prf1 %% prf2')
  1279                   | NONE => NONE)
  1280             end)
  1281       | rew2 Ts skel (Abst (s, T, prf)) = (case rew1 (the_default dummyT T :: Ts)
  1282               (case skel of Abst (_, _, skel') => skel' | _ => no_skel) prf of
  1283             SOME prf' => SOME (Abst (s, T, prf'))
  1284           | NONE => NONE)
  1285       | rew2 Ts skel (AbsP (s, t, prf)) = (case rew1 Ts
  1286               (case skel of AbsP (_, _, skel') => skel' | _ => no_skel) prf of
  1287             SOME prf' => SOME (AbsP (s, t, prf'))
  1288           | NONE => NONE)
  1289       | rew2 _ _ _ = NONE;
  1290 
  1291   in the_default prf (rew1 [] no_skel prf) end;
  1292 
  1293 fun rewrite_proof thy = rewrite_prf (fn (tyenv, f) =>
  1294   Sign.typ_match thy (f ()) tyenv handle Type.TYPE_MATCH => raise PMatch);
  1295 
  1296 fun rewrite_proof_notypes rews = rewrite_prf fst rews;
  1297 
  1298 
  1299 (**** theory data ****)
  1300 
  1301 structure ProofData = Theory_Data
  1302 (
  1303   type T =
  1304     (stamp * (proof * proof)) list *
  1305     (stamp * (typ list -> proof -> (proof * proof) option)) list;
  1306 
  1307   val empty = ([], []);
  1308   val extend = I;
  1309   fun merge ((rules1, procs1), (rules2, procs2)) : T =
  1310     (AList.merge (op =) (K true) (rules1, rules2),
  1311       AList.merge (op =) (K true) (procs1, procs2));
  1312 );
  1313 
  1314 fun get_data thy = let val (rules, procs) = ProofData.get thy in (map #2 rules, map #2 procs) end;
  1315 fun rew_proof thy = rewrite_prf fst (get_data thy);
  1316 
  1317 fun add_prf_rrule r = (ProofData.map o apfst) (cons (stamp (), r));
  1318 fun add_prf_rproc p = (ProofData.map o apsnd) (cons (stamp (), p));
  1319 
  1320 
  1321 (***** promises *****)
  1322 
  1323 fun promise_proof thy i prop =
  1324   let
  1325     val _ = prop |> Term.exists_subterm (fn t =>
  1326       (Term.is_Free t orelse Term.is_Var t) andalso
  1327         error ("promise_proof: illegal variable " ^ Syntax.string_of_term_global thy t));
  1328     val _ = prop |> Term.exists_type (Term.exists_subtype
  1329       (fn TFree (a, _) => error ("promise_proof: illegal type variable " ^ quote a)
  1330         | _ => false));
  1331   in Promise (i, prop, map TVar (Term.add_tvars prop [])) end;
  1332 
  1333 fun fulfill_norm_proof thy ps body0 =
  1334   let
  1335     val PBody {oracles = oracles0, thms = thms0, proof = proof0} = body0;
  1336     val oracles = fold (fn (_, PBody {oracles, ...}) => merge_oracles oracles) ps oracles0;
  1337     val thms = fold (fn (_, PBody {thms, ...}) => merge_thms thms) ps thms0;
  1338     val proofs = fold (fn (i, PBody {proof, ...}) => Inttab.update (i, proof)) ps Inttab.empty;
  1339 
  1340     fun fill (Promise (i, prop, Ts)) =
  1341           (case Inttab.lookup proofs i of
  1342             NONE => NONE
  1343           | SOME prf => SOME (instantiate (Term.add_tvars prop [] ~~ Ts, []) prf, normal_skel))
  1344       | fill _ = NONE;
  1345     val (rules, procs) = get_data thy;
  1346     val proof = rewrite_prf fst (rules, K fill :: procs) proof0;
  1347   in PBody {oracles = oracles, thms = thms, proof = proof} end;
  1348 
  1349 fun fulfill_proof_future _ [] body = Future.value body
  1350   | fulfill_proof_future thy promises body =
  1351       Future.fork_deps (map snd promises) (fn () =>
  1352         fulfill_norm_proof thy (map (apsnd Future.join) promises) body);
  1353 
  1354 
  1355 (***** theorems *****)
  1356 
  1357 fun thm_proof thy name hyps concl promises body =
  1358   let
  1359     val PBody {oracles = oracles0, thms = thms0, proof = prf} = body;
  1360     val prop = Logic.list_implies (hyps, concl);
  1361     val nvs = needed_vars prop;
  1362     val args = map (fn (v as Var (ixn, _)) =>
  1363         if member (op =) nvs ixn then SOME v else NONE) (vars_of prop) @
  1364       map SOME (frees_of prop);
  1365 
  1366     val proof0 =
  1367       if ! proofs = 2 then
  1368         #4 (shrink_proof [] 0 (rew_proof thy (fold_rev implies_intr_proof hyps prf)))
  1369       else MinProof;
  1370     val body0 = PBody {oracles = oracles0, thms = thms0, proof = proof0};
  1371 
  1372     fun new_prf () = (serial (), name, prop, fulfill_proof_future thy promises body0);
  1373     val (i, name, prop, body') =
  1374       (case strip_combt (fst (strip_combP prf)) of
  1375         (PThm (i, ((old_name, prop', NONE), body')), args') =>
  1376           if (old_name = "" orelse old_name = name) andalso prop = prop' andalso args = args'
  1377           then (i, name, prop, body')
  1378           else new_prf ()
  1379       | _ => new_prf ());
  1380     val head = PThm (i, ((name, prop, NONE), body'));
  1381   in
  1382     ((i, (name, prop, body')), proof_combP (proof_combt' (head, args), map Hyp hyps))
  1383   end;
  1384 
  1385 fun get_name hyps prop prf =
  1386   let val prop = Logic.list_implies (hyps, prop) in
  1387     (case strip_combt (fst (strip_combP prf)) of
  1388       (PThm (_, ((name, prop', _), _)), _) => if prop = prop' then name else ""
  1389     | _ => "")
  1390   end;
  1391 
  1392 end;
  1393 
  1394 structure Basic_Proofterm : BASIC_PROOFTERM = Proofterm;
  1395 open Basic_Proofterm;