src/Pure/proofterm.ML
author wenzelm
Thu Jun 09 16:34:49 2011 +0200 (2011-06-09 ago)
changeset 43324 2b47822868e4
parent 43278 1fbdcebb364b
child 43326 47cf4bc789aa
permissions -rw-r--r--
discontinued Name.variant to emphasize that this is old-style / indirect;
     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) Ord_List.T,
    28      thms: (serial * (string * term * proof_body future)) Ord_List.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 Ord_List.T -> oracle Ord_List.T -> oracle Ord_List.T
    50   val merge_thms: pthm Ord_List.T -> pthm Ord_List.T -> pthm Ord_List.T
    51   val all_oracles_of: proof_body -> oracle Ord_List.T
    52   val approximate_proof_body: proof -> proof_body
    53 
    54   (** primitive operations **)
    55   val proofs_enabled: unit -> bool
    56   val proof_combt: proof * term list -> proof
    57   val proof_combt': proof * term option list -> proof
    58   val proof_combP: proof * proof list -> proof
    59   val strip_combt: proof -> proof * term option list
    60   val strip_combP: proof -> proof * proof list
    61   val strip_thm: proof_body -> proof_body
    62   val map_proof_same: term Same.operation -> typ Same.operation
    63     -> (typ * class -> proof) -> proof Same.operation
    64   val map_proof_terms_same: term Same.operation -> typ Same.operation -> proof Same.operation
    65   val map_proof_types_same: typ Same.operation -> proof Same.operation
    66   val map_proof_terms: (term -> term) -> (typ -> typ) -> proof -> proof
    67   val map_proof_types: (typ -> typ) -> proof -> proof
    68   val fold_proof_terms: (term -> 'a -> 'a) -> (typ -> 'a -> 'a) -> proof -> 'a -> 'a
    69   val maxidx_proof: proof -> int -> int
    70   val size_of_proof: proof -> int
    71   val change_type: typ list option -> proof -> proof
    72   val prf_abstract_over: term -> proof -> proof
    73   val prf_incr_bv: int -> int -> int -> int -> proof -> proof
    74   val incr_pboundvars: int -> int -> proof -> proof
    75   val prf_loose_bvar1: proof -> int -> bool
    76   val prf_loose_Pbvar1: proof -> int -> bool
    77   val prf_add_loose_bnos: int -> int -> proof -> int list * int list -> int list * int list
    78   val norm_proof: Envir.env -> proof -> proof
    79   val norm_proof': Envir.env -> proof -> proof
    80   val prf_subst_bounds: term list -> proof -> proof
    81   val prf_subst_pbounds: proof list -> proof -> proof
    82   val freeze_thaw_prf: proof -> proof * (proof -> proof)
    83 
    84   (** proof terms for specific inference rules **)
    85   val implies_intr_proof: term -> proof -> proof
    86   val implies_intr_proof': term -> proof -> proof
    87   val forall_intr_proof: term -> string -> proof -> proof
    88   val forall_intr_proof': term -> proof -> proof
    89   val varify_proof: term -> (string * sort) list -> proof -> proof
    90   val legacy_freezeT: term -> proof -> proof
    91   val rotate_proof: term list -> term -> int -> proof -> proof
    92   val permute_prems_proof: term list -> int -> int -> proof -> proof
    93   val generalize: string list * string list -> int -> proof -> proof
    94   val instantiate: ((indexname * sort) * typ) list * ((indexname * typ) * term) list
    95     -> proof -> proof
    96   val lift_proof: term -> int -> term -> proof -> proof
    97   val incr_indexes: int -> proof -> proof
    98   val assumption_proof: term list -> term -> int -> proof -> proof
    99   val bicompose_proof: bool -> term list -> term list -> term list -> term option ->
   100     int -> int -> proof -> proof -> proof
   101   val equality_axms: (string * term) list
   102   val reflexive_axm: proof
   103   val symmetric_axm: proof
   104   val transitive_axm: proof
   105   val equal_intr_axm: proof
   106   val equal_elim_axm: proof
   107   val abstract_rule_axm: proof
   108   val combination_axm: proof
   109   val reflexive: proof
   110   val symmetric: proof -> proof
   111   val transitive: term -> typ -> proof -> proof -> proof
   112   val abstract_rule: term -> string -> proof -> proof
   113   val combination: term -> term -> term -> term -> typ -> proof -> proof -> proof
   114   val equal_intr: term -> term -> proof -> proof -> proof
   115   val equal_elim: term -> term -> proof -> proof -> proof
   116   val strip_shyps_proof: Sorts.algebra -> (typ * sort) list -> (typ * sort) list ->
   117     sort list -> proof -> proof
   118   val classrel_proof: theory -> class * class -> proof
   119   val arity_proof: theory -> string * sort list * class -> proof
   120   val of_sort_proof: theory -> (typ * class -> proof) -> typ * sort -> proof list
   121   val install_axclass_proofs:
   122    {classrel_proof: theory -> class * class -> proof,
   123     arity_proof: theory -> string * sort list * class -> proof} -> unit
   124   val axm_proof: string -> term -> proof
   125   val oracle_proof: string -> term -> oracle * proof
   126 
   127   (** rewriting on proof terms **)
   128   val add_prf_rrule: proof * proof -> theory -> theory
   129   val add_prf_rproc: (typ list -> term option list -> proof -> (proof * proof) option) -> theory -> theory
   130   val no_skel: proof
   131   val normal_skel: proof
   132   val rewrite_proof: theory -> (proof * proof) list *
   133     (typ list -> term option list -> proof -> (proof * proof) option) list -> proof -> proof
   134   val rewrite_proof_notypes: (proof * proof) list *
   135     (typ list -> term option list -> proof -> (proof * proof) option) list -> proof -> proof
   136   val rew_proof: theory -> proof -> proof
   137 
   138   val promise_proof: theory -> serial -> term -> proof
   139   val fulfill_norm_proof: theory -> (serial * proof_body) list -> proof_body -> proof_body
   140   val thm_proof: theory -> string -> sort list -> term list -> term ->
   141     (serial * proof_body future) list -> proof_body -> pthm * proof
   142   val unconstrain_thm_proof: theory -> sort list -> term ->
   143     (serial * proof_body future) list -> proof_body -> pthm * proof
   144   val get_name: sort list -> term list -> term -> proof -> string
   145   val guess_name: proof -> string
   146 end
   147 
   148 structure Proofterm : PROOFTERM =
   149 struct
   150 
   151 (***** datatype proof *****)
   152 
   153 datatype proof =
   154    MinProof
   155  | PBound of int
   156  | Abst of string * typ option * proof
   157  | AbsP of string * term option * proof
   158  | op % of proof * term option
   159  | op %% of proof * proof
   160  | Hyp of term
   161  | PAxm of string * term * typ list option
   162  | OfClass of typ * class
   163  | Oracle of string * term * typ list option
   164  | Promise of serial * term * typ list
   165  | PThm of serial * ((string * term * typ list option) * proof_body future)
   166 and proof_body = PBody of
   167   {oracles: (string * term) Ord_List.T,
   168    thms: (serial * (string * term * proof_body future)) Ord_List.T,
   169    proof: proof};
   170 
   171 type oracle = string * term;
   172 type pthm = serial * (string * term * proof_body future);
   173 
   174 fun proof_of (PBody {proof, ...}) = proof;
   175 val join_proof = Future.join #> proof_of;
   176 
   177 
   178 (***** proof atoms *****)
   179 
   180 fun fold_proof_atoms all f =
   181   let
   182     fun app (Abst (_, _, prf)) = app prf
   183       | app (AbsP (_, _, prf)) = app prf
   184       | app (prf % _) = app prf
   185       | app (prf1 %% prf2) = app prf1 #> app prf2
   186       | app (prf as PThm (i, (_, body))) = (fn (x, seen) =>
   187           if Inttab.defined seen i then (x, seen)
   188           else
   189             let val (x', seen') =
   190               (if all then app (join_proof body) else I) (x, Inttab.update (i, ()) seen)
   191             in (f prf x', seen') end)
   192       | app prf = (fn (x, seen) => (f prf x, seen));
   193   in fn prfs => fn x => #1 (fold app prfs (x, Inttab.empty)) end;
   194 
   195 fun fold_body_thms f =
   196   let
   197     fun app (PBody {thms, ...}) =
   198      (Future.join_results (map (#3 o #2) thms);
   199       thms |> fold (fn (i, (name, prop, body)) => fn (x, seen) =>
   200         if Inttab.defined seen i then (x, seen)
   201         else
   202           let
   203             val body' = Future.join body;
   204             val (x', seen') = app body' (x, Inttab.update (i, ()) seen);
   205           in (f (name, prop, body') x', seen') end));
   206   in fn bodies => fn x => #1 (fold app bodies (x, Inttab.empty)) end;
   207 
   208 fun join_bodies bodies = fold_body_thms (fn _ => fn () => ()) bodies ();
   209 
   210 fun status_of bodies =
   211   let
   212     fun status (PBody {oracles, thms, ...}) x =
   213       let
   214         val ((oracle, unfinished, failed), seen) =
   215           (thms, x) |-> fold (fn (i, (_, _, body)) => fn (st, seen) =>
   216             if Inttab.defined seen i then (st, seen)
   217             else
   218               let val seen' = Inttab.update (i, ()) seen in
   219                 (case Future.peek body of
   220                   SOME (Exn.Result body') => status body' (st, seen')
   221                 | SOME (Exn.Exn _) =>
   222                     let val (oracle, unfinished, _) = st
   223                     in ((oracle, unfinished, true), seen') end
   224                 | NONE =>
   225                     let val (oracle, _, failed) = st
   226                     in ((oracle, true, failed), seen') end)
   227               end);
   228       in ((oracle orelse not (null oracles), unfinished, failed), seen) end;
   229     val (oracle, unfinished, failed) =
   230       #1 (fold status bodies ((false, false, false), Inttab.empty));
   231   in {oracle = oracle, unfinished = unfinished, failed = failed} end;
   232 
   233 
   234 (* proof body *)
   235 
   236 val oracle_ord = prod_ord fast_string_ord Term_Ord.fast_term_ord;
   237 fun thm_ord ((i, _): pthm, (j, _)) = int_ord (j, i);
   238 
   239 val merge_oracles = Ord_List.union oracle_ord;
   240 val merge_thms = Ord_List.union thm_ord;
   241 
   242 val all_oracles_of =
   243   let
   244     fun collect (PBody {oracles, thms, ...}) =
   245      (Future.join_results (map (#3 o #2) thms);
   246       thms |> fold (fn (i, (_, _, body)) => fn (x, seen) =>
   247         if Inttab.defined seen i then (x, seen)
   248         else
   249           let
   250             val body' = Future.join body;
   251             val (x', seen') = collect body' (x, Inttab.update (i, ()) seen);
   252           in (merge_oracles oracles x', seen') end));
   253   in fn body => #1 (collect body ([], Inttab.empty)) end;
   254 
   255 fun approximate_proof_body prf =
   256   let
   257     val (oracles, thms) = fold_proof_atoms false
   258       (fn Oracle (s, prop, _) => apfst (cons (s, prop))
   259         | PThm (i, ((name, prop, _), body)) => apsnd (cons (i, (name, prop, body)))
   260         | _ => I) [prf] ([], []);
   261   in
   262     PBody
   263      {oracles = Ord_List.make oracle_ord oracles,
   264       thms = Ord_List.make thm_ord thms,
   265       proof = prf}
   266   end;
   267 
   268 
   269 (***** proof objects with different levels of detail *****)
   270 
   271 fun (prf %> t) = prf % SOME t;
   272 
   273 val proof_combt = Library.foldl (op %>);
   274 val proof_combt' = Library.foldl (op %);
   275 val proof_combP = Library.foldl (op %%);
   276 
   277 fun strip_combt prf =
   278     let fun stripc (prf % t, ts) = stripc (prf, t::ts)
   279           | stripc  x =  x
   280     in  stripc (prf, [])  end;
   281 
   282 fun strip_combP prf =
   283     let fun stripc (prf %% prf', prfs) = stripc (prf, prf'::prfs)
   284           | stripc  x =  x
   285     in  stripc (prf, [])  end;
   286 
   287 fun strip_thm (body as PBody {proof, ...}) =
   288   (case strip_combt (fst (strip_combP proof)) of
   289     (PThm (_, (_, body')), _) => Future.join body'
   290   | _ => body);
   291 
   292 val mk_Abst = fold_rev (fn (s, T:typ) => fn prf => Abst (s, NONE, prf));
   293 fun mk_AbsP (i, prf) = funpow i (fn prf => AbsP ("H", NONE, prf)) prf;
   294 
   295 fun map_proof_same term typ ofclass =
   296   let
   297     val typs = Same.map typ;
   298 
   299     fun proof (Abst (s, T, prf)) =
   300           (Abst (s, Same.map_option typ T, Same.commit proof prf)
   301             handle Same.SAME => Abst (s, T, proof prf))
   302       | proof (AbsP (s, t, prf)) =
   303           (AbsP (s, Same.map_option term t, Same.commit proof prf)
   304             handle Same.SAME => AbsP (s, t, proof prf))
   305       | proof (prf % t) =
   306           (proof prf % Same.commit (Same.map_option term) t
   307             handle Same.SAME => prf % Same.map_option term t)
   308       | proof (prf1 %% prf2) =
   309           (proof prf1 %% Same.commit proof prf2
   310             handle Same.SAME => prf1 %% proof prf2)
   311       | proof (PAxm (a, prop, SOME Ts)) = PAxm (a, prop, SOME (typs Ts))
   312       | proof (OfClass T_c) = ofclass T_c
   313       | proof (Oracle (a, prop, SOME Ts)) = Oracle (a, prop, SOME (typs Ts))
   314       | proof (Promise (i, prop, Ts)) = Promise (i, prop, typs Ts)
   315       | proof (PThm (i, ((a, prop, SOME Ts), body))) =
   316           PThm (i, ((a, prop, SOME (typs Ts)), body))
   317       | proof _ = raise Same.SAME;
   318   in proof end;
   319 
   320 fun map_proof_terms_same term typ = map_proof_same term typ (fn (T, c) => OfClass (typ T, c));
   321 fun map_proof_types_same typ = map_proof_terms_same (Term_Subst.map_types_same typ) typ;
   322 
   323 fun same eq f x =
   324   let val x' = f x
   325   in if eq (x, x') then raise Same.SAME else x' end;
   326 
   327 fun map_proof_terms f g = Same.commit (map_proof_terms_same (same (op =) f) (same (op =) g));
   328 fun map_proof_types f = Same.commit (map_proof_types_same (same (op =) f));
   329 
   330 fun fold_proof_terms f g (Abst (_, SOME T, prf)) = g T #> fold_proof_terms f g prf
   331   | fold_proof_terms f g (Abst (_, NONE, prf)) = fold_proof_terms f g prf
   332   | fold_proof_terms f g (AbsP (_, SOME t, prf)) = f t #> fold_proof_terms f g prf
   333   | fold_proof_terms f g (AbsP (_, NONE, prf)) = fold_proof_terms f g prf
   334   | fold_proof_terms f g (prf % SOME t) = fold_proof_terms f g prf #> f t
   335   | fold_proof_terms f g (prf % NONE) = fold_proof_terms f g prf
   336   | fold_proof_terms f g (prf1 %% prf2) =
   337       fold_proof_terms f g prf1 #> fold_proof_terms f g prf2
   338   | fold_proof_terms _ g (PAxm (_, _, SOME Ts)) = fold g Ts
   339   | fold_proof_terms _ g (OfClass (T, _)) = g T
   340   | fold_proof_terms _ g (Oracle (_, _, SOME Ts)) = fold g Ts
   341   | fold_proof_terms _ g (Promise (_, _, Ts)) = fold g Ts
   342   | fold_proof_terms _ g (PThm (_, ((_, _, SOME Ts), _))) = fold g Ts
   343   | fold_proof_terms _ _ _ = I;
   344 
   345 fun maxidx_proof prf = fold_proof_terms Term.maxidx_term Term.maxidx_typ prf;
   346 
   347 fun size_of_proof (Abst (_, _, prf)) = 1 + size_of_proof prf
   348   | size_of_proof (AbsP (_, t, prf)) = 1 + size_of_proof prf
   349   | size_of_proof (prf % _) = 1 + size_of_proof prf
   350   | size_of_proof (prf1 %% prf2) = size_of_proof prf1 + size_of_proof prf2
   351   | size_of_proof _ = 1;
   352 
   353 fun change_type opTs (PAxm (name, prop, _)) = PAxm (name, prop, opTs)
   354   | change_type (SOME [T]) (OfClass (_, c)) = OfClass (T, c)
   355   | change_type opTs (Oracle (name, prop, _)) = Oracle (name, prop, opTs)
   356   | change_type opTs (Promise _) = raise Fail "change_type: unexpected promise"
   357   | change_type opTs (PThm (i, ((name, prop, _), body))) =
   358       PThm (i, ((name, prop, opTs), body))
   359   | change_type _ prf = prf;
   360 
   361 
   362 (***** utilities *****)
   363 
   364 fun strip_abs (_::Ts) (Abs (_, _, t)) = strip_abs Ts t
   365   | strip_abs _ t = t;
   366 
   367 fun mk_abs Ts t = Library.foldl (fn (t', T) => Abs ("", T, t')) (t, Ts);
   368 
   369 
   370 (*Abstraction of a proof term over its occurrences of v,
   371     which must contain no loose bound variables.
   372   The resulting proof term is ready to become the body of an Abst.*)
   373 
   374 fun prf_abstract_over v =
   375   let
   376     fun abst' lev u = if v aconv u then Bound lev else
   377       (case u of
   378          Abs (a, T, t) => Abs (a, T, abst' (lev + 1) t)
   379        | f $ t => (abst' lev f $ absth' lev t handle Same.SAME => f $ abst' lev t)
   380        | _ => raise Same.SAME)
   381     and absth' lev t = (abst' lev t handle Same.SAME => t);
   382 
   383     fun abst lev (AbsP (a, t, prf)) =
   384           (AbsP (a, Same.map_option (abst' lev) t, absth lev prf)
   385            handle Same.SAME => AbsP (a, t, abst lev prf))
   386       | abst lev (Abst (a, T, prf)) = Abst (a, T, abst (lev + 1) prf)
   387       | abst lev (prf1 %% prf2) = (abst lev prf1 %% absth lev prf2
   388           handle Same.SAME => prf1 %% abst lev prf2)
   389       | abst lev (prf % t) = (abst lev prf % Option.map (absth' lev) t
   390           handle Same.SAME => prf % Same.map_option (abst' lev) t)
   391       | abst _ _ = raise Same.SAME
   392     and absth lev prf = (abst lev prf handle Same.SAME => prf);
   393 
   394   in absth 0 end;
   395 
   396 
   397 (*increments a proof term's non-local bound variables
   398   required when moving a proof term within abstractions
   399      inc is  increment for bound variables
   400      lev is  level at which a bound variable is considered 'loose'*)
   401 
   402 fun incr_bv' inct tlev t = incr_bv (inct, tlev, t);
   403 
   404 fun prf_incr_bv' incP inct Plev tlev (PBound i) =
   405       if i >= Plev then PBound (i+incP) else raise Same.SAME
   406   | prf_incr_bv' incP inct Plev tlev (AbsP (a, t, body)) =
   407       (AbsP (a, Same.map_option (same (op =) (incr_bv' inct tlev)) t,
   408          prf_incr_bv incP inct (Plev+1) tlev body) handle Same.SAME =>
   409            AbsP (a, t, prf_incr_bv' incP inct (Plev+1) tlev body))
   410   | prf_incr_bv' incP inct Plev tlev (Abst (a, T, body)) =
   411       Abst (a, T, prf_incr_bv' incP inct Plev (tlev+1) body)
   412   | prf_incr_bv' incP inct Plev tlev (prf %% prf') =
   413       (prf_incr_bv' incP inct Plev tlev prf %% prf_incr_bv incP inct Plev tlev prf'
   414        handle Same.SAME => prf %% prf_incr_bv' incP inct Plev tlev prf')
   415   | prf_incr_bv' incP inct Plev tlev (prf % t) =
   416       (prf_incr_bv' incP inct Plev tlev prf % Option.map (incr_bv' inct tlev) t
   417        handle Same.SAME => prf % Same.map_option (same (op =) (incr_bv' inct tlev)) t)
   418   | prf_incr_bv' _ _ _ _ _ = raise Same.SAME
   419 and prf_incr_bv incP inct Plev tlev prf =
   420       (prf_incr_bv' incP inct Plev tlev prf handle Same.SAME => prf);
   421 
   422 fun incr_pboundvars  0 0 prf = prf
   423   | incr_pboundvars incP inct prf = prf_incr_bv incP inct 0 0 prf;
   424 
   425 
   426 fun prf_loose_bvar1 (prf1 %% prf2) k = prf_loose_bvar1 prf1 k orelse prf_loose_bvar1 prf2 k
   427   | prf_loose_bvar1 (prf % SOME t) k = prf_loose_bvar1 prf k orelse loose_bvar1 (t, k)
   428   | prf_loose_bvar1 (_ % NONE) _ = true
   429   | prf_loose_bvar1 (AbsP (_, SOME t, prf)) k = loose_bvar1 (t, k) orelse prf_loose_bvar1 prf k
   430   | prf_loose_bvar1 (AbsP (_, NONE, _)) k = true
   431   | prf_loose_bvar1 (Abst (_, _, prf)) k = prf_loose_bvar1 prf (k+1)
   432   | prf_loose_bvar1 _ _ = false;
   433 
   434 fun prf_loose_Pbvar1 (PBound i) k = i = k
   435   | prf_loose_Pbvar1 (prf1 %% prf2) k = prf_loose_Pbvar1 prf1 k orelse prf_loose_Pbvar1 prf2 k
   436   | prf_loose_Pbvar1 (prf % _) k = prf_loose_Pbvar1 prf k
   437   | prf_loose_Pbvar1 (AbsP (_, _, prf)) k = prf_loose_Pbvar1 prf (k+1)
   438   | prf_loose_Pbvar1 (Abst (_, _, prf)) k = prf_loose_Pbvar1 prf k
   439   | prf_loose_Pbvar1 _ _ = false;
   440 
   441 fun prf_add_loose_bnos plev tlev (PBound i) (is, js) =
   442       if i < plev then (is, js) else (insert (op =) (i-plev) is, js)
   443   | prf_add_loose_bnos plev tlev (prf1 %% prf2) p =
   444       prf_add_loose_bnos plev tlev prf2
   445         (prf_add_loose_bnos plev tlev prf1 p)
   446   | prf_add_loose_bnos plev tlev (prf % opt) (is, js) =
   447       prf_add_loose_bnos plev tlev prf (case opt of
   448           NONE => (is, insert (op =) ~1 js)
   449         | SOME t => (is, add_loose_bnos (t, tlev, js)))
   450   | prf_add_loose_bnos plev tlev (AbsP (_, opt, prf)) (is, js) =
   451       prf_add_loose_bnos (plev+1) tlev prf (case opt of
   452           NONE => (is, insert (op =) ~1 js)
   453         | SOME t => (is, add_loose_bnos (t, tlev, js)))
   454   | prf_add_loose_bnos plev tlev (Abst (_, _, prf)) p =
   455       prf_add_loose_bnos plev (tlev+1) prf p
   456   | prf_add_loose_bnos _ _ _ _ = ([], []);
   457 
   458 
   459 (**** substitutions ****)
   460 
   461 fun del_conflicting_tvars envT T = Term_Subst.instantiateT
   462   (map_filter (fn ixnS as (_, S) =>
   463      (Type.lookup envT ixnS; NONE) handle TYPE _ =>
   464         SOME (ixnS, TFree ("'dummy", S))) (OldTerm.typ_tvars T)) T;
   465 
   466 fun del_conflicting_vars env t = Term_Subst.instantiate
   467   (map_filter (fn ixnS as (_, S) =>
   468      (Type.lookup (Envir.type_env env) ixnS; NONE) handle TYPE _ =>
   469         SOME (ixnS, TFree ("'dummy", S))) (OldTerm.term_tvars t),
   470    map_filter (fn Var (ixnT as (_, T)) =>
   471      (Envir.lookup (env, ixnT); NONE) handle TYPE _ =>
   472         SOME (ixnT, Free ("dummy", T))) (OldTerm.term_vars t)) t;
   473 
   474 fun norm_proof env =
   475   let
   476     val envT = Envir.type_env env;
   477     fun msg s = warning ("type conflict in norm_proof:\n" ^ s);
   478     fun htype f t = f env t handle TYPE (s, _, _) =>
   479       (msg s; f env (del_conflicting_vars env t));
   480     fun htypeT f T = f envT T handle TYPE (s, _, _) =>
   481       (msg s; f envT (del_conflicting_tvars envT T));
   482     fun htypeTs f Ts = f envT Ts handle TYPE (s, _, _) =>
   483       (msg s; f envT (map (del_conflicting_tvars envT) Ts));
   484 
   485     fun norm (Abst (s, T, prf)) =
   486           (Abst (s, Same.map_option (htypeT Envir.norm_type_same) T, Same.commit norm prf)
   487             handle Same.SAME => Abst (s, T, norm prf))
   488       | norm (AbsP (s, t, prf)) =
   489           (AbsP (s, Same.map_option (htype Envir.norm_term_same) t, Same.commit norm prf)
   490             handle Same.SAME => AbsP (s, t, norm prf))
   491       | norm (prf % t) =
   492           (norm prf % Option.map (htype Envir.norm_term) t
   493             handle Same.SAME => prf % Same.map_option (htype Envir.norm_term_same) t)
   494       | norm (prf1 %% prf2) =
   495           (norm prf1 %% Same.commit norm prf2
   496             handle Same.SAME => prf1 %% norm prf2)
   497       | norm (PAxm (s, prop, Ts)) =
   498           PAxm (s, prop, Same.map_option (htypeTs Envir.norm_types_same) Ts)
   499       | norm (OfClass (T, c)) =
   500           OfClass (htypeT Envir.norm_type_same T, c)
   501       | norm (Oracle (s, prop, Ts)) =
   502           Oracle (s, prop, Same.map_option (htypeTs Envir.norm_types_same) Ts)
   503       | norm (Promise (i, prop, Ts)) =
   504           Promise (i, prop, htypeTs Envir.norm_types_same Ts)
   505       | norm (PThm (i, ((s, t, Ts), body))) =
   506           PThm (i, ((s, t, Same.map_option (htypeTs Envir.norm_types_same) Ts), body))
   507       | norm _ = raise Same.SAME;
   508   in Same.commit norm end;
   509 
   510 
   511 (***** Remove some types in proof term (to save space) *****)
   512 
   513 fun remove_types (Abs (s, _, t)) = Abs (s, dummyT, remove_types t)
   514   | remove_types (t $ u) = remove_types t $ remove_types u
   515   | remove_types (Const (s, _)) = Const (s, dummyT)
   516   | remove_types t = t;
   517 
   518 fun remove_types_env (Envir.Envir {maxidx, tenv, tyenv}) =
   519   Envir.Envir {maxidx = maxidx, tenv = Vartab.map (K (apsnd remove_types)) tenv, tyenv = tyenv};
   520 
   521 fun norm_proof' env prf = norm_proof (remove_types_env env) prf;
   522 
   523 
   524 (**** substitution of bound variables ****)
   525 
   526 fun prf_subst_bounds args prf =
   527   let
   528     val n = length args;
   529     fun subst' lev (Bound i) =
   530          (if i<lev then raise Same.SAME    (*var is locally bound*)
   531           else  incr_boundvars lev (nth args (i-lev))
   532                   handle General.Subscript => Bound (i-n))  (*loose: change it*)
   533       | subst' lev (Abs (a, T, body)) = Abs (a, T,  subst' (lev+1) body)
   534       | subst' lev (f $ t) = (subst' lev f $ substh' lev t
   535           handle Same.SAME => f $ subst' lev t)
   536       | subst' _ _ = raise Same.SAME
   537     and substh' lev t = (subst' lev t handle Same.SAME => t);
   538 
   539     fun subst lev (AbsP (a, t, body)) =
   540         (AbsP (a, Same.map_option (subst' lev) t, substh lev body)
   541           handle Same.SAME => AbsP (a, t, subst lev body))
   542       | subst lev (Abst (a, T, body)) = Abst (a, T, subst (lev+1) body)
   543       | subst lev (prf %% prf') = (subst lev prf %% substh lev prf'
   544           handle Same.SAME => prf %% subst lev prf')
   545       | subst lev (prf % t) = (subst lev prf % Option.map (substh' lev) t
   546           handle Same.SAME => prf % Same.map_option (subst' lev) t)
   547       | subst _ _ = raise Same.SAME
   548     and substh lev prf = (subst lev prf handle Same.SAME => prf);
   549   in case args of [] => prf | _ => substh 0 prf end;
   550 
   551 fun prf_subst_pbounds args prf =
   552   let
   553     val n = length args;
   554     fun subst (PBound i) Plev tlev =
   555          (if i < Plev then raise Same.SAME    (*var is locally bound*)
   556           else incr_pboundvars Plev tlev (nth args (i-Plev))
   557                  handle General.Subscript => PBound (i-n)  (*loose: change it*))
   558       | subst (AbsP (a, t, body)) Plev tlev = AbsP (a, t, subst body (Plev+1) tlev)
   559       | subst (Abst (a, T, body)) Plev tlev = Abst (a, T, subst body Plev (tlev+1))
   560       | subst (prf %% prf') Plev tlev = (subst prf Plev tlev %% substh prf' Plev tlev
   561           handle Same.SAME => prf %% subst prf' Plev tlev)
   562       | subst (prf % t) Plev tlev = subst prf Plev tlev % t
   563       | subst  prf _ _ = raise Same.SAME
   564     and substh prf Plev tlev = (subst prf Plev tlev handle Same.SAME => prf)
   565   in case args of [] => prf | _ => substh prf 0 0 end;
   566 
   567 
   568 (**** Freezing and thawing of variables in proof terms ****)
   569 
   570 fun frzT names =
   571   map_type_tvar (fn (ixn, xs) => TFree ((the o AList.lookup (op =) names) ixn, xs));
   572 
   573 fun thawT names =
   574   map_type_tfree (fn (s, xs) => case AList.lookup (op =) names s of
   575       NONE => TFree (s, xs)
   576     | SOME ixn => TVar (ixn, xs));
   577 
   578 fun freeze names names' (t $ u) =
   579       freeze names names' t $ freeze names names' u
   580   | freeze names names' (Abs (s, T, t)) =
   581       Abs (s, frzT names' T, freeze names names' t)
   582   | freeze names names' (Const (s, T)) = Const (s, frzT names' T)
   583   | freeze names names' (Free (s, T)) = Free (s, frzT names' T)
   584   | freeze names names' (Var (ixn, T)) =
   585       Free ((the o AList.lookup (op =) names) ixn, frzT names' T)
   586   | freeze names names' t = t;
   587 
   588 fun thaw names names' (t $ u) =
   589       thaw names names' t $ thaw names names' u
   590   | thaw names names' (Abs (s, T, t)) =
   591       Abs (s, thawT names' T, thaw names names' t)
   592   | thaw names names' (Const (s, T)) = Const (s, thawT names' T)
   593   | thaw names names' (Free (s, T)) =
   594       let val T' = thawT names' T
   595       in case AList.lookup (op =) names s of
   596           NONE => Free (s, T')
   597         | SOME ixn => Var (ixn, T')
   598       end
   599   | thaw names names' (Var (ixn, T)) = Var (ixn, thawT names' T)
   600   | thaw names names' t = t;
   601 
   602 fun freeze_thaw_prf prf =
   603   let
   604     val (fs, Tfs, vs, Tvs) = fold_proof_terms
   605       (fn t => fn (fs, Tfs, vs, Tvs) =>
   606          (Term.add_free_names t fs, Term.add_tfree_names t Tfs,
   607           Term.add_var_names t vs, Term.add_tvar_names t Tvs))
   608       (fn T => fn (fs, Tfs, vs, Tvs) =>
   609          (fs, Term.add_tfree_namesT T Tfs,
   610           vs, Term.add_tvar_namesT T Tvs))
   611       prf ([], [], [], []);
   612     val names = vs ~~ Name.variant_list fs (map fst vs);
   613     val names' = Tvs ~~ Name.variant_list Tfs (map fst Tvs);
   614     val rnames = map swap names;
   615     val rnames' = map swap names';
   616   in
   617     (map_proof_terms (freeze names names') (frzT names') prf,
   618      map_proof_terms (thaw rnames rnames') (thawT rnames'))
   619   end;
   620 
   621 
   622 (***** implication introduction *****)
   623 
   624 fun gen_implies_intr_proof f h prf =
   625   let
   626     fun abshyp i (Hyp t) = if h aconv t then PBound i else raise Same.SAME
   627       | abshyp i (Abst (s, T, prf)) = Abst (s, T, abshyp i prf)
   628       | abshyp i (AbsP (s, t, prf)) = AbsP (s, t, abshyp (i + 1) prf)
   629       | abshyp i (prf % t) = abshyp i prf % t
   630       | abshyp i (prf1 %% prf2) =
   631           (abshyp i prf1 %% abshyph i prf2
   632             handle Same.SAME => prf1 %% abshyp i prf2)
   633       | abshyp _ _ = raise Same.SAME
   634     and abshyph i prf = (abshyp i prf handle Same.SAME => prf);
   635   in
   636     AbsP ("H", f h, abshyph 0 prf)
   637   end;
   638 
   639 val implies_intr_proof = gen_implies_intr_proof (K NONE);
   640 val implies_intr_proof' = gen_implies_intr_proof SOME;
   641 
   642 
   643 (***** forall introduction *****)
   644 
   645 fun forall_intr_proof x a prf = Abst (a, NONE, prf_abstract_over x prf);
   646 
   647 fun forall_intr_proof' t prf =
   648   let val (a, T) = (case t of Var ((a, _), T) => (a, T) | Free p => p)
   649   in Abst (a, SOME T, prf_abstract_over t prf) end;
   650 
   651 
   652 (***** varify *****)
   653 
   654 fun varify_proof t fixed prf =
   655   let
   656     val fs = Term.fold_types (Term.fold_atyps
   657       (fn TFree v => if member (op =) fixed v then I else insert (op =) v | _ => I)) t [];
   658     val used = Name.context
   659       |> fold_types (fold_atyps (fn TVar ((a, _), _) => Name.declare a | _ => I)) t;
   660     val fmap = fs ~~ #1 (Name.variants (map fst fs) used);
   661     fun thaw (f as (a, S)) =
   662       (case AList.lookup (op =) fmap f of
   663         NONE => TFree f
   664       | SOME b => TVar ((b, 0), S));
   665   in map_proof_terms (map_types (map_type_tfree thaw)) (map_type_tfree thaw) prf end;
   666 
   667 
   668 local
   669 
   670 fun new_name (ix, (pairs,used)) =
   671   let val v = singleton (Name.variant_list used) (string_of_indexname ix)
   672   in  ((ix, v) :: pairs, v :: used)  end;
   673 
   674 fun freeze_one alist (ix, sort) = (case AList.lookup (op =) alist ix of
   675     NONE => TVar (ix, sort)
   676   | SOME name => TFree (name, sort));
   677 
   678 in
   679 
   680 fun legacy_freezeT t prf =
   681   let
   682     val used = OldTerm.it_term_types OldTerm.add_typ_tfree_names (t, [])
   683     and tvars = map #1 (OldTerm.it_term_types OldTerm.add_typ_tvars (t, []));
   684     val (alist, _) = List.foldr new_name ([], used) tvars;
   685   in
   686     (case alist of
   687       [] => prf (*nothing to do!*)
   688     | _ =>
   689       let val frzT = map_type_tvar (freeze_one alist)
   690       in map_proof_terms (map_types frzT) frzT prf end)
   691   end;
   692 
   693 end;
   694 
   695 
   696 (***** rotate assumptions *****)
   697 
   698 fun rotate_proof Bs Bi m prf =
   699   let
   700     val params = Term.strip_all_vars Bi;
   701     val asms = Logic.strip_imp_prems (Term.strip_all_body Bi);
   702     val i = length asms;
   703     val j = length Bs;
   704   in
   705     mk_AbsP (j+1, proof_combP (prf, map PBound
   706       (j downto 1) @ [mk_Abst params (mk_AbsP (i,
   707         proof_combP (proof_combt (PBound i, map Bound ((length params - 1) downto 0)),
   708           map PBound (((i-m-1) downto 0) @ ((i-1) downto (i-m))))))]))
   709   end;
   710 
   711 
   712 (***** permute premises *****)
   713 
   714 fun permute_prems_proof prems j k prf =
   715   let val n = length prems
   716   in mk_AbsP (n, proof_combP (prf,
   717     map PBound ((n-1 downto n-j) @ (k-1 downto 0) @ (n-j-1 downto k))))
   718   end;
   719 
   720 
   721 (***** generalization *****)
   722 
   723 fun generalize (tfrees, frees) idx =
   724   Same.commit (map_proof_terms_same
   725     (Term_Subst.generalize_same (tfrees, frees) idx)
   726     (Term_Subst.generalizeT_same tfrees idx));
   727 
   728 
   729 (***** instantiation *****)
   730 
   731 fun instantiate (instT, inst) =
   732   Same.commit (map_proof_terms_same
   733     (Term_Subst.instantiate_same (instT, map (apsnd remove_types) inst))
   734     (Term_Subst.instantiateT_same instT));
   735 
   736 
   737 (***** lifting *****)
   738 
   739 fun lift_proof Bi inc prop prf =
   740   let
   741     fun lift'' Us Ts t =
   742       strip_abs Ts (Logic.incr_indexes (Us, inc) (mk_abs Ts t));
   743 
   744     fun lift' Us Ts (Abst (s, T, prf)) =
   745           (Abst (s, Same.map_option (Logic.incr_tvar_same inc) T, lifth' Us (dummyT::Ts) prf)
   746            handle Same.SAME => Abst (s, T, lift' Us (dummyT::Ts) prf))
   747       | lift' Us Ts (AbsP (s, t, prf)) =
   748           (AbsP (s, Same.map_option (same (op =) (lift'' Us Ts)) t, lifth' Us Ts prf)
   749            handle Same.SAME => AbsP (s, t, lift' Us Ts prf))
   750       | lift' Us Ts (prf % t) = (lift' Us Ts prf % Option.map (lift'' Us Ts) t
   751           handle Same.SAME => prf % Same.map_option (same (op =) (lift'' Us Ts)) t)
   752       | lift' Us Ts (prf1 %% prf2) = (lift' Us Ts prf1 %% lifth' Us Ts prf2
   753           handle Same.SAME => prf1 %% lift' Us Ts prf2)
   754       | lift' _ _ (PAxm (s, prop, Ts)) =
   755           PAxm (s, prop, (Same.map_option o Same.map) (Logic.incr_tvar_same inc) Ts)
   756       | lift' _ _ (OfClass (T, c)) =
   757           OfClass (Logic.incr_tvar_same inc T, c)
   758       | lift' _ _ (Oracle (s, prop, Ts)) =
   759           Oracle (s, prop, (Same.map_option o Same.map) (Logic.incr_tvar_same inc) Ts)
   760       | lift' _ _ (Promise (i, prop, Ts)) =
   761           Promise (i, prop, Same.map (Logic.incr_tvar_same inc) Ts)
   762       | lift' _ _ (PThm (i, ((s, prop, Ts), body))) =
   763           PThm (i, ((s, prop, (Same.map_option o Same.map) (Logic.incr_tvar inc) Ts), body))
   764       | lift' _ _ _ = raise Same.SAME
   765     and lifth' Us Ts prf = (lift' Us Ts prf handle Same.SAME => prf);
   766 
   767     val ps = map (Logic.lift_all inc Bi) (Logic.strip_imp_prems prop);
   768     val k = length ps;
   769 
   770     fun mk_app b (i, j, prf) =
   771           if b then (i-1, j, prf %% PBound i) else (i, j-1, prf %> Bound j);
   772 
   773     fun lift Us bs i j (Const ("==>", _) $ A $ B) =
   774             AbsP ("H", NONE (*A*), lift Us (true::bs) (i+1) j B)
   775       | lift Us bs i j (Const ("all", _) $ Abs (a, T, t)) =
   776             Abst (a, NONE (*T*), lift (T::Us) (false::bs) i (j+1) t)
   777       | lift Us bs i j _ = proof_combP (lifth' (rev Us) [] prf,
   778             map (fn k => (#3 (fold_rev mk_app bs (i-1, j-1, PBound k))))
   779               (i + k - 1 downto i));
   780   in
   781     mk_AbsP (k, lift [] [] 0 0 Bi)
   782   end;
   783 
   784 fun incr_indexes i =
   785   Same.commit (map_proof_terms_same
   786     (Logic.incr_indexes_same ([], i)) (Logic.incr_tvar_same i));
   787 
   788 
   789 (***** proof by assumption *****)
   790 
   791 fun mk_asm_prf t i m =
   792   let
   793     fun imp_prf _ i 0 = PBound i
   794       | imp_prf (Const ("==>", _) $ A $ B) i m = AbsP ("H", NONE (*A*), imp_prf B (i+1) (m-1))
   795       | imp_prf _ i _ = PBound i;
   796     fun all_prf (Const ("all", _) $ Abs (a, T, t)) = Abst (a, NONE (*T*), all_prf t)
   797       | all_prf t = imp_prf t (~i) m
   798   in all_prf t end;
   799 
   800 fun assumption_proof Bs Bi n prf =
   801   mk_AbsP (length Bs, proof_combP (prf,
   802     map PBound (length Bs - 1 downto 0) @ [mk_asm_prf Bi n ~1]));
   803 
   804 
   805 (***** Composition of object rule with proof state *****)
   806 
   807 fun flatten_params_proof i j n (Const ("==>", _) $ A $ B, k) =
   808       AbsP ("H", NONE (*A*), flatten_params_proof (i+1) j n (B, k))
   809   | flatten_params_proof i j n (Const ("all", _) $ Abs (a, T, t), k) =
   810       Abst (a, NONE (*T*), flatten_params_proof i (j+1) n (t, k))
   811   | flatten_params_proof i j n (_, k) = proof_combP (proof_combt (PBound (k+i),
   812       map Bound (j-1 downto 0)), map PBound (remove (op =) (i-n) (i-1 downto 0)));
   813 
   814 fun bicompose_proof flatten Bs oldAs newAs A n m rprf sprf =
   815   let
   816     val la = length newAs;
   817     val lb = length Bs;
   818   in
   819     mk_AbsP (lb+la, proof_combP (sprf,
   820       map PBound (lb + la - 1 downto la)) %%
   821         proof_combP (rprf, (if n>0 then [mk_asm_prf (the A) n m] else []) @
   822           map (if flatten then flatten_params_proof 0 0 n else PBound o snd)
   823             (oldAs ~~ (la - 1 downto 0))))
   824   end;
   825 
   826 
   827 (***** axioms for equality *****)
   828 
   829 val aT = TFree ("'a", []);
   830 val bT = TFree ("'b", []);
   831 val x = Free ("x", aT);
   832 val y = Free ("y", aT);
   833 val z = Free ("z", aT);
   834 val A = Free ("A", propT);
   835 val B = Free ("B", propT);
   836 val f = Free ("f", aT --> bT);
   837 val g = Free ("g", aT --> bT);
   838 
   839 val equality_axms =
   840  [("reflexive", Logic.mk_equals (x, x)),
   841   ("symmetric", Logic.mk_implies (Logic.mk_equals (x, y), Logic.mk_equals (y, x))),
   842   ("transitive",
   843     Logic.list_implies ([Logic.mk_equals (x, y), Logic.mk_equals (y, z)], Logic.mk_equals (x, z))),
   844   ("equal_intr",
   845     Logic.list_implies ([Logic.mk_implies (A, B), Logic.mk_implies (B, A)], Logic.mk_equals (A, B))),
   846   ("equal_elim", Logic.list_implies ([Logic.mk_equals (A, B), A], B)),
   847   ("abstract_rule",
   848     Logic.mk_implies
   849       (Logic.all x
   850         (Logic.mk_equals (f $ x, g $ x)), Logic.mk_equals (lambda x (f $ x), lambda x (g $ x)))),
   851   ("combination", Logic.list_implies
   852     ([Logic.mk_equals (f, g), Logic.mk_equals (x, y)], Logic.mk_equals (f $ x, g $ y)))];
   853 
   854 val [reflexive_axm, symmetric_axm, transitive_axm, equal_intr_axm,
   855   equal_elim_axm, abstract_rule_axm, combination_axm] =
   856     map (fn (s, t) => PAxm ("Pure." ^ s, Logic.varify_global t, NONE)) equality_axms;
   857 
   858 val reflexive = reflexive_axm % NONE;
   859 
   860 fun symmetric (prf as PAxm ("Pure.reflexive", _, _) % _) = prf
   861   | symmetric prf = symmetric_axm % NONE % NONE %% prf;
   862 
   863 fun transitive _ _ (PAxm ("Pure.reflexive", _, _) % _) prf2 = prf2
   864   | transitive _ _ prf1 (PAxm ("Pure.reflexive", _, _) % _) = prf1
   865   | transitive u (Type ("prop", [])) prf1 prf2 =
   866       transitive_axm % NONE % SOME (remove_types u) % NONE %% prf1 %% prf2
   867   | transitive u T prf1 prf2 =
   868       transitive_axm % NONE % NONE % NONE %% prf1 %% prf2;
   869 
   870 fun abstract_rule x a prf =
   871   abstract_rule_axm % NONE % NONE %% forall_intr_proof x a prf;
   872 
   873 fun check_comb (PAxm ("Pure.combination", _, _) % f % g % _ % _ %% prf %% _) =
   874       is_some f orelse check_comb prf
   875   | check_comb (PAxm ("Pure.transitive", _, _) % _ % _ % _ %% prf1 %% prf2) =
   876       check_comb prf1 andalso check_comb prf2
   877   | check_comb (PAxm ("Pure.symmetric", _, _) % _ % _ %% prf) = check_comb prf
   878   | check_comb _ = false;
   879 
   880 fun combination f g t u (Type (_, [T, U])) prf1 prf2 =
   881   let
   882     val f = Envir.beta_norm f;
   883     val g = Envir.beta_norm g;
   884     val prf =  if check_comb prf1 then
   885         combination_axm % NONE % NONE
   886       else (case prf1 of
   887           PAxm ("Pure.reflexive", _, _) % _ =>
   888             combination_axm %> remove_types f % NONE
   889         | _ => combination_axm %> remove_types f %> remove_types g)
   890   in
   891     (case T of
   892        Type ("fun", _) => prf %
   893          (case head_of f of
   894             Abs _ => SOME (remove_types t)
   895           | Var _ => SOME (remove_types t)
   896           | _ => NONE) %
   897          (case head_of g of
   898             Abs _ => SOME (remove_types u)
   899           | Var _ => SOME (remove_types u)
   900           | _ => NONE) %% prf1 %% prf2
   901      | _ => prf % NONE % NONE %% prf1 %% prf2)
   902   end;
   903 
   904 fun equal_intr A B prf1 prf2 =
   905   equal_intr_axm %> remove_types A %> remove_types B %% prf1 %% prf2;
   906 
   907 fun equal_elim A B prf1 prf2 =
   908   equal_elim_axm %> remove_types A %> remove_types B %% prf1 %% prf2;
   909 
   910 
   911 (**** type classes ****)
   912 
   913 fun strip_shyps_proof algebra present witnessed extra_sorts prf =
   914   let
   915     fun get S2 (T, S1) = if Sorts.sort_le algebra (S1, S2) then SOME T else NONE;
   916     val extra = map (fn S => (TFree ("'dummy", S), S)) extra_sorts;
   917     val replacements = present @ extra @ witnessed;
   918     fun replace T =
   919       if exists (fn (T', _) => T' = T) present then raise Same.SAME
   920       else
   921         (case get_first (get (Type.sort_of_atyp T)) replacements of
   922           SOME T' => T'
   923         | NONE => raise Fail "strip_shyps_proof: bad type variable in proof term");
   924   in Same.commit (map_proof_types_same (Term_Subst.map_atypsT_same replace)) prf end;
   925 
   926 
   927 local
   928 
   929 type axclass_proofs =
   930  {classrel_proof: theory -> class * class -> proof,
   931   arity_proof: theory -> string * sort list * class -> proof};
   932 
   933 val axclass_proofs: axclass_proofs Single_Assignment.var =
   934   Single_Assignment.var "Proofterm.axclass_proofs";
   935 
   936 fun axclass_proof which thy x =
   937   (case Single_Assignment.peek axclass_proofs of
   938     NONE => raise Fail "Axclass proof operations not installed"
   939   | SOME prfs => which prfs thy x);
   940 
   941 in
   942 
   943 val classrel_proof = axclass_proof #classrel_proof;
   944 val arity_proof = axclass_proof #arity_proof;
   945 
   946 fun install_axclass_proofs prfs = Single_Assignment.assign axclass_proofs prfs;
   947 
   948 end;
   949 
   950 
   951 local
   952 
   953 fun canonical_instance typs =
   954   let
   955     val names = Name.invents Name.context Name.aT (length typs);
   956     val instT = map2 (fn a => fn T => (((a, 0), []), Type.strip_sorts T)) names typs;
   957   in instantiate (instT, []) end;
   958 
   959 in
   960 
   961 fun of_sort_proof thy hyps =
   962   Sorts.of_sort_derivation (Sign.classes_of thy)
   963    {class_relation = fn typ => fn (prf, c1) => fn c2 =>
   964       if c1 = c2 then prf
   965       else canonical_instance [typ] (classrel_proof thy (c1, c2)) %% prf,
   966     type_constructor = fn (a, typs) => fn dom => fn c =>
   967       let val Ss = map (map snd) dom and prfs = maps (map fst) dom
   968       in proof_combP (canonical_instance typs (arity_proof thy (a, Ss, c)), prfs) end,
   969     type_variable = fn typ => map (fn c => (hyps (typ, c), c)) (Type.sort_of_atyp typ)};
   970 
   971 end;
   972 
   973 
   974 (***** axioms and theorems *****)
   975 
   976 val proofs = Unsynchronized.ref 2;
   977 fun proofs_enabled () = ! proofs >= 2;
   978 
   979 fun vars_of t = map Var (rev (Term.add_vars t []));
   980 fun frees_of t = map Free (rev (Term.add_frees t []));
   981 
   982 fun test_args _ [] = true
   983   | test_args is (Bound i :: ts) =
   984       not (member (op =) is i) andalso test_args (i :: is) ts
   985   | test_args _ _ = false;
   986 
   987 fun is_fun (Type ("fun", _)) = true
   988   | is_fun (TVar _) = true
   989   | is_fun _ = false;
   990 
   991 fun add_funvars Ts (vs, t) =
   992   if is_fun (fastype_of1 (Ts, t)) then
   993     union (op =) vs (map_filter (fn Var (ixn, T) =>
   994       if is_fun T then SOME ixn else NONE | _ => NONE) (vars_of t))
   995   else vs;
   996 
   997 fun add_npvars q p Ts (vs, Const ("==>", _) $ t $ u) =
   998       add_npvars q p Ts (add_npvars q (not p) Ts (vs, t), u)
   999   | add_npvars q p Ts (vs, Const ("all", Type (_, [Type (_, [T, _]), _])) $ t) =
  1000       add_npvars q p Ts (vs, if p andalso q then betapply (t, Var (("",0), T)) else t)
  1001   | add_npvars q p Ts (vs, Abs (_, T, t)) = add_npvars q p (T::Ts) (vs, t)
  1002   | add_npvars _ _ Ts (vs, t) = add_npvars' Ts (vs, t)
  1003 and add_npvars' Ts (vs, t) = (case strip_comb t of
  1004     (Var (ixn, _), ts) => if test_args [] ts then vs
  1005       else Library.foldl (add_npvars' Ts)
  1006         (AList.update (op =) (ixn,
  1007           Library.foldl (add_funvars Ts) ((these ooo AList.lookup) (op =) vs ixn, ts)) vs, ts)
  1008   | (Abs (_, T, u), ts) => Library.foldl (add_npvars' (T::Ts)) (vs, u :: ts)
  1009   | (_, ts) => Library.foldl (add_npvars' Ts) (vs, ts));
  1010 
  1011 fun prop_vars (Const ("==>", _) $ P $ Q) = union (op =) (prop_vars P) (prop_vars Q)
  1012   | prop_vars (Const ("all", _) $ Abs (_, _, t)) = prop_vars t
  1013   | prop_vars t = (case strip_comb t of
  1014       (Var (ixn, _), _) => [ixn] | _ => []);
  1015 
  1016 fun is_proj t =
  1017   let
  1018     fun is_p i t = (case strip_comb t of
  1019         (Bound j, []) => false
  1020       | (Bound j, ts) => j >= i orelse exists (is_p i) ts
  1021       | (Abs (_, _, u), _) => is_p (i+1) u
  1022       | (_, ts) => exists (is_p i) ts)
  1023   in (case strip_abs_body t of
  1024         Bound _ => true
  1025       | t' => is_p 0 t')
  1026   end;
  1027 
  1028 fun needed_vars prop =
  1029   union (op =) (Library.foldl (uncurry (union (op =)))
  1030     ([], map (uncurry (insert (op =))) (add_npvars true true [] ([], prop))))
  1031   (prop_vars prop);
  1032 
  1033 fun gen_axm_proof c name prop =
  1034   let
  1035     val nvs = needed_vars prop;
  1036     val args = map (fn (v as Var (ixn, _)) =>
  1037         if member (op =) nvs ixn then SOME v else NONE) (vars_of prop) @
  1038       map SOME (frees_of prop);
  1039   in
  1040     proof_combt' (c (name, prop, NONE), args)
  1041   end;
  1042 
  1043 val axm_proof = gen_axm_proof PAxm;
  1044 
  1045 val dummy = Const (Term.dummy_patternN, dummyT);
  1046 
  1047 fun oracle_proof name prop =
  1048   if ! proofs = 0 then ((name, dummy), Oracle (name, dummy, NONE))
  1049   else ((name, prop), gen_axm_proof Oracle name prop);
  1050 
  1051 val shrink_proof =
  1052   let
  1053     fun shrink ls lev (prf as Abst (a, T, body)) =
  1054           let val (b, is, ch, body') = shrink ls (lev+1) body
  1055           in (b, is, ch, if ch then Abst (a, T, body') else prf) end
  1056       | shrink ls lev (prf as AbsP (a, t, body)) =
  1057           let val (b, is, ch, body') = shrink (lev::ls) lev body
  1058           in (b orelse member (op =) is 0, map_filter (fn 0 => NONE | i => SOME (i-1)) is,
  1059             ch, if ch then AbsP (a, t, body') else prf)
  1060           end
  1061       | shrink ls lev prf =
  1062           let val (is, ch, _, prf') = shrink' ls lev [] [] prf
  1063           in (false, is, ch, prf') end
  1064     and shrink' ls lev ts prfs (prf as prf1 %% prf2) =
  1065           let
  1066             val p as (_, is', ch', prf') = shrink ls lev prf2;
  1067             val (is, ch, ts', prf'') = shrink' ls lev ts (p::prfs) prf1
  1068           in (union (op =) is is', ch orelse ch', ts',
  1069               if ch orelse ch' then prf'' %% prf' else prf)
  1070           end
  1071       | shrink' ls lev ts prfs (prf as prf1 % t) =
  1072           let val (is, ch, (ch', t')::ts', prf') = shrink' ls lev (t::ts) prfs prf1
  1073           in (is, ch orelse ch', ts',
  1074               if ch orelse ch' then prf' % t' else prf) end
  1075       | shrink' ls lev ts prfs (prf as PBound i) =
  1076           (if exists (fn SOME (Bound j) => lev-j <= nth ls i | _ => true) ts
  1077              orelse has_duplicates (op =)
  1078                (Library.foldl (fn (js, SOME (Bound j)) => j :: js | (js, _) => js) ([], ts))
  1079              orelse exists #1 prfs then [i] else [], false, map (pair false) ts, prf)
  1080       | shrink' ls lev ts prfs (prf as Hyp _) = ([], false, map (pair false) ts, prf)
  1081       | shrink' ls lev ts prfs (prf as MinProof) = ([], false, map (pair false) ts, prf)
  1082       | shrink' ls lev ts prfs (prf as OfClass _) = ([], false, map (pair false) ts, prf)
  1083       | shrink' ls lev ts prfs prf =
  1084           let
  1085             val prop =
  1086               (case prf of
  1087                 PAxm (_, prop, _) => prop
  1088               | Oracle (_, prop, _) => prop
  1089               | Promise (_, prop, _) => prop
  1090               | PThm (_, ((_, prop, _), _)) => prop
  1091               | _ => raise Fail "shrink: proof not in normal form");
  1092             val vs = vars_of prop;
  1093             val (ts', ts'') = chop (length vs) ts;
  1094             val insts = take (length ts') (map (fst o dest_Var) vs) ~~ ts';
  1095             val nvs = Library.foldl (fn (ixns', (ixn, ixns)) =>
  1096               insert (op =) ixn (case AList.lookup (op =) insts ixn of
  1097                   SOME (SOME t) => if is_proj t then union (op =) ixns ixns' else ixns'
  1098                 | _ => union (op =) ixns ixns'))
  1099                   (needed prop ts'' prfs, add_npvars false true [] ([], prop));
  1100             val insts' = map
  1101               (fn (ixn, x as SOME _) => if member (op =) nvs ixn then (false, x) else (true, NONE)
  1102                 | (_, x) => (false, x)) insts
  1103           in ([], false, insts' @ map (pair false) ts'', prf) end
  1104     and needed (Const ("==>", _) $ t $ u) ts ((b, _, _, _)::prfs) =
  1105           union (op =) (if b then map (fst o dest_Var) (vars_of t) else []) (needed u ts prfs)
  1106       | needed (Var (ixn, _)) (_::_) _ = [ixn]
  1107       | needed _ _ _ = [];
  1108   in shrink end;
  1109 
  1110 
  1111 (**** Simple first order matching functions for terms and proofs ****)
  1112 
  1113 exception PMatch;
  1114 
  1115 (** see pattern.ML **)
  1116 
  1117 fun flt (i: int) = filter (fn n => n < i);
  1118 
  1119 fun fomatch Ts tymatch j instsp p =
  1120   let
  1121     fun mtch (instsp as (tyinsts, insts)) = fn
  1122         (Var (ixn, T), t)  =>
  1123           if j>0 andalso not (null (flt j (loose_bnos t)))
  1124           then raise PMatch
  1125           else (tymatch (tyinsts, fn () => (T, fastype_of1 (Ts, t))),
  1126             (ixn, t) :: insts)
  1127       | (Free (a, T), Free (b, U)) =>
  1128           if a=b then (tymatch (tyinsts, K (T, U)), insts) else raise PMatch
  1129       | (Const (a, T), Const (b, U))  =>
  1130           if a=b then (tymatch (tyinsts, K (T, U)), insts) else raise PMatch
  1131       | (f $ t, g $ u) => mtch (mtch instsp (f, g)) (t, u)
  1132       | (Bound i, Bound j) => if i=j then instsp else raise PMatch
  1133       | _ => raise PMatch
  1134   in mtch instsp (pairself Envir.beta_eta_contract p) end;
  1135 
  1136 fun match_proof Ts tymatch =
  1137   let
  1138     fun optmatch _ inst (NONE, _) = inst
  1139       | optmatch _ _ (SOME _, NONE) = raise PMatch
  1140       | optmatch mtch inst (SOME x, SOME y) = mtch inst (x, y)
  1141 
  1142     fun matcht Ts j (pinst, tinst) (t, u) =
  1143       (pinst, fomatch Ts tymatch j tinst (t, Envir.beta_norm u));
  1144     fun matchT (pinst, (tyinsts, insts)) p =
  1145       (pinst, (tymatch (tyinsts, K p), insts));
  1146     fun matchTs inst (Ts, Us) = Library.foldl (uncurry matchT) (inst, Ts ~~ Us);
  1147 
  1148     fun mtch Ts i j (pinst, tinst) (Hyp (Var (ixn, _)), prf) =
  1149           if i = 0 andalso j = 0 then ((ixn, prf) :: pinst, tinst)
  1150           else (case apfst (flt i) (apsnd (flt j)
  1151                   (prf_add_loose_bnos 0 0 prf ([], []))) of
  1152               ([], []) => ((ixn, incr_pboundvars (~i) (~j) prf) :: pinst, tinst)
  1153             | ([], _) => if j = 0 then
  1154                    ((ixn, incr_pboundvars (~i) (~j) prf) :: pinst, tinst)
  1155                  else raise PMatch
  1156             | _ => raise PMatch)
  1157       | mtch Ts i j inst (prf1 % opt1, prf2 % opt2) =
  1158           optmatch (matcht Ts j) (mtch Ts i j inst (prf1, prf2)) (opt1, opt2)
  1159       | mtch Ts i j inst (prf1 %% prf2, prf1' %% prf2') =
  1160           mtch Ts i j (mtch Ts i j inst (prf1, prf1')) (prf2, prf2')
  1161       | mtch Ts i j inst (Abst (_, opT, prf1), Abst (_, opU, prf2)) =
  1162           mtch (the_default dummyT opU :: Ts) i (j+1)
  1163             (optmatch matchT inst (opT, opU)) (prf1, prf2)
  1164       | mtch Ts i j inst (prf1, Abst (_, opU, prf2)) =
  1165           mtch (the_default dummyT opU :: Ts) i (j+1) inst
  1166             (incr_pboundvars 0 1 prf1 %> Bound 0, prf2)
  1167       | mtch Ts i j inst (AbsP (_, opt, prf1), AbsP (_, opu, prf2)) =
  1168           mtch Ts (i+1) j (optmatch (matcht Ts j) inst (opt, opu)) (prf1, prf2)
  1169       | mtch Ts i j inst (prf1, AbsP (_, _, prf2)) =
  1170           mtch Ts (i+1) j inst (incr_pboundvars 1 0 prf1 %% PBound 0, prf2)
  1171       | mtch Ts i j inst (PAxm (s1, _, opTs), PAxm (s2, _, opUs)) =
  1172           if s1 = s2 then optmatch matchTs inst (opTs, opUs)
  1173           else raise PMatch
  1174       | mtch Ts i j inst (OfClass (T1, c1), OfClass (T2, c2)) =
  1175           if c1 = c2 then matchT inst (T1, T2)
  1176           else raise PMatch
  1177       | mtch Ts i j inst (PThm (_, ((name1, prop1, opTs), _)), PThm (_, ((name2, prop2, opUs), _))) =
  1178           if name1 = name2 andalso prop1 = prop2 then
  1179             optmatch matchTs inst (opTs, opUs)
  1180           else raise PMatch
  1181       | mtch _ _ _ inst (PBound i, PBound j) = if i = j then inst else raise PMatch
  1182       | mtch _ _ _ _ _ = raise PMatch
  1183   in mtch Ts 0 0 end;
  1184 
  1185 fun prf_subst (pinst, (tyinsts, insts)) =
  1186   let
  1187     val substT = Envir.subst_type_same tyinsts;
  1188     val substTs = Same.map substT;
  1189 
  1190     fun subst' lev (Var (xi, _)) =
  1191         (case AList.lookup (op =) insts xi of
  1192           NONE => raise Same.SAME
  1193         | SOME u => incr_boundvars lev u)
  1194       | subst' _ (Const (s, T)) = Const (s, substT T)
  1195       | subst' _ (Free (s, T)) = Free (s, substT T)
  1196       | subst' lev (Abs (a, T, body)) =
  1197           (Abs (a, substT T, Same.commit (subst' (lev + 1)) body)
  1198             handle Same.SAME => Abs (a, T, subst' (lev + 1) body))
  1199       | subst' lev (f $ t) =
  1200           (subst' lev f $ Same.commit (subst' lev) t
  1201             handle Same.SAME => f $ subst' lev t)
  1202       | subst' _ _ = raise Same.SAME;
  1203 
  1204     fun subst plev tlev (AbsP (a, t, body)) =
  1205           (AbsP (a, Same.map_option (subst' tlev) t, Same.commit (subst (plev + 1) tlev) body)
  1206             handle Same.SAME => AbsP (a, t, subst (plev + 1) tlev body))
  1207       | subst plev tlev (Abst (a, T, body)) =
  1208           (Abst (a, Same.map_option substT T, Same.commit (subst plev (tlev + 1)) body)
  1209             handle Same.SAME => Abst (a, T, subst plev (tlev + 1) body))
  1210       | subst plev tlev (prf %% prf') =
  1211           (subst plev tlev prf %% Same.commit (subst plev tlev) prf'
  1212             handle Same.SAME => prf %% subst plev tlev prf')
  1213       | subst plev tlev (prf % t) =
  1214           (subst plev tlev prf % Same.commit (Same.map_option (subst' tlev)) t
  1215             handle Same.SAME => prf % Same.map_option (subst' tlev) t)
  1216       | subst plev tlev (Hyp (Var (xi, _))) =
  1217           (case AList.lookup (op =) pinst xi of
  1218             NONE => raise Same.SAME
  1219           | SOME prf' => incr_pboundvars plev tlev prf')
  1220       | subst _ _ (PAxm (id, prop, Ts)) = PAxm (id, prop, Same.map_option substTs Ts)
  1221       | subst _ _ (OfClass (T, c)) = OfClass (substT T, c)
  1222       | subst _ _ (Oracle (id, prop, Ts)) = Oracle (id, prop, Same.map_option substTs Ts)
  1223       | subst _ _ (Promise (i, prop, Ts)) = Promise (i, prop, substTs Ts)
  1224       | subst _ _ (PThm (i, ((id, prop, Ts), body))) =
  1225           PThm (i, ((id, prop, Same.map_option substTs Ts), body))
  1226       | subst _ _ _ = raise Same.SAME;
  1227   in fn t => subst 0 0 t handle Same.SAME => t end;
  1228 
  1229 (*A fast unification filter: true unless the two terms cannot be unified.
  1230   Terms must be NORMAL.  Treats all Vars as distinct. *)
  1231 fun could_unify prf1 prf2 =
  1232   let
  1233     fun matchrands (prf1 %% prf2) (prf1' %% prf2') =
  1234           could_unify prf2 prf2' andalso matchrands prf1 prf1'
  1235       | matchrands (prf % SOME t) (prf' % SOME t') =
  1236           Term.could_unify (t, t') andalso matchrands prf prf'
  1237       | matchrands (prf % _) (prf' % _) = matchrands prf prf'
  1238       | matchrands _ _ = true
  1239 
  1240     fun head_of (prf %% _) = head_of prf
  1241       | head_of (prf % _) = head_of prf
  1242       | head_of prf = prf
  1243 
  1244   in case (head_of prf1, head_of prf2) of
  1245         (_, Hyp (Var _)) => true
  1246       | (Hyp (Var _), _) => true
  1247       | (PAxm (a, _, _), PAxm (b, _, _)) => a = b andalso matchrands prf1 prf2
  1248       | (OfClass (_, c), OfClass (_, d)) => c = d andalso matchrands prf1 prf2
  1249       | (PThm (_, ((a, propa, _), _)), PThm (_, ((b, propb, _), _))) =>
  1250           a = b andalso propa = propb andalso matchrands prf1 prf2
  1251       | (PBound i, PBound j) => i = j andalso matchrands prf1 prf2
  1252       | (AbsP _, _) =>  true   (*because of possible eta equality*)
  1253       | (Abst _, _) =>  true
  1254       | (_, AbsP _) =>  true
  1255       | (_, Abst _) =>  true
  1256       | _ => false
  1257   end;
  1258 
  1259 
  1260 (**** rewriting on proof terms ****)
  1261 
  1262 val no_skel = PBound 0;
  1263 val normal_skel = Hyp (Var ((Name.uu, 0), propT));
  1264 
  1265 fun rewrite_prf tymatch (rules, procs) prf =
  1266   let
  1267     fun rew _ _ (Abst (_, _, body) % SOME t) = SOME (prf_subst_bounds [t] body, no_skel)
  1268       | rew _ _ (AbsP (_, _, body) %% prf) = SOME (prf_subst_pbounds [prf] body, no_skel)
  1269       | rew Ts hs prf =
  1270           (case get_first (fn r => r Ts hs prf) procs of
  1271             NONE => get_first (fn (prf1, prf2) => SOME (prf_subst
  1272               (match_proof Ts tymatch ([], (Vartab.empty, [])) (prf1, prf)) prf2, prf2)
  1273                  handle PMatch => NONE) (filter (could_unify prf o fst) rules)
  1274           | some => some);
  1275 
  1276     fun rew0 Ts hs (prf as AbsP (_, _, prf' %% PBound 0)) =
  1277           if prf_loose_Pbvar1 prf' 0 then rew Ts hs prf
  1278           else
  1279             let val prf'' = incr_pboundvars (~1) 0 prf'
  1280             in SOME (the_default (prf'', no_skel) (rew Ts hs prf'')) end
  1281       | rew0 Ts hs (prf as Abst (_, _, prf' % SOME (Bound 0))) =
  1282           if prf_loose_bvar1 prf' 0 then rew Ts hs prf
  1283           else
  1284             let val prf'' = incr_pboundvars 0 (~1) prf'
  1285             in SOME (the_default (prf'', no_skel) (rew Ts hs prf'')) end
  1286       | rew0 Ts hs prf = rew Ts hs prf;
  1287 
  1288     fun rew1 _ _ (Hyp (Var _)) _ = NONE
  1289       | rew1 Ts hs skel prf = (case rew2 Ts hs skel prf of
  1290           SOME prf1 => (case rew0 Ts hs prf1 of
  1291               SOME (prf2, skel') => SOME (the_default prf2 (rew1 Ts hs skel' prf2))
  1292             | NONE => SOME prf1)
  1293         | NONE => (case rew0 Ts hs prf of
  1294               SOME (prf1, skel') => SOME (the_default prf1 (rew1 Ts hs skel' prf1))
  1295             | NONE => NONE))
  1296 
  1297     and rew2 Ts hs skel (prf % SOME t) = (case prf of
  1298             Abst (_, _, body) =>
  1299               let val prf' = prf_subst_bounds [t] body
  1300               in SOME (the_default prf' (rew2 Ts hs no_skel prf')) end
  1301           | _ => (case rew1 Ts hs (case skel of skel' % _ => skel' | _ => no_skel) prf of
  1302               SOME prf' => SOME (prf' % SOME t)
  1303             | NONE => NONE))
  1304       | rew2 Ts hs skel (prf % NONE) = Option.map (fn prf' => prf' % NONE)
  1305           (rew1 Ts hs (case skel of skel' % _ => skel' | _ => no_skel) prf)
  1306       | rew2 Ts hs skel (prf1 %% prf2) = (case prf1 of
  1307             AbsP (_, _, body) =>
  1308               let val prf' = prf_subst_pbounds [prf2] body
  1309               in SOME (the_default prf' (rew2 Ts hs no_skel prf')) end
  1310           | _ =>
  1311             let val (skel1, skel2) = (case skel of
  1312                 skel1 %% skel2 => (skel1, skel2)
  1313               | _ => (no_skel, no_skel))
  1314             in case rew1 Ts hs skel1 prf1 of
  1315                 SOME prf1' => (case rew1 Ts hs skel2 prf2 of
  1316                     SOME prf2' => SOME (prf1' %% prf2')
  1317                   | NONE => SOME (prf1' %% prf2))
  1318               | NONE => (case rew1 Ts hs skel2 prf2 of
  1319                     SOME prf2' => SOME (prf1 %% prf2')
  1320                   | NONE => NONE)
  1321             end)
  1322       | rew2 Ts hs skel (Abst (s, T, prf)) = (case rew1 (the_default dummyT T :: Ts) hs
  1323               (case skel of Abst (_, _, skel') => skel' | _ => no_skel) prf of
  1324             SOME prf' => SOME (Abst (s, T, prf'))
  1325           | NONE => NONE)
  1326       | rew2 Ts hs skel (AbsP (s, t, prf)) = (case rew1 Ts (t :: hs)
  1327               (case skel of AbsP (_, _, skel') => skel' | _ => no_skel) prf of
  1328             SOME prf' => SOME (AbsP (s, t, prf'))
  1329           | NONE => NONE)
  1330       | rew2 _ _ _ _ = NONE;
  1331 
  1332   in the_default prf (rew1 [] [] no_skel prf) end;
  1333 
  1334 fun rewrite_proof thy = rewrite_prf (fn (tyenv, f) =>
  1335   Sign.typ_match thy (f ()) tyenv handle Type.TYPE_MATCH => raise PMatch);
  1336 
  1337 fun rewrite_proof_notypes rews = rewrite_prf fst rews;
  1338 
  1339 
  1340 (**** theory data ****)
  1341 
  1342 structure Data = Theory_Data
  1343 (
  1344   type T =
  1345     (stamp * (proof * proof)) list *
  1346     (stamp * (typ list -> term option list -> proof -> (proof * proof) option)) list;
  1347 
  1348   val empty = ([], []);
  1349   val extend = I;
  1350   fun merge ((rules1, procs1), (rules2, procs2)) : T =
  1351     (AList.merge (op =) (K true) (rules1, rules2),
  1352       AList.merge (op =) (K true) (procs1, procs2));
  1353 );
  1354 
  1355 fun get_data thy = let val (rules, procs) = Data.get thy in (map #2 rules, map #2 procs) end;
  1356 fun rew_proof thy = rewrite_prf fst (get_data thy);
  1357 
  1358 fun add_prf_rrule r = (Data.map o apfst) (cons (stamp (), r));
  1359 fun add_prf_rproc p = (Data.map o apsnd) (cons (stamp (), p));
  1360 
  1361 
  1362 (***** promises *****)
  1363 
  1364 fun promise_proof thy i prop =
  1365   let
  1366     val _ = prop |> Term.exists_subterm (fn t =>
  1367       (Term.is_Free t orelse Term.is_Var t) andalso
  1368         raise Fail ("promise_proof: illegal variable " ^ Syntax.string_of_term_global thy t));
  1369     val _ = prop |> Term.exists_type (Term.exists_subtype
  1370       (fn TFree (a, _) => raise Fail ("promise_proof: illegal type variable " ^ quote a)
  1371         | _ => false));
  1372   in Promise (i, prop, map TVar (Term.add_tvars prop [])) end;
  1373 
  1374 fun fulfill_norm_proof thy ps body0 =
  1375   let
  1376     val PBody {oracles = oracles0, thms = thms0, proof = proof0} = body0;
  1377     val oracles = fold (fn (_, PBody {oracles, ...}) => merge_oracles oracles) ps oracles0;
  1378     val thms = fold (fn (_, PBody {thms, ...}) => merge_thms thms) ps thms0;
  1379     val proofs = fold (fn (i, PBody {proof, ...}) => Inttab.update (i, proof)) ps Inttab.empty;
  1380 
  1381     fun fill (Promise (i, prop, Ts)) =
  1382           (case Inttab.lookup proofs i of
  1383             NONE => NONE
  1384           | SOME prf => SOME (instantiate (Term.add_tvars prop [] ~~ Ts, []) prf, normal_skel))
  1385       | fill _ = NONE;
  1386     val (rules, procs) = get_data thy;
  1387     val proof = rewrite_prf fst (rules, K (K fill) :: procs) proof0;
  1388   in PBody {oracles = oracles, thms = thms, proof = proof} end;
  1389 
  1390 fun fulfill_proof_future _ [] postproc body =
  1391       if not (Multithreading.enabled ()) then Future.value (postproc (Future.join body))
  1392       else Future.map postproc body
  1393   | fulfill_proof_future thy promises postproc body =
  1394       singleton
  1395         (Future.forks {name = "Proofterm.fulfill_proof_future", group = NONE,
  1396             deps = Future.task_of body :: map (Future.task_of o snd) promises, pri = 0})
  1397         (fn () =>
  1398           postproc (fulfill_norm_proof thy (map (apsnd Future.join) promises) (Future.join body)));
  1399 
  1400 
  1401 (***** abstraction over sort constraints *****)
  1402 
  1403 fun unconstrainT_prf thy (atyp_map, constraints) =
  1404   let
  1405     fun hyp_map hyp =
  1406       (case AList.lookup (op =) constraints hyp of
  1407         SOME t => Hyp t
  1408       | NONE => raise Fail "unconstrainT_prf: missing constraint");
  1409 
  1410     val typ = Term_Subst.map_atypsT_same (Type.strip_sorts o atyp_map);
  1411     fun ofclass (ty, c) =
  1412       let val ty' = Term.map_atyps atyp_map ty;
  1413       in the_single (of_sort_proof thy hyp_map (ty', [c])) end;
  1414   in
  1415     Same.commit (map_proof_same (Term_Subst.map_types_same typ) typ ofclass)
  1416     #> fold_rev (implies_intr_proof o snd) constraints
  1417   end;
  1418 
  1419 fun unconstrainT_body thy constrs (PBody {oracles, thms, proof}) =
  1420   PBody
  1421    {oracles = oracles,  (* FIXME merge (!), unconstrain (!?!) *)
  1422     thms = thms,  (* FIXME merge (!) *)
  1423     proof = unconstrainT_prf thy constrs proof};
  1424 
  1425 
  1426 (***** theorems *****)
  1427 
  1428 fun prepare_thm_proof thy name shyps hyps concl promises body =
  1429   let
  1430     val PBody {oracles = oracles0, thms = thms0, proof = prf} = body;
  1431     val prop = Logic.list_implies (hyps, concl);
  1432     val nvs = needed_vars prop;
  1433     val args = map (fn (v as Var (ixn, _)) =>
  1434         if member (op =) nvs ixn then SOME v else NONE) (vars_of prop) @
  1435       map SOME (frees_of prop);
  1436 
  1437     val ((atyp_map, constraints, outer_constraints), prop1) = Logic.unconstrainT shyps prop;
  1438     val postproc = unconstrainT_body thy (atyp_map, constraints);
  1439     val args1 =
  1440       (map o Option.map o Term.map_types o Term.map_atyps)
  1441         (Type.strip_sorts o atyp_map) args;
  1442     val argsP = map OfClass outer_constraints @ map Hyp hyps;
  1443 
  1444     fun full_proof0 () =
  1445       #4 (shrink_proof [] 0 (rew_proof thy (fold_rev implies_intr_proof hyps prf)));
  1446 
  1447     fun make_body0 proof0 = PBody {oracles = oracles0, thms = thms0, proof = proof0};
  1448     val body0 =
  1449       if not (proofs_enabled ()) then Future.value (make_body0 MinProof)
  1450       else if not (Multithreading.enabled ()) then Future.value (make_body0 (full_proof0 ()))
  1451       else
  1452         singleton
  1453           (Future.forks {name = "Proofterm.prepare_thm_proof", group = NONE, deps = [], pri = ~1})
  1454           (make_body0 o full_proof0);
  1455 
  1456     fun new_prf () = (serial (), fulfill_proof_future thy promises postproc body0);
  1457     val (i, body') =
  1458       (*non-deterministic, depends on unknown promises*)
  1459       (case strip_combt (fst (strip_combP prf)) of
  1460         (PThm (i, ((old_name, prop', NONE), body')), args') =>
  1461           if (old_name = "" orelse old_name = name) andalso prop1 = prop' andalso args = args'
  1462           then (i, body')
  1463           else new_prf ()
  1464       | _ => new_prf ());
  1465     val head = PThm (i, ((name, prop1, NONE), body'));
  1466   in ((i, (name, prop1, body')), head, args, argsP, args1) end;
  1467 
  1468 fun thm_proof thy name shyps hyps concl promises body =
  1469   let val (pthm, head, args, argsP, _) = prepare_thm_proof thy name shyps hyps concl promises body
  1470   in (pthm, proof_combP (proof_combt' (head, args), argsP)) end;
  1471 
  1472 fun unconstrain_thm_proof thy shyps concl promises body =
  1473   let
  1474     val (pthm, head, _, _, args) = prepare_thm_proof thy "" shyps [] concl promises body
  1475   in (pthm, proof_combt' (head, args)) end;
  1476 
  1477 
  1478 fun get_name shyps hyps prop prf =
  1479   let val (_, prop) = Logic.unconstrainT shyps (Logic.list_implies (hyps, prop)) in
  1480     (case strip_combt (fst (strip_combP prf)) of
  1481       (PThm (_, ((name, prop', _), _)), _) => if prop = prop' then name else ""
  1482     | _ => "")
  1483   end;
  1484 
  1485 fun guess_name (PThm (_, ((name, _, _), _))) = name
  1486   | guess_name (prf %% Hyp _) = guess_name prf
  1487   | guess_name (prf %% OfClass _) = guess_name prf
  1488   | guess_name (prf % NONE) = guess_name prf
  1489   | guess_name (prf % SOME (Var _)) = guess_name prf
  1490   | guess_name _ = "";
  1491 
  1492 end;
  1493 
  1494 structure Basic_Proofterm : BASIC_PROOFTERM = Proofterm;
  1495 open Basic_Proofterm;