src/Pure/proofterm.ML
author wenzelm
Sat Aug 20 15:52:29 2011 +0200 (2011-08-20 ago)
changeset 44330 b28e091f683a
parent 44303 4e2abb045eac
child 44331 aa9c1e9ef2ce
permissions -rw-r--r--
added Future.joins convenience;
clarified Future.map: based on Future.cond_forks;
     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 join_body: proof_body -> unit
    41   val proof_of: proof_body -> proof
    42   val join_proof: proof_body future -> proof
    43   val fold_proof_atoms: bool -> (proof -> 'a -> 'a) -> proof list -> 'a -> 'a
    44   val fold_body_thms: (string * term * proof_body -> 'a -> 'a) -> proof_body list -> 'a -> 'a
    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 join_thms thms = ignore (Future.joins (map (#3 o #2) thms));
   175 fun join_body (PBody {thms, ...}) = join_thms thms;
   176 
   177 fun proof_of (PBody {proof, ...}) = proof;
   178 val join_proof = Future.join #> proof_of;
   179 
   180 
   181 (***** proof atoms *****)
   182 
   183 fun fold_proof_atoms all f =
   184   let
   185     fun app (Abst (_, _, prf)) = app prf
   186       | app (AbsP (_, _, prf)) = app prf
   187       | app (prf % _) = app prf
   188       | app (prf1 %% prf2) = app prf1 #> app prf2
   189       | app (prf as PThm (i, (_, body))) = (fn (x, seen) =>
   190           if Inttab.defined seen i then (x, seen)
   191           else
   192             let val (x', seen') =
   193               (if all then app (join_proof body) else I) (x, Inttab.update (i, ()) seen)
   194             in (f prf x', seen') end)
   195       | app prf = (fn (x, seen) => (f prf x, seen));
   196   in fn prfs => fn x => #1 (fold app prfs (x, Inttab.empty)) end;
   197 
   198 fun fold_body_thms f =
   199   let
   200     fun app (PBody {thms, ...}) =
   201       tap join_thms thms |> fold (fn (i, (name, prop, body)) => fn (x, seen) =>
   202         if Inttab.defined seen i then (x, seen)
   203         else
   204           let
   205             val body' = Future.join body;
   206             val (x', seen') = app body' (x, Inttab.update (i, ()) seen);
   207           in (f (name, prop, body') x', seen') end);
   208   in fn bodies => fn x => #1 (fold app bodies (x, Inttab.empty)) end;
   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.Res 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       tap join_thms thms |> fold (fn (i, (_, _, body)) => fn (x, seen) =>
   246         if Inttab.defined seen i then (x, seen)
   247         else
   248           let
   249             val body' = Future.join body;
   250             val (x', seen') = collect body' (x, Inttab.update (i, ()) seen);
   251           in (merge_oracles oracles x', seen') end);
   252   in fn body => #1 (collect body ([], Inttab.empty)) end;
   253 
   254 fun approximate_proof_body prf =
   255   let
   256     val (oracles, thms) = fold_proof_atoms false
   257       (fn Oracle (s, prop, _) => apfst (cons (s, prop))
   258         | PThm (i, ((name, prop, _), body)) => apsnd (cons (i, (name, prop, body)))
   259         | _ => I) [prf] ([], []);
   260   in
   261     PBody
   262      {oracles = Ord_List.make oracle_ord oracles,
   263       thms = Ord_List.make thm_ord thms,
   264       proof = prf}
   265   end;
   266 
   267 
   268 (***** proof objects with different levels of detail *****)
   269 
   270 fun (prf %> t) = prf % SOME t;
   271 
   272 val proof_combt = Library.foldl (op %>);
   273 val proof_combt' = Library.foldl (op %);
   274 val proof_combP = Library.foldl (op %%);
   275 
   276 fun strip_combt prf =
   277     let fun stripc (prf % t, ts) = stripc (prf, t::ts)
   278           | stripc  x =  x
   279     in  stripc (prf, [])  end;
   280 
   281 fun strip_combP prf =
   282     let fun stripc (prf %% prf', prfs) = stripc (prf, prf'::prfs)
   283           | stripc  x =  x
   284     in  stripc (prf, [])  end;
   285 
   286 fun strip_thm (body as PBody {proof, ...}) =
   287   (case strip_combt (fst (strip_combP proof)) of
   288     (PThm (_, (_, body')), _) => Future.join body'
   289   | _ => body);
   290 
   291 val mk_Abst = fold_rev (fn (s, T:typ) => fn prf => Abst (s, NONE, prf));
   292 fun mk_AbsP (i, prf) = funpow i (fn prf => AbsP ("H", NONE, prf)) prf;
   293 
   294 fun map_proof_same term typ ofclass =
   295   let
   296     val typs = Same.map typ;
   297 
   298     fun proof (Abst (s, T, prf)) =
   299           (Abst (s, Same.map_option typ T, Same.commit proof prf)
   300             handle Same.SAME => Abst (s, T, proof prf))
   301       | proof (AbsP (s, t, prf)) =
   302           (AbsP (s, Same.map_option term t, Same.commit proof prf)
   303             handle Same.SAME => AbsP (s, t, proof prf))
   304       | proof (prf % t) =
   305           (proof prf % Same.commit (Same.map_option term) t
   306             handle Same.SAME => prf % Same.map_option term t)
   307       | proof (prf1 %% prf2) =
   308           (proof prf1 %% Same.commit proof prf2
   309             handle Same.SAME => prf1 %% proof prf2)
   310       | proof (PAxm (a, prop, SOME Ts)) = PAxm (a, prop, SOME (typs Ts))
   311       | proof (OfClass T_c) = ofclass T_c
   312       | proof (Oracle (a, prop, SOME Ts)) = Oracle (a, prop, SOME (typs Ts))
   313       | proof (Promise (i, prop, Ts)) = Promise (i, prop, typs Ts)
   314       | proof (PThm (i, ((a, prop, SOME Ts), body))) =
   315           PThm (i, ((a, prop, SOME (typs Ts)), body))
   316       | proof _ = raise Same.SAME;
   317   in proof end;
   318 
   319 fun map_proof_terms_same term typ = map_proof_same term typ (fn (T, c) => OfClass (typ T, c));
   320 fun map_proof_types_same typ = map_proof_terms_same (Term_Subst.map_types_same typ) typ;
   321 
   322 fun same eq f x =
   323   let val x' = f x
   324   in if eq (x, x') then raise Same.SAME else x' end;
   325 
   326 fun map_proof_terms f g = Same.commit (map_proof_terms_same (same (op =) f) (same (op =) g));
   327 fun map_proof_types f = Same.commit (map_proof_types_same (same (op =) f));
   328 
   329 fun fold_proof_terms f g (Abst (_, SOME T, prf)) = g T #> fold_proof_terms f g prf
   330   | fold_proof_terms f g (Abst (_, NONE, prf)) = fold_proof_terms f g prf
   331   | fold_proof_terms f g (AbsP (_, SOME t, prf)) = f t #> fold_proof_terms f g prf
   332   | fold_proof_terms f g (AbsP (_, NONE, prf)) = fold_proof_terms f g prf
   333   | fold_proof_terms f g (prf % SOME t) = fold_proof_terms f g prf #> f t
   334   | fold_proof_terms f g (prf % NONE) = fold_proof_terms f g prf
   335   | fold_proof_terms f g (prf1 %% prf2) =
   336       fold_proof_terms f g prf1 #> fold_proof_terms f g prf2
   337   | fold_proof_terms _ g (PAxm (_, _, SOME Ts)) = fold g Ts
   338   | fold_proof_terms _ g (OfClass (T, _)) = g T
   339   | fold_proof_terms _ g (Oracle (_, _, SOME Ts)) = fold g Ts
   340   | fold_proof_terms _ g (Promise (_, _, Ts)) = fold g Ts
   341   | fold_proof_terms _ g (PThm (_, ((_, _, SOME Ts), _))) = fold g Ts
   342   | fold_proof_terms _ _ _ = I;
   343 
   344 fun maxidx_proof prf = fold_proof_terms Term.maxidx_term Term.maxidx_typ prf;
   345 
   346 fun size_of_proof (Abst (_, _, prf)) = 1 + size_of_proof prf
   347   | size_of_proof (AbsP (_, t, prf)) = 1 + size_of_proof prf
   348   | size_of_proof (prf % _) = 1 + size_of_proof prf
   349   | size_of_proof (prf1 %% prf2) = size_of_proof prf1 + size_of_proof prf2
   350   | size_of_proof _ = 1;
   351 
   352 fun change_type opTs (PAxm (name, prop, _)) = PAxm (name, prop, opTs)
   353   | change_type (SOME [T]) (OfClass (_, c)) = OfClass (T, c)
   354   | change_type opTs (Oracle (name, prop, _)) = Oracle (name, prop, opTs)
   355   | change_type opTs (Promise _) = raise Fail "change_type: unexpected promise"
   356   | change_type opTs (PThm (i, ((name, prop, _), body))) =
   357       PThm (i, ((name, prop, opTs), body))
   358   | change_type _ prf = prf;
   359 
   360 
   361 (***** utilities *****)
   362 
   363 fun strip_abs (_::Ts) (Abs (_, _, t)) = strip_abs Ts t
   364   | strip_abs _ t = t;
   365 
   366 fun mk_abs Ts t = Library.foldl (fn (t', T) => Abs ("", T, t')) (t, Ts);
   367 
   368 
   369 (*Abstraction of a proof term over its occurrences of v,
   370     which must contain no loose bound variables.
   371   The resulting proof term is ready to become the body of an Abst.*)
   372 
   373 fun prf_abstract_over v =
   374   let
   375     fun abst' lev u = if v aconv u then Bound lev else
   376       (case u of
   377          Abs (a, T, t) => Abs (a, T, abst' (lev + 1) t)
   378        | f $ t => (abst' lev f $ absth' lev t handle Same.SAME => f $ abst' lev t)
   379        | _ => raise Same.SAME)
   380     and absth' lev t = (abst' lev t handle Same.SAME => t);
   381 
   382     fun abst lev (AbsP (a, t, prf)) =
   383           (AbsP (a, Same.map_option (abst' lev) t, absth lev prf)
   384            handle Same.SAME => AbsP (a, t, abst lev prf))
   385       | abst lev (Abst (a, T, prf)) = Abst (a, T, abst (lev + 1) prf)
   386       | abst lev (prf1 %% prf2) = (abst lev prf1 %% absth lev prf2
   387           handle Same.SAME => prf1 %% abst lev prf2)
   388       | abst lev (prf % t) = (abst lev prf % Option.map (absth' lev) t
   389           handle Same.SAME => prf % Same.map_option (abst' lev) t)
   390       | abst _ _ = raise Same.SAME
   391     and absth lev prf = (abst lev prf handle Same.SAME => prf);
   392 
   393   in absth 0 end;
   394 
   395 
   396 (*increments a proof term's non-local bound variables
   397   required when moving a proof term within abstractions
   398      inc is  increment for bound variables
   399      lev is  level at which a bound variable is considered 'loose'*)
   400 
   401 fun incr_bv' inct tlev t = incr_bv (inct, tlev, t);
   402 
   403 fun prf_incr_bv' incP inct Plev tlev (PBound i) =
   404       if i >= Plev then PBound (i+incP) else raise Same.SAME
   405   | prf_incr_bv' incP inct Plev tlev (AbsP (a, t, body)) =
   406       (AbsP (a, Same.map_option (same (op =) (incr_bv' inct tlev)) t,
   407          prf_incr_bv incP inct (Plev+1) tlev body) handle Same.SAME =>
   408            AbsP (a, t, prf_incr_bv' incP inct (Plev+1) tlev body))
   409   | prf_incr_bv' incP inct Plev tlev (Abst (a, T, body)) =
   410       Abst (a, T, prf_incr_bv' incP inct Plev (tlev+1) body)
   411   | prf_incr_bv' incP inct Plev tlev (prf %% prf') =
   412       (prf_incr_bv' incP inct Plev tlev prf %% prf_incr_bv incP inct Plev tlev prf'
   413        handle Same.SAME => prf %% prf_incr_bv' incP inct Plev tlev prf')
   414   | prf_incr_bv' incP inct Plev tlev (prf % t) =
   415       (prf_incr_bv' incP inct Plev tlev prf % Option.map (incr_bv' inct tlev) t
   416        handle Same.SAME => prf % Same.map_option (same (op =) (incr_bv' inct tlev)) t)
   417   | prf_incr_bv' _ _ _ _ _ = raise Same.SAME
   418 and prf_incr_bv incP inct Plev tlev prf =
   419       (prf_incr_bv' incP inct Plev tlev prf handle Same.SAME => prf);
   420 
   421 fun incr_pboundvars  0 0 prf = prf
   422   | incr_pboundvars incP inct prf = prf_incr_bv incP inct 0 0 prf;
   423 
   424 
   425 fun prf_loose_bvar1 (prf1 %% prf2) k = prf_loose_bvar1 prf1 k orelse prf_loose_bvar1 prf2 k
   426   | prf_loose_bvar1 (prf % SOME t) k = prf_loose_bvar1 prf k orelse loose_bvar1 (t, k)
   427   | prf_loose_bvar1 (_ % NONE) _ = true
   428   | prf_loose_bvar1 (AbsP (_, SOME t, prf)) k = loose_bvar1 (t, k) orelse prf_loose_bvar1 prf k
   429   | prf_loose_bvar1 (AbsP (_, NONE, _)) k = true
   430   | prf_loose_bvar1 (Abst (_, _, prf)) k = prf_loose_bvar1 prf (k+1)
   431   | prf_loose_bvar1 _ _ = false;
   432 
   433 fun prf_loose_Pbvar1 (PBound i) k = i = k
   434   | prf_loose_Pbvar1 (prf1 %% prf2) k = prf_loose_Pbvar1 prf1 k orelse prf_loose_Pbvar1 prf2 k
   435   | prf_loose_Pbvar1 (prf % _) k = prf_loose_Pbvar1 prf k
   436   | prf_loose_Pbvar1 (AbsP (_, _, prf)) k = prf_loose_Pbvar1 prf (k+1)
   437   | prf_loose_Pbvar1 (Abst (_, _, prf)) k = prf_loose_Pbvar1 prf k
   438   | prf_loose_Pbvar1 _ _ = false;
   439 
   440 fun prf_add_loose_bnos plev tlev (PBound i) (is, js) =
   441       if i < plev then (is, js) else (insert (op =) (i-plev) is, js)
   442   | prf_add_loose_bnos plev tlev (prf1 %% prf2) p =
   443       prf_add_loose_bnos plev tlev prf2
   444         (prf_add_loose_bnos plev tlev prf1 p)
   445   | prf_add_loose_bnos plev tlev (prf % opt) (is, js) =
   446       prf_add_loose_bnos plev tlev prf (case opt of
   447           NONE => (is, insert (op =) ~1 js)
   448         | SOME t => (is, add_loose_bnos (t, tlev, js)))
   449   | prf_add_loose_bnos plev tlev (AbsP (_, opt, prf)) (is, js) =
   450       prf_add_loose_bnos (plev+1) tlev prf (case opt of
   451           NONE => (is, insert (op =) ~1 js)
   452         | SOME t => (is, add_loose_bnos (t, tlev, js)))
   453   | prf_add_loose_bnos plev tlev (Abst (_, _, prf)) p =
   454       prf_add_loose_bnos plev (tlev+1) prf p
   455   | prf_add_loose_bnos _ _ _ _ = ([], []);
   456 
   457 
   458 (**** substitutions ****)
   459 
   460 fun del_conflicting_tvars envT T = Term_Subst.instantiateT
   461   (map_filter (fn ixnS as (_, S) =>
   462      (Type.lookup envT ixnS; NONE) handle TYPE _ =>
   463         SOME (ixnS, TFree ("'dummy", S))) (Term.add_tvarsT T [])) T;
   464 
   465 fun del_conflicting_vars env t = Term_Subst.instantiate
   466   (map_filter (fn ixnS as (_, S) =>
   467      (Type.lookup (Envir.type_env env) ixnS; NONE) handle TYPE _ =>
   468         SOME (ixnS, TFree ("'dummy", S))) (Term.add_tvars t []),
   469    map_filter (fn (ixnT as (_, T)) =>
   470      (Envir.lookup (env, ixnT); NONE) handle TYPE _ =>
   471         SOME (ixnT, Free ("dummy", T))) (Term.add_vars t [])) t;
   472 
   473 fun norm_proof env =
   474   let
   475     val envT = Envir.type_env env;
   476     fun msg s = warning ("type conflict in norm_proof:\n" ^ s);
   477     fun htype f t = f env t handle TYPE (s, _, _) =>
   478       (msg s; f env (del_conflicting_vars env t));
   479     fun htypeT f T = f envT T handle TYPE (s, _, _) =>
   480       (msg s; f envT (del_conflicting_tvars envT T));
   481     fun htypeTs f Ts = f envT Ts handle TYPE (s, _, _) =>
   482       (msg s; f envT (map (del_conflicting_tvars envT) Ts));
   483 
   484     fun norm (Abst (s, T, prf)) =
   485           (Abst (s, Same.map_option (htypeT Envir.norm_type_same) T, Same.commit norm prf)
   486             handle Same.SAME => Abst (s, T, norm prf))
   487       | norm (AbsP (s, t, prf)) =
   488           (AbsP (s, Same.map_option (htype Envir.norm_term_same) t, Same.commit norm prf)
   489             handle Same.SAME => AbsP (s, t, norm prf))
   490       | norm (prf % t) =
   491           (norm prf % Option.map (htype Envir.norm_term) t
   492             handle Same.SAME => prf % Same.map_option (htype Envir.norm_term_same) t)
   493       | norm (prf1 %% prf2) =
   494           (norm prf1 %% Same.commit norm prf2
   495             handle Same.SAME => prf1 %% norm prf2)
   496       | norm (PAxm (s, prop, Ts)) =
   497           PAxm (s, prop, Same.map_option (htypeTs Envir.norm_types_same) Ts)
   498       | norm (OfClass (T, c)) =
   499           OfClass (htypeT Envir.norm_type_same T, c)
   500       | norm (Oracle (s, prop, Ts)) =
   501           Oracle (s, prop, Same.map_option (htypeTs Envir.norm_types_same) Ts)
   502       | norm (Promise (i, prop, Ts)) =
   503           Promise (i, prop, htypeTs Envir.norm_types_same Ts)
   504       | norm (PThm (i, ((s, t, Ts), body))) =
   505           PThm (i, ((s, t, Same.map_option (htypeTs Envir.norm_types_same) Ts), body))
   506       | norm _ = raise Same.SAME;
   507   in Same.commit norm end;
   508 
   509 
   510 (***** Remove some types in proof term (to save space) *****)
   511 
   512 fun remove_types (Abs (s, _, t)) = Abs (s, dummyT, remove_types t)
   513   | remove_types (t $ u) = remove_types t $ remove_types u
   514   | remove_types (Const (s, _)) = Const (s, dummyT)
   515   | remove_types t = t;
   516 
   517 fun remove_types_env (Envir.Envir {maxidx, tenv, tyenv}) =
   518   Envir.Envir {maxidx = maxidx, tenv = Vartab.map (K (apsnd remove_types)) tenv, tyenv = tyenv};
   519 
   520 fun norm_proof' env prf = norm_proof (remove_types_env env) prf;
   521 
   522 
   523 (**** substitution of bound variables ****)
   524 
   525 fun prf_subst_bounds args prf =
   526   let
   527     val n = length args;
   528     fun subst' lev (Bound i) =
   529          (if i<lev then raise Same.SAME    (*var is locally bound*)
   530           else  incr_boundvars lev (nth args (i-lev))
   531                   handle General.Subscript => Bound (i-n))  (*loose: change it*)
   532       | subst' lev (Abs (a, T, body)) = Abs (a, T,  subst' (lev+1) body)
   533       | subst' lev (f $ t) = (subst' lev f $ substh' lev t
   534           handle Same.SAME => f $ subst' lev t)
   535       | subst' _ _ = raise Same.SAME
   536     and substh' lev t = (subst' lev t handle Same.SAME => t);
   537 
   538     fun subst lev (AbsP (a, t, body)) =
   539         (AbsP (a, Same.map_option (subst' lev) t, substh lev body)
   540           handle Same.SAME => AbsP (a, t, subst lev body))
   541       | subst lev (Abst (a, T, body)) = Abst (a, T, subst (lev+1) body)
   542       | subst lev (prf %% prf') = (subst lev prf %% substh lev prf'
   543           handle Same.SAME => prf %% subst lev prf')
   544       | subst lev (prf % t) = (subst lev prf % Option.map (substh' lev) t
   545           handle Same.SAME => prf % Same.map_option (subst' lev) t)
   546       | subst _ _ = raise Same.SAME
   547     and substh lev prf = (subst lev prf handle Same.SAME => prf);
   548   in case args of [] => prf | _ => substh 0 prf end;
   549 
   550 fun prf_subst_pbounds args prf =
   551   let
   552     val n = length args;
   553     fun subst (PBound i) Plev tlev =
   554          (if i < Plev then raise Same.SAME    (*var is locally bound*)
   555           else incr_pboundvars Plev tlev (nth args (i-Plev))
   556                  handle General.Subscript => PBound (i-n)  (*loose: change it*))
   557       | subst (AbsP (a, t, body)) Plev tlev = AbsP (a, t, subst body (Plev+1) tlev)
   558       | subst (Abst (a, T, body)) Plev tlev = Abst (a, T, subst body Plev (tlev+1))
   559       | subst (prf %% prf') Plev tlev = (subst prf Plev tlev %% substh prf' Plev tlev
   560           handle Same.SAME => prf %% subst prf' Plev tlev)
   561       | subst (prf % t) Plev tlev = subst prf Plev tlev % t
   562       | subst  prf _ _ = raise Same.SAME
   563     and substh prf Plev tlev = (subst prf Plev tlev handle Same.SAME => prf)
   564   in case args of [] => prf | _ => substh prf 0 0 end;
   565 
   566 
   567 (**** Freezing and thawing of variables in proof terms ****)
   568 
   569 local
   570 
   571 fun frzT names =
   572   map_type_tvar (fn (ixn, S) => TFree (the (AList.lookup (op =) names ixn), S));
   573 
   574 fun thawT names =
   575   map_type_tfree (fn (a, S) =>
   576     (case AList.lookup (op =) names a of
   577       NONE => TFree (a, S)
   578     | SOME ixn => TVar (ixn, S)));
   579 
   580 fun freeze names names' (t $ u) =
   581       freeze names names' t $ freeze names names' u
   582   | freeze names names' (Abs (s, T, t)) =
   583       Abs (s, frzT names' T, freeze names names' t)
   584   | freeze names names' (Const (s, T)) = Const (s, frzT names' T)
   585   | freeze names names' (Free (s, T)) = Free (s, frzT names' T)
   586   | freeze names names' (Var (ixn, T)) =
   587       Free (the (AList.lookup (op =) names ixn), frzT names' T)
   588   | freeze names names' t = t;
   589 
   590 fun thaw names names' (t $ u) =
   591       thaw names names' t $ thaw names names' u
   592   | thaw names names' (Abs (s, T, t)) =
   593       Abs (s, thawT names' T, thaw names names' t)
   594   | thaw names names' (Const (s, T)) = Const (s, thawT names' T)
   595   | thaw names names' (Free (s, T)) =
   596       let val T' = thawT names' T in
   597         (case AList.lookup (op =) names s of
   598           NONE => Free (s, T')
   599         | SOME ixn => Var (ixn, T'))
   600       end
   601   | thaw names names' (Var (ixn, T)) = Var (ixn, thawT names' T)
   602   | thaw names names' t = t;
   603 
   604 in
   605 
   606 fun freeze_thaw_prf prf =
   607   let
   608     val (fs, Tfs, vs, Tvs) = fold_proof_terms
   609       (fn t => fn (fs, Tfs, vs, Tvs) =>
   610          (Term.add_free_names t fs, Term.add_tfree_names t Tfs,
   611           Term.add_var_names t vs, Term.add_tvar_names t Tvs))
   612       (fn T => fn (fs, Tfs, vs, Tvs) =>
   613          (fs, Term.add_tfree_namesT T Tfs,
   614           vs, Term.add_tvar_namesT T Tvs))
   615       prf ([], [], [], []);
   616     val names = vs ~~ Name.variant_list fs (map fst vs);
   617     val names' = Tvs ~~ Name.variant_list Tfs (map fst Tvs);
   618     val rnames = map swap names;
   619     val rnames' = map swap names';
   620   in
   621     (map_proof_terms (freeze names names') (frzT names') prf,
   622      map_proof_terms (thaw rnames rnames') (thawT rnames'))
   623   end;
   624 
   625 end;
   626 
   627 
   628 (***** implication introduction *****)
   629 
   630 fun gen_implies_intr_proof f h prf =
   631   let
   632     fun abshyp i (Hyp t) = if h aconv t then PBound i else raise Same.SAME
   633       | abshyp i (Abst (s, T, prf)) = Abst (s, T, abshyp i prf)
   634       | abshyp i (AbsP (s, t, prf)) = AbsP (s, t, abshyp (i + 1) prf)
   635       | abshyp i (prf % t) = abshyp i prf % t
   636       | abshyp i (prf1 %% prf2) =
   637           (abshyp i prf1 %% abshyph i prf2
   638             handle Same.SAME => prf1 %% abshyp i prf2)
   639       | abshyp _ _ = raise Same.SAME
   640     and abshyph i prf = (abshyp i prf handle Same.SAME => prf);
   641   in
   642     AbsP ("H", f h, abshyph 0 prf)
   643   end;
   644 
   645 val implies_intr_proof = gen_implies_intr_proof (K NONE);
   646 val implies_intr_proof' = gen_implies_intr_proof SOME;
   647 
   648 
   649 (***** forall introduction *****)
   650 
   651 fun forall_intr_proof x a prf = Abst (a, NONE, prf_abstract_over x prf);
   652 
   653 fun forall_intr_proof' t prf =
   654   let val (a, T) = (case t of Var ((a, _), T) => (a, T) | Free p => p)
   655   in Abst (a, SOME T, prf_abstract_over t prf) end;
   656 
   657 
   658 (***** varify *****)
   659 
   660 fun varify_proof t fixed prf =
   661   let
   662     val fs = Term.fold_types (Term.fold_atyps
   663       (fn TFree v => if member (op =) fixed v then I else insert (op =) v | _ => I)) t [];
   664     val used = Name.context
   665       |> fold_types (fold_atyps (fn TVar ((a, _), _) => Name.declare a | _ => I)) t;
   666     val fmap = fs ~~ #1 (fold_map Name.variant (map fst fs) used);
   667     fun thaw (f as (a, S)) =
   668       (case AList.lookup (op =) fmap f of
   669         NONE => TFree f
   670       | SOME b => TVar ((b, 0), S));
   671   in map_proof_terms (map_types (map_type_tfree thaw)) (map_type_tfree thaw) prf end;
   672 
   673 
   674 local
   675 
   676 fun new_name ix (pairs, used) =
   677   let val v = singleton (Name.variant_list used) (string_of_indexname ix)
   678   in ((ix, v) :: pairs, v :: used) end;
   679 
   680 fun freeze_one alist (ix, sort) =
   681   (case AList.lookup (op =) alist ix of
   682     NONE => TVar (ix, sort)
   683   | SOME name => TFree (name, sort));
   684 
   685 in
   686 
   687 fun legacy_freezeT t prf =
   688   let
   689     val used = Term.add_tfree_names t [];
   690     val (alist, _) = fold_rev new_name (map #1 (Term.add_tvars t [])) ([], used);
   691   in
   692     (case alist of
   693       [] => prf (*nothing to do!*)
   694     | _ =>
   695         let val frzT = map_type_tvar (freeze_one alist)
   696         in map_proof_terms (map_types frzT) frzT prf end)
   697   end;
   698 
   699 end;
   700 
   701 
   702 (***** rotate assumptions *****)
   703 
   704 fun rotate_proof Bs Bi m prf =
   705   let
   706     val params = Term.strip_all_vars Bi;
   707     val asms = Logic.strip_imp_prems (Term.strip_all_body Bi);
   708     val i = length asms;
   709     val j = length Bs;
   710   in
   711     mk_AbsP (j+1, proof_combP (prf, map PBound
   712       (j downto 1) @ [mk_Abst params (mk_AbsP (i,
   713         proof_combP (proof_combt (PBound i, map Bound ((length params - 1) downto 0)),
   714           map PBound (((i-m-1) downto 0) @ ((i-1) downto (i-m))))))]))
   715   end;
   716 
   717 
   718 (***** permute premises *****)
   719 
   720 fun permute_prems_proof prems j k prf =
   721   let val n = length prems
   722   in mk_AbsP (n, proof_combP (prf,
   723     map PBound ((n-1 downto n-j) @ (k-1 downto 0) @ (n-j-1 downto k))))
   724   end;
   725 
   726 
   727 (***** generalization *****)
   728 
   729 fun generalize (tfrees, frees) idx =
   730   Same.commit (map_proof_terms_same
   731     (Term_Subst.generalize_same (tfrees, frees) idx)
   732     (Term_Subst.generalizeT_same tfrees idx));
   733 
   734 
   735 (***** instantiation *****)
   736 
   737 fun instantiate (instT, inst) =
   738   Same.commit (map_proof_terms_same
   739     (Term_Subst.instantiate_same (instT, map (apsnd remove_types) inst))
   740     (Term_Subst.instantiateT_same instT));
   741 
   742 
   743 (***** lifting *****)
   744 
   745 fun lift_proof Bi inc prop prf =
   746   let
   747     fun lift'' Us Ts t =
   748       strip_abs Ts (Logic.incr_indexes (Us, inc) (mk_abs Ts t));
   749 
   750     fun lift' Us Ts (Abst (s, T, prf)) =
   751           (Abst (s, Same.map_option (Logic.incr_tvar_same inc) T, lifth' Us (dummyT::Ts) prf)
   752            handle Same.SAME => Abst (s, T, lift' Us (dummyT::Ts) prf))
   753       | lift' Us Ts (AbsP (s, t, prf)) =
   754           (AbsP (s, Same.map_option (same (op =) (lift'' Us Ts)) t, lifth' Us Ts prf)
   755            handle Same.SAME => AbsP (s, t, lift' Us Ts prf))
   756       | lift' Us Ts (prf % t) = (lift' Us Ts prf % Option.map (lift'' Us Ts) t
   757           handle Same.SAME => prf % Same.map_option (same (op =) (lift'' Us Ts)) t)
   758       | lift' Us Ts (prf1 %% prf2) = (lift' Us Ts prf1 %% lifth' Us Ts prf2
   759           handle Same.SAME => prf1 %% lift' Us Ts prf2)
   760       | lift' _ _ (PAxm (s, prop, Ts)) =
   761           PAxm (s, prop, (Same.map_option o Same.map) (Logic.incr_tvar_same inc) Ts)
   762       | lift' _ _ (OfClass (T, c)) =
   763           OfClass (Logic.incr_tvar_same inc T, c)
   764       | lift' _ _ (Oracle (s, prop, Ts)) =
   765           Oracle (s, prop, (Same.map_option o Same.map) (Logic.incr_tvar_same inc) Ts)
   766       | lift' _ _ (Promise (i, prop, Ts)) =
   767           Promise (i, prop, Same.map (Logic.incr_tvar_same inc) Ts)
   768       | lift' _ _ (PThm (i, ((s, prop, Ts), body))) =
   769           PThm (i, ((s, prop, (Same.map_option o Same.map) (Logic.incr_tvar inc) Ts), body))
   770       | lift' _ _ _ = raise Same.SAME
   771     and lifth' Us Ts prf = (lift' Us Ts prf handle Same.SAME => prf);
   772 
   773     val ps = map (Logic.lift_all inc Bi) (Logic.strip_imp_prems prop);
   774     val k = length ps;
   775 
   776     fun mk_app b (i, j, prf) =
   777           if b then (i-1, j, prf %% PBound i) else (i, j-1, prf %> Bound j);
   778 
   779     fun lift Us bs i j (Const ("==>", _) $ A $ B) =
   780             AbsP ("H", NONE (*A*), lift Us (true::bs) (i+1) j B)
   781       | lift Us bs i j (Const ("all", _) $ Abs (a, T, t)) =
   782             Abst (a, NONE (*T*), lift (T::Us) (false::bs) i (j+1) t)
   783       | lift Us bs i j _ = proof_combP (lifth' (rev Us) [] prf,
   784             map (fn k => (#3 (fold_rev mk_app bs (i-1, j-1, PBound k))))
   785               (i + k - 1 downto i));
   786   in
   787     mk_AbsP (k, lift [] [] 0 0 Bi)
   788   end;
   789 
   790 fun incr_indexes i =
   791   Same.commit (map_proof_terms_same
   792     (Logic.incr_indexes_same ([], i)) (Logic.incr_tvar_same i));
   793 
   794 
   795 (***** proof by assumption *****)
   796 
   797 fun mk_asm_prf t i m =
   798   let
   799     fun imp_prf _ i 0 = PBound i
   800       | imp_prf (Const ("==>", _) $ A $ B) i m = AbsP ("H", NONE (*A*), imp_prf B (i+1) (m-1))
   801       | imp_prf _ i _ = PBound i;
   802     fun all_prf (Const ("all", _) $ Abs (a, T, t)) = Abst (a, NONE (*T*), all_prf t)
   803       | all_prf t = imp_prf t (~i) m
   804   in all_prf t end;
   805 
   806 fun assumption_proof Bs Bi n prf =
   807   mk_AbsP (length Bs, proof_combP (prf,
   808     map PBound (length Bs - 1 downto 0) @ [mk_asm_prf Bi n ~1]));
   809 
   810 
   811 (***** Composition of object rule with proof state *****)
   812 
   813 fun flatten_params_proof i j n (Const ("==>", _) $ A $ B, k) =
   814       AbsP ("H", NONE (*A*), flatten_params_proof (i+1) j n (B, k))
   815   | flatten_params_proof i j n (Const ("all", _) $ Abs (a, T, t), k) =
   816       Abst (a, NONE (*T*), flatten_params_proof i (j+1) n (t, k))
   817   | flatten_params_proof i j n (_, k) = proof_combP (proof_combt (PBound (k+i),
   818       map Bound (j-1 downto 0)), map PBound (remove (op =) (i-n) (i-1 downto 0)));
   819 
   820 fun bicompose_proof flatten Bs oldAs newAs A n m rprf sprf =
   821   let
   822     val la = length newAs;
   823     val lb = length Bs;
   824   in
   825     mk_AbsP (lb+la, proof_combP (sprf,
   826       map PBound (lb + la - 1 downto la)) %%
   827         proof_combP (rprf, (if n>0 then [mk_asm_prf (the A) n m] else []) @
   828           map (if flatten then flatten_params_proof 0 0 n else PBound o snd)
   829             (oldAs ~~ (la - 1 downto 0))))
   830   end;
   831 
   832 
   833 (***** axioms for equality *****)
   834 
   835 val aT = TFree ("'a", []);
   836 val bT = TFree ("'b", []);
   837 val x = Free ("x", aT);
   838 val y = Free ("y", aT);
   839 val z = Free ("z", aT);
   840 val A = Free ("A", propT);
   841 val B = Free ("B", propT);
   842 val f = Free ("f", aT --> bT);
   843 val g = Free ("g", aT --> bT);
   844 
   845 val equality_axms =
   846  [("reflexive", Logic.mk_equals (x, x)),
   847   ("symmetric", Logic.mk_implies (Logic.mk_equals (x, y), Logic.mk_equals (y, x))),
   848   ("transitive",
   849     Logic.list_implies ([Logic.mk_equals (x, y), Logic.mk_equals (y, z)], Logic.mk_equals (x, z))),
   850   ("equal_intr",
   851     Logic.list_implies ([Logic.mk_implies (A, B), Logic.mk_implies (B, A)], Logic.mk_equals (A, B))),
   852   ("equal_elim", Logic.list_implies ([Logic.mk_equals (A, B), A], B)),
   853   ("abstract_rule",
   854     Logic.mk_implies
   855       (Logic.all x
   856         (Logic.mk_equals (f $ x, g $ x)), Logic.mk_equals (lambda x (f $ x), lambda x (g $ x)))),
   857   ("combination", Logic.list_implies
   858     ([Logic.mk_equals (f, g), Logic.mk_equals (x, y)], Logic.mk_equals (f $ x, g $ y)))];
   859 
   860 val [reflexive_axm, symmetric_axm, transitive_axm, equal_intr_axm,
   861   equal_elim_axm, abstract_rule_axm, combination_axm] =
   862     map (fn (s, t) => PAxm ("Pure." ^ s, Logic.varify_global t, NONE)) equality_axms;
   863 
   864 val reflexive = reflexive_axm % NONE;
   865 
   866 fun symmetric (prf as PAxm ("Pure.reflexive", _, _) % _) = prf
   867   | symmetric prf = symmetric_axm % NONE % NONE %% prf;
   868 
   869 fun transitive _ _ (PAxm ("Pure.reflexive", _, _) % _) prf2 = prf2
   870   | transitive _ _ prf1 (PAxm ("Pure.reflexive", _, _) % _) = prf1
   871   | transitive u (Type ("prop", [])) prf1 prf2 =
   872       transitive_axm % NONE % SOME (remove_types u) % NONE %% prf1 %% prf2
   873   | transitive u T prf1 prf2 =
   874       transitive_axm % NONE % NONE % NONE %% prf1 %% prf2;
   875 
   876 fun abstract_rule x a prf =
   877   abstract_rule_axm % NONE % NONE %% forall_intr_proof x a prf;
   878 
   879 fun check_comb (PAxm ("Pure.combination", _, _) % f % g % _ % _ %% prf %% _) =
   880       is_some f orelse check_comb prf
   881   | check_comb (PAxm ("Pure.transitive", _, _) % _ % _ % _ %% prf1 %% prf2) =
   882       check_comb prf1 andalso check_comb prf2
   883   | check_comb (PAxm ("Pure.symmetric", _, _) % _ % _ %% prf) = check_comb prf
   884   | check_comb _ = false;
   885 
   886 fun combination f g t u (Type (_, [T, U])) prf1 prf2 =
   887   let
   888     val f = Envir.beta_norm f;
   889     val g = Envir.beta_norm g;
   890     val prf =
   891       if check_comb prf1 then
   892         combination_axm % NONE % NONE
   893       else
   894         (case prf1 of
   895           PAxm ("Pure.reflexive", _, _) % _ =>
   896             combination_axm %> remove_types f % NONE
   897         | _ => combination_axm %> remove_types f %> remove_types g)
   898   in
   899     (case T of
   900       Type ("fun", _) => prf %
   901         (case head_of f of
   902           Abs _ => SOME (remove_types t)
   903         | Var _ => SOME (remove_types t)
   904         | _ => NONE) %
   905         (case head_of g of
   906            Abs _ => SOME (remove_types u)
   907         | Var _ => SOME (remove_types u)
   908         | _ => NONE) %% prf1 %% prf2
   909      | _ => prf % NONE % NONE %% prf1 %% prf2)
   910   end;
   911 
   912 fun equal_intr A B prf1 prf2 =
   913   equal_intr_axm %> remove_types A %> remove_types B %% prf1 %% prf2;
   914 
   915 fun equal_elim A B prf1 prf2 =
   916   equal_elim_axm %> remove_types A %> remove_types B %% prf1 %% prf2;
   917 
   918 
   919 (**** type classes ****)
   920 
   921 fun strip_shyps_proof algebra present witnessed extra_sorts prf =
   922   let
   923     fun get S2 (T, S1) = if Sorts.sort_le algebra (S1, S2) then SOME T else NONE;
   924     val extra = map (fn S => (TFree ("'dummy", S), S)) extra_sorts;
   925     val replacements = present @ extra @ witnessed;
   926     fun replace T =
   927       if exists (fn (T', _) => T' = T) present then raise Same.SAME
   928       else
   929         (case get_first (get (Type.sort_of_atyp T)) replacements of
   930           SOME T' => T'
   931         | NONE => raise Fail "strip_shyps_proof: bad type variable in proof term");
   932   in Same.commit (map_proof_types_same (Term_Subst.map_atypsT_same replace)) prf end;
   933 
   934 
   935 local
   936 
   937 type axclass_proofs =
   938  {classrel_proof: theory -> class * class -> proof,
   939   arity_proof: theory -> string * sort list * class -> proof};
   940 
   941 val axclass_proofs: axclass_proofs Single_Assignment.var =
   942   Single_Assignment.var "Proofterm.axclass_proofs";
   943 
   944 fun axclass_proof which thy x =
   945   (case Single_Assignment.peek axclass_proofs of
   946     NONE => raise Fail "Axclass proof operations not installed"
   947   | SOME prfs => which prfs thy x);
   948 
   949 in
   950 
   951 val classrel_proof = axclass_proof #classrel_proof;
   952 val arity_proof = axclass_proof #arity_proof;
   953 
   954 fun install_axclass_proofs prfs = Single_Assignment.assign axclass_proofs prfs;
   955 
   956 end;
   957 
   958 
   959 local
   960 
   961 fun canonical_instance typs =
   962   let
   963     val names = Name.invent Name.context Name.aT (length typs);
   964     val instT = map2 (fn a => fn T => (((a, 0), []), Type.strip_sorts T)) names typs;
   965   in instantiate (instT, []) end;
   966 
   967 in
   968 
   969 fun of_sort_proof thy hyps =
   970   Sorts.of_sort_derivation (Sign.classes_of thy)
   971    {class_relation = fn typ => fn (prf, c1) => fn c2 =>
   972       if c1 = c2 then prf
   973       else canonical_instance [typ] (classrel_proof thy (c1, c2)) %% prf,
   974     type_constructor = fn (a, typs) => fn dom => fn c =>
   975       let val Ss = map (map snd) dom and prfs = maps (map fst) dom
   976       in proof_combP (canonical_instance typs (arity_proof thy (a, Ss, c)), prfs) end,
   977     type_variable = fn typ => map (fn c => (hyps (typ, c), c)) (Type.sort_of_atyp typ)};
   978 
   979 end;
   980 
   981 
   982 (***** axioms and theorems *****)
   983 
   984 val proofs = Unsynchronized.ref 2;
   985 fun proofs_enabled () = ! proofs >= 2;
   986 
   987 fun vars_of t = map Var (rev (Term.add_vars t []));
   988 fun frees_of t = map Free (rev (Term.add_frees t []));
   989 
   990 fun test_args _ [] = true
   991   | test_args is (Bound i :: ts) =
   992       not (member (op =) is i) andalso test_args (i :: is) ts
   993   | test_args _ _ = false;
   994 
   995 fun is_fun (Type ("fun", _)) = true
   996   | is_fun (TVar _) = true
   997   | is_fun _ = false;
   998 
   999 fun add_funvars Ts (vs, t) =
  1000   if is_fun (fastype_of1 (Ts, t)) then
  1001     union (op =) vs (map_filter (fn Var (ixn, T) =>
  1002       if is_fun T then SOME ixn else NONE | _ => NONE) (vars_of t))
  1003   else vs;
  1004 
  1005 fun add_npvars q p Ts (vs, Const ("==>", _) $ t $ u) =
  1006       add_npvars q p Ts (add_npvars q (not p) Ts (vs, t), u)
  1007   | add_npvars q p Ts (vs, Const ("all", Type (_, [Type (_, [T, _]), _])) $ t) =
  1008       add_npvars q p Ts (vs, if p andalso q then betapply (t, Var (("",0), T)) else t)
  1009   | add_npvars q p Ts (vs, Abs (_, T, t)) = add_npvars q p (T::Ts) (vs, t)
  1010   | add_npvars _ _ Ts (vs, t) = add_npvars' Ts (vs, t)
  1011 and add_npvars' Ts (vs, t) = (case strip_comb t of
  1012     (Var (ixn, _), ts) => if test_args [] ts then vs
  1013       else Library.foldl (add_npvars' Ts)
  1014         (AList.update (op =) (ixn,
  1015           Library.foldl (add_funvars Ts) ((these ooo AList.lookup) (op =) vs ixn, ts)) vs, ts)
  1016   | (Abs (_, T, u), ts) => Library.foldl (add_npvars' (T::Ts)) (vs, u :: ts)
  1017   | (_, ts) => Library.foldl (add_npvars' Ts) (vs, ts));
  1018 
  1019 fun prop_vars (Const ("==>", _) $ P $ Q) = union (op =) (prop_vars P) (prop_vars Q)
  1020   | prop_vars (Const ("all", _) $ Abs (_, _, t)) = prop_vars t
  1021   | prop_vars t = (case strip_comb t of
  1022       (Var (ixn, _), _) => [ixn] | _ => []);
  1023 
  1024 fun is_proj t =
  1025   let
  1026     fun is_p i t = (case strip_comb t of
  1027         (Bound j, []) => false
  1028       | (Bound j, ts) => j >= i orelse exists (is_p i) ts
  1029       | (Abs (_, _, u), _) => is_p (i+1) u
  1030       | (_, ts) => exists (is_p i) ts)
  1031   in (case strip_abs_body t of
  1032         Bound _ => true
  1033       | t' => is_p 0 t')
  1034   end;
  1035 
  1036 fun needed_vars prop =
  1037   union (op =) (Library.foldl (uncurry (union (op =)))
  1038     ([], map (uncurry (insert (op =))) (add_npvars true true [] ([], prop))))
  1039   (prop_vars prop);
  1040 
  1041 fun gen_axm_proof c name prop =
  1042   let
  1043     val nvs = needed_vars prop;
  1044     val args = map (fn (v as Var (ixn, _)) =>
  1045         if member (op =) nvs ixn then SOME v else NONE) (vars_of prop) @
  1046       map SOME (frees_of prop);
  1047   in
  1048     proof_combt' (c (name, prop, NONE), args)
  1049   end;
  1050 
  1051 val axm_proof = gen_axm_proof PAxm;
  1052 
  1053 val dummy = Const (Term.dummy_patternN, dummyT);
  1054 
  1055 fun oracle_proof name prop =
  1056   if ! proofs = 0 then ((name, dummy), Oracle (name, dummy, NONE))
  1057   else ((name, prop), gen_axm_proof Oracle name prop);
  1058 
  1059 fun shrink_proof thy =
  1060   let
  1061     val (typ, term) = Term_Sharing.init thy;
  1062 
  1063     fun shrink ls lev (prf as Abst (a, T, body)) =
  1064           let val (b, is, ch, body') = shrink ls (lev+1) body
  1065           in (b, is, ch, if ch then Abst (a, Option.map typ T, body') else prf) end
  1066       | shrink ls lev (prf as AbsP (a, t, body)) =
  1067           let val (b, is, ch, body') = shrink (lev::ls) lev body
  1068           in (b orelse member (op =) is 0, map_filter (fn 0 => NONE | i => SOME (i-1)) is,
  1069             ch, if ch then AbsP (a, Option.map term t, body') else prf)
  1070           end
  1071       | shrink ls lev prf =
  1072           let val (is, ch, _, prf') = shrink' ls lev [] [] prf
  1073           in (false, is, ch, prf') end
  1074     and shrink' ls lev ts prfs (prf as prf1 %% prf2) =
  1075           let
  1076             val p as (_, is', ch', prf') = shrink ls lev prf2;
  1077             val (is, ch, ts', prf'') = shrink' ls lev ts (p::prfs) prf1
  1078           in (union (op =) is is', ch orelse ch', ts',
  1079               if ch orelse ch' then prf'' %% prf' else prf)
  1080           end
  1081       | shrink' ls lev ts prfs (prf as prf1 % t) =
  1082           let val (is, ch, (ch', t')::ts', prf') = shrink' ls lev (t::ts) prfs prf1
  1083           in (is, ch orelse ch', ts',
  1084               if ch orelse ch' then prf' % Option.map term t' else prf) end
  1085       | shrink' ls lev ts prfs (prf as PBound i) =
  1086           (if exists (fn SOME (Bound j) => lev-j <= nth ls i | _ => true) ts
  1087              orelse has_duplicates (op =)
  1088                (Library.foldl (fn (js, SOME (Bound j)) => j :: js | (js, _) => js) ([], ts))
  1089              orelse exists #1 prfs then [i] else [], false, map (pair false) ts, prf)
  1090       | shrink' ls lev ts prfs (Hyp t) = ([], false, map (pair false) ts, Hyp (term t))
  1091       | shrink' ls lev ts prfs (prf as MinProof) = ([], false, map (pair false) ts, prf)
  1092       | shrink' ls lev ts prfs (prf as OfClass _) = ([], false, map (pair false) ts, prf)
  1093       | shrink' ls lev ts prfs prf =
  1094           let
  1095             val prop =
  1096               (case prf of
  1097                 PAxm (_, prop, _) => prop
  1098               | Oracle (_, prop, _) => prop
  1099               | Promise (_, prop, _) => prop
  1100               | PThm (_, ((_, prop, _), _)) => prop
  1101               | _ => raise Fail "shrink: proof not in normal form");
  1102             val vs = vars_of prop;
  1103             val (ts', ts'') = chop (length vs) ts;
  1104             val insts = take (length ts') (map (fst o dest_Var) vs) ~~ ts';
  1105             val nvs = Library.foldl (fn (ixns', (ixn, ixns)) =>
  1106               insert (op =) ixn (case AList.lookup (op =) insts ixn of
  1107                   SOME (SOME t) => if is_proj t then union (op =) ixns ixns' else ixns'
  1108                 | _ => union (op =) ixns ixns'))
  1109                   (needed prop ts'' prfs, add_npvars false true [] ([], prop));
  1110             val insts' = map
  1111               (fn (ixn, x as SOME _) => if member (op =) nvs ixn then (false, x) else (true, NONE)
  1112                 | (_, x) => (false, x)) insts
  1113           in ([], false, insts' @ map (pair false) ts'', prf) end
  1114     and needed (Const ("==>", _) $ t $ u) ts ((b, _, _, _)::prfs) =
  1115           union (op =) (if b then map (fst o dest_Var) (vars_of t) else []) (needed u ts prfs)
  1116       | needed (Var (ixn, _)) (_::_) _ = [ixn]
  1117       | needed _ _ _ = [];
  1118   in shrink end;
  1119 
  1120 
  1121 (**** Simple first order matching functions for terms and proofs ****)
  1122 
  1123 exception PMatch;
  1124 
  1125 (** see pattern.ML **)
  1126 
  1127 fun flt (i: int) = filter (fn n => n < i);
  1128 
  1129 fun fomatch Ts tymatch j instsp p =
  1130   let
  1131     fun mtch (instsp as (tyinsts, insts)) = fn
  1132         (Var (ixn, T), t)  =>
  1133           if j>0 andalso not (null (flt j (loose_bnos t)))
  1134           then raise PMatch
  1135           else (tymatch (tyinsts, fn () => (T, fastype_of1 (Ts, t))),
  1136             (ixn, t) :: insts)
  1137       | (Free (a, T), Free (b, U)) =>
  1138           if a=b then (tymatch (tyinsts, K (T, U)), insts) else raise PMatch
  1139       | (Const (a, T), Const (b, U))  =>
  1140           if a=b then (tymatch (tyinsts, K (T, U)), insts) else raise PMatch
  1141       | (f $ t, g $ u) => mtch (mtch instsp (f, g)) (t, u)
  1142       | (Bound i, Bound j) => if i=j then instsp else raise PMatch
  1143       | _ => raise PMatch
  1144   in mtch instsp (pairself Envir.beta_eta_contract p) end;
  1145 
  1146 fun match_proof Ts tymatch =
  1147   let
  1148     fun optmatch _ inst (NONE, _) = inst
  1149       | optmatch _ _ (SOME _, NONE) = raise PMatch
  1150       | optmatch mtch inst (SOME x, SOME y) = mtch inst (x, y)
  1151 
  1152     fun matcht Ts j (pinst, tinst) (t, u) =
  1153       (pinst, fomatch Ts tymatch j tinst (t, Envir.beta_norm u));
  1154     fun matchT (pinst, (tyinsts, insts)) p =
  1155       (pinst, (tymatch (tyinsts, K p), insts));
  1156     fun matchTs inst (Ts, Us) = Library.foldl (uncurry matchT) (inst, Ts ~~ Us);
  1157 
  1158     fun mtch Ts i j (pinst, tinst) (Hyp (Var (ixn, _)), prf) =
  1159           if i = 0 andalso j = 0 then ((ixn, prf) :: pinst, tinst)
  1160           else (case apfst (flt i) (apsnd (flt j)
  1161                   (prf_add_loose_bnos 0 0 prf ([], []))) of
  1162               ([], []) => ((ixn, incr_pboundvars (~i) (~j) prf) :: pinst, tinst)
  1163             | ([], _) => if j = 0 then
  1164                    ((ixn, incr_pboundvars (~i) (~j) prf) :: pinst, tinst)
  1165                  else raise PMatch
  1166             | _ => raise PMatch)
  1167       | mtch Ts i j inst (prf1 % opt1, prf2 % opt2) =
  1168           optmatch (matcht Ts j) (mtch Ts i j inst (prf1, prf2)) (opt1, opt2)
  1169       | mtch Ts i j inst (prf1 %% prf2, prf1' %% prf2') =
  1170           mtch Ts i j (mtch Ts i j inst (prf1, prf1')) (prf2, prf2')
  1171       | mtch Ts i j inst (Abst (_, opT, prf1), Abst (_, opU, prf2)) =
  1172           mtch (the_default dummyT opU :: Ts) i (j+1)
  1173             (optmatch matchT inst (opT, opU)) (prf1, prf2)
  1174       | mtch Ts i j inst (prf1, Abst (_, opU, prf2)) =
  1175           mtch (the_default dummyT opU :: Ts) i (j+1) inst
  1176             (incr_pboundvars 0 1 prf1 %> Bound 0, prf2)
  1177       | mtch Ts i j inst (AbsP (_, opt, prf1), AbsP (_, opu, prf2)) =
  1178           mtch Ts (i+1) j (optmatch (matcht Ts j) inst (opt, opu)) (prf1, prf2)
  1179       | mtch Ts i j inst (prf1, AbsP (_, _, prf2)) =
  1180           mtch Ts (i+1) j inst (incr_pboundvars 1 0 prf1 %% PBound 0, prf2)
  1181       | mtch Ts i j inst (PAxm (s1, _, opTs), PAxm (s2, _, opUs)) =
  1182           if s1 = s2 then optmatch matchTs inst (opTs, opUs)
  1183           else raise PMatch
  1184       | mtch Ts i j inst (OfClass (T1, c1), OfClass (T2, c2)) =
  1185           if c1 = c2 then matchT inst (T1, T2)
  1186           else raise PMatch
  1187       | mtch Ts i j inst (PThm (_, ((name1, prop1, opTs), _)), PThm (_, ((name2, prop2, opUs), _))) =
  1188           if name1 = name2 andalso prop1 = prop2 then
  1189             optmatch matchTs inst (opTs, opUs)
  1190           else raise PMatch
  1191       | mtch _ _ _ inst (PBound i, PBound j) = if i = j then inst else raise PMatch
  1192       | mtch _ _ _ _ _ = raise PMatch
  1193   in mtch Ts 0 0 end;
  1194 
  1195 fun prf_subst (pinst, (tyinsts, insts)) =
  1196   let
  1197     val substT = Envir.subst_type_same tyinsts;
  1198     val substTs = Same.map substT;
  1199 
  1200     fun subst' lev (Var (xi, _)) =
  1201         (case AList.lookup (op =) insts xi of
  1202           NONE => raise Same.SAME
  1203         | SOME u => incr_boundvars lev u)
  1204       | subst' _ (Const (s, T)) = Const (s, substT T)
  1205       | subst' _ (Free (s, T)) = Free (s, substT T)
  1206       | subst' lev (Abs (a, T, body)) =
  1207           (Abs (a, substT T, Same.commit (subst' (lev + 1)) body)
  1208             handle Same.SAME => Abs (a, T, subst' (lev + 1) body))
  1209       | subst' lev (f $ t) =
  1210           (subst' lev f $ Same.commit (subst' lev) t
  1211             handle Same.SAME => f $ subst' lev t)
  1212       | subst' _ _ = raise Same.SAME;
  1213 
  1214     fun subst plev tlev (AbsP (a, t, body)) =
  1215           (AbsP (a, Same.map_option (subst' tlev) t, Same.commit (subst (plev + 1) tlev) body)
  1216             handle Same.SAME => AbsP (a, t, subst (plev + 1) tlev body))
  1217       | subst plev tlev (Abst (a, T, body)) =
  1218           (Abst (a, Same.map_option substT T, Same.commit (subst plev (tlev + 1)) body)
  1219             handle Same.SAME => Abst (a, T, subst plev (tlev + 1) body))
  1220       | subst plev tlev (prf %% prf') =
  1221           (subst plev tlev prf %% Same.commit (subst plev tlev) prf'
  1222             handle Same.SAME => prf %% subst plev tlev prf')
  1223       | subst plev tlev (prf % t) =
  1224           (subst plev tlev prf % Same.commit (Same.map_option (subst' tlev)) t
  1225             handle Same.SAME => prf % Same.map_option (subst' tlev) t)
  1226       | subst plev tlev (Hyp (Var (xi, _))) =
  1227           (case AList.lookup (op =) pinst xi of
  1228             NONE => raise Same.SAME
  1229           | SOME prf' => incr_pboundvars plev tlev prf')
  1230       | subst _ _ (PAxm (id, prop, Ts)) = PAxm (id, prop, Same.map_option substTs Ts)
  1231       | subst _ _ (OfClass (T, c)) = OfClass (substT T, c)
  1232       | subst _ _ (Oracle (id, prop, Ts)) = Oracle (id, prop, Same.map_option substTs Ts)
  1233       | subst _ _ (Promise (i, prop, Ts)) = Promise (i, prop, substTs Ts)
  1234       | subst _ _ (PThm (i, ((id, prop, Ts), body))) =
  1235           PThm (i, ((id, prop, Same.map_option substTs Ts), body))
  1236       | subst _ _ _ = raise Same.SAME;
  1237   in fn t => subst 0 0 t handle Same.SAME => t end;
  1238 
  1239 (*A fast unification filter: true unless the two terms cannot be unified.
  1240   Terms must be NORMAL.  Treats all Vars as distinct. *)
  1241 fun could_unify prf1 prf2 =
  1242   let
  1243     fun matchrands (prf1 %% prf2) (prf1' %% prf2') =
  1244           could_unify prf2 prf2' andalso matchrands prf1 prf1'
  1245       | matchrands (prf % SOME t) (prf' % SOME t') =
  1246           Term.could_unify (t, t') andalso matchrands prf prf'
  1247       | matchrands (prf % _) (prf' % _) = matchrands prf prf'
  1248       | matchrands _ _ = true
  1249 
  1250     fun head_of (prf %% _) = head_of prf
  1251       | head_of (prf % _) = head_of prf
  1252       | head_of prf = prf
  1253 
  1254   in case (head_of prf1, head_of prf2) of
  1255         (_, Hyp (Var _)) => true
  1256       | (Hyp (Var _), _) => true
  1257       | (PAxm (a, _, _), PAxm (b, _, _)) => a = b andalso matchrands prf1 prf2
  1258       | (OfClass (_, c), OfClass (_, d)) => c = d andalso matchrands prf1 prf2
  1259       | (PThm (_, ((a, propa, _), _)), PThm (_, ((b, propb, _), _))) =>
  1260           a = b andalso propa = propb andalso matchrands prf1 prf2
  1261       | (PBound i, PBound j) => i = j andalso matchrands prf1 prf2
  1262       | (AbsP _, _) =>  true   (*because of possible eta equality*)
  1263       | (Abst _, _) =>  true
  1264       | (_, AbsP _) =>  true
  1265       | (_, Abst _) =>  true
  1266       | _ => false
  1267   end;
  1268 
  1269 
  1270 (**** rewriting on proof terms ****)
  1271 
  1272 val no_skel = PBound 0;
  1273 val normal_skel = Hyp (Var ((Name.uu, 0), propT));
  1274 
  1275 fun rewrite_prf tymatch (rules, procs) prf =
  1276   let
  1277     fun rew _ _ (Abst (_, _, body) % SOME t) = SOME (prf_subst_bounds [t] body, no_skel)
  1278       | rew _ _ (AbsP (_, _, body) %% prf) = SOME (prf_subst_pbounds [prf] body, no_skel)
  1279       | rew Ts hs prf =
  1280           (case get_first (fn r => r Ts hs prf) procs of
  1281             NONE => get_first (fn (prf1, prf2) => SOME (prf_subst
  1282               (match_proof Ts tymatch ([], (Vartab.empty, [])) (prf1, prf)) prf2, prf2)
  1283                  handle PMatch => NONE) (filter (could_unify prf o fst) rules)
  1284           | some => some);
  1285 
  1286     fun rew0 Ts hs (prf as AbsP (_, _, prf' %% PBound 0)) =
  1287           if prf_loose_Pbvar1 prf' 0 then rew Ts hs prf
  1288           else
  1289             let val prf'' = incr_pboundvars (~1) 0 prf'
  1290             in SOME (the_default (prf'', no_skel) (rew Ts hs prf'')) end
  1291       | rew0 Ts hs (prf as Abst (_, _, prf' % SOME (Bound 0))) =
  1292           if prf_loose_bvar1 prf' 0 then rew Ts hs prf
  1293           else
  1294             let val prf'' = incr_pboundvars 0 (~1) prf'
  1295             in SOME (the_default (prf'', no_skel) (rew Ts hs prf'')) end
  1296       | rew0 Ts hs prf = rew Ts hs prf;
  1297 
  1298     fun rew1 _ _ (Hyp (Var _)) _ = NONE
  1299       | rew1 Ts hs skel prf = (case rew2 Ts hs skel prf of
  1300           SOME prf1 => (case rew0 Ts hs prf1 of
  1301               SOME (prf2, skel') => SOME (the_default prf2 (rew1 Ts hs skel' prf2))
  1302             | NONE => SOME prf1)
  1303         | NONE => (case rew0 Ts hs prf of
  1304               SOME (prf1, skel') => SOME (the_default prf1 (rew1 Ts hs skel' prf1))
  1305             | NONE => NONE))
  1306 
  1307     and rew2 Ts hs skel (prf % SOME t) = (case prf of
  1308             Abst (_, _, body) =>
  1309               let val prf' = prf_subst_bounds [t] body
  1310               in SOME (the_default prf' (rew2 Ts hs no_skel prf')) end
  1311           | _ => (case rew1 Ts hs (case skel of skel' % _ => skel' | _ => no_skel) prf of
  1312               SOME prf' => SOME (prf' % SOME t)
  1313             | NONE => NONE))
  1314       | rew2 Ts hs skel (prf % NONE) = Option.map (fn prf' => prf' % NONE)
  1315           (rew1 Ts hs (case skel of skel' % _ => skel' | _ => no_skel) prf)
  1316       | rew2 Ts hs skel (prf1 %% prf2) = (case prf1 of
  1317             AbsP (_, _, body) =>
  1318               let val prf' = prf_subst_pbounds [prf2] body
  1319               in SOME (the_default prf' (rew2 Ts hs no_skel prf')) end
  1320           | _ =>
  1321             let val (skel1, skel2) = (case skel of
  1322                 skel1 %% skel2 => (skel1, skel2)
  1323               | _ => (no_skel, no_skel))
  1324             in case rew1 Ts hs skel1 prf1 of
  1325                 SOME prf1' => (case rew1 Ts hs skel2 prf2 of
  1326                     SOME prf2' => SOME (prf1' %% prf2')
  1327                   | NONE => SOME (prf1' %% prf2))
  1328               | NONE => (case rew1 Ts hs skel2 prf2 of
  1329                     SOME prf2' => SOME (prf1 %% prf2')
  1330                   | NONE => NONE)
  1331             end)
  1332       | rew2 Ts hs skel (Abst (s, T, prf)) = (case rew1 (the_default dummyT T :: Ts) hs
  1333               (case skel of Abst (_, _, skel') => skel' | _ => no_skel) prf of
  1334             SOME prf' => SOME (Abst (s, T, prf'))
  1335           | NONE => NONE)
  1336       | rew2 Ts hs skel (AbsP (s, t, prf)) = (case rew1 Ts (t :: hs)
  1337               (case skel of AbsP (_, _, skel') => skel' | _ => no_skel) prf of
  1338             SOME prf' => SOME (AbsP (s, t, prf'))
  1339           | NONE => NONE)
  1340       | rew2 _ _ _ _ = NONE;
  1341 
  1342   in the_default prf (rew1 [] [] no_skel prf) end;
  1343 
  1344 fun rewrite_proof thy = rewrite_prf (fn (tyenv, f) =>
  1345   Sign.typ_match thy (f ()) tyenv handle Type.TYPE_MATCH => raise PMatch);
  1346 
  1347 fun rewrite_proof_notypes rews = rewrite_prf fst rews;
  1348 
  1349 
  1350 (**** theory data ****)
  1351 
  1352 structure Data = Theory_Data
  1353 (
  1354   type T =
  1355     (stamp * (proof * proof)) list *
  1356     (stamp * (typ list -> term option list -> proof -> (proof * proof) option)) list;
  1357 
  1358   val empty = ([], []);
  1359   val extend = I;
  1360   fun merge ((rules1, procs1), (rules2, procs2)) : T =
  1361     (AList.merge (op =) (K true) (rules1, rules2),
  1362       AList.merge (op =) (K true) (procs1, procs2));
  1363 );
  1364 
  1365 fun get_data thy = let val (rules, procs) = Data.get thy in (map #2 rules, map #2 procs) end;
  1366 fun rew_proof thy = rewrite_prf fst (get_data thy);
  1367 
  1368 fun add_prf_rrule r = (Data.map o apfst) (cons (stamp (), r));
  1369 fun add_prf_rproc p = (Data.map o apsnd) (cons (stamp (), p));
  1370 
  1371 
  1372 (***** promises *****)
  1373 
  1374 fun promise_proof thy i prop =
  1375   let
  1376     val _ = prop |> Term.exists_subterm (fn t =>
  1377       (Term.is_Free t orelse Term.is_Var t) andalso
  1378         raise Fail ("promise_proof: illegal variable " ^ Syntax.string_of_term_global thy t));
  1379     val _ = prop |> Term.exists_type (Term.exists_subtype
  1380       (fn TFree (a, _) => raise Fail ("promise_proof: illegal type variable " ^ quote a)
  1381         | _ => false));
  1382   in Promise (i, prop, map TVar (Term.add_tvars prop [])) end;
  1383 
  1384 fun fulfill_norm_proof thy ps body0 =
  1385   let
  1386     val PBody {oracles = oracles0, thms = thms0, proof = proof0} = body0;
  1387     val oracles = fold (fn (_, PBody {oracles, ...}) => merge_oracles oracles) ps oracles0;
  1388     val thms = fold (fn (_, PBody {thms, ...}) => merge_thms thms) ps thms0;
  1389     val proofs = fold (fn (i, PBody {proof, ...}) => Inttab.update (i, proof)) ps Inttab.empty;
  1390 
  1391     fun fill (Promise (i, prop, Ts)) =
  1392           (case Inttab.lookup proofs i of
  1393             NONE => NONE
  1394           | SOME prf => SOME (instantiate (Term.add_tvars prop [] ~~ Ts, []) prf, normal_skel))
  1395       | fill _ = NONE;
  1396     val (rules, procs) = get_data thy;
  1397     val proof = rewrite_prf fst (rules, K (K fill) :: procs) proof0;
  1398     val _ = join_thms thms;
  1399   in PBody {oracles = oracles, thms = thms, proof = proof} end;
  1400 
  1401 fun fulfill_proof_future _ [] postproc body =
  1402       if not (Multithreading.enabled ()) then Future.value (postproc (Future.join body))
  1403       else Future.map postproc body
  1404   | fulfill_proof_future thy promises postproc body =
  1405       (singleton o Future.forks)
  1406         {name = "Proofterm.fulfill_proof_future", group = NONE,
  1407           deps = Future.task_of body :: map (Future.task_of o snd) promises, pri = 0,
  1408           interrupts = true}
  1409         (fn () =>
  1410           postproc (fulfill_norm_proof thy (map (apsnd Future.join) promises) (Future.join body)));
  1411 
  1412 
  1413 (***** abstraction over sort constraints *****)
  1414 
  1415 fun unconstrainT_prf thy (atyp_map, constraints) =
  1416   let
  1417     fun hyp_map hyp =
  1418       (case AList.lookup (op =) constraints hyp of
  1419         SOME t => Hyp t
  1420       | NONE => raise Fail "unconstrainT_prf: missing constraint");
  1421 
  1422     val typ = Term_Subst.map_atypsT_same (Type.strip_sorts o atyp_map);
  1423     fun ofclass (ty, c) =
  1424       let val ty' = Term.map_atyps atyp_map ty;
  1425       in the_single (of_sort_proof thy hyp_map (ty', [c])) end;
  1426   in
  1427     Same.commit (map_proof_same (Term_Subst.map_types_same typ) typ ofclass)
  1428     #> fold_rev (implies_intr_proof o snd) constraints
  1429   end;
  1430 
  1431 fun unconstrainT_body thy constrs (PBody {oracles, thms, proof}) =
  1432   PBody
  1433    {oracles = oracles,  (* FIXME merge (!), unconstrain (!?!) *)
  1434     thms = thms,  (* FIXME merge (!) *)
  1435     proof = unconstrainT_prf thy constrs proof};
  1436 
  1437 
  1438 (***** theorems *****)
  1439 
  1440 fun prepare_thm_proof thy name shyps hyps concl promises body =
  1441   let
  1442     val PBody {oracles = oracles0, thms = thms0, proof = prf} = body;
  1443     val prop = Logic.list_implies (hyps, concl);
  1444     val nvs = needed_vars prop;
  1445     val args = map (fn (v as Var (ixn, _)) =>
  1446         if member (op =) nvs ixn then SOME v else NONE) (vars_of prop) @
  1447       map SOME (frees_of prop);
  1448 
  1449     val ((atyp_map, constraints, outer_constraints), prop1) = Logic.unconstrainT shyps prop;
  1450     val postproc = unconstrainT_body thy (atyp_map, constraints);
  1451     val args1 =
  1452       (map o Option.map o Term.map_types o Term.map_atyps)
  1453         (Type.strip_sorts o atyp_map) args;
  1454     val argsP = map OfClass outer_constraints @ map Hyp hyps;
  1455 
  1456     fun full_proof0 () =
  1457       #4 (shrink_proof thy [] 0 (rew_proof thy (fold_rev implies_intr_proof hyps prf)));
  1458 
  1459     fun make_body0 proof0 = PBody {oracles = oracles0, thms = thms0, proof = proof0};
  1460     val body0 =
  1461       if not (proofs_enabled ()) then Future.value (make_body0 MinProof)
  1462       else if not (Multithreading.enabled ()) then Future.value (make_body0 (full_proof0 ()))
  1463       else
  1464         (singleton o Future.forks)
  1465           {name = "Proofterm.prepare_thm_proof", group = NONE,
  1466             deps = [], pri = ~1, interrupts = true}
  1467           (make_body0 o full_proof0);
  1468 
  1469     fun new_prf () = (serial (), fulfill_proof_future thy promises postproc body0);
  1470     val (i, body') =
  1471       (*non-deterministic, depends on unknown promises*)
  1472       (case strip_combt (fst (strip_combP prf)) of
  1473         (PThm (i, ((old_name, prop', NONE), body')), args') =>
  1474           if (old_name = "" orelse old_name = name) andalso prop1 = prop' andalso args = args'
  1475           then (i, body')
  1476           else new_prf ()
  1477       | _ => new_prf ());
  1478     val head = PThm (i, ((name, prop1, NONE), body'));
  1479   in ((i, (name, prop1, body')), head, args, argsP, args1) end;
  1480 
  1481 fun thm_proof thy name shyps hyps concl promises body =
  1482   let val (pthm, head, args, argsP, _) = prepare_thm_proof thy name shyps hyps concl promises body
  1483   in (pthm, proof_combP (proof_combt' (head, args), argsP)) end;
  1484 
  1485 fun unconstrain_thm_proof thy shyps concl promises body =
  1486   let
  1487     val (pthm, head, _, _, args) = prepare_thm_proof thy "" shyps [] concl promises body
  1488   in (pthm, proof_combt' (head, args)) end;
  1489 
  1490 
  1491 fun get_name shyps hyps prop prf =
  1492   let val (_, prop) = Logic.unconstrainT shyps (Logic.list_implies (hyps, prop)) in
  1493     (case strip_combt (fst (strip_combP prf)) of
  1494       (PThm (_, ((name, prop', _), _)), _) => if prop = prop' then name else ""
  1495     | _ => "")
  1496   end;
  1497 
  1498 fun guess_name (PThm (_, ((name, _, _), _))) = name
  1499   | guess_name (prf %% Hyp _) = guess_name prf
  1500   | guess_name (prf %% OfClass _) = guess_name prf
  1501   | guess_name (prf % NONE) = guess_name prf
  1502   | guess_name (prf % SOME (Var _)) = guess_name prf
  1503   | guess_name _ = "";
  1504 
  1505 end;
  1506 
  1507 structure Basic_Proofterm : BASIC_PROOFTERM = Proofterm;
  1508 open Basic_Proofterm;