src/Pure/proofterm.ML
author wenzelm
Fri Oct 07 21:16:48 2016 +0200 (2016-10-07)
changeset 64092 95469c544b82
parent 63857 0883c1cc655c
child 64566 679710d324f1
permissions -rw-r--r--
accept obscure timezone used in 2011;
     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    | % of proof * term option
    19    | %% 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 peek_status: 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 unions_oracles: oracle Ord_List.T list -> oracle Ord_List.T
    50   val unions_thms: pthm Ord_List.T list -> pthm Ord_List.T
    51   val all_oracles_of: proof_body -> oracle Ord_List.T
    52   val approximate_proof_body: proof -> proof_body
    53   val no_proof_body: proof_body
    54   val no_thm_proofs: proof -> proof
    55 
    56   val encode: proof XML.Encode.T
    57   val encode_body: proof_body XML.Encode.T
    58   val decode: proof XML.Decode.T
    59   val decode_body: proof_body XML.Decode.T
    60 
    61   (** primitive operations **)
    62   val proofs_enabled: unit -> bool
    63   val proof_combt: proof * term list -> proof
    64   val proof_combt': proof * term option list -> proof
    65   val proof_combP: proof * proof list -> proof
    66   val strip_combt: proof -> proof * term option list
    67   val strip_combP: proof -> proof * proof list
    68   val strip_thm: proof_body -> proof_body
    69   val map_proof_same: term Same.operation -> typ Same.operation
    70     -> (typ * class -> proof) -> proof Same.operation
    71   val map_proof_terms_same: term Same.operation -> typ Same.operation -> proof Same.operation
    72   val map_proof_types_same: typ Same.operation -> proof Same.operation
    73   val map_proof_terms: (term -> term) -> (typ -> typ) -> proof -> proof
    74   val map_proof_types: (typ -> typ) -> proof -> proof
    75   val fold_proof_terms: (term -> 'a -> 'a) -> (typ -> 'a -> 'a) -> proof -> 'a -> 'a
    76   val maxidx_proof: proof -> int -> int
    77   val size_of_proof: proof -> int
    78   val change_type: typ list option -> proof -> proof
    79   val prf_abstract_over: term -> proof -> proof
    80   val prf_incr_bv: int -> int -> int -> int -> proof -> proof
    81   val incr_pboundvars: int -> int -> proof -> proof
    82   val prf_loose_bvar1: proof -> int -> bool
    83   val prf_loose_Pbvar1: proof -> int -> bool
    84   val prf_add_loose_bnos: int -> int -> proof -> int list * int list -> int list * int list
    85   val norm_proof: Envir.env -> proof -> proof
    86   val norm_proof': Envir.env -> proof -> proof
    87   val prf_subst_bounds: term list -> proof -> proof
    88   val prf_subst_pbounds: proof list -> proof -> proof
    89   val freeze_thaw_prf: proof -> proof * (proof -> proof)
    90 
    91   (** proof terms for specific inference rules **)
    92   val implies_intr_proof: term -> proof -> proof
    93   val implies_intr_proof': term -> proof -> proof
    94   val forall_intr_proof: term -> string -> proof -> proof
    95   val forall_intr_proof': term -> proof -> proof
    96   val varify_proof: term -> (string * sort) list -> proof -> proof
    97   val legacy_freezeT: term -> proof -> proof
    98   val rotate_proof: term list -> term -> int -> proof -> proof
    99   val permute_prems_proof: term list -> int -> int -> proof -> proof
   100   val generalize: string list * string list -> int -> proof -> proof
   101   val instantiate: ((indexname * sort) * typ) list * ((indexname * typ) * term) list
   102     -> proof -> proof
   103   val lift_proof: term -> int -> term -> proof -> proof
   104   val incr_indexes: int -> proof -> proof
   105   val assumption_proof: term list -> term -> int -> proof -> proof
   106   val bicompose_proof: bool -> term list -> term list -> term list -> term option ->
   107     int -> int -> proof -> proof -> proof
   108   val equality_axms: (string * term) list
   109   val reflexive_axm: proof
   110   val symmetric_axm: proof
   111   val transitive_axm: proof
   112   val equal_intr_axm: proof
   113   val equal_elim_axm: proof
   114   val abstract_rule_axm: proof
   115   val combination_axm: proof
   116   val reflexive: proof
   117   val symmetric: proof -> proof
   118   val transitive: term -> typ -> proof -> proof -> proof
   119   val abstract_rule: term -> string -> proof -> proof
   120   val combination: term -> term -> term -> term -> typ -> proof -> proof -> proof
   121   val equal_intr: term -> term -> proof -> proof -> proof
   122   val equal_elim: term -> term -> proof -> proof -> proof
   123   val strip_shyps_proof: Sorts.algebra -> (typ * sort) list -> (typ * sort) list ->
   124     sort list -> proof -> proof
   125   val classrel_proof: theory -> class * class -> proof
   126   val arity_proof: theory -> string * sort list * class -> proof
   127   val of_sort_proof: theory -> (typ * class -> proof) -> typ * sort -> proof list
   128   val install_axclass_proofs:
   129    {classrel_proof: theory -> class * class -> proof,
   130     arity_proof: theory -> string * sort list * class -> proof} -> theory -> theory
   131   val axm_proof: string -> term -> proof
   132   val oracle_proof: string -> term -> oracle * proof
   133   val shrink_proof: proof -> proof
   134 
   135   (** rewriting on proof terms **)
   136   val add_prf_rrule: proof * proof -> theory -> theory
   137   val add_prf_rproc: (typ list -> term option list -> proof -> (proof * proof) option) -> theory -> theory
   138   val no_skel: proof
   139   val normal_skel: proof
   140   val rewrite_proof: theory -> (proof * proof) list *
   141     (typ list -> term option list -> proof -> (proof * proof) option) list -> proof -> proof
   142   val rewrite_proof_notypes: (proof * proof) list *
   143     (typ list -> term option list -> proof -> (proof * proof) option) list -> proof -> proof
   144   val rew_proof: theory -> proof -> proof
   145 
   146   val promise_proof: theory -> serial -> term -> proof
   147   val fulfill_norm_proof: theory -> (serial * proof_body) list -> proof_body -> proof_body
   148   val thm_proof: theory -> string -> sort list -> term list -> term ->
   149     (serial * proof_body future) list -> proof_body -> pthm * proof
   150   val unconstrain_thm_proof: theory -> sort list -> term ->
   151     (serial * proof_body future) list -> proof_body -> pthm * proof
   152   val get_name: sort list -> term list -> term -> proof -> string
   153   val guess_name: proof -> string
   154 end
   155 
   156 structure Proofterm : PROOFTERM =
   157 struct
   158 
   159 (***** datatype proof *****)
   160 
   161 datatype proof =
   162    MinProof
   163  | PBound of int
   164  | Abst of string * typ option * proof
   165  | AbsP of string * term option * proof
   166  | op % of proof * term option
   167  | op %% of proof * proof
   168  | Hyp of term
   169  | PAxm of string * term * typ list option
   170  | OfClass of typ * class
   171  | Oracle of string * term * typ list option
   172  | Promise of serial * term * typ list
   173  | PThm of serial * ((string * term * typ list option) * proof_body future)
   174 and proof_body = PBody of
   175   {oracles: (string * term) Ord_List.T,
   176    thms: (serial * (string * term * proof_body future)) Ord_List.T,
   177    proof: proof};
   178 
   179 type oracle = string * term;
   180 type pthm = serial * (string * term * proof_body future);
   181 
   182 fun proof_of (PBody {proof, ...}) = proof;
   183 val join_proof = Future.join #> proof_of;
   184 
   185 fun join_thms (thms: pthm list) = ignore (Future.joins (map (#3 o #2) thms));
   186 
   187 
   188 (***** proof atoms *****)
   189 
   190 fun fold_proof_atoms all f =
   191   let
   192     fun app (Abst (_, _, prf)) = app prf
   193       | app (AbsP (_, _, prf)) = app prf
   194       | app (prf % _) = app prf
   195       | app (prf1 %% prf2) = app prf1 #> app prf2
   196       | app (prf as PThm (i, (_, body))) = (fn (x, seen) =>
   197           if Inttab.defined seen i then (x, seen)
   198           else
   199             let val (x', seen') =
   200               (if all then app (join_proof body) else I) (x, Inttab.update (i, ()) seen)
   201             in (f prf x', seen') end)
   202       | app prf = (fn (x, seen) => (f prf x, seen));
   203   in fn prfs => fn x => #1 (fold app prfs (x, Inttab.empty)) end;
   204 
   205 fun fold_body_thms f =
   206   let
   207     fun app (PBody {thms, ...}) =
   208       tap join_thms thms |> fold (fn (i, (name, prop, body)) => fn (x, seen) =>
   209         if Inttab.defined seen i then (x, seen)
   210         else
   211           let
   212             val body' = Future.join body;
   213             val (x', seen') = app body' (x, Inttab.update (i, ()) seen);
   214           in (f (name, prop, body') x', seen') end);
   215   in fn bodies => fn x => #1 (fold app bodies (x, Inttab.empty)) end;
   216 
   217 fun join_bodies bodies = fold_body_thms (fn _ => fn () => ()) bodies ();
   218 
   219 fun peek_status bodies =
   220   let
   221     fun status (PBody {oracles, thms, ...}) x =
   222       let
   223         val ((oracle, unfinished, failed), seen) =
   224           (thms, x) |-> fold (fn (i, (_, _, body)) => fn (st, seen) =>
   225             if Inttab.defined seen i then (st, seen)
   226             else
   227               let val seen' = Inttab.update (i, ()) seen in
   228                 (case Future.peek body of
   229                   SOME (Exn.Res body') => status body' (st, seen')
   230                 | SOME (Exn.Exn _) =>
   231                     let val (oracle, unfinished, _) = st
   232                     in ((oracle, unfinished, true), seen') end
   233                 | NONE =>
   234                     let val (oracle, _, failed) = st
   235                     in ((oracle, true, failed), seen') end)
   236               end);
   237       in ((oracle orelse not (null oracles), unfinished, failed), seen) end;
   238     val (oracle, unfinished, failed) =
   239       #1 (fold status bodies ((false, false, false), Inttab.empty));
   240   in {oracle = oracle, unfinished = unfinished, failed = failed} end;
   241 
   242 
   243 (* proof body *)
   244 
   245 val oracle_ord = prod_ord fast_string_ord Term_Ord.fast_term_ord;
   246 fun thm_ord ((i, _): pthm, (j, _)) = int_ord (j, i);
   247 
   248 val unions_oracles = Ord_List.unions oracle_ord;
   249 val unions_thms = Ord_List.unions thm_ord;
   250 
   251 val all_oracles_of =
   252   let
   253     fun collect (PBody {oracles, thms, ...}) =
   254       tap join_thms thms |> fold (fn (i, (_, _, body)) => fn (x, seen) =>
   255         if Inttab.defined seen i then (x, seen)
   256         else
   257           let
   258             val body' = Future.join body;
   259             val (x', seen') = collect body' (x, Inttab.update (i, ()) seen);
   260           in (if null oracles then x' else oracles :: x', seen') end);
   261   in fn body => unions_oracles (#1 (collect body ([], Inttab.empty))) end;
   262 
   263 fun approximate_proof_body prf =
   264   let
   265     val (oracles, thms) = fold_proof_atoms false
   266       (fn Oracle (s, prop, _) => apfst (cons (s, prop))
   267         | PThm (i, ((name, prop, _), body)) => apsnd (cons (i, (name, prop, body)))
   268         | _ => I) [prf] ([], []);
   269   in
   270     PBody
   271      {oracles = Ord_List.make oracle_ord oracles,
   272       thms = Ord_List.make thm_ord thms,
   273       proof = prf}
   274   end;
   275 
   276 val no_proof_body = PBody {oracles = [], thms = [], proof = MinProof};
   277 val no_body = Future.value no_proof_body;
   278 
   279 fun no_thm_proofs (PThm (i, (a, _))) = PThm (i, (a, no_body))
   280   | no_thm_proofs (Abst (x, T, prf)) = Abst (x, T, no_thm_proofs prf)
   281   | no_thm_proofs (AbsP (x, t, prf)) = AbsP (x, t, no_thm_proofs prf)
   282   | no_thm_proofs (prf % t) = no_thm_proofs prf % t
   283   | no_thm_proofs (prf1 %% prf2) = no_thm_proofs prf1 %% no_thm_proofs prf2
   284   | no_thm_proofs a = a;
   285 
   286 
   287 (***** XML data representation *****)
   288 
   289 (* encode *)
   290 
   291 local
   292 
   293 open XML.Encode Term_XML.Encode;
   294 
   295 fun proof prf = prf |> variant
   296  [fn MinProof => ([], []),
   297   fn PBound a => ([int_atom a], []),
   298   fn Abst (a, b, c) => ([a], pair (option typ) proof (b, c)),
   299   fn AbsP (a, b, c) => ([a], pair (option term) proof (b, c)),
   300   fn a % b => ([], pair proof (option term) (a, b)),
   301   fn a %% b => ([], pair proof proof (a, b)),
   302   fn Hyp a => ([], term a),
   303   fn PAxm (a, b, c) => ([a], pair term (option (list typ)) (b, c)),
   304   fn OfClass (a, b) => ([b], typ a),
   305   fn Oracle (a, b, c) => ([a], pair term (option (list typ)) (b, c)),
   306   fn Promise (a, b, c) => ([int_atom a], pair term (list typ) (b, c)),
   307   fn PThm (a, ((b, c, d), body)) =>
   308     ([int_atom a, b], triple term (option (list typ)) proof_body (c, d, Future.join body))]
   309 and proof_body (PBody {oracles, thms, proof = prf}) =
   310   triple (list (pair string term)) (list pthm) proof (oracles, thms, prf)
   311 and pthm (a, (b, c, body)) =
   312   pair int (triple string term proof_body) (a, (b, c, Future.join body));
   313 
   314 in
   315 
   316 val encode = proof;
   317 val encode_body = proof_body;
   318 
   319 end;
   320 
   321 
   322 (* decode *)
   323 
   324 local
   325 
   326 open XML.Decode Term_XML.Decode;
   327 
   328 fun proof prf = prf |> variant
   329  [fn ([], []) => MinProof,
   330   fn ([a], []) => PBound (int_atom a),
   331   fn ([a], b) => let val (c, d) = pair (option typ) proof b in Abst (a, c, d) end,
   332   fn ([a], b) => let val (c, d) = pair (option term) proof b in AbsP (a, c, d) end,
   333   fn ([], a) => op % (pair proof (option term) a),
   334   fn ([], a) => op %% (pair proof proof a),
   335   fn ([], a) => Hyp (term a),
   336   fn ([a], b) => let val (c, d) = pair term (option (list typ)) b in PAxm (a, c, d) end,
   337   fn ([b], a) => OfClass (typ a, b),
   338   fn ([a], b) => let val (c, d) = pair term (option (list typ)) b in Oracle (a, c, d) end,
   339   fn ([a], b) => let val (c, d) = pair term (list typ) b in Promise (int_atom a, c, d) end,
   340   fn ([a, b], c) =>
   341     let val (d, e, f) = triple term (option (list typ)) proof_body c
   342     in PThm (int_atom a, ((b, d, e), Future.value f)) end]
   343 and proof_body x =
   344   let val (a, b, c) = triple (list (pair string term)) (list pthm) proof x
   345   in PBody {oracles = a, thms = b, proof = c} end
   346 and pthm x =
   347   let val (a, (b, c, d)) = pair int (triple string term proof_body) x
   348   in (a, (b, c, Future.value d)) end;
   349 
   350 in
   351 
   352 val decode = proof;
   353 val decode_body = proof_body;
   354 
   355 end;
   356 
   357 
   358 (***** proof objects with different levels of detail *****)
   359 
   360 fun (prf %> t) = prf % SOME t;
   361 
   362 val proof_combt = Library.foldl (op %>);
   363 val proof_combt' = Library.foldl (op %);
   364 val proof_combP = Library.foldl (op %%);
   365 
   366 fun strip_combt prf =
   367     let fun stripc (prf % t, ts) = stripc (prf, t::ts)
   368           | stripc  x =  x
   369     in  stripc (prf, [])  end;
   370 
   371 fun strip_combP prf =
   372     let fun stripc (prf %% prf', prfs) = stripc (prf, prf'::prfs)
   373           | stripc  x =  x
   374     in  stripc (prf, [])  end;
   375 
   376 fun strip_thm (body as PBody {proof, ...}) =
   377   (case strip_combt (fst (strip_combP proof)) of
   378     (PThm (_, (_, body')), _) => Future.join body'
   379   | _ => body);
   380 
   381 val mk_Abst = fold_rev (fn (s, _: typ) => fn prf => Abst (s, NONE, prf));
   382 fun mk_AbsP (i, prf) = funpow i (fn prf => AbsP ("H", NONE, prf)) prf;
   383 
   384 fun map_proof_same term typ ofclass =
   385   let
   386     val typs = Same.map typ;
   387 
   388     fun proof (Abst (s, T, prf)) =
   389           (Abst (s, Same.map_option typ T, Same.commit proof prf)
   390             handle Same.SAME => Abst (s, T, proof prf))
   391       | proof (AbsP (s, t, prf)) =
   392           (AbsP (s, Same.map_option term t, Same.commit proof prf)
   393             handle Same.SAME => AbsP (s, t, proof prf))
   394       | proof (prf % t) =
   395           (proof prf % Same.commit (Same.map_option term) t
   396             handle Same.SAME => prf % Same.map_option term t)
   397       | proof (prf1 %% prf2) =
   398           (proof prf1 %% Same.commit proof prf2
   399             handle Same.SAME => prf1 %% proof prf2)
   400       | proof (PAxm (a, prop, SOME Ts)) = PAxm (a, prop, SOME (typs Ts))
   401       | proof (OfClass T_c) = ofclass T_c
   402       | proof (Oracle (a, prop, SOME Ts)) = Oracle (a, prop, SOME (typs Ts))
   403       | proof (Promise (i, prop, Ts)) = Promise (i, prop, typs Ts)
   404       | proof (PThm (i, ((a, prop, SOME Ts), body))) =
   405           PThm (i, ((a, prop, SOME (typs Ts)), body))
   406       | proof _ = raise Same.SAME;
   407   in proof end;
   408 
   409 fun map_proof_terms_same term typ = map_proof_same term typ (fn (T, c) => OfClass (typ T, c));
   410 fun map_proof_types_same typ = map_proof_terms_same (Term_Subst.map_types_same typ) typ;
   411 
   412 fun same eq f x =
   413   let val x' = f x
   414   in if eq (x, x') then raise Same.SAME else x' end;
   415 
   416 fun map_proof_terms f g = Same.commit (map_proof_terms_same (same (op =) f) (same (op =) g));
   417 fun map_proof_types f = Same.commit (map_proof_types_same (same (op =) f));
   418 
   419 fun fold_proof_terms f g (Abst (_, SOME T, prf)) = g T #> fold_proof_terms f g prf
   420   | fold_proof_terms f g (Abst (_, NONE, prf)) = fold_proof_terms f g prf
   421   | fold_proof_terms f g (AbsP (_, SOME t, prf)) = f t #> fold_proof_terms f g prf
   422   | fold_proof_terms f g (AbsP (_, NONE, prf)) = fold_proof_terms f g prf
   423   | fold_proof_terms f g (prf % SOME t) = fold_proof_terms f g prf #> f t
   424   | fold_proof_terms f g (prf % NONE) = fold_proof_terms f g prf
   425   | fold_proof_terms f g (prf1 %% prf2) =
   426       fold_proof_terms f g prf1 #> fold_proof_terms f g prf2
   427   | fold_proof_terms _ g (PAxm (_, _, SOME Ts)) = fold g Ts
   428   | fold_proof_terms _ g (OfClass (T, _)) = g T
   429   | fold_proof_terms _ g (Oracle (_, _, SOME Ts)) = fold g Ts
   430   | fold_proof_terms _ g (Promise (_, _, Ts)) = fold g Ts
   431   | fold_proof_terms _ g (PThm (_, ((_, _, SOME Ts), _))) = fold g Ts
   432   | fold_proof_terms _ _ _ = I;
   433 
   434 fun maxidx_proof prf = fold_proof_terms Term.maxidx_term Term.maxidx_typ prf;
   435 
   436 fun size_of_proof (Abst (_, _, prf)) = 1 + size_of_proof prf
   437   | size_of_proof (AbsP (_, _, prf)) = 1 + size_of_proof prf
   438   | size_of_proof (prf % _) = 1 + size_of_proof prf
   439   | size_of_proof (prf1 %% prf2) = size_of_proof prf1 + size_of_proof prf2
   440   | size_of_proof _ = 1;
   441 
   442 fun change_type opTs (PAxm (name, prop, _)) = PAxm (name, prop, opTs)
   443   | change_type (SOME [T]) (OfClass (_, c)) = OfClass (T, c)
   444   | change_type opTs (Oracle (name, prop, _)) = Oracle (name, prop, opTs)
   445   | change_type _ (Promise _) = raise Fail "change_type: unexpected promise"
   446   | change_type opTs (PThm (i, ((name, prop, _), body))) =
   447       PThm (i, ((name, prop, opTs), body))
   448   | change_type _ prf = prf;
   449 
   450 
   451 (***** utilities *****)
   452 
   453 fun strip_abs (_::Ts) (Abs (_, _, t)) = strip_abs Ts t
   454   | strip_abs _ t = t;
   455 
   456 fun mk_abs Ts t = Library.foldl (fn (t', T) => Abs ("", T, t')) (t, Ts);
   457 
   458 
   459 (*Abstraction of a proof term over its occurrences of v,
   460     which must contain no loose bound variables.
   461   The resulting proof term is ready to become the body of an Abst.*)
   462 
   463 fun prf_abstract_over v =
   464   let
   465     fun abst' lev u = if v aconv u then Bound lev else
   466       (case u of
   467          Abs (a, T, t) => Abs (a, T, abst' (lev + 1) t)
   468        | f $ t => (abst' lev f $ absth' lev t handle Same.SAME => f $ abst' lev t)
   469        | _ => raise Same.SAME)
   470     and absth' lev t = (abst' lev t handle Same.SAME => t);
   471 
   472     fun abst lev (AbsP (a, t, prf)) =
   473           (AbsP (a, Same.map_option (abst' lev) t, absth lev prf)
   474            handle Same.SAME => AbsP (a, t, abst lev prf))
   475       | abst lev (Abst (a, T, prf)) = Abst (a, T, abst (lev + 1) prf)
   476       | abst lev (prf1 %% prf2) = (abst lev prf1 %% absth lev prf2
   477           handle Same.SAME => prf1 %% abst lev prf2)
   478       | abst lev (prf % t) = (abst lev prf % Option.map (absth' lev) t
   479           handle Same.SAME => prf % Same.map_option (abst' lev) t)
   480       | abst _ _ = raise Same.SAME
   481     and absth lev prf = (abst lev prf handle Same.SAME => prf);
   482 
   483   in absth 0 end;
   484 
   485 
   486 (*increments a proof term's non-local bound variables
   487   required when moving a proof term within abstractions
   488      inc is  increment for bound variables
   489      lev is  level at which a bound variable is considered 'loose'*)
   490 
   491 fun incr_bv' inct tlev t = incr_bv (inct, tlev, t);
   492 
   493 fun prf_incr_bv' incP _ Plev _ (PBound i) =
   494       if i >= Plev then PBound (i+incP) else raise Same.SAME
   495   | prf_incr_bv' incP inct Plev tlev (AbsP (a, t, body)) =
   496       (AbsP (a, Same.map_option (same (op =) (incr_bv' inct tlev)) t,
   497          prf_incr_bv incP inct (Plev+1) tlev body) handle Same.SAME =>
   498            AbsP (a, t, prf_incr_bv' incP inct (Plev+1) tlev body))
   499   | prf_incr_bv' incP inct Plev tlev (Abst (a, T, body)) =
   500       Abst (a, T, prf_incr_bv' incP inct Plev (tlev+1) body)
   501   | prf_incr_bv' incP inct Plev tlev (prf %% prf') =
   502       (prf_incr_bv' incP inct Plev tlev prf %% prf_incr_bv incP inct Plev tlev prf'
   503        handle Same.SAME => prf %% prf_incr_bv' incP inct Plev tlev prf')
   504   | prf_incr_bv' incP inct Plev tlev (prf % t) =
   505       (prf_incr_bv' incP inct Plev tlev prf % Option.map (incr_bv' inct tlev) t
   506        handle Same.SAME => prf % Same.map_option (same (op =) (incr_bv' inct tlev)) t)
   507   | prf_incr_bv' _ _ _ _ _ = raise Same.SAME
   508 and prf_incr_bv incP inct Plev tlev prf =
   509       (prf_incr_bv' incP inct Plev tlev prf handle Same.SAME => prf);
   510 
   511 fun incr_pboundvars  0 0 prf = prf
   512   | incr_pboundvars incP inct prf = prf_incr_bv incP inct 0 0 prf;
   513 
   514 
   515 fun prf_loose_bvar1 (prf1 %% prf2) k = prf_loose_bvar1 prf1 k orelse prf_loose_bvar1 prf2 k
   516   | prf_loose_bvar1 (prf % SOME t) k = prf_loose_bvar1 prf k orelse loose_bvar1 (t, k)
   517   | prf_loose_bvar1 (_ % NONE) _ = true
   518   | prf_loose_bvar1 (AbsP (_, SOME t, prf)) k = loose_bvar1 (t, k) orelse prf_loose_bvar1 prf k
   519   | prf_loose_bvar1 (AbsP (_, NONE, _)) _ = true
   520   | prf_loose_bvar1 (Abst (_, _, prf)) k = prf_loose_bvar1 prf (k+1)
   521   | prf_loose_bvar1 _ _ = false;
   522 
   523 fun prf_loose_Pbvar1 (PBound i) k = i = k
   524   | prf_loose_Pbvar1 (prf1 %% prf2) k = prf_loose_Pbvar1 prf1 k orelse prf_loose_Pbvar1 prf2 k
   525   | prf_loose_Pbvar1 (prf % _) k = prf_loose_Pbvar1 prf k
   526   | prf_loose_Pbvar1 (AbsP (_, _, prf)) k = prf_loose_Pbvar1 prf (k+1)
   527   | prf_loose_Pbvar1 (Abst (_, _, prf)) k = prf_loose_Pbvar1 prf k
   528   | prf_loose_Pbvar1 _ _ = false;
   529 
   530 fun prf_add_loose_bnos plev _ (PBound i) (is, js) =
   531       if i < plev then (is, js) else (insert (op =) (i-plev) is, js)
   532   | prf_add_loose_bnos plev tlev (prf1 %% prf2) p =
   533       prf_add_loose_bnos plev tlev prf2
   534         (prf_add_loose_bnos plev tlev prf1 p)
   535   | prf_add_loose_bnos plev tlev (prf % opt) (is, js) =
   536       prf_add_loose_bnos plev tlev prf (case opt of
   537           NONE => (is, insert (op =) ~1 js)
   538         | SOME t => (is, add_loose_bnos (t, tlev, js)))
   539   | prf_add_loose_bnos plev tlev (AbsP (_, opt, prf)) (is, js) =
   540       prf_add_loose_bnos (plev+1) tlev prf (case opt of
   541           NONE => (is, insert (op =) ~1 js)
   542         | SOME t => (is, add_loose_bnos (t, tlev, js)))
   543   | prf_add_loose_bnos plev tlev (Abst (_, _, prf)) p =
   544       prf_add_loose_bnos plev (tlev+1) prf p
   545   | prf_add_loose_bnos _ _ _ _ = ([], []);
   546 
   547 
   548 (**** substitutions ****)
   549 
   550 fun del_conflicting_tvars envT T = Term_Subst.instantiateT
   551   (map_filter (fn ixnS as (_, S) =>
   552      (Type.lookup envT ixnS; NONE) handle TYPE _ =>
   553         SOME (ixnS, TFree ("'dummy", S))) (Term.add_tvarsT T [])) T;
   554 
   555 fun del_conflicting_vars env t = Term_Subst.instantiate
   556   (map_filter (fn ixnS as (_, S) =>
   557      (Type.lookup (Envir.type_env env) ixnS; NONE) handle TYPE _ =>
   558         SOME (ixnS, TFree ("'dummy", S))) (Term.add_tvars t []),
   559    map_filter (fn (ixnT as (_, T)) =>
   560      (Envir.lookup env ixnT; NONE) handle TYPE _ =>
   561         SOME (ixnT, Free ("dummy", T))) (Term.add_vars t [])) t;
   562 
   563 fun norm_proof env =
   564   let
   565     val envT = Envir.type_env env;
   566     fun msg s = warning ("type conflict in norm_proof:\n" ^ s);
   567     fun htype f t = f env t handle TYPE (s, _, _) =>
   568       (msg s; f env (del_conflicting_vars env t));
   569     fun htypeT f T = f envT T handle TYPE (s, _, _) =>
   570       (msg s; f envT (del_conflicting_tvars envT T));
   571     fun htypeTs f Ts = f envT Ts handle TYPE (s, _, _) =>
   572       (msg s; f envT (map (del_conflicting_tvars envT) Ts));
   573 
   574     fun norm (Abst (s, T, prf)) =
   575           (Abst (s, Same.map_option (htypeT Envir.norm_type_same) T, Same.commit norm prf)
   576             handle Same.SAME => Abst (s, T, norm prf))
   577       | norm (AbsP (s, t, prf)) =
   578           (AbsP (s, Same.map_option (htype Envir.norm_term_same) t, Same.commit norm prf)
   579             handle Same.SAME => AbsP (s, t, norm prf))
   580       | norm (prf % t) =
   581           (norm prf % Option.map (htype Envir.norm_term) t
   582             handle Same.SAME => prf % Same.map_option (htype Envir.norm_term_same) t)
   583       | norm (prf1 %% prf2) =
   584           (norm prf1 %% Same.commit norm prf2
   585             handle Same.SAME => prf1 %% norm prf2)
   586       | norm (PAxm (s, prop, Ts)) =
   587           PAxm (s, prop, Same.map_option (htypeTs Envir.norm_types_same) Ts)
   588       | norm (OfClass (T, c)) =
   589           OfClass (htypeT Envir.norm_type_same T, c)
   590       | norm (Oracle (s, prop, Ts)) =
   591           Oracle (s, prop, Same.map_option (htypeTs Envir.norm_types_same) Ts)
   592       | norm (Promise (i, prop, Ts)) =
   593           Promise (i, prop, htypeTs Envir.norm_types_same Ts)
   594       | norm (PThm (i, ((s, t, Ts), body))) =
   595           PThm (i, ((s, t, Same.map_option (htypeTs Envir.norm_types_same) Ts), body))
   596       | norm _ = raise Same.SAME;
   597   in Same.commit norm end;
   598 
   599 
   600 (***** Remove some types in proof term (to save space) *****)
   601 
   602 fun remove_types (Abs (s, _, t)) = Abs (s, dummyT, remove_types t)
   603   | remove_types (t $ u) = remove_types t $ remove_types u
   604   | remove_types (Const (s, _)) = Const (s, dummyT)
   605   | remove_types t = t;
   606 
   607 fun remove_types_env (Envir.Envir {maxidx, tenv, tyenv}) =
   608   Envir.Envir {maxidx = maxidx, tenv = Vartab.map (K (apsnd remove_types)) tenv, tyenv = tyenv};
   609 
   610 fun norm_proof' env prf = norm_proof (remove_types_env env) prf;
   611 
   612 
   613 (**** substitution of bound variables ****)
   614 
   615 fun prf_subst_bounds args prf =
   616   let
   617     val n = length args;
   618     fun subst' lev (Bound i) =
   619          (if i<lev then raise Same.SAME    (*var is locally bound*)
   620           else  incr_boundvars lev (nth args (i-lev))
   621                   handle General.Subscript => Bound (i-n))  (*loose: change it*)
   622       | subst' lev (Abs (a, T, body)) = Abs (a, T,  subst' (lev+1) body)
   623       | subst' lev (f $ t) = (subst' lev f $ substh' lev t
   624           handle Same.SAME => f $ subst' lev t)
   625       | subst' _ _ = raise Same.SAME
   626     and substh' lev t = (subst' lev t handle Same.SAME => t);
   627 
   628     fun subst lev (AbsP (a, t, body)) =
   629         (AbsP (a, Same.map_option (subst' lev) t, substh lev body)
   630           handle Same.SAME => AbsP (a, t, subst lev body))
   631       | subst lev (Abst (a, T, body)) = Abst (a, T, subst (lev+1) body)
   632       | subst lev (prf %% prf') = (subst lev prf %% substh lev prf'
   633           handle Same.SAME => prf %% subst lev prf')
   634       | subst lev (prf % t) = (subst lev prf % Option.map (substh' lev) t
   635           handle Same.SAME => prf % Same.map_option (subst' lev) t)
   636       | subst _ _ = raise Same.SAME
   637     and substh lev prf = (subst lev prf handle Same.SAME => prf);
   638   in case args of [] => prf | _ => substh 0 prf end;
   639 
   640 fun prf_subst_pbounds args prf =
   641   let
   642     val n = length args;
   643     fun subst (PBound i) Plev tlev =
   644          (if i < Plev then raise Same.SAME    (*var is locally bound*)
   645           else incr_pboundvars Plev tlev (nth args (i-Plev))
   646                  handle General.Subscript => PBound (i-n)  (*loose: change it*))
   647       | subst (AbsP (a, t, body)) Plev tlev = AbsP (a, t, subst body (Plev+1) tlev)
   648       | subst (Abst (a, T, body)) Plev tlev = Abst (a, T, subst body Plev (tlev+1))
   649       | subst (prf %% prf') Plev tlev = (subst prf Plev tlev %% substh prf' Plev tlev
   650           handle Same.SAME => prf %% subst prf' Plev tlev)
   651       | subst (prf % t) Plev tlev = subst prf Plev tlev % t
   652       | subst  _ _ _ = raise Same.SAME
   653     and substh prf Plev tlev = (subst prf Plev tlev handle Same.SAME => prf)
   654   in case args of [] => prf | _ => substh prf 0 0 end;
   655 
   656 
   657 (**** Freezing and thawing of variables in proof terms ****)
   658 
   659 local
   660 
   661 fun frzT names =
   662   map_type_tvar (fn (ixn, S) => TFree (the (AList.lookup (op =) names ixn), S));
   663 
   664 fun thawT names =
   665   map_type_tfree (fn (a, S) =>
   666     (case AList.lookup (op =) names a of
   667       NONE => TFree (a, S)
   668     | SOME ixn => TVar (ixn, S)));
   669 
   670 fun freeze names names' (t $ u) =
   671       freeze names names' t $ freeze names names' u
   672   | freeze names names' (Abs (s, T, t)) =
   673       Abs (s, frzT names' T, freeze names names' t)
   674   | freeze _ names' (Const (s, T)) = Const (s, frzT names' T)
   675   | freeze _ names' (Free (s, T)) = Free (s, frzT names' T)
   676   | freeze names names' (Var (ixn, T)) =
   677       Free (the (AList.lookup (op =) names ixn), frzT names' T)
   678   | freeze _ _ t = t;
   679 
   680 fun thaw names names' (t $ u) =
   681       thaw names names' t $ thaw names names' u
   682   | thaw names names' (Abs (s, T, t)) =
   683       Abs (s, thawT names' T, thaw names names' t)
   684   | thaw _ names' (Const (s, T)) = Const (s, thawT names' T)
   685   | thaw names names' (Free (s, T)) =
   686       let val T' = thawT names' T in
   687         (case AList.lookup (op =) names s of
   688           NONE => Free (s, T')
   689         | SOME ixn => Var (ixn, T'))
   690       end
   691   | thaw _ names' (Var (ixn, T)) = Var (ixn, thawT names' T)
   692   | thaw _ _ t = t;
   693 
   694 in
   695 
   696 fun freeze_thaw_prf prf =
   697   let
   698     val (fs, Tfs, vs, Tvs) = fold_proof_terms
   699       (fn t => fn (fs, Tfs, vs, Tvs) =>
   700          (Term.add_free_names t fs, Term.add_tfree_names t Tfs,
   701           Term.add_var_names t vs, Term.add_tvar_names t Tvs))
   702       (fn T => fn (fs, Tfs, vs, Tvs) =>
   703          (fs, Term.add_tfree_namesT T Tfs,
   704           vs, Term.add_tvar_namesT T Tvs))
   705       prf ([], [], [], []);
   706     val names = vs ~~ Name.variant_list fs (map fst vs);
   707     val names' = Tvs ~~ Name.variant_list Tfs (map fst Tvs);
   708     val rnames = map swap names;
   709     val rnames' = map swap names';
   710   in
   711     (map_proof_terms (freeze names names') (frzT names') prf,
   712      map_proof_terms (thaw rnames rnames') (thawT rnames'))
   713   end;
   714 
   715 end;
   716 
   717 
   718 (***** implication introduction *****)
   719 
   720 fun gen_implies_intr_proof f h prf =
   721   let
   722     fun abshyp i (Hyp t) = if h aconv t then PBound i else raise Same.SAME
   723       | abshyp i (Abst (s, T, prf)) = Abst (s, T, abshyp i prf)
   724       | abshyp i (AbsP (s, t, prf)) = AbsP (s, t, abshyp (i + 1) prf)
   725       | abshyp i (prf % t) = abshyp i prf % t
   726       | abshyp i (prf1 %% prf2) =
   727           (abshyp i prf1 %% abshyph i prf2
   728             handle Same.SAME => prf1 %% abshyp i prf2)
   729       | abshyp _ _ = raise Same.SAME
   730     and abshyph i prf = (abshyp i prf handle Same.SAME => prf);
   731   in
   732     AbsP ("H", f h, abshyph 0 prf)
   733   end;
   734 
   735 val implies_intr_proof = gen_implies_intr_proof (K NONE);
   736 val implies_intr_proof' = gen_implies_intr_proof SOME;
   737 
   738 
   739 (***** forall introduction *****)
   740 
   741 fun forall_intr_proof x a prf = Abst (a, NONE, prf_abstract_over x prf);
   742 
   743 fun forall_intr_proof' t prf =
   744   let val (a, T) = (case t of Var ((a, _), T) => (a, T) | Free p => p)
   745   in Abst (a, SOME T, prf_abstract_over t prf) end;
   746 
   747 
   748 (***** varify *****)
   749 
   750 fun varify_proof t fixed prf =
   751   let
   752     val fs = Term.fold_types (Term.fold_atyps
   753       (fn TFree v => if member (op =) fixed v then I else insert (op =) v | _ => I)) t [];
   754     val used = Name.context
   755       |> fold_types (fold_atyps (fn TVar ((a, _), _) => Name.declare a | _ => I)) t;
   756     val fmap = fs ~~ #1 (fold_map Name.variant (map fst fs) used);
   757     fun thaw (a, S) =
   758       (case AList.lookup (op =) fmap (a, S) of
   759         NONE => TFree (a, S)
   760       | SOME b => TVar ((b, 0), S));
   761   in map_proof_terms (map_types (map_type_tfree thaw)) (map_type_tfree thaw) prf end;
   762 
   763 
   764 local
   765 
   766 fun new_name ix (pairs, used) =
   767   let val v = singleton (Name.variant_list used) (string_of_indexname ix)
   768   in ((ix, v) :: pairs, v :: used) end;
   769 
   770 fun freeze_one alist (ix, sort) =
   771   (case AList.lookup (op =) alist ix of
   772     NONE => TVar (ix, sort)
   773   | SOME name => TFree (name, sort));
   774 
   775 in
   776 
   777 fun legacy_freezeT t prf =
   778   let
   779     val used = Term.add_tfree_names t [];
   780     val (alist, _) = fold_rev new_name (map #1 (Term.add_tvars t [])) ([], used);
   781   in
   782     (case alist of
   783       [] => prf (*nothing to do!*)
   784     | _ =>
   785         let val frzT = map_type_tvar (freeze_one alist)
   786         in map_proof_terms (map_types frzT) frzT prf end)
   787   end;
   788 
   789 end;
   790 
   791 
   792 (***** rotate assumptions *****)
   793 
   794 fun rotate_proof Bs Bi m prf =
   795   let
   796     val params = Term.strip_all_vars Bi;
   797     val asms = Logic.strip_imp_prems (Term.strip_all_body Bi);
   798     val i = length asms;
   799     val j = length Bs;
   800   in
   801     mk_AbsP (j+1, proof_combP (prf, map PBound
   802       (j downto 1) @ [mk_Abst params (mk_AbsP (i,
   803         proof_combP (proof_combt (PBound i, map Bound ((length params - 1) downto 0)),
   804           map PBound (((i-m-1) downto 0) @ ((i-1) downto (i-m))))))]))
   805   end;
   806 
   807 
   808 (***** permute premises *****)
   809 
   810 fun permute_prems_proof prems j k prf =
   811   let val n = length prems
   812   in mk_AbsP (n, proof_combP (prf,
   813     map PBound ((n-1 downto n-j) @ (k-1 downto 0) @ (n-j-1 downto k))))
   814   end;
   815 
   816 
   817 (***** generalization *****)
   818 
   819 fun generalize (tfrees, frees) idx =
   820   Same.commit (map_proof_terms_same
   821     (Term_Subst.generalize_same (tfrees, frees) idx)
   822     (Term_Subst.generalizeT_same tfrees idx));
   823 
   824 
   825 (***** instantiation *****)
   826 
   827 fun instantiate (instT, inst) =
   828   Same.commit (map_proof_terms_same
   829     (Term_Subst.instantiate_same (instT, map (apsnd remove_types) inst))
   830     (Term_Subst.instantiateT_same instT));
   831 
   832 
   833 (***** lifting *****)
   834 
   835 fun lift_proof Bi inc prop prf =
   836   let
   837     fun lift'' Us Ts t =
   838       strip_abs Ts (Logic.incr_indexes ([], Us, inc) (mk_abs Ts t));
   839 
   840     fun lift' Us Ts (Abst (s, T, prf)) =
   841           (Abst (s, Same.map_option (Logic.incr_tvar_same inc) T, lifth' Us (dummyT::Ts) prf)
   842            handle Same.SAME => Abst (s, T, lift' Us (dummyT::Ts) prf))
   843       | lift' Us Ts (AbsP (s, t, prf)) =
   844           (AbsP (s, Same.map_option (same (op =) (lift'' Us Ts)) t, lifth' Us Ts prf)
   845            handle Same.SAME => AbsP (s, t, lift' Us Ts prf))
   846       | lift' Us Ts (prf % t) = (lift' Us Ts prf % Option.map (lift'' Us Ts) t
   847           handle Same.SAME => prf % Same.map_option (same (op =) (lift'' Us Ts)) t)
   848       | lift' Us Ts (prf1 %% prf2) = (lift' Us Ts prf1 %% lifth' Us Ts prf2
   849           handle Same.SAME => prf1 %% lift' Us Ts prf2)
   850       | lift' _ _ (PAxm (s, prop, Ts)) =
   851           PAxm (s, prop, (Same.map_option o Same.map) (Logic.incr_tvar_same inc) Ts)
   852       | lift' _ _ (OfClass (T, c)) =
   853           OfClass (Logic.incr_tvar_same inc T, c)
   854       | lift' _ _ (Oracle (s, prop, Ts)) =
   855           Oracle (s, prop, (Same.map_option o Same.map) (Logic.incr_tvar_same inc) Ts)
   856       | lift' _ _ (Promise (i, prop, Ts)) =
   857           Promise (i, prop, Same.map (Logic.incr_tvar_same inc) Ts)
   858       | lift' _ _ (PThm (i, ((s, prop, Ts), body))) =
   859           PThm (i, ((s, prop, (Same.map_option o Same.map) (Logic.incr_tvar inc) Ts), body))
   860       | lift' _ _ _ = raise Same.SAME
   861     and lifth' Us Ts prf = (lift' Us Ts prf handle Same.SAME => prf);
   862 
   863     val ps = map (Logic.lift_all inc Bi) (Logic.strip_imp_prems prop);
   864     val k = length ps;
   865 
   866     fun mk_app b (i, j, prf) =
   867           if b then (i-1, j, prf %% PBound i) else (i, j-1, prf %> Bound j);
   868 
   869     fun lift Us bs i j (Const ("Pure.imp", _) $ A $ B) =
   870             AbsP ("H", NONE (*A*), lift Us (true::bs) (i+1) j B)
   871       | lift Us bs i j (Const ("Pure.all", _) $ Abs (a, T, t)) =
   872             Abst (a, NONE (*T*), lift (T::Us) (false::bs) i (j+1) t)
   873       | lift Us bs i j _ = proof_combP (lifth' (rev Us) [] prf,
   874             map (fn k => (#3 (fold_rev mk_app bs (i-1, j-1, PBound k))))
   875               (i + k - 1 downto i));
   876   in
   877     mk_AbsP (k, lift [] [] 0 0 Bi)
   878   end;
   879 
   880 fun incr_indexes i =
   881   Same.commit (map_proof_terms_same
   882     (Logic.incr_indexes_same ([], [], i)) (Logic.incr_tvar_same i));
   883 
   884 
   885 (***** proof by assumption *****)
   886 
   887 fun mk_asm_prf t i m =
   888   let
   889     fun imp_prf _ i 0 = PBound i
   890       | imp_prf (Const ("Pure.imp", _) $ A $ B) i m = AbsP ("H", NONE (*A*), imp_prf B (i+1) (m-1))
   891       | imp_prf _ i _ = PBound i;
   892     fun all_prf (Const ("Pure.all", _) $ Abs (a, T, t)) = Abst (a, NONE (*T*), all_prf t)
   893       | all_prf t = imp_prf t (~i) m
   894   in all_prf t end;
   895 
   896 fun assumption_proof Bs Bi n prf =
   897   mk_AbsP (length Bs, proof_combP (prf,
   898     map PBound (length Bs - 1 downto 0) @ [mk_asm_prf Bi n ~1]));
   899 
   900 
   901 (***** Composition of object rule with proof state *****)
   902 
   903 fun flatten_params_proof i j n (Const ("Pure.imp", _) $ A $ B, k) =
   904       AbsP ("H", NONE (*A*), flatten_params_proof (i+1) j n (B, k))
   905   | flatten_params_proof i j n (Const ("Pure.all", _) $ Abs (a, T, t), k) =
   906       Abst (a, NONE (*T*), flatten_params_proof i (j+1) n (t, k))
   907   | flatten_params_proof i j n (_, k) = proof_combP (proof_combt (PBound (k+i),
   908       map Bound (j-1 downto 0)), map PBound (remove (op =) (i-n) (i-1 downto 0)));
   909 
   910 fun bicompose_proof flatten Bs oldAs newAs A n m rprf sprf =
   911   let
   912     val la = length newAs;
   913     val lb = length Bs;
   914   in
   915     mk_AbsP (lb+la, proof_combP (sprf,
   916       map PBound (lb + la - 1 downto la)) %%
   917         proof_combP (rprf, (if n>0 then [mk_asm_prf (the A) n m] else []) @
   918           map (if flatten then flatten_params_proof 0 0 n else PBound o snd)
   919             (oldAs ~~ (la - 1 downto 0))))
   920   end;
   921 
   922 
   923 (***** axioms for equality *****)
   924 
   925 val aT = TFree ("'a", []);
   926 val bT = TFree ("'b", []);
   927 val x = Free ("x", aT);
   928 val y = Free ("y", aT);
   929 val z = Free ("z", aT);
   930 val A = Free ("A", propT);
   931 val B = Free ("B", propT);
   932 val f = Free ("f", aT --> bT);
   933 val g = Free ("g", aT --> bT);
   934 
   935 val equality_axms =
   936  [("reflexive", Logic.mk_equals (x, x)),
   937   ("symmetric", Logic.mk_implies (Logic.mk_equals (x, y), Logic.mk_equals (y, x))),
   938   ("transitive",
   939     Logic.list_implies ([Logic.mk_equals (x, y), Logic.mk_equals (y, z)], Logic.mk_equals (x, z))),
   940   ("equal_intr",
   941     Logic.list_implies ([Logic.mk_implies (A, B), Logic.mk_implies (B, A)], Logic.mk_equals (A, B))),
   942   ("equal_elim", Logic.list_implies ([Logic.mk_equals (A, B), A], B)),
   943   ("abstract_rule",
   944     Logic.mk_implies
   945       (Logic.all x
   946         (Logic.mk_equals (f $ x, g $ x)), Logic.mk_equals (lambda x (f $ x), lambda x (g $ x)))),
   947   ("combination", Logic.list_implies
   948     ([Logic.mk_equals (f, g), Logic.mk_equals (x, y)], Logic.mk_equals (f $ x, g $ y)))];
   949 
   950 val [reflexive_axm, symmetric_axm, transitive_axm, equal_intr_axm,
   951   equal_elim_axm, abstract_rule_axm, combination_axm] =
   952     map (fn (s, t) => PAxm ("Pure." ^ s, Logic.varify_global t, NONE)) equality_axms;
   953 
   954 val reflexive = reflexive_axm % NONE;
   955 
   956 fun symmetric (prf as PAxm ("Pure.reflexive", _, _) % _) = prf
   957   | symmetric prf = symmetric_axm % NONE % NONE %% prf;
   958 
   959 fun transitive _ _ (PAxm ("Pure.reflexive", _, _) % _) prf2 = prf2
   960   | transitive _ _ prf1 (PAxm ("Pure.reflexive", _, _) % _) = prf1
   961   | transitive u (Type ("prop", [])) prf1 prf2 =
   962       transitive_axm % NONE % SOME (remove_types u) % NONE %% prf1 %% prf2
   963   | transitive _ _ prf1 prf2 = transitive_axm % NONE % NONE % NONE %% prf1 %% prf2;
   964 
   965 fun abstract_rule x a prf =
   966   abstract_rule_axm % NONE % NONE %% forall_intr_proof x a prf;
   967 
   968 fun check_comb (PAxm ("Pure.combination", _, _) % f % _ % _ % _ %% prf %% _) =
   969       is_some f orelse check_comb prf
   970   | check_comb (PAxm ("Pure.transitive", _, _) % _ % _ % _ %% prf1 %% prf2) =
   971       check_comb prf1 andalso check_comb prf2
   972   | check_comb (PAxm ("Pure.symmetric", _, _) % _ % _ %% prf) = check_comb prf
   973   | check_comb _ = false;
   974 
   975 fun combination f g t u (Type (_, [T, U])) prf1 prf2 =
   976   let
   977     val f = Envir.beta_norm f;
   978     val g = Envir.beta_norm g;
   979     val prf =
   980       if check_comb prf1 then
   981         combination_axm % NONE % NONE
   982       else
   983         (case prf1 of
   984           PAxm ("Pure.reflexive", _, _) % _ =>
   985             combination_axm %> remove_types f % NONE
   986         | _ => combination_axm %> remove_types f %> remove_types g)
   987   in
   988     (case T of
   989       Type ("fun", _) => prf %
   990         (case head_of f of
   991           Abs _ => SOME (remove_types t)
   992         | Var _ => SOME (remove_types t)
   993         | _ => NONE) %
   994         (case head_of g of
   995            Abs _ => SOME (remove_types u)
   996         | Var _ => SOME (remove_types u)
   997         | _ => NONE) %% prf1 %% prf2
   998      | _ => prf % NONE % NONE %% prf1 %% prf2)
   999   end;
  1000 
  1001 fun equal_intr A B prf1 prf2 =
  1002   equal_intr_axm %> remove_types A %> remove_types B %% prf1 %% prf2;
  1003 
  1004 fun equal_elim A B prf1 prf2 =
  1005   equal_elim_axm %> remove_types A %> remove_types B %% prf1 %% prf2;
  1006 
  1007 
  1008 (**** type classes ****)
  1009 
  1010 fun strip_shyps_proof algebra present witnessed extra_sorts prf =
  1011   let
  1012     fun get S2 (T, S1) = if Sorts.sort_le algebra (S1, S2) then SOME T else NONE;
  1013     val extra = map (fn S => (TFree ("'dummy", S), S)) extra_sorts;
  1014     val replacements = present @ extra @ witnessed;
  1015     fun replace T =
  1016       if exists (fn (T', _) => T' = T) present then raise Same.SAME
  1017       else
  1018         (case get_first (get (Type.sort_of_atyp T)) replacements of
  1019           SOME T' => T'
  1020         | NONE => raise Fail "strip_shyps_proof: bad type variable in proof term");
  1021   in Same.commit (map_proof_types_same (Term_Subst.map_atypsT_same replace)) prf end;
  1022 
  1023 
  1024 local
  1025 
  1026 type axclass_proofs =
  1027  {classrel_proof: theory -> class * class -> proof,
  1028   arity_proof: theory -> string * sort list * class -> proof};
  1029 
  1030 structure Axclass_Proofs = Theory_Data
  1031 (
  1032   type T = axclass_proofs option;
  1033   val empty = NONE;
  1034   val extend = I;
  1035   val merge = merge_options;
  1036 );
  1037 
  1038 fun the_axclass_proofs which thy x =
  1039   (case Axclass_Proofs.get thy of
  1040     NONE => raise Fail "Axclass proof operations not installed"
  1041   | SOME proofs => which proofs thy x);
  1042 
  1043 in
  1044 
  1045 val classrel_proof = the_axclass_proofs #classrel_proof;
  1046 val arity_proof = the_axclass_proofs #arity_proof;
  1047 
  1048 fun install_axclass_proofs proofs =
  1049   Axclass_Proofs.map
  1050     (fn NONE => SOME proofs
  1051       | SOME _ => raise Fail "Axclass proof operations already installed");
  1052 
  1053 end;
  1054 
  1055 
  1056 local
  1057 
  1058 fun canonical_instance typs =
  1059   let
  1060     val names = Name.invent Name.context Name.aT (length typs);
  1061     val instT = map2 (fn a => fn T => (((a, 0), []), Type.strip_sorts T)) names typs;
  1062   in instantiate (instT, []) end;
  1063 
  1064 in
  1065 
  1066 fun of_sort_proof thy hyps =
  1067   Sorts.of_sort_derivation (Sign.classes_of thy)
  1068    {class_relation = fn typ => fn _ => fn (prf, c1) => fn c2 =>
  1069       if c1 = c2 then prf
  1070       else canonical_instance [typ] (classrel_proof thy (c1, c2)) %% prf,
  1071     type_constructor = fn (a, typs) => fn dom => fn c =>
  1072       let val Ss = map (map snd) dom and prfs = maps (map fst) dom
  1073       in proof_combP (canonical_instance typs (arity_proof thy (a, Ss, c)), prfs) end,
  1074     type_variable = fn typ => map (fn c => (hyps (typ, c), c)) (Type.sort_of_atyp typ)};
  1075 
  1076 end;
  1077 
  1078 
  1079 (***** axioms and theorems *****)
  1080 
  1081 val proofs = Unsynchronized.ref 2;
  1082 fun proofs_enabled () = ! proofs >= 2;
  1083 
  1084 fun vars_of t = map Var (rev (Term.add_vars t []));
  1085 fun frees_of t = map Free (rev (Term.add_frees t []));
  1086 
  1087 fun test_args _ [] = true
  1088   | test_args is (Bound i :: ts) =
  1089       not (member (op =) is i) andalso test_args (i :: is) ts
  1090   | test_args _ _ = false;
  1091 
  1092 fun is_fun (Type ("fun", _)) = true
  1093   | is_fun (TVar _) = true
  1094   | is_fun _ = false;
  1095 
  1096 fun add_funvars Ts (vs, t) =
  1097   if is_fun (fastype_of1 (Ts, t)) then
  1098     union (op =) vs (map_filter (fn Var (ixn, T) =>
  1099       if is_fun T then SOME ixn else NONE | _ => NONE) (vars_of t))
  1100   else vs;
  1101 
  1102 fun add_npvars q p Ts (vs, Const ("Pure.imp", _) $ t $ u) =
  1103       add_npvars q p Ts (add_npvars q (not p) Ts (vs, t), u)
  1104   | add_npvars q p Ts (vs, Const ("Pure.all", Type (_, [Type (_, [T, _]), _])) $ t) =
  1105       add_npvars q p Ts (vs, if p andalso q then betapply (t, Var (("",0), T)) else t)
  1106   | add_npvars q p Ts (vs, Abs (_, T, t)) = add_npvars q p (T::Ts) (vs, t)
  1107   | add_npvars _ _ Ts (vs, t) = add_npvars' Ts (vs, t)
  1108 and add_npvars' Ts (vs, t) = (case strip_comb t of
  1109     (Var (ixn, _), ts) => if test_args [] ts then vs
  1110       else Library.foldl (add_npvars' Ts)
  1111         (AList.update (op =) (ixn,
  1112           Library.foldl (add_funvars Ts) ((these ooo AList.lookup) (op =) vs ixn, ts)) vs, ts)
  1113   | (Abs (_, T, u), ts) => Library.foldl (add_npvars' (T::Ts)) (vs, u :: ts)
  1114   | (_, ts) => Library.foldl (add_npvars' Ts) (vs, ts));
  1115 
  1116 fun prop_vars (Const ("Pure.imp", _) $ P $ Q) = union (op =) (prop_vars P) (prop_vars Q)
  1117   | prop_vars (Const ("Pure.all", _) $ Abs (_, _, t)) = prop_vars t
  1118   | prop_vars t = (case strip_comb t of
  1119       (Var (ixn, _), _) => [ixn] | _ => []);
  1120 
  1121 fun is_proj t =
  1122   let
  1123     fun is_p i t = (case strip_comb t of
  1124         (Bound _, []) => false
  1125       | (Bound j, ts) => j >= i orelse exists (is_p i) ts
  1126       | (Abs (_, _, u), _) => is_p (i+1) u
  1127       | (_, ts) => exists (is_p i) ts)
  1128   in (case strip_abs_body t of
  1129         Bound _ => true
  1130       | t' => is_p 0 t')
  1131   end;
  1132 
  1133 fun needed_vars prop =
  1134   union (op =) (Library.foldl (uncurry (union (op =)))
  1135     ([], map (uncurry (insert (op =))) (add_npvars true true [] ([], prop))))
  1136   (prop_vars prop);
  1137 
  1138 fun gen_axm_proof c name prop =
  1139   let
  1140     val nvs = needed_vars prop;
  1141     val args = map (fn (v as Var (ixn, _)) =>
  1142         if member (op =) nvs ixn then SOME v else NONE) (vars_of prop) @
  1143       map SOME (frees_of prop);
  1144   in
  1145     proof_combt' (c (name, prop, NONE), args)
  1146   end;
  1147 
  1148 val axm_proof = gen_axm_proof PAxm;
  1149 
  1150 fun oracle_proof name prop =
  1151   if ! proofs = 0 then ((name, Term.dummy), Oracle (name, Term.dummy, NONE))
  1152   else ((name, prop), gen_axm_proof Oracle name prop);
  1153 
  1154 val shrink_proof =
  1155   let
  1156     fun shrink ls lev (prf as Abst (a, T, body)) =
  1157           let val (b, is, ch, body') = shrink ls (lev+1) body
  1158           in (b, is, ch, if ch then Abst (a, T, body') else prf) end
  1159       | shrink ls lev (prf as AbsP (a, t, body)) =
  1160           let val (b, is, ch, body') = shrink (lev::ls) lev body
  1161           in (b orelse member (op =) is 0, map_filter (fn 0 => NONE | i => SOME (i-1)) is,
  1162             ch, if ch then AbsP (a, t, body') else prf)
  1163           end
  1164       | shrink ls lev prf =
  1165           let val (is, ch, _, prf') = shrink' ls lev [] [] prf
  1166           in (false, is, ch, prf') end
  1167     and shrink' ls lev ts prfs (prf as prf1 %% prf2) =
  1168           let
  1169             val p as (_, is', ch', prf') = shrink ls lev prf2;
  1170             val (is, ch, ts', prf'') = shrink' ls lev ts (p::prfs) prf1
  1171           in (union (op =) is is', ch orelse ch', ts',
  1172               if ch orelse ch' then prf'' %% prf' else prf)
  1173           end
  1174       | shrink' ls lev ts prfs (prf as prf1 % t) =
  1175           let val (is, ch, (ch', t')::ts', prf') = shrink' ls lev (t::ts) prfs prf1
  1176           in (is, ch orelse ch', ts',
  1177               if ch orelse ch' then prf' % t' else prf) end
  1178       | shrink' ls lev ts prfs (prf as PBound i) =
  1179           (if exists (fn SOME (Bound j) => lev-j <= nth ls i | _ => true) ts
  1180              orelse has_duplicates (op =)
  1181                (Library.foldl (fn (js, SOME (Bound j)) => j :: js | (js, _) => js) ([], ts))
  1182              orelse exists #1 prfs then [i] else [], false, map (pair false) ts, prf)
  1183       | shrink' _ _ ts _ (Hyp t) = ([], false, map (pair false) ts, Hyp t)
  1184       | shrink' _ _ ts _ (prf as MinProof) = ([], false, map (pair false) ts, prf)
  1185       | shrink' _ _ ts _ (prf as OfClass _) = ([], false, map (pair false) ts, prf)
  1186       | shrink' _ _ ts prfs prf =
  1187           let
  1188             val prop =
  1189               (case prf of
  1190                 PAxm (_, prop, _) => prop
  1191               | Oracle (_, prop, _) => prop
  1192               | Promise (_, prop, _) => prop
  1193               | PThm (_, ((_, prop, _), _)) => prop
  1194               | _ => raise Fail "shrink: proof not in normal form");
  1195             val vs = vars_of prop;
  1196             val (ts', ts'') = chop (length vs) ts;
  1197             val insts = take (length ts') (map (fst o dest_Var) vs) ~~ ts';
  1198             val nvs = Library.foldl (fn (ixns', (ixn, ixns)) =>
  1199               insert (op =) ixn (case AList.lookup (op =) insts ixn of
  1200                   SOME (SOME t) => if is_proj t then union (op =) ixns ixns' else ixns'
  1201                 | _ => union (op =) ixns ixns'))
  1202                   (needed prop ts'' prfs, add_npvars false true [] ([], prop));
  1203             val insts' = map
  1204               (fn (ixn, x as SOME _) => if member (op =) nvs ixn then (false, x) else (true, NONE)
  1205                 | (_, x) => (false, x)) insts
  1206           in ([], false, insts' @ map (pair false) ts'', prf) end
  1207     and needed (Const ("Pure.imp", _) $ t $ u) ts ((b, _, _, _)::prfs) =
  1208           union (op =) (if b then map (fst o dest_Var) (vars_of t) else []) (needed u ts prfs)
  1209       | needed (Var (ixn, _)) (_::_) _ = [ixn]
  1210       | needed _ _ _ = [];
  1211   in fn prf => #4 (shrink [] 0 prf) end;
  1212 
  1213 
  1214 (**** Simple first order matching functions for terms and proofs ****)
  1215 
  1216 exception PMatch;
  1217 
  1218 (** see pattern.ML **)
  1219 
  1220 fun flt (i: int) = filter (fn n => n < i);
  1221 
  1222 fun fomatch Ts tymatch j instsp p =
  1223   let
  1224     fun mtch (instsp as (tyinsts, insts)) = fn
  1225         (Var (ixn, T), t)  =>
  1226           if j>0 andalso not (null (flt j (loose_bnos t)))
  1227           then raise PMatch
  1228           else (tymatch (tyinsts, fn () => (T, fastype_of1 (Ts, t))),
  1229             (ixn, t) :: insts)
  1230       | (Free (a, T), Free (b, U)) =>
  1231           if a=b then (tymatch (tyinsts, K (T, U)), insts) else raise PMatch
  1232       | (Const (a, T), Const (b, U))  =>
  1233           if a=b then (tymatch (tyinsts, K (T, U)), insts) else raise PMatch
  1234       | (f $ t, g $ u) => mtch (mtch instsp (f, g)) (t, u)
  1235       | (Bound i, Bound j) => if i=j then instsp else raise PMatch
  1236       | _ => raise PMatch
  1237   in mtch instsp (apply2 Envir.beta_eta_contract p) end;
  1238 
  1239 fun match_proof Ts tymatch =
  1240   let
  1241     fun optmatch _ inst (NONE, _) = inst
  1242       | optmatch _ _ (SOME _, NONE) = raise PMatch
  1243       | optmatch mtch inst (SOME x, SOME y) = mtch inst (x, y)
  1244 
  1245     fun matcht Ts j (pinst, tinst) (t, u) =
  1246       (pinst, fomatch Ts tymatch j tinst (t, Envir.beta_norm u));
  1247     fun matchT (pinst, (tyinsts, insts)) p =
  1248       (pinst, (tymatch (tyinsts, K p), insts));
  1249     fun matchTs inst (Ts, Us) = Library.foldl (uncurry matchT) (inst, Ts ~~ Us);
  1250 
  1251     fun mtch Ts i j (pinst, tinst) (Hyp (Var (ixn, _)), prf) =
  1252           if i = 0 andalso j = 0 then ((ixn, prf) :: pinst, tinst)
  1253           else (case apfst (flt i) (apsnd (flt j)
  1254                   (prf_add_loose_bnos 0 0 prf ([], []))) of
  1255               ([], []) => ((ixn, incr_pboundvars (~i) (~j) prf) :: pinst, tinst)
  1256             | ([], _) => if j = 0 then
  1257                    ((ixn, incr_pboundvars (~i) (~j) prf) :: pinst, tinst)
  1258                  else raise PMatch
  1259             | _ => raise PMatch)
  1260       | mtch Ts i j inst (prf1 % opt1, prf2 % opt2) =
  1261           optmatch (matcht Ts j) (mtch Ts i j inst (prf1, prf2)) (opt1, opt2)
  1262       | mtch Ts i j inst (prf1 %% prf2, prf1' %% prf2') =
  1263           mtch Ts i j (mtch Ts i j inst (prf1, prf1')) (prf2, prf2')
  1264       | mtch Ts i j inst (Abst (_, opT, prf1), Abst (_, opU, prf2)) =
  1265           mtch (the_default dummyT opU :: Ts) i (j+1)
  1266             (optmatch matchT inst (opT, opU)) (prf1, prf2)
  1267       | mtch Ts i j inst (prf1, Abst (_, opU, prf2)) =
  1268           mtch (the_default dummyT opU :: Ts) i (j+1) inst
  1269             (incr_pboundvars 0 1 prf1 %> Bound 0, prf2)
  1270       | mtch Ts i j inst (AbsP (_, opt, prf1), AbsP (_, opu, prf2)) =
  1271           mtch Ts (i+1) j (optmatch (matcht Ts j) inst (opt, opu)) (prf1, prf2)
  1272       | mtch Ts i j inst (prf1, AbsP (_, _, prf2)) =
  1273           mtch Ts (i+1) j inst (incr_pboundvars 1 0 prf1 %% PBound 0, prf2)
  1274       | mtch Ts i j inst (PAxm (s1, _, opTs), PAxm (s2, _, opUs)) =
  1275           if s1 = s2 then optmatch matchTs inst (opTs, opUs)
  1276           else raise PMatch
  1277       | mtch Ts i j inst (OfClass (T1, c1), OfClass (T2, c2)) =
  1278           if c1 = c2 then matchT inst (T1, T2)
  1279           else raise PMatch
  1280       | mtch Ts i j inst (PThm (_, ((name1, prop1, opTs), _)), PThm (_, ((name2, prop2, opUs), _))) =
  1281           if name1 = name2 andalso prop1 = prop2 then
  1282             optmatch matchTs inst (opTs, opUs)
  1283           else raise PMatch
  1284       | mtch _ _ _ inst (PBound i, PBound j) = if i = j then inst else raise PMatch
  1285       | mtch _ _ _ _ _ = raise PMatch
  1286   in mtch Ts 0 0 end;
  1287 
  1288 fun prf_subst (pinst, (tyinsts, insts)) =
  1289   let
  1290     val substT = Envir.subst_type_same tyinsts;
  1291     val substTs = Same.map substT;
  1292 
  1293     fun subst' lev (Var (xi, _)) =
  1294         (case AList.lookup (op =) insts xi of
  1295           NONE => raise Same.SAME
  1296         | SOME u => incr_boundvars lev u)
  1297       | subst' _ (Const (s, T)) = Const (s, substT T)
  1298       | subst' _ (Free (s, T)) = Free (s, substT T)
  1299       | subst' lev (Abs (a, T, body)) =
  1300           (Abs (a, substT T, Same.commit (subst' (lev + 1)) body)
  1301             handle Same.SAME => Abs (a, T, subst' (lev + 1) body))
  1302       | subst' lev (f $ t) =
  1303           (subst' lev f $ Same.commit (subst' lev) t
  1304             handle Same.SAME => f $ subst' lev t)
  1305       | subst' _ _ = raise Same.SAME;
  1306 
  1307     fun subst plev tlev (AbsP (a, t, body)) =
  1308           (AbsP (a, Same.map_option (subst' tlev) t, Same.commit (subst (plev + 1) tlev) body)
  1309             handle Same.SAME => AbsP (a, t, subst (plev + 1) tlev body))
  1310       | subst plev tlev (Abst (a, T, body)) =
  1311           (Abst (a, Same.map_option substT T, Same.commit (subst plev (tlev + 1)) body)
  1312             handle Same.SAME => Abst (a, T, subst plev (tlev + 1) body))
  1313       | subst plev tlev (prf %% prf') =
  1314           (subst plev tlev prf %% Same.commit (subst plev tlev) prf'
  1315             handle Same.SAME => prf %% subst plev tlev prf')
  1316       | subst plev tlev (prf % t) =
  1317           (subst plev tlev prf % Same.commit (Same.map_option (subst' tlev)) t
  1318             handle Same.SAME => prf % Same.map_option (subst' tlev) t)
  1319       | subst plev tlev (Hyp (Var (xi, _))) =
  1320           (case AList.lookup (op =) pinst xi of
  1321             NONE => raise Same.SAME
  1322           | SOME prf' => incr_pboundvars plev tlev prf')
  1323       | subst _ _ (PAxm (id, prop, Ts)) = PAxm (id, prop, Same.map_option substTs Ts)
  1324       | subst _ _ (OfClass (T, c)) = OfClass (substT T, c)
  1325       | subst _ _ (Oracle (id, prop, Ts)) = Oracle (id, prop, Same.map_option substTs Ts)
  1326       | subst _ _ (Promise (i, prop, Ts)) = Promise (i, prop, substTs Ts)
  1327       | subst _ _ (PThm (i, ((id, prop, Ts), body))) =
  1328           PThm (i, ((id, prop, Same.map_option substTs Ts), body))
  1329       | subst _ _ _ = raise Same.SAME;
  1330   in fn t => subst 0 0 t handle Same.SAME => t end;
  1331 
  1332 (*A fast unification filter: true unless the two terms cannot be unified.
  1333   Terms must be NORMAL.  Treats all Vars as distinct. *)
  1334 fun could_unify prf1 prf2 =
  1335   let
  1336     fun matchrands (prf1 %% prf2) (prf1' %% prf2') =
  1337           could_unify prf2 prf2' andalso matchrands prf1 prf1'
  1338       | matchrands (prf % SOME t) (prf' % SOME t') =
  1339           Term.could_unify (t, t') andalso matchrands prf prf'
  1340       | matchrands (prf % _) (prf' % _) = matchrands prf prf'
  1341       | matchrands _ _ = true
  1342 
  1343     fun head_of (prf %% _) = head_of prf
  1344       | head_of (prf % _) = head_of prf
  1345       | head_of prf = prf
  1346 
  1347   in case (head_of prf1, head_of prf2) of
  1348         (_, Hyp (Var _)) => true
  1349       | (Hyp (Var _), _) => true
  1350       | (PAxm (a, _, _), PAxm (b, _, _)) => a = b andalso matchrands prf1 prf2
  1351       | (OfClass (_, c), OfClass (_, d)) => c = d andalso matchrands prf1 prf2
  1352       | (PThm (_, ((a, propa, _), _)), PThm (_, ((b, propb, _), _))) =>
  1353           a = b andalso propa = propb andalso matchrands prf1 prf2
  1354       | (PBound i, PBound j) => i = j andalso matchrands prf1 prf2
  1355       | (AbsP _, _) =>  true   (*because of possible eta equality*)
  1356       | (Abst _, _) =>  true
  1357       | (_, AbsP _) =>  true
  1358       | (_, Abst _) =>  true
  1359       | _ => false
  1360   end;
  1361 
  1362 
  1363 (**** rewriting on proof terms ****)
  1364 
  1365 val no_skel = PBound 0;
  1366 val normal_skel = Hyp (Var ((Name.uu, 0), propT));
  1367 
  1368 fun rewrite_prf tymatch (rules, procs) prf =
  1369   let
  1370     fun rew _ _ (Abst (_, _, body) % SOME t) = SOME (prf_subst_bounds [t] body, no_skel)
  1371       | rew _ _ (AbsP (_, _, body) %% prf) = SOME (prf_subst_pbounds [prf] body, no_skel)
  1372       | rew Ts hs prf =
  1373           (case get_first (fn r => r Ts hs prf) procs of
  1374             NONE => get_first (fn (prf1, prf2) => SOME (prf_subst
  1375               (match_proof Ts tymatch ([], (Vartab.empty, [])) (prf1, prf)) prf2, prf2)
  1376                  handle PMatch => NONE) (filter (could_unify prf o fst) rules)
  1377           | some => some);
  1378 
  1379     fun rew0 Ts hs (prf as AbsP (_, _, prf' %% PBound 0)) =
  1380           if prf_loose_Pbvar1 prf' 0 then rew Ts hs prf
  1381           else
  1382             let val prf'' = incr_pboundvars (~1) 0 prf'
  1383             in SOME (the_default (prf'', no_skel) (rew Ts hs prf'')) end
  1384       | rew0 Ts hs (prf as Abst (_, _, prf' % SOME (Bound 0))) =
  1385           if prf_loose_bvar1 prf' 0 then rew Ts hs prf
  1386           else
  1387             let val prf'' = incr_pboundvars 0 (~1) prf'
  1388             in SOME (the_default (prf'', no_skel) (rew Ts hs prf'')) end
  1389       | rew0 Ts hs prf = rew Ts hs prf;
  1390 
  1391     fun rew1 _ _ (Hyp (Var _)) _ = NONE
  1392       | rew1 Ts hs skel prf = (case rew2 Ts hs skel prf of
  1393           SOME prf1 => (case rew0 Ts hs prf1 of
  1394               SOME (prf2, skel') => SOME (the_default prf2 (rew1 Ts hs skel' prf2))
  1395             | NONE => SOME prf1)
  1396         | NONE => (case rew0 Ts hs prf of
  1397               SOME (prf1, skel') => SOME (the_default prf1 (rew1 Ts hs skel' prf1))
  1398             | NONE => NONE))
  1399 
  1400     and rew2 Ts hs skel (prf % SOME t) = (case prf of
  1401             Abst (_, _, body) =>
  1402               let val prf' = prf_subst_bounds [t] body
  1403               in SOME (the_default prf' (rew2 Ts hs no_skel prf')) end
  1404           | _ => (case rew1 Ts hs (case skel of skel' % _ => skel' | _ => no_skel) prf of
  1405               SOME prf' => SOME (prf' % SOME t)
  1406             | NONE => NONE))
  1407       | rew2 Ts hs skel (prf % NONE) = Option.map (fn prf' => prf' % NONE)
  1408           (rew1 Ts hs (case skel of skel' % _ => skel' | _ => no_skel) prf)
  1409       | rew2 Ts hs skel (prf1 %% prf2) = (case prf1 of
  1410             AbsP (_, _, body) =>
  1411               let val prf' = prf_subst_pbounds [prf2] body
  1412               in SOME (the_default prf' (rew2 Ts hs no_skel prf')) end
  1413           | _ =>
  1414             let val (skel1, skel2) = (case skel of
  1415                 skel1 %% skel2 => (skel1, skel2)
  1416               | _ => (no_skel, no_skel))
  1417             in case rew1 Ts hs skel1 prf1 of
  1418                 SOME prf1' => (case rew1 Ts hs skel2 prf2 of
  1419                     SOME prf2' => SOME (prf1' %% prf2')
  1420                   | NONE => SOME (prf1' %% prf2))
  1421               | NONE => (case rew1 Ts hs skel2 prf2 of
  1422                     SOME prf2' => SOME (prf1 %% prf2')
  1423                   | NONE => NONE)
  1424             end)
  1425       | rew2 Ts hs skel (Abst (s, T, prf)) = (case rew1 (the_default dummyT T :: Ts) hs
  1426               (case skel of Abst (_, _, skel') => skel' | _ => no_skel) prf of
  1427             SOME prf' => SOME (Abst (s, T, prf'))
  1428           | NONE => NONE)
  1429       | rew2 Ts hs skel (AbsP (s, t, prf)) = (case rew1 Ts (t :: hs)
  1430               (case skel of AbsP (_, _, skel') => skel' | _ => no_skel) prf of
  1431             SOME prf' => SOME (AbsP (s, t, prf'))
  1432           | NONE => NONE)
  1433       | rew2 _ _ _ _ = NONE;
  1434 
  1435   in the_default prf (rew1 [] [] no_skel prf) end;
  1436 
  1437 fun rewrite_proof thy = rewrite_prf (fn (tyenv, f) =>
  1438   Sign.typ_match thy (f ()) tyenv handle Type.TYPE_MATCH => raise PMatch);
  1439 
  1440 fun rewrite_proof_notypes rews = rewrite_prf fst rews;
  1441 
  1442 
  1443 (**** theory data ****)
  1444 
  1445 structure Data = Theory_Data
  1446 (
  1447   type T =
  1448     (stamp * (proof * proof)) list *
  1449     (stamp * (typ list -> term option list -> proof -> (proof * proof) option)) list;
  1450 
  1451   val empty = ([], []);
  1452   val extend = I;
  1453   fun merge ((rules1, procs1), (rules2, procs2)) : T =
  1454     (AList.merge (op =) (K true) (rules1, rules2),
  1455       AList.merge (op =) (K true) (procs1, procs2));
  1456 );
  1457 
  1458 fun get_data thy = let val (rules, procs) = Data.get thy in (map #2 rules, map #2 procs) end;
  1459 fun rew_proof thy = rewrite_prf fst (get_data thy);
  1460 
  1461 fun add_prf_rrule r = (Data.map o apfst) (cons (stamp (), r));
  1462 fun add_prf_rproc p = (Data.map o apsnd) (cons (stamp (), p));
  1463 
  1464 
  1465 (***** promises *****)
  1466 
  1467 fun promise_proof thy i prop =
  1468   let
  1469     val _ = prop |> Term.exists_subterm (fn t =>
  1470       (Term.is_Free t orelse Term.is_Var t) andalso
  1471         raise Fail ("promise_proof: illegal variable " ^ Syntax.string_of_term_global thy t));
  1472     val _ = prop |> Term.exists_type (Term.exists_subtype
  1473       (fn TFree (a, _) => raise Fail ("promise_proof: illegal type variable " ^ quote a)
  1474         | _ => false));
  1475   in Promise (i, prop, map TVar (Term.add_tvars prop [])) end;
  1476 
  1477 fun fulfill_norm_proof thy ps body0 =
  1478   let
  1479     val PBody {oracles = oracles0, thms = thms0, proof = proof0} = body0;
  1480     val oracles =
  1481       unions_oracles
  1482         (fold (fn (_, PBody {oracles, ...}) => not (null oracles) ? cons oracles) ps [oracles0]);
  1483     val thms =
  1484       unions_thms (fold (fn (_, PBody {thms, ...}) => not (null thms) ? cons thms) ps [thms0]);
  1485     val proofs = fold (fn (i, PBody {proof, ...}) => Inttab.update (i, proof)) ps Inttab.empty;
  1486 
  1487     fun fill (Promise (i, prop, Ts)) =
  1488           (case Inttab.lookup proofs i of
  1489             NONE => NONE
  1490           | SOME prf => SOME (instantiate (Term.add_tvars prop [] ~~ Ts, []) prf, normal_skel))
  1491       | fill _ = NONE;
  1492     val (rules, procs) = get_data thy;
  1493     val proof = rewrite_prf fst (rules, K (K fill) :: procs) proof0;
  1494   in PBody {oracles = oracles, thms = thms, proof = proof} end;
  1495 
  1496 fun fulfill_proof_future thy promises postproc body =
  1497   let
  1498     fun fulfill () =
  1499       postproc (fulfill_norm_proof thy (map (apsnd Future.join) promises) (Future.join body));
  1500   in
  1501     if null promises then Future.map postproc body
  1502     else if Future.is_finished body andalso length promises = 1 then
  1503       Future.map (fn _ => fulfill ()) (snd (hd promises))
  1504     else
  1505       (singleton o Future.forks)
  1506         {name = "Proofterm.fulfill_proof_future", group = NONE,
  1507           deps = Future.task_of body :: map (Future.task_of o snd) promises, pri = 0,
  1508           interrupts = true}
  1509         fulfill
  1510   end;
  1511 
  1512 
  1513 (***** abstraction over sort constraints *****)
  1514 
  1515 fun unconstrainT_prf thy (atyp_map, constraints) =
  1516   let
  1517     fun hyp_map hyp =
  1518       (case AList.lookup (op =) constraints hyp of
  1519         SOME t => Hyp t
  1520       | NONE => raise Fail "unconstrainT_prf: missing constraint");
  1521 
  1522     val typ = Term_Subst.map_atypsT_same (Type.strip_sorts o atyp_map);
  1523     fun ofclass (ty, c) =
  1524       let val ty' = Term.map_atyps atyp_map ty;
  1525       in the_single (of_sort_proof thy hyp_map (ty', [c])) end;
  1526   in
  1527     Same.commit (map_proof_same (Term_Subst.map_types_same typ) typ ofclass)
  1528     #> fold_rev (implies_intr_proof o snd) constraints
  1529   end;
  1530 
  1531 fun unconstrainT_body thy constrs (PBody {oracles, thms, proof}) =
  1532   PBody
  1533    {oracles = oracles,  (* FIXME merge (!), unconstrain (!?!) *)
  1534     thms = thms,  (* FIXME merge (!) *)
  1535     proof = unconstrainT_prf thy constrs proof};
  1536 
  1537 
  1538 (***** theorems *****)
  1539 
  1540 fun prepare_thm_proof thy name shyps hyps concl promises body =
  1541   let
  1542     val PBody {oracles = oracles0, thms = thms0, proof = prf} = body;
  1543     val prop = Logic.list_implies (hyps, concl);
  1544     val nvs = needed_vars prop;
  1545     val args = map (fn (v as Var (ixn, _)) =>
  1546         if member (op =) nvs ixn then SOME v else NONE) (vars_of prop) @
  1547       map SOME (frees_of prop);
  1548 
  1549     val ((atyp_map, constraints, outer_constraints), prop1) = Logic.unconstrainT shyps prop;
  1550     val postproc = unconstrainT_body thy (atyp_map, constraints);
  1551     val args1 =
  1552       (map o Option.map o Term.map_types o Term.map_atyps)
  1553         (Type.strip_sorts o atyp_map) args;
  1554     val argsP = map OfClass outer_constraints @ map Hyp hyps;
  1555 
  1556     fun make_body0 proof0 = PBody {oracles = oracles0, thms = thms0, proof = proof0};
  1557     val body0 =
  1558       if not (proofs_enabled ()) then Future.value (make_body0 MinProof)
  1559       else
  1560         (singleton o Future.cond_forks)
  1561           {name = "Proofterm.prepare_thm_proof", group = NONE,
  1562             deps = [], pri = 0, interrupts = true}
  1563           (fn () =>
  1564             make_body0 (shrink_proof (rew_proof thy (fold_rev implies_intr_proof hyps prf))));
  1565 
  1566     fun new_prf () = (serial (), fulfill_proof_future thy promises postproc body0);
  1567     val (i, body') =
  1568       (*non-deterministic, depends on unknown promises*)
  1569       (case strip_combt (fst (strip_combP prf)) of
  1570         (PThm (i, ((old_name, prop', NONE), body')), args') =>
  1571           if (old_name = "" orelse old_name = name) andalso prop1 = prop' andalso args = args'
  1572           then (i, body')
  1573           else new_prf ()
  1574       | _ => new_prf ());
  1575     val head = PThm (i, ((name, prop1, NONE), body'));
  1576   in ((i, (name, prop1, body')), head, args, argsP, args1) end;
  1577 
  1578 fun thm_proof thy name shyps hyps concl promises body =
  1579   let val (pthm, head, args, argsP, _) = prepare_thm_proof thy name shyps hyps concl promises body
  1580   in (pthm, proof_combP (proof_combt' (head, args), argsP)) end;
  1581 
  1582 fun unconstrain_thm_proof thy shyps concl promises body =
  1583   let
  1584     val (pthm, head, _, _, args) = prepare_thm_proof thy "" shyps [] concl promises body
  1585   in (pthm, proof_combt' (head, args)) end;
  1586 
  1587 
  1588 fun get_name shyps hyps prop prf =
  1589   let val (_, prop) = Logic.unconstrainT shyps (Logic.list_implies (hyps, prop)) in
  1590     (case strip_combt (fst (strip_combP prf)) of
  1591       (PThm (_, ((name, prop', _), _)), _) => if prop = prop' then name else ""
  1592     | _ => "")
  1593   end;
  1594 
  1595 fun guess_name (PThm (_, ((name, _, _), _))) = name
  1596   | guess_name (prf %% Hyp _) = guess_name prf
  1597   | guess_name (prf %% OfClass _) = guess_name prf
  1598   | guess_name (prf % NONE) = guess_name prf
  1599   | guess_name (prf % SOME (Var _)) = guess_name prf
  1600   | guess_name _ = "";
  1601 
  1602 end;
  1603 
  1604 structure Basic_Proofterm : BASIC_PROOFTERM = Proofterm;
  1605 open Basic_Proofterm;