src/HOL/Tools/record.ML

qualified Subgoal.FOCUS;

(*  Title:      HOL/Tools/record.ML
    Author:     Wolfgang Naraschewski, Norbert Schirmer and Markus Wenzel, TU Muenchen

Extensible records with structural subtyping in HOL.
*)


signature BASIC_RECORD =
sig
  val record_simproc: simproc
  val record_eq_simproc: simproc
  val record_upd_simproc: simproc
  val record_split_simproc: (term -> int) -> simproc
  val record_ex_sel_eq_simproc: simproc
  val record_split_tac: int -> tactic
  val record_split_simp_tac: thm list -> (term -> int) -> int -> tactic
  val record_split_name: string
  val record_split_wrapper: string * wrapper
  val print_record_type_abbr: bool ref
  val print_record_type_as_fields: bool ref
end;

signature RECORD =
sig
  include BASIC_RECORD
  val timing: bool ref
  val record_quick_and_dirty_sensitive: bool ref
  val updateN: string
  val updN: string
  val ext_typeN: string
  val extN: string
  val makeN: string
  val moreN: string
  val ext_dest: string

  val last_extT: typ -> (string * typ list) option
  val dest_recTs : typ -> (string * typ list) list
  val get_extT_fields:  theory -> typ -> (string * typ) list * (string * typ)
  val get_recT_fields:  theory -> typ -> (string * typ) list * (string * typ)
  val get_parent: theory -> string -> (typ list * string) option
  val get_extension: theory -> string -> (string * typ list) option
  val get_extinjects: theory -> thm list
  val get_simpset: theory -> simpset
  val print_records: theory -> unit
  val read_typ: Proof.context -> string -> (string * sort) list -> typ * (string * sort) list
  val cert_typ: Proof.context -> typ -> (string * sort) list -> typ * (string * sort) list
  val add_record: bool -> string list * string -> string option -> (string * string * mixfix) list
    -> theory -> theory
  val add_record_i: bool -> string list * string -> (typ list * string) option
    -> (string * typ * mixfix) list -> theory -> theory
  val setup: theory -> theory
end;


structure Record: RECORD =
struct

val eq_reflection = thm "eq_reflection";
val rec_UNIV_I = thm "rec_UNIV_I";
val rec_True_simp = thm "rec_True_simp";
val Pair_eq = thm "Product_Type.prod.inject";
val atomize_all = thm "HOL.atomize_all";
val atomize_imp = thm "HOL.atomize_imp";
val meta_allE = thm "Pure.meta_allE";
val prop_subst = thm "prop_subst";
val Pair_sel_convs = [fst_conv,snd_conv];
val K_record_comp = @{thm "K_record_comp"};
val K_comp_convs = [@{thm o_apply}, K_record_comp]

(** name components **)

val rN = "r";
val wN = "w";
val moreN = "more";
val schemeN = "_scheme";
val ext_typeN = "_ext_type";
val extN ="_ext";
val casesN = "_cases";
val ext_dest = "_sel";
val updateN = "_update";
val updN = "_upd";
val makeN = "make";
val fields_selN = "fields";
val extendN = "extend";
val truncateN = "truncate";

(*see typedef.ML*)
val RepN = "Rep_";
val AbsN = "Abs_";

(*** utilities ***)

fun but_last xs = fst (split_last xs);

fun varifyT midx =
  let fun varify (a, S) = TVar ((a, midx + 1), S);
  in map_type_tfree varify end;

fun domain_type' T =
    domain_type T handle Match => T;

fun range_type' T =
    range_type T handle Match => T;

(* messages *)

fun trace_thm str thm =
    tracing (str ^ (Pretty.string_of (Display.pretty_thm_without_context thm)));

fun trace_thms str thms =
    (tracing str; map (trace_thm "") thms);

fun trace_term str t =
    tracing (str ^ Syntax.string_of_term_global Pure.thy t);

(* timing *)

val timing = ref false;
fun timeit_msg s x = if !timing then (warning s; timeit x) else x ();
fun timing_msg s = if !timing then warning s else ();

(* syntax *)

fun prune n xs = Library.drop (n, xs);
fun prefix_base s = Long_Name.map_base_name (fn bname => s ^ bname);

val Trueprop = HOLogic.mk_Trueprop;
fun All xs t = Term.list_all_free (xs, t);

infix 9 $$;
infix 0 :== ===;
infixr 0 ==>;

val (op $$) = Term.list_comb;
val (op :==) = PrimitiveDefs.mk_defpair;
val (op ===) = Trueprop o HOLogic.mk_eq;
val (op ==>) = Logic.mk_implies;

(* morphisms *)

fun mk_RepN name = suffix ext_typeN (prefix_base RepN name);
fun mk_AbsN name = suffix ext_typeN (prefix_base AbsN name);

fun mk_Rep name repT absT  =
  Const (suffix ext_typeN (prefix_base RepN name),absT --> repT);

fun mk_Abs name repT absT =
  Const (mk_AbsN name,repT --> absT);

(* constructor *)

fun mk_extC (name,T) Ts  = (suffix extN name, Ts ---> T);

fun mk_ext (name,T) ts =
  let val Ts = map fastype_of ts
  in list_comb (Const (mk_extC (name,T) Ts),ts) end;

(* cases *)

fun mk_casesC (name,T,vT) Ts = (suffix casesN name, (Ts ---> vT) --> T --> vT)

fun mk_cases (name,T,vT) f =
  let val Ts = binder_types (fastype_of f)
  in Const (mk_casesC (name,T,vT) Ts) $ f end;

(* selector *)

fun mk_selC sT (c,T) = (c,sT --> T);

fun mk_sel s (c,T) =
  let val sT = fastype_of s
  in Const (mk_selC sT (c,T)) $ s end;

(* updates *)

fun mk_updC sfx sT (c,T) = (suffix sfx c, (T --> T) --> sT --> sT);

fun mk_upd' sfx c v sT =
  let val vT = domain_type (fastype_of v);
  in Const (mk_updC sfx sT (c, vT)) $ v  end;

fun mk_upd sfx c v s = mk_upd' sfx c v (fastype_of s) $ s

(* types *)

fun dest_recT (typ as Type (c_ext_type, Ts as (T::_))) =
      (case try (unsuffix ext_typeN) c_ext_type of
        NONE => raise TYPE ("Record.dest_recT", [typ], [])
      | SOME c => ((c, Ts), List.last Ts))
  | dest_recT typ = raise TYPE ("Record.dest_recT", [typ], []);

fun is_recT T =
  (case try dest_recT T of NONE => false | SOME _ => true);

fun dest_recTs T =
  let val ((c, Ts), U) = dest_recT T
  in (c, Ts) :: dest_recTs U
  end handle TYPE _ => [];

fun last_extT T =
  let val ((c, Ts), U) = dest_recT T
  in (case last_extT U of
        NONE => SOME (c,Ts)
      | SOME l => SOME l)
  end handle TYPE _ => NONE

fun rec_id i T =
  let val rTs = dest_recTs T
      val rTs' = if i < 0 then rTs else Library.take (i,rTs)
  in Library.foldl (fn (s,(c,T)) => s ^ c) ("",rTs') end;

(*** extend theory by record definition ***)

(** record info **)

(* type record_info and parent_info  *)

type record_info =
 {args: (string * sort) list,
  parent: (typ list * string) option,
  fields: (string * typ) list,
  extension: (string * typ list),
  induct: thm
 };

fun make_record_info args parent fields extension induct =
 {args = args, parent = parent, fields = fields, extension = extension,
  induct = induct}: record_info;


type parent_info =
 {name: string,
  fields: (string * typ) list,
  extension: (string * typ list),
  induct: thm
};

fun make_parent_info name fields extension induct =
 {name = name, fields = fields, extension = extension, induct = induct}: parent_info;


(* theory data *)

type record_data =
 {records: record_info Symtab.table,
  sel_upd:
   {selectors: unit Symtab.table,
    updates: string Symtab.table,
    simpset: Simplifier.simpset},
  equalities: thm Symtab.table,
  extinjects: thm list,
  extsplit: thm Symtab.table, (* maps extension name to split rule *)
  splits: (thm*thm*thm*thm) Symtab.table,    (* !!,!,EX - split-equalities,induct rule *)
  extfields: (string*typ) list Symtab.table, (* maps extension to its fields *)
  fieldext: (string*typ list) Symtab.table   (* maps field to its extension *)
};

fun make_record_data
      records sel_upd equalities extinjects extsplit splits extfields fieldext =
 {records = records, sel_upd = sel_upd,
  equalities = equalities, extinjects=extinjects, extsplit = extsplit, splits = splits,
  extfields = extfields, fieldext = fieldext }: record_data;

structure RecordsData = TheoryDataFun
(
  type T = record_data;
  val empty =
    make_record_data Symtab.empty
      {selectors = Symtab.empty, updates = Symtab.empty, simpset = HOL_basic_ss}
       Symtab.empty [] Symtab.empty Symtab.empty Symtab.empty Symtab.empty;

  val copy = I;
  val extend = I;
  fun merge _
   ({records = recs1,
     sel_upd = {selectors = sels1, updates = upds1, simpset = ss1},
     equalities = equalities1,
     extinjects = extinjects1,
     extsplit = extsplit1,
     splits = splits1,
     extfields = extfields1,
     fieldext = fieldext1},
    {records = recs2,
     sel_upd = {selectors = sels2, updates = upds2, simpset = ss2},
     equalities = equalities2,
     extinjects = extinjects2,
     extsplit = extsplit2,
     splits = splits2,
     extfields = extfields2,
     fieldext = fieldext2}) =
    make_record_data
      (Symtab.merge (K true) (recs1, recs2))
      {selectors = Symtab.merge (K true) (sels1, sels2),
        updates = Symtab.merge (K true) (upds1, upds2),
        simpset = Simplifier.merge_ss (ss1, ss2)}
      (Symtab.merge Thm.eq_thm_prop (equalities1, equalities2))
      (Library.merge Thm.eq_thm_prop (extinjects1, extinjects2))
      (Symtab.merge Thm.eq_thm_prop (extsplit1,extsplit2))
      (Symtab.merge (fn ((a,b,c,d),(w,x,y,z))
                     => Thm.eq_thm (a,w) andalso Thm.eq_thm (b,x) andalso
                        Thm.eq_thm (c,y) andalso Thm.eq_thm (d,z))
                    (splits1, splits2))
      (Symtab.merge (K true) (extfields1,extfields2))
      (Symtab.merge (K true) (fieldext1,fieldext2));
);

fun print_records thy =
  let
    val {records = recs, ...} = RecordsData.get thy;
    val prt_typ = Syntax.pretty_typ_global thy;

    fun pretty_parent NONE = []
      | pretty_parent (SOME (Ts, name)) =
          [Pretty.block [prt_typ (Type (name, Ts)), Pretty.str " +"]];

    fun pretty_field (c, T) = Pretty.block
      [Pretty.str (Sign.extern_const thy c), Pretty.str " ::",
        Pretty.brk 1, Pretty.quote (prt_typ T)];

    fun pretty_record (name, {args, parent, fields, ...}: record_info) =
      Pretty.block (Pretty.fbreaks (Pretty.block
        [prt_typ (Type (name, map TFree args)), Pretty.str " = "] ::
        pretty_parent parent @ map pretty_field fields));
  in map pretty_record (Symtab.dest recs) |> Pretty.chunks |> Pretty.writeln end;


(* access 'records' *)

val get_record = Symtab.lookup o #records o RecordsData.get;

fun put_record name info thy =
  let
    val {records, sel_upd, equalities, extinjects,extsplit,splits,extfields,fieldext} =
          RecordsData.get thy;
    val data = make_record_data (Symtab.update (name, info) records)
      sel_upd equalities extinjects extsplit splits extfields fieldext;
  in RecordsData.put data thy end;


(* access 'sel_upd' *)

val get_sel_upd = #sel_upd o RecordsData.get;

val is_selector = Symtab.defined o #selectors o get_sel_upd;
val get_updates = Symtab.lookup o #updates o get_sel_upd;
fun get_simpset thy = Simplifier.theory_context thy (#simpset (get_sel_upd thy));

fun put_sel_upd names simps = RecordsData.map (fn {records,
  sel_upd = {selectors, updates, simpset},
    equalities, extinjects, extsplit, splits, extfields, fieldext} =>
  make_record_data records
    {selectors = fold (fn name => Symtab.update (name, ())) names selectors,
      updates = fold (fn name => Symtab.update ((suffix updateN) name, name)) names updates,
      simpset = Simplifier.addsimps (simpset, simps)}
      equalities extinjects extsplit splits extfields fieldext);


(* access 'equalities' *)

fun add_record_equalities name thm thy =
  let
    val {records, sel_upd, equalities, extinjects, extsplit, splits, extfields,fieldext} =
          RecordsData.get thy;
    val data = make_record_data records sel_upd
           (Symtab.update_new (name, thm) equalities) extinjects extsplit
           splits extfields fieldext;
  in RecordsData.put data thy end;

val get_equalities =Symtab.lookup o #equalities o RecordsData.get;


(* access 'extinjects' *)

fun add_extinjects thm thy =
  let
    val {records, sel_upd, equalities, extinjects, extsplit, splits, extfields,fieldext} =
          RecordsData.get thy;
    val data =
      make_record_data records sel_upd equalities (insert Thm.eq_thm_prop thm extinjects) extsplit
        splits extfields fieldext;
  in RecordsData.put data thy end;

val get_extinjects = rev o #extinjects o RecordsData.get;


(* access 'extsplit' *)

fun add_extsplit name thm thy =
  let
    val {records, sel_upd, equalities, extinjects, extsplit, splits, extfields,fieldext} =
          RecordsData.get thy;
    val data = make_record_data records sel_upd
      equalities extinjects (Symtab.update_new (name, thm) extsplit) splits
      extfields fieldext;
  in RecordsData.put data thy end;

val get_extsplit = Symtab.lookup o #extsplit o RecordsData.get;


(* access 'splits' *)

fun add_record_splits name thmP thy =
  let
    val {records, sel_upd, equalities, extinjects, extsplit, splits, extfields,fieldext} =
          RecordsData.get thy;
    val data = make_record_data records sel_upd
      equalities extinjects extsplit (Symtab.update_new (name, thmP) splits)
      extfields fieldext;
  in RecordsData.put data thy end;

val get_splits = Symtab.lookup o #splits o RecordsData.get;


(* parent/extension of named record *)

val get_parent = (Option.join o Option.map #parent) oo (Symtab.lookup o #records o RecordsData.get);
val get_extension = Option.map #extension oo (Symtab.lookup o #records o RecordsData.get);


(* access 'extfields' *)

fun add_extfields name fields thy =
  let
    val {records, sel_upd, equalities, extinjects, extsplit,splits, extfields, fieldext} =
          RecordsData.get thy;
    val data = make_record_data records sel_upd
         equalities extinjects extsplit splits
         (Symtab.update_new (name, fields) extfields) fieldext;
  in RecordsData.put data thy end;

val get_extfields = Symtab.lookup o #extfields o RecordsData.get;

fun get_extT_fields thy T =
  let
    val ((name,Ts),moreT) = dest_recT T;
    val recname = let val (nm::recn::rst) = rev (Long_Name.explode name)
                  in Long_Name.implode (rev (nm::rst)) end;
    val midx = maxidx_of_typs (moreT::Ts);
    val varifyT = varifyT midx;
    val {records,extfields,...} = RecordsData.get thy;
    val (flds,(more,_)) = split_last (Symtab.lookup_list extfields name);
    val args = map varifyT (snd (#extension (the (Symtab.lookup records recname))));

    val subst = fold (Sign.typ_match thy) (but_last args ~~ but_last Ts) (Vartab.empty);
    val flds' = map (apsnd ((Envir.norm_type subst) o varifyT)) flds;
  in (flds',(more,moreT)) end;

fun get_recT_fields thy T =
  let
    val (root_flds,(root_more,root_moreT)) = get_extT_fields thy T;
    val (rest_flds,rest_more) =
           if is_recT root_moreT then get_recT_fields thy root_moreT
           else ([],(root_more,root_moreT));
  in (root_flds@rest_flds,rest_more) end;


(* access 'fieldext' *)

fun add_fieldext extname_types fields thy =
  let
    val {records, sel_upd, equalities, extinjects, extsplit, splits, extfields, fieldext} =
           RecordsData.get thy;
    val fieldext' =
      fold (fn field => Symtab.update_new (field, extname_types)) fields fieldext;
    val data=make_record_data records sel_upd equalities extinjects extsplit
              splits extfields fieldext';
  in RecordsData.put data thy end;


val get_fieldext = Symtab.lookup o #fieldext o RecordsData.get;


(* parent records *)

fun add_parents thy NONE parents = parents
  | add_parents thy (SOME (types, name)) parents =
      let
        fun err msg = error (msg ^ " parent record " ^ quote name);

        val {args, parent, fields, extension, induct} =
          (case get_record thy name of SOME info => info | NONE => err "Unknown");
        val _ = if length types <> length args then err "Bad number of arguments for" else ();

        fun bad_inst ((x, S), T) =
          if Sign.of_sort thy (T, S) then NONE else SOME x
        val bads = List.mapPartial bad_inst (args ~~ types);
        val _ = null bads orelse err ("Ill-sorted instantiation of " ^ commas bads ^ " in");

        val inst = map fst args ~~ types;
        val subst = Term.map_type_tfree (the o AList.lookup (op =) inst o fst);
        val parent' = Option.map (apfst (map subst)) parent;
        val fields' = map (apsnd subst) fields;
        val extension' = apsnd (map subst) extension;
      in
        add_parents thy parent'
          (make_parent_info name fields' extension' induct :: parents)
      end;



(** concrete syntax for records **)

(* decode type *)

fun decode_type thy t =
  let
    fun get_sort xs n = AList.lookup (op =) xs (n: indexname) |> the_default (Sign.defaultS thy);
    val map_sort = Sign.intern_sort thy;
  in
    Syntax.typ_of_term (get_sort (Syntax.term_sorts map_sort t)) map_sort t
    |> Sign.intern_tycons thy
  end;


(* parse translations *)

fun gen_field_tr mark sfx (t as Const (c, _) $ Const (name, _) $ arg) =
      if c = mark then Syntax.const (suffix sfx name) $ (Abs ("_",dummyT, arg))
      else raise TERM ("gen_field_tr: " ^ mark, [t])
  | gen_field_tr mark _ t = raise TERM ("gen_field_tr: " ^ mark, [t]);

fun gen_fields_tr sep mark sfx (tm as Const (c, _) $ t $ u) =
      if c = sep then gen_field_tr mark sfx t :: gen_fields_tr sep mark sfx u
      else [gen_field_tr mark sfx tm]
  | gen_fields_tr _ mark sfx tm = [gen_field_tr mark sfx tm];


fun record_update_tr [t, u] =
      Library.foldr (op $) (rev (gen_fields_tr "_updates" "_update" updateN u), t)
  | record_update_tr ts = raise TERM ("record_update_tr", ts);

fun update_name_tr (Free (x, T) :: ts) = Free (suffix updateN x, T) $$ ts
  | update_name_tr (Const (x, T) :: ts) = Const (suffix updateN x, T) $$ ts
  | update_name_tr (((c as Const ("_constrain", _)) $ t $ ty) :: ts) =
      (c $ update_name_tr [t] $ (Syntax.const "fun" $ ty $ Syntax.const "dummy")) $$ ts
  | update_name_tr ts = raise TERM ("update_name_tr", ts);

fun dest_ext_field mark (t as (Const (c,_) $ Const (name,_) $ arg)) =
     if c = mark then (name,arg) else raise TERM ("dest_ext_field: " ^ mark, [t])
  | dest_ext_field _ t = raise TERM ("dest_ext_field", [t])

fun dest_ext_fields sep mark (trm as (Const (c,_) $ t $ u)) =
     if c = sep then dest_ext_field mark t::dest_ext_fields sep mark u
     else [dest_ext_field mark trm]
  | dest_ext_fields _ mark t = [dest_ext_field mark t]

fun gen_ext_fields_tr sep mark sfx more ctxt t =
  let
    val thy = ProofContext.theory_of ctxt;
    val msg = "error in record input: ";
    val fieldargs = dest_ext_fields sep mark t;
    fun splitargs (field::fields) ((name,arg)::fargs) =
          if can (unsuffix name) field
          then let val (args,rest) = splitargs fields fargs
               in (arg::args,rest) end
          else raise TERM (msg ^ "expecting field " ^ field ^ " but got " ^ name, [t])
      | splitargs [] (fargs as (_::_)) = ([],fargs)
      | splitargs (_::_) [] = raise TERM (msg ^ "expecting more fields", [t])
      | splitargs _ _ = ([],[]);

    fun mk_ext (fargs as (name,arg)::_) =
         (case get_fieldext thy (Sign.intern_const thy name) of
            SOME (ext,_) => (case get_extfields thy ext of
                               SOME flds
                                 => let val (args,rest) =
                                               splitargs (map fst (but_last flds)) fargs;
                                        val more' = mk_ext rest;
                                    in list_comb (Syntax.const (suffix sfx ext),args@[more'])
                                    end
                             | NONE => raise TERM(msg ^ "no fields defined for "
                                                   ^ ext,[t]))
          | NONE => raise TERM (msg ^ name ^" is no proper field",[t]))
      | mk_ext [] = more

  in mk_ext fieldargs end;

fun gen_ext_type_tr sep mark sfx more ctxt t =
  let
    val thy = ProofContext.theory_of ctxt;
    val msg = "error in record-type input: ";
    val fieldargs = dest_ext_fields sep mark t;
    fun splitargs (field::fields) ((name,arg)::fargs) =
          if can (unsuffix name) field
          then let val (args,rest) = splitargs fields fargs
               in (arg::args,rest) end
          else raise TERM (msg ^ "expecting field " ^ field ^ " but got " ^ name, [t])
      | splitargs [] (fargs as (_::_)) = ([],fargs)
      | splitargs (_::_) [] = raise TERM (msg ^ "expecting more fields", [t])
      | splitargs _ _ = ([],[]);

    fun mk_ext (fargs as (name,arg)::_) =
         (case get_fieldext thy (Sign.intern_const thy name) of
            SOME (ext,alphas) =>
              (case get_extfields thy ext of
                 SOME flds
                  => (let
                       val flds' = but_last flds;
                       val types = map snd flds';
                       val (args,rest) = splitargs (map fst flds') fargs;
                       val argtypes = map (Sign.certify_typ thy o decode_type thy) args;
                       val midx =  fold (fn T => fn i => Int.max (maxidx_of_typ T, i))
                                    argtypes 0;
                       val varifyT = varifyT midx;
                       val vartypes = map varifyT types;

                       val subst = fold (Sign.typ_match thy) (vartypes ~~ argtypes)
                                            Vartab.empty;
                       val alphas' = map ((Syntax.term_of_typ (! Syntax.show_sorts)) o
                                          Envir.norm_type subst o varifyT)
                                         (but_last alphas);

                       val more' = mk_ext rest;
                     in list_comb (Syntax.const (suffix sfx ext),alphas'@[more'])
                     end handle TYPE_MATCH => raise
                           TERM (msg ^ "type is no proper record (extension)", [t]))
               | NONE => raise TERM (msg ^ "no fields defined for " ^ ext,[t]))
          | NONE => raise TERM (msg ^ name ^" is no proper field",[t]))
      | mk_ext [] = more

  in mk_ext fieldargs end;

fun gen_adv_record_tr sep mark sfx unit ctxt [t] =
      gen_ext_fields_tr sep mark sfx unit ctxt t
  | gen_adv_record_tr _ _ _ _ _ ts = raise TERM ("gen_record_tr", ts);

fun gen_adv_record_scheme_tr sep mark sfx ctxt [t, more] =
      gen_ext_fields_tr sep mark sfx more ctxt t
  | gen_adv_record_scheme_tr _ _ _ _ ts = raise TERM ("gen_record_scheme_tr", ts);

fun gen_adv_record_type_tr sep mark sfx unit ctxt [t] =
      gen_ext_type_tr sep mark sfx unit ctxt t
  | gen_adv_record_type_tr _ _ _ _ _ ts = raise TERM ("gen_record_tr", ts);

fun gen_adv_record_type_scheme_tr sep mark sfx ctxt [t, more] =
      gen_ext_type_tr sep mark sfx more ctxt t
  | gen_adv_record_type_scheme_tr _ _ _ _ ts = raise TERM ("gen_record_scheme_tr", ts);

val adv_record_tr = gen_adv_record_tr "_fields" "_field" extN HOLogic.unit;
val adv_record_scheme_tr = gen_adv_record_scheme_tr "_fields" "_field" extN;

val adv_record_type_tr =
      gen_adv_record_type_tr "_field_types" "_field_type" ext_typeN
        (Syntax.term_of_typ false (HOLogic.unitT));
val adv_record_type_scheme_tr =
      gen_adv_record_type_scheme_tr "_field_types" "_field_type" ext_typeN;


val parse_translation =
 [("_record_update", record_update_tr),
  ("_update_name", update_name_tr)];


val adv_parse_translation =
 [("_record",adv_record_tr),
  ("_record_scheme",adv_record_scheme_tr),
  ("_record_type",adv_record_type_tr),
  ("_record_type_scheme",adv_record_type_scheme_tr)];


(* print translations *)

val print_record_type_abbr = ref true;
val print_record_type_as_fields = ref true;

fun gen_field_upds_tr' mark sfx (tm as Const (name_field, _) $ k $ u) =
  let val t = (case k of (Abs (_,_,(Abs (_,_,t)$Bound 0))) 
                  => if null (loose_bnos t) then t else raise Match
               | Abs (x,_,t) => if null (loose_bnos t) then t else raise Match
               | _ => raise Match)

      (* (case k of (Const ("K_record",_)$t) => t
               | Abs (x,_,Const ("K_record",_)$t$Bound 0) => t
               | _ => raise Match)*)
  in
    (case try (unsuffix sfx) name_field of
      SOME name =>
        apfst (cons (Syntax.const mark $ Syntax.free name $ t)) (gen_field_upds_tr' mark sfx u)
     | NONE => ([], tm))
  end
  | gen_field_upds_tr' _ _ tm = ([], tm);

fun record_update_tr' tm =
  let val (ts, u) = gen_field_upds_tr' "_update" updateN tm in
    if null ts then raise Match
    else Syntax.const "_record_update" $ u $
          foldr1 (fn (v, w) => Syntax.const "_updates" $ v $ w) (rev ts)
  end;

fun gen_field_tr' sfx tr' name =
  let val name_sfx = suffix sfx name
  in (name_sfx, fn [t, u] => tr' (Syntax.const name_sfx $ t $ u) | _ => raise Match) end;

fun record_tr' sep mark record record_scheme unit ctxt t =
  let
    val thy = ProofContext.theory_of ctxt;
    fun field_lst t =
      (case strip_comb t of
        (Const (ext,_),args as (_::_))
         => (case try (unsuffix extN) (Sign.intern_const thy ext) of
               SOME ext'
               => (case get_extfields thy ext' of
                     SOME flds
                     => (let
                          val (f::fs) = but_last (map fst flds);
                          val flds' = Sign.extern_const thy f :: map Long_Name.base_name fs;
                          val (args',more) = split_last args;
                         in (flds'~~args')@field_lst more end
                         handle Library.UnequalLengths => [("",t)])
                   | NONE => [("",t)])
             | NONE => [("",t)])
       | _ => [("",t)])

    val (flds,(_,more)) = split_last (field_lst t);
    val _ = if null flds then raise Match else ();
    val flds' = map (fn (n,t)=>Syntax.const mark$Syntax.const n$t) flds;
    val flds'' = foldr1 (fn (x,y) => Syntax.const sep$x$y) flds';

  in if unit more
     then Syntax.const record$flds''
     else Syntax.const record_scheme$flds''$more
  end

fun gen_record_tr' name =
  let val name_sfx = suffix extN name;
      val unit = (fn Const (@{const_syntax "Product_Type.Unity"},_) => true | _ => false);
      fun tr' ctxt ts = record_tr' "_fields" "_field" "_record" "_record_scheme" unit ctxt
                       (list_comb (Syntax.const name_sfx,ts))
  in (name_sfx,tr')
  end

fun print_translation names =
  map (gen_field_tr' updateN record_update_tr') names;


(* record_type_abbr_tr' tries to reconstruct the record name type abbreviation from *)
(* the (nested) extension types.                                                    *)
fun record_type_abbr_tr' default_tr' abbr alphas zeta lastExt schemeT ctxt tm =
  let
      val thy = ProofContext.theory_of ctxt;
      (* tm is term representation of a (nested) field type. We first reconstruct the      *)
      (* type from tm so that we can continue on the type level rather then the term level.*)

      (* WORKAROUND:
       * If a record type occurs in an error message of type inference there
       * may be some internal frees donoted by ??:
       * (Const "_tfree",_)$Free ("??'a",_).

       * This will unfortunately be translated to Type ("??'a",[]) instead of
       * TFree ("??'a",_) by typ_of_term, which will confuse unify below.
       * fixT works around.
       *)
      fun fixT (T as Type (x,[])) =
            if String.isPrefix "??'" x then TFree (x,Sign.defaultS thy) else T
        | fixT (Type (x,xs)) = Type (x,map fixT xs)
        | fixT T = T;

      val T = fixT (decode_type thy tm);
      val midx = maxidx_of_typ T;
      val varifyT = varifyT midx;

      fun mk_type_abbr subst name alphas =
          let val abbrT = Type (name, map (fn a => varifyT (TFree (a, Sign.defaultS thy))) alphas);
          in Syntax.term_of_typ (! Syntax.show_sorts)
               (Sign.extern_typ thy (Envir.norm_type subst abbrT)) end;

      fun match rT T = (Sign.typ_match thy (varifyT rT,T)
                                                Vartab.empty);

   in if !print_record_type_abbr
      then (case last_extT T of
             SOME (name,_)
              => if name = lastExt
                 then
                  (let
                     val subst = match schemeT T
                   in
                    if HOLogic.is_unitT (Envir.norm_type subst (varifyT (TFree(zeta,Sign.defaultS thy))))
                    then mk_type_abbr subst abbr alphas
                    else mk_type_abbr subst (suffix schemeN abbr) (alphas@[zeta])
                   end handle TYPE_MATCH => default_tr' ctxt tm)
                 else raise Match (* give print translation of specialised record a chance *)
            | _ => raise Match)
       else default_tr' ctxt tm
  end

fun record_type_tr' sep mark record record_scheme ctxt t =
  let
    val thy = ProofContext.theory_of ctxt;

    val T = decode_type thy t;
    val varifyT = varifyT (Term.maxidx_of_typ T);

    fun term_of_type T = Syntax.term_of_typ (!Syntax.show_sorts) (Sign.extern_typ thy T);

    fun field_lst T =
      (case T of
        Type (ext, args)
         => (case try (unsuffix ext_typeN) ext of
               SOME ext'
               => (case get_extfields thy ext' of
                     SOME flds
                     => (case get_fieldext thy (fst (hd flds)) of
                           SOME (_, alphas)
                           => (let
                                val (f :: fs) = but_last flds;
                                val flds' = apfst (Sign.extern_const thy) f
                                  :: map (apfst Long_Name.base_name) fs;
                                val (args', more) = split_last args;
                                val alphavars = map varifyT (but_last alphas);
                                val subst = fold2 (curry (Sign.typ_match thy))
                                  alphavars args' Vartab.empty;
                                val flds'' = (map o apsnd)
                                  (Envir.norm_type subst o varifyT) flds';
                              in flds'' @ field_lst more end
                              handle TYPE_MATCH => [("", T)]
                                  | Library.UnequalLengths => [("", T)])
                         | NONE => [("", T)])
                   | NONE => [("", T)])
             | NONE => [("", T)])
        | _ => [("", T)])

    val (flds, (_, moreT)) = split_last (field_lst T);
    val flds' = map (fn (n, T) => Syntax.const mark $ Syntax.const n $ term_of_type T) flds;
    val flds'' = foldr1 (fn (x, y) => Syntax.const sep $ x $ y) flds' handle Empty => raise Match;

  in if not (!print_record_type_as_fields) orelse null flds then raise Match
     else if moreT = HOLogic.unitT
          then Syntax.const record$flds''
          else Syntax.const record_scheme$flds''$term_of_type moreT
  end


fun gen_record_type_tr' name =
  let val name_sfx = suffix ext_typeN name;
      fun tr' ctxt ts = record_type_tr' "_field_types" "_field_type"
                       "_record_type" "_record_type_scheme" ctxt
                       (list_comb (Syntax.const name_sfx,ts))
  in (name_sfx,tr')
  end


fun gen_record_type_abbr_tr' abbr alphas zeta lastExt schemeT name =
  let val name_sfx = suffix ext_typeN name;
      val default_tr' = record_type_tr' "_field_types" "_field_type"
                               "_record_type" "_record_type_scheme"
      fun tr' ctxt ts =
          record_type_abbr_tr' default_tr' abbr alphas zeta lastExt schemeT ctxt
                               (list_comb (Syntax.const name_sfx,ts))
  in (name_sfx, tr') end;

(** record simprocs **)

val record_quick_and_dirty_sensitive = ref false;


fun quick_and_dirty_prove stndrd thy asms prop tac =
  if !record_quick_and_dirty_sensitive andalso !quick_and_dirty
  then Goal.prove (ProofContext.init thy) [] []
        (Logic.list_implies (map Logic.varify asms,Logic.varify prop))
        (K (SkipProof.cheat_tac @{theory HOL}))
        (* standard can take quite a while for large records, thats why
         * we varify the proposition manually here.*)
  else let val prf = Goal.prove (ProofContext.init thy) [] asms prop tac;
       in if stndrd then standard prf else prf end;

fun quick_and_dirty_prf noopt opt () =
      if !record_quick_and_dirty_sensitive andalso !quick_and_dirty
      then noopt ()
      else opt ();

local
fun abstract_over_fun_app (Abs (f,fT,t)) =
  let
     val (f',t') = Term.dest_abs (f,fT,t);
     val T = domain_type fT;
     val (x,T') = hd (Term.variant_frees t' [("x",T)]);
     val f_x = Free (f',fT)$(Free (x,T'));
     fun is_constr (Const (c,_)$_) = can (unsuffix extN) c
       | is_constr _ = false;
     fun subst (t as u$w) = if Free (f',fT)=u
                            then if is_constr w then f_x
                                 else raise TERM ("abstract_over_fun_app",[t])
                            else subst u$subst w
       | subst (Abs (x,T,t)) = (Abs (x,T,subst t))
       | subst t = t
     val t'' = abstract_over (f_x,subst t');
     val vars = strip_qnt_vars "all" t'';
     val bdy = strip_qnt_body "all" t'';

  in list_abs ((x,T')::vars,bdy) end
  | abstract_over_fun_app t = raise TERM ("abstract_over_fun_app",[t]);
(* Generates a theorem of the kind:
 * !!f x*. PROP P (f ( r x* ) x* == !!r x*. PROP P r x*
 *)
fun mk_fun_apply_eq (Abs (f, fT, t)) thy =
  let
    val rT = domain_type fT;
    val vars = Term.strip_qnt_vars "all" t;
    val Ts = map snd vars;
    val n = length vars;
    fun app_bounds 0 t = t$Bound 0
      | app_bounds n t = if n > 0 then app_bounds (n-1) (t$Bound n) else t


    val [P,r] = Term.variant_frees t [("P",rT::Ts--->Term.propT),("r",Ts--->rT)];
    val prop = Logic.mk_equals
                (list_all ((f,fT)::vars,
                           app_bounds (n - 1) ((Free P)$(Bound n$app_bounds (n-1) (Free r)))),
                 list_all ((fst r,rT)::vars,
                           app_bounds (n - 1) ((Free P)$Bound n)));
    val prove_standard = quick_and_dirty_prove true thy;
    val thm = prove_standard [] prop (fn _ =>
	 EVERY [rtac equal_intr_rule 1,
                Goal.norm_hhf_tac 1,REPEAT (etac meta_allE 1), atac 1,
                Goal.norm_hhf_tac 1,REPEAT (etac meta_allE 1), atac 1]);
  in thm end
  | mk_fun_apply_eq t thy = raise TERM ("mk_fun_apply_eq",[t]);

in
(* During proof of theorems produced by record_simproc you can end up in
 * situations like "!!f ... . ... f r ..." where f is an extension update function.
 * In order to split "f r" we transform this to "!!r ... . ... r ..." so that the
 * usual split rules for extensions can apply.
 *)
val record_split_f_more_simproc =
  Simplifier.simproc @{theory HOL} "record_split_f_more_simp" ["x"]
    (fn thy => fn _ => fn t =>
      (case t of (Const ("all", Type (_, [Type (_, [Type("fun",[T,T']), _]), _])))$
                  (trm as Abs _) =>
         (case rec_id (~1) T of
            "" => NONE
          | n => if T=T'
                 then (let
                        val P=cterm_of thy (abstract_over_fun_app trm);
                        val thm = mk_fun_apply_eq trm thy;
                        val PV = cterm_of thy (hd (OldTerm.term_vars (prop_of thm)));
                        val thm' = cterm_instantiate [(PV,P)] thm;
                       in SOME  thm' end handle TERM _ => NONE)
                else NONE)
       | _ => NONE))
end

fun prove_split_simp thy ss T prop =
  let
    val {sel_upd={simpset,...},extsplit,...} = RecordsData.get thy;
    val extsplits =
            Library.foldl (fn (thms,(n,_)) => the_list (Symtab.lookup extsplit n) @ thms)
                    ([],dest_recTs T);
    val thms = (case get_splits thy (rec_id (~1) T) of
                   SOME (all_thm,_,_,_) =>
                     all_thm::(case extsplits of [thm] => [] | _ => extsplits)
                              (* [thm] is the same as all_thm *)
                 | NONE => extsplits)
    val thms'=K_comp_convs@thms;
    val ss' = (Simplifier.inherit_context ss simpset
                addsimps thms'
                addsimprocs [record_split_f_more_simproc]);
  in
    quick_and_dirty_prove true thy [] prop (fn _ => simp_tac ss' 1)
  end;


local
fun eq (s1:string) (s2:string) = (s1 = s2);
fun has_field extfields f T =
     exists (fn (eN,_) => exists (eq f o fst) (Symtab.lookup_list extfields eN))
       (dest_recTs T);

fun K_skeleton n (T as Type (_,[_,kT])) (b as Bound i) (Abs (x,xT,t)) =
     if null (loose_bnos t) then ((n,kT),(Abs (x,xT,Bound (i+1)))) else ((n,T),b)
  | K_skeleton n T b _ = ((n,T),b);

(*
fun K_skeleton n _ b ((K_rec as Const ("Record.K_record",Type (_,[kT,_])))$_) = 
      ((n,kT),K_rec$b)
  | K_skeleton n _ (Bound i) 
      (Abs (x,T,(K_rec as Const ("Record.K_record",Type (_,[kT,_])))$_$Bound 0)) =
        ((n,kT),Abs (x,T,(K_rec$Bound (i+1)$Bound 0)))
  | K_skeleton n T b  _ = ((n,T),b);
 *)

fun normalize_rhs thm =
  let
     val ss = HOL_basic_ss addsimps K_comp_convs; 
     val rhs = thm |> Thm.cprop_of |> Thm.dest_comb |> snd;
     val rhs' = (Simplifier.rewrite ss rhs);
  in Thm.transitive thm rhs' end;
in
(* record_simproc *)
(* Simplifies selections of an record update:
 *  (1)  S (S_update k r) = k (S r)
 *  (2)  S (X_update k r) = S r
 * The simproc skips multiple updates at once, eg:
 *  S (X_update x (Y_update y (S_update k r))) = k (S r)
 * But be careful in (2) because of the extendibility of records.
 * - If S is a more-selector we have to make sure that the update on component
 *   X does not affect the selected subrecord.
 * - If X is a more-selector we have to make sure that S is not in the updated
 *   subrecord.
 *)
val record_simproc =
  Simplifier.simproc @{theory HOL} "record_simp" ["x"]
    (fn thy => fn ss => fn t =>
      (case t of (sel as Const (s, Type (_,[domS,rangeS])))$
                   ((upd as Const (u,Type(_,[_,Type (_,[rT,_])]))) $ k $ r)=>
        if is_selector thy s then
          (case get_updates thy u of SOME u_name =>
            let
              val {sel_upd={updates,...},extfields,...} = RecordsData.get thy;

              fun mk_eq_terms ((upd as Const (u,Type(_,[kT,_]))) $ k $ r) =
                  (case Symtab.lookup updates u of
                     NONE => NONE
                   | SOME u_name
                     => if u_name = s
                        then (case mk_eq_terms r of
                               NONE =>
                                 let
                                   val rv = ("r",rT)
                                   val rb = Bound 0
                                   val (kv,kb) = K_skeleton "k" kT (Bound 1) k;
                                  in SOME (upd$kb$rb,kb$(sel$rb),[kv,rv]) end
                              | SOME (trm,trm',vars) =>
                                 let
                                   val (kv,kb) = K_skeleton "k" kT (Bound (length vars)) k;
                                 in SOME (upd$kb$trm,kb$trm',kv::vars) end)
                        else if has_field extfields u_name rangeS
                             orelse has_field extfields s (domain_type kT)
                             then NONE
                             else (case mk_eq_terms r of
                                     SOME (trm,trm',vars)
                                     => let
                                          val (kv,kb) = 
                                                 K_skeleton "k" kT (Bound (length vars)) k;
                                        in SOME (upd$kb$trm,trm',kv::vars) end
                                   | NONE
                                     => let
                                          val rv = ("r",rT)
                                          val rb = Bound 0
                                          val (kv,kb) = K_skeleton "k" kT (Bound 1) k;
                                        in SOME (upd$kb$rb,sel$rb,[kv,rv]) end))
                | mk_eq_terms r = NONE
            in
              (case mk_eq_terms (upd$k$r) of
                 SOME (trm,trm',vars)
                 => SOME (prove_split_simp thy ss domS
                                 (list_all(vars, Logic.mk_equals (sel $ trm, trm'))))
               | NONE => NONE)
            end
          | NONE => NONE)
        else NONE
      | _ => NONE));

(* record_upd_simproc *)
(* simplify multiple updates:
 *  (1)  "N_update y (M_update g (N_update x (M_update f r))) =
          (N_update (y o x) (M_update (g o f) r))"
 *  (2)  "r(|M:= M r|) = r"
 * For (2) special care of "more" updates has to be taken:
 *    r(|more := m; A := A r|)
 * If A is contained in the fields of m we cannot remove the update A := A r!
 * (But r(|more := r; A := A (r(|more := r|))|) = r(|more := r|)
*)
val record_upd_simproc =
  Simplifier.simproc @{theory HOL} "record_upd_simp" ["x"]
    (fn thy => fn ss => fn t =>
      (case t of ((upd as Const (u, Type(_,[_,Type(_,[rT,_])]))) $ k $ r) =>
         let datatype ('a,'b) calc = Init of 'b | Inter of 'a
             val {sel_upd={selectors,updates,...},extfields,...} = RecordsData.get thy;

             (*fun mk_abs_var x t = (x, fastype_of t);*)
             fun sel_name u = Long_Name.base_name (unsuffix updateN u);

             fun seed s (upd as Const (more,Type(_,[mT,_]))$ k $ r) =
                  if has_field extfields s (domain_type' mT) then upd else seed s r
               | seed _ r = r;

             fun grow u uT k kT vars (sprout,skeleton) =
                   if sel_name u = moreN
                   then let val (kv,kb) = K_skeleton "k" kT (Bound (length vars)) k;
                        in ((Const (u,uT)$k$sprout,Const (u,uT)$kb$skeleton),kv::vars) end
                   else ((sprout,skeleton),vars);


             fun dest_k (Abs (x,T,((sel as Const (s,_))$r))) =
                  if null (loose_bnos r) then SOME (x,T,sel,s,r) else NONE
               | dest_k (Abs (_,_,(Abs (x,T,((sel as Const (s,_))$r)))$Bound 0)) =
                  (* eta expanded variant *)
                  if null (loose_bnos r) then SOME (x,T,sel,s,r) else NONE
               | dest_k _ = NONE;

             fun is_upd_same (sprout,skeleton) u k =
               (case dest_k k of SOME (x,T,sel,s,r) =>
                   if (unsuffix updateN u) = s andalso (seed s sprout) = r
                   then SOME (fn t => Abs (x,T,incr_boundvars 1 t),sel,seed s skeleton)
                   else NONE
                | NONE => NONE);

             fun init_seed r = ((r,Bound 0), [("r", rT)]);

             fun add (n:string) f fmaps =
               (case AList.lookup (op =) fmaps n of
                  NONE => AList.update (op =) (n,[f]) fmaps
                | SOME fs => AList.update (op =) (n,f::fs) fmaps)

             fun comps (n:string) T fmaps =
               (case AList.lookup (op =) fmaps n of
                 SOME fs =>
                   foldr1 (fn (f,g) => Const ("Fun.comp",(T-->T)-->(T-->T)-->(T-->T))$f$g) fs
                | NONE => error ("record_upd_simproc.comps"))

             (* mk_updterm returns either
              *  - Init (orig-term, orig-term-skeleton, vars) if no optimisation can be made,
              *     where vars are the bound variables in the skeleton
              *  - Inter (orig-term-skeleton,simplified-term-skeleton,
              *           vars, (term-sprout, skeleton-sprout))
              *     where "All vars. orig-term-skeleton = simplified-term-skeleton" is
              *     the desired simplification rule,
              *     the sprouts accumulate the "more-updates" on the way from the seed
              *     to the outermost update. It is only relevant to calculate the
              *     possible simplification for (2)
              * The algorithm first walks down the updates to the seed-record while
              * memorising the updates in the already-table. While walking up the
              * updates again, the optimised term is constructed.
              *)
             fun mk_updterm upds already
                 (t as ((upd as Const (u,uT as (Type (_,[kT,_])))) $ k $ r)) =
                 if Symtab.defined upds u
                 then let
                         fun rest already = mk_updterm upds already
                      in if u mem_string already
                         then (case (rest already r) of
                                 Init ((sprout,skel),vars) =>
                                 let
                                   val n = sel_name u;
                                   val (kv,kb) = K_skeleton n kT (Bound (length vars)) k;
                                   val (sprout',vars')= grow u uT k kT (kv::vars) (sprout,skel);
                                 in Inter (upd$kb$skel,skel,vars',add n kb [],sprout') end
                               | Inter (trm,trm',vars,fmaps,sprout) =>
                                 let
                                   val n = sel_name u;
                                   val (kv,kb) = K_skeleton n kT (Bound (length vars)) k;
                                   val (sprout',vars') = grow u uT k kT (kv::vars) sprout;
                                 in Inter(upd$kb$trm,trm',kv::vars',add n kb fmaps,sprout')
                                 end)
                         else
                          (case rest (u::already) r of
                             Init ((sprout,skel),vars) =>
                              (case is_upd_same (sprout,skel) u k of
                                 SOME (K_rec,sel,skel') =>
                                 let
                                   val (sprout',vars') = grow u uT k kT vars (sprout,skel);
                                  in Inter(upd$(K_rec (sel$skel'))$skel,skel,vars',[],sprout')
                                  end
                               | NONE =>
                                 let
                                   val n = sel_name u;
                                   val (kv,kb) = K_skeleton n kT (Bound (length vars)) k;
                                 in Init ((upd$k$sprout,upd$kb$skel),kv::vars) end)
                           | Inter (trm,trm',vars,fmaps,sprout) =>
                               (case is_upd_same sprout u k of
                                  SOME (K_rec,sel,skel) =>
                                  let
                                    val (sprout',vars') = grow u uT k kT vars sprout
                                  in Inter(upd$(K_rec (sel$skel))$trm,trm',vars',fmaps,sprout')
                                  end
                                | NONE =>
                                  let
                                    val n = sel_name u
                                    val T = domain_type kT
                                    val (kv,kb) = K_skeleton n kT (Bound (length vars)) k;
                                    val (sprout',vars') = grow u uT k kT (kv::vars) sprout
                                    val fmaps' = add n kb fmaps
                                  in Inter (upd$kb$trm,upd$comps n T fmaps'$trm'
                                           ,vars',fmaps',sprout') end))
                     end
                 else Init (init_seed t)
               | mk_updterm _ _ t = Init (init_seed t);

         in (case mk_updterm updates [] t of
               Inter (trm,trm',vars,_,_)
                => SOME (normalize_rhs 
                          (prove_split_simp thy ss rT
                            (list_all(vars, Logic.mk_equals (trm, trm')))))
             | _ => NONE)
         end
       | _ => NONE))
end

(* record_eq_simproc *)
(* looks up the most specific record-equality.
 * Note on efficiency:
 * Testing equality of records boils down to the test of equality of all components.
 * Therefore the complexity is: #components * complexity for single component.
 * Especially if a record has a lot of components it may be better to split up
 * the record first and do simplification on that (record_split_simp_tac).
 * e.g. r(|lots of updates|) = x
 *
 *               record_eq_simproc       record_split_simp_tac
 * Complexity: #components * #updates     #updates
 *
 *)
val record_eq_simproc =
  Simplifier.simproc @{theory HOL} "record_eq_simp" ["r = s"]
    (fn thy => fn _ => fn t =>
      (case t of Const ("op =", Type (_, [T, _])) $ _ $ _ =>