src/HOL/Tools/Datatype/datatype_data.ML
author haftmann
Mon, 30 Nov 2009 12:28:12 +0100
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parent 33968 src/HOL/Tools/Datatype/datatype.ML@f94fb13ecbb3
permissions -rw-r--r--
dropped some unused bindings
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(*  Title:      HOL/Tools/Datatype/datatype_data.ML
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    Author:     Stefan Berghofer, TU Muenchen
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Datatype package: bookkeeping; interpretation of existing types as datatypes.
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*)
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signature DATATYPE_DATA =
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sig
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  include DATATYPE_COMMON
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  val derive_datatype_props : config -> string list -> string list option
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    -> descr list -> (string * sort) list -> thm -> thm list list -> thm list list
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    -> theory -> string list * theory
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  val rep_datatype : config -> (string list -> Proof.context -> Proof.context)
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    -> string list option -> term list -> theory -> Proof.state
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  val rep_datatype_cmd : string list option -> string list -> theory -> Proof.state
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  val get_info : theory -> string -> info option
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  val the_info : theory -> string -> info
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  val the_descr : theory -> string list
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    -> descr * (string * sort) list * string list
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      * string * (string list * string list) * (typ list * typ list)
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  val the_spec : theory -> string -> (string * sort) list * (string * typ list) list
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  val all_distincts : theory -> typ list -> thm list list
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  val get_constrs : theory -> string -> (string * typ) list option
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  val get_all : theory -> info Symtab.table
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  val info_of_constr : theory -> string * typ -> info option
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  val info_of_case : theory -> string -> info option
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  val interpretation : (config -> string list -> theory -> theory) -> theory -> theory
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  val make_case :  Proof.context -> Datatype_Case.config -> string list -> term ->
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    (term * term) list -> term * (term * (int * bool)) list
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  val strip_case : Proof.context -> bool -> term -> (term * (term * term) list) option
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  val read_typ: theory -> string -> (string * sort) list -> typ * (string * sort) list
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  val cert_typ: theory -> typ -> (string * sort) list -> typ * (string * sort) list
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  val mk_case_names_induct: descr -> attribute
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  val setup: theory -> theory
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end;
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structure Datatype_Data: DATATYPE_DATA =
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struct
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open Datatype_Aux;
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(** theory data **)
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(* data management *)
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structure DatatypesData = Theory_Data
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(
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  type T =
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    {types: info Symtab.table,
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     constrs: (string * info) list Symtab.table,
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     cases: info Symtab.table};
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  val empty =
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    {types = Symtab.empty, constrs = Symtab.empty, cases = Symtab.empty};
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  val extend = I;
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  fun merge
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    ({types = types1, constrs = constrs1, cases = cases1},
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     {types = types2, constrs = constrs2, cases = cases2}) : T =
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    {types = Symtab.merge (K true) (types1, types2),
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     constrs = Symtab.join (K (AList.merge (op =) (K true))) (constrs1, constrs2),
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     cases = Symtab.merge (K true) (cases1, cases2)};
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);
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val get_all = #types o DatatypesData.get;
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val get_info = Symtab.lookup o get_all;
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fun the_info thy name =
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  (case get_info thy name of
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    SOME info => info
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  | NONE => error ("Unknown datatype " ^ quote name));
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fun info_of_constr thy (c, T) =
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  let
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    val tab = Symtab.lookup_list ((#constrs o DatatypesData.get) thy) c;
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    val hint = case strip_type T of (_, Type (tyco, _)) => SOME tyco | _ => NONE;
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    val default = if null tab then NONE
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      else SOME (snd (Library.last_elem tab))
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        (*conservative wrt. overloaded constructors*);
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  in case hint
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   of NONE => default
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    | SOME tyco => case AList.lookup (op =) tab tyco
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       of NONE => default (*permissive*)
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        | SOME info => SOME info
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  end;
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val info_of_case = Symtab.lookup o #cases o DatatypesData.get;
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fun register (dt_infos : (string * info) list) =
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  DatatypesData.map (fn {types, constrs, cases} =>
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    {types = types |> fold Symtab.update dt_infos,
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     constrs = constrs |> fold (fn (constr, dtname_info) =>
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         Symtab.map_default (constr, []) (cons dtname_info))
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       (maps (fn (dtname, info as {descr, index, ...}) =>
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          map (rpair (dtname, info) o fst)
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            (#3 (the (AList.lookup op = descr index)))) dt_infos),
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     cases = cases |> fold Symtab.update
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       (map (fn (_, info as {case_name, ...}) => (case_name, info)) dt_infos)});
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(* complex queries *)
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fun the_spec thy dtco =
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  let
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    val { descr, index, sorts = raw_sorts, ... } = the_info thy dtco;
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    val SOME (_, dtys, raw_cos) = AList.lookup (op =) descr index;
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    val sorts = map ((fn v => (v, (the o AList.lookup (op =) raw_sorts) v))
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      o Datatype_Aux.dest_DtTFree) dtys;
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    val cos = map
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      (fn (co, tys) => (co, map (Datatype_Aux.typ_of_dtyp descr sorts) tys)) raw_cos;
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  in (sorts, cos) end;
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fun the_descr thy (raw_tycos as raw_tyco :: _) =
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  let
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    val info = the_info thy raw_tyco;
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    val descr = #descr info;
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    val SOME (_, dtys, _) = AList.lookup (op =) descr (#index info);
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    val vs = map ((fn v => (v, (the o AList.lookup (op =) (#sorts info)) v))
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      o dest_DtTFree) dtys;
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    fun is_DtTFree (DtTFree _) = true
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      | is_DtTFree _ = false
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    val k = find_index (fn (_, (_, dTs, _)) => not (forall is_DtTFree dTs)) descr;
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    val protoTs as (dataTs, _) = chop k descr
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      |> (pairself o map) (fn (_, (tyco, dTs, _)) => (tyco, map (typ_of_dtyp descr vs) dTs));
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    val tycos = map fst dataTs;
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    val _ = if eq_set (op =) (tycos, raw_tycos) then ()
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      else error ("Type constructors " ^ commas (map quote raw_tycos)
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        ^ " do not belong exhaustively to one mutual recursive datatype");
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    val (Ts, Us) = (pairself o map) Type protoTs;
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    val names = map Long_Name.base_name (the_default tycos (#alt_names info));
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    val (auxnames, _) = Name.make_context names
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      |> fold_map (yield_singleton Name.variants o name_of_typ) Us;
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    val prefix = space_implode "_" names;
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  in (descr, vs, tycos, prefix, (names, auxnames), (Ts, Us)) end;
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fun all_distincts thy Ts =
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  let
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    fun add_tycos (Type (tyco, Ts)) = insert (op =) tyco #> fold add_tycos Ts
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      | add_tycos _ = I;
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    val tycos = fold add_tycos Ts [];
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  in map_filter (Option.map #distinct o get_info thy) tycos end;
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fun get_constrs thy dtco =
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  case try (the_spec thy) dtco
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   of SOME (sorts, cos) =>
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        let
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          fun subst (v, sort) = TVar ((v, 0), sort);
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          fun subst_ty (TFree v) = subst v
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            | subst_ty ty = ty;
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          val dty = Type (dtco, map subst sorts);
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          fun mk_co (co, tys) = (co, map (Term.map_atyps subst_ty) tys ---> dty);
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        in SOME (map mk_co cos) end
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    | NONE => NONE;
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(** various auxiliary **)
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(* prepare datatype specifications *)
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fun read_typ thy str sorts =
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  let
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    val ctxt = ProofContext.init thy
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      |> fold (Variable.declare_typ o TFree) sorts;
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    val T = Syntax.read_typ ctxt str;
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  in (T, Term.add_tfreesT T sorts) end;
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fun cert_typ sign raw_T sorts =
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  let
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    val T = Type.no_tvars (Sign.certify_typ sign raw_T)
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      handle TYPE (msg, _, _) => error msg;
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    val sorts' = Term.add_tfreesT T sorts;
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    val _ =
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      case duplicates (op =) (map fst sorts') of
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        [] => ()
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      | dups => error ("Inconsistent sort constraints for " ^ commas dups)
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  in (T, sorts') end;
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(* case names *)
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local
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fun dt_recs (DtTFree _) = []
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  | dt_recs (DtType (_, dts)) = maps dt_recs dts
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  | dt_recs (DtRec i) = [i];
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fun dt_cases (descr: descr) (_, args, constrs) =
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  let
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    fun the_bname i = Long_Name.base_name (#1 (the (AList.lookup (op =) descr i)));
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    val bnames = map the_bname (distinct (op =) (maps dt_recs args));
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  in map (fn (c, _) => space_implode "_" (Long_Name.base_name c :: bnames)) constrs end;
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fun induct_cases descr =
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  Datatype_Prop.indexify_names (maps (dt_cases descr) (map #2 descr));
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fun exhaust_cases descr i = dt_cases descr (the (AList.lookup (op =) descr i));
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in
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fun mk_case_names_induct descr = Rule_Cases.case_names (induct_cases descr);
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fun mk_case_names_exhausts descr new =
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  map (Rule_Cases.case_names o exhaust_cases descr o #1)
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    (filter (fn ((_, (name, _, _))) => member (op =) new name) descr);
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end;
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(* translation rules for case *)
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fun make_case ctxt = Datatype_Case.make_case
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  (info_of_constr (ProofContext.theory_of ctxt)) ctxt;
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fun strip_case ctxt = Datatype_Case.strip_case
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  (info_of_case (ProofContext.theory_of ctxt));
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fun add_case_tr' case_names thy =
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  Sign.add_advanced_trfuns ([], [],
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    map (fn case_name =>
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      let val case_name' = Sign.const_syntax_name thy case_name
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      in (case_name', Datatype_Case.case_tr' info_of_case case_name')
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      end) case_names, []) thy;
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val trfun_setup =
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  Sign.add_advanced_trfuns ([],
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    [("_case_syntax", Datatype_Case.case_tr true info_of_constr)],
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    [], []);
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(** document antiquotation **)
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val _ = ThyOutput.antiquotation "datatype" Args.tyname
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  (fn {source = src, context = ctxt, ...} => fn dtco =>
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    let
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      val thy = ProofContext.theory_of ctxt;
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      val (vs, cos) = the_spec thy dtco;
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      val ty = Type (dtco, map TFree vs);
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      fun pretty_typ_bracket (ty as Type (_, _ :: _)) =
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            Pretty.enclose "(" ")" [Syntax.pretty_typ ctxt ty]
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        | pretty_typ_bracket ty =
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            Syntax.pretty_typ ctxt ty;
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      fun pretty_constr (co, tys) =
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        (Pretty.block o Pretty.breaks)
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          (Syntax.pretty_term ctxt (Const (co, tys ---> ty)) ::
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            map pretty_typ_bracket tys);
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      val pretty_datatype =
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        Pretty.block
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          (Pretty.command "datatype" :: Pretty.brk 1 ::
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           Syntax.pretty_typ ctxt ty ::
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           Pretty.str " =" :: Pretty.brk 1 ::
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           flat (separate [Pretty.brk 1, Pretty.str "| "]
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             (map (single o pretty_constr) cos)));
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    in ThyOutput.output (ThyOutput.maybe_pretty_source (K pretty_datatype) src [()]) end);
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(** abstract theory extensions relative to a datatype characterisation **)
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structure Datatype_Interpretation = Interpretation
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  (type T = config * string list val eq: T * T -> bool = eq_snd op =);
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fun interpretation f = Datatype_Interpretation.interpretation (uncurry f);
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fun make_dt_info alt_names descr sorts induct inducts rec_names rec_rewrites
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    (index, (((((((((((_, (tname, _, _))), inject), distinct),
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      exhaust), nchotomy), case_name), case_rewrites), case_cong), weak_case_cong),
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        (split, split_asm))) =
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  (tname,
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   {index = index,
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    alt_names = alt_names,
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    descr = descr,
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    sorts = sorts,
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    inject = inject,
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    distinct = distinct,
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    induct = induct,
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    inducts = inducts,
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    exhaust = exhaust,
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    nchotomy = nchotomy,
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    rec_names = rec_names,
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    rec_rewrites = rec_rewrites,
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    case_name = case_name,
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    case_rewrites = case_rewrites,
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    case_cong = case_cong,
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    weak_case_cong = weak_case_cong,
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    split = split,
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    split_asm = split_asm});
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fun derive_datatype_props config dt_names alt_names descr sorts
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    induct inject distinct thy1 =
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  let
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    val thy2 = thy1 |> Theory.checkpoint;
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    val flat_descr = flat descr;
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    val new_type_names = map Long_Name.base_name (the_default dt_names alt_names);
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    val _ = message config ("Deriving properties for datatype(s) " ^ commas_quote new_type_names);
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    val (exhaust, thy3) = Datatype_Abs_Proofs.prove_casedist_thms config new_type_names
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      descr sorts induct (mk_case_names_exhausts flat_descr dt_names) thy2;
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    val (nchotomys, thy4) = Datatype_Abs_Proofs.prove_nchotomys config new_type_names
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      descr sorts exhaust thy3;
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    val ((rec_names, rec_rewrites), thy5) = Datatype_Abs_Proofs.prove_primrec_thms
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      config new_type_names descr sorts (#inject o the o Symtab.lookup (get_all thy4))
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      inject (distinct, all_distincts thy2 (get_rec_types flat_descr sorts))
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      induct thy4;
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    val ((case_rewrites, case_names), thy6) = Datatype_Abs_Proofs.prove_case_thms
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      config new_type_names descr sorts rec_names rec_rewrites thy5;
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    val (case_congs, thy7) = Datatype_Abs_Proofs.prove_case_congs new_type_names
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      descr sorts nchotomys case_rewrites thy6;
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    val (weak_case_congs, thy8) = Datatype_Abs_Proofs.prove_weak_case_congs new_type_names
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      descr sorts thy7;
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    val (splits, thy9) = Datatype_Abs_Proofs.prove_split_thms
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      config new_type_names descr sorts inject distinct exhaust case_rewrites thy8;
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    val inducts = Project_Rule.projections (ProofContext.init thy2) induct;
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    val dt_infos = map_index
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      (make_dt_info alt_names flat_descr sorts induct inducts rec_names rec_rewrites)
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      (hd descr ~~ inject ~~ distinct ~~ exhaust ~~ nchotomys ~~
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        case_names ~~ case_rewrites ~~ case_congs ~~ weak_case_congs ~~ splits);
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    val dt_names = map fst dt_infos;
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    val prfx = Binding.qualify true (space_implode "_" new_type_names);
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    val simps = flat (inject @ distinct @ case_rewrites) @ rec_rewrites;
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    val named_rules = flat (map_index (fn (index, tname) =>
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      [((Binding.empty, [nth inducts index]), [Induct.induct_type tname]),
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       ((Binding.empty, [nth exhaust index]), [Induct.cases_type tname])]) dt_names);
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    val unnamed_rules = map (fn induct =>
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      ((Binding.empty, [induct]), [Rule_Cases.inner_rule, Induct.induct_type ""]))
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        (drop (length dt_names) inducts);
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  in
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    thy9
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    |> PureThy.add_thmss ([((prfx (Binding.name "simps"), simps), []),
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        ((prfx (Binding.name "inducts"), inducts), []),
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        ((prfx (Binding.name "splits"), maps (fn (x, y) => [x, y]) splits), []),
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        ((Binding.empty, flat case_rewrites @ flat distinct @ rec_rewrites),
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          [Simplifier.simp_add]),
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        ((Binding.empty, rec_rewrites), [Code.add_default_eqn_attribute]),
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        ((Binding.empty, flat inject), [iff_add]),
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        ((Binding.empty, map (fn th => th RS notE) (flat distinct)),
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          [Classical.safe_elim NONE]),
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        ((Binding.empty, weak_case_congs), [Simplifier.attrib (op addcongs)])]
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        @ named_rules @ unnamed_rules)
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    |> snd
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    |> add_case_tr' case_names
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    |> register dt_infos
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    |> Datatype_Interpretation.data (config, dt_names)
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    |> pair dt_names
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  end;
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(** declare existing type as datatype **)
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   356
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fun prove_rep_datatype config dt_names alt_names descr sorts
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    raw_inject half_distinct raw_induct thy1 =
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  let
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    val raw_distinct = (map o maps) (fn thm => [thm, thm RS not_sym]) half_distinct;
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    val new_type_names = map Long_Name.base_name (the_default dt_names alt_names);
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    val (((inject, distinct), [induct]), thy2) =
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      thy1
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      |> store_thmss "inject" new_type_names raw_inject
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      ||>> store_thmss "distinct" new_type_names raw_distinct
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      ||> Sign.add_path (space_implode "_" new_type_names)
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      ||>> PureThy.add_thms [((Binding.name "induct", raw_induct), [mk_case_names_induct descr])]
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      ||> Sign.restore_naming thy1;
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  in
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    thy2
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    |> derive_datatype_props config dt_names alt_names [descr] sorts
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         induct inject distinct
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 end;
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   374
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fun gen_rep_datatype prep_term config after_qed alt_names raw_ts thy =
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  let
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    fun constr_of_term (Const (c, T)) = (c, T)
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      | constr_of_term t =
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          error ("Not a constant: " ^ Syntax.string_of_term_global thy t);
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    fun no_constr (c, T) = error ("Bad constructor: "
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      ^ Sign.extern_const thy c ^ "::"
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      ^ Syntax.string_of_typ_global thy T);
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    fun type_of_constr (cT as (_, T)) =
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      let
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        val frees = OldTerm.typ_tfrees T;
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        val (tyco, vs) = ((apsnd o map) (dest_TFree) o dest_Type o snd o strip_type) T
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          handle TYPE _ => no_constr cT
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        val _ = if has_duplicates (eq_fst (op =)) vs then no_constr cT else ();
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        val _ = if length frees <> length vs then no_constr cT else ();
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      in (tyco, (vs, cT)) end;
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   391
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    val raw_cs = AList.group (op =) (map (type_of_constr o constr_of_term o prep_term thy) raw_ts);
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    val _ = case map_filter (fn (tyco, _) =>
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        if Symtab.defined (get_all thy) tyco then SOME tyco else NONE) raw_cs
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     of [] => ()
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      | tycos => error ("Type(s) " ^ commas (map quote tycos)
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   397
          ^ " already represented inductivly");
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   398
    val raw_vss = maps (map (map snd o fst) o snd) raw_cs;
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   399
    val ms = case distinct (op =) (map length raw_vss)
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     of [n] => 0 upto n - 1
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      | _ => error ("Different types in given constructors");
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   402
    fun inter_sort m = map (fn xs => nth xs m) raw_vss
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   403
      |> Library.foldr1 (Sorts.inter_sort (Sign.classes_of thy))
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    val sorts = map inter_sort ms;
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   405
    val vs = Name.names Name.context Name.aT sorts;
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   406
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   407
    fun norm_constr (raw_vs, (c, T)) = (c, map_atyps
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   408
      (TFree o (the o AList.lookup (op =) (map fst raw_vs ~~ vs)) o fst o dest_TFree) T);
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   409
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   410
    val cs = map (apsnd (map norm_constr)) raw_cs;
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   411
    val dtyps_of_typ = map (dtyp_of_typ (map (rpair (map fst vs) o fst) cs))
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   412
      o fst o strip_type;
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   413
    val dt_names = map fst cs;
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   414
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   415
    fun mk_spec (i, (tyco, constr)) = (i, (tyco,
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   416
      map (DtTFree o fst) vs,
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   417
      (map o apsnd) dtyps_of_typ constr))
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   418
    val descr = map_index mk_spec cs;
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   419
    val injs = Datatype_Prop.make_injs [descr] vs;
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   420
    val half_distincts = map snd (Datatype_Prop.make_distincts [descr] vs);
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    val ind = Datatype_Prop.make_ind [descr] vs;
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   422
    val rules = (map o map o map) Logic.close_form [[[ind]], injs, half_distincts];
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   423
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   424
    fun after_qed' raw_thms =
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   425
      let
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   426
        val [[[raw_induct]], raw_inject, half_distinct] =
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   427
          unflat rules (map Drule.zero_var_indexes_list raw_thms);
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   428
            (*FIXME somehow dubious*)
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   429
      in
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   430
        ProofContext.theory_result
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   431
          (prove_rep_datatype config dt_names alt_names descr vs
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   432
            raw_inject half_distinct raw_induct)
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   433
        #-> after_qed
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   434
      end;
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   435
  in
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   436
    thy
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   437
    |> ProofContext.init
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   438
    |> Proof.theorem_i NONE after_qed' ((map o map) (rpair []) (flat rules))
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   439
  end;
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   440
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   441
val rep_datatype = gen_rep_datatype Sign.cert_term;
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val rep_datatype_cmd = gen_rep_datatype Syntax.read_term_global default_config (K I);
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   443
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   444
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   445
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   446
(** package setup **)
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   447
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   448
(* setup theory *)
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   449
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   450
val setup =
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   451
  trfun_setup #>
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   452
  Datatype_Interpretation.init;
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   453
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   454
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   455
(* outer syntax *)
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   456
f94fb13ecbb3 modernized structures and tuned headers of datatype package modules; joined former datatype.ML and datatype_rep_proofs.ML
haftmann
parents: 33963
diff changeset
   457
local
f94fb13ecbb3 modernized structures and tuned headers of datatype package modules; joined former datatype.ML and datatype_rep_proofs.ML
haftmann
parents: 33963
diff changeset
   458
f94fb13ecbb3 modernized structures and tuned headers of datatype package modules; joined former datatype.ML and datatype_rep_proofs.ML
haftmann
parents: 33963
diff changeset
   459
structure P = OuterParse and K = OuterKeyword
f94fb13ecbb3 modernized structures and tuned headers of datatype package modules; joined former datatype.ML and datatype_rep_proofs.ML
haftmann
parents: 33963
diff changeset
   460
f94fb13ecbb3 modernized structures and tuned headers of datatype package modules; joined former datatype.ML and datatype_rep_proofs.ML
haftmann
parents: 33963
diff changeset
   461
in
f94fb13ecbb3 modernized structures and tuned headers of datatype package modules; joined former datatype.ML and datatype_rep_proofs.ML
haftmann
parents: 33963
diff changeset
   462
f94fb13ecbb3 modernized structures and tuned headers of datatype package modules; joined former datatype.ML and datatype_rep_proofs.ML
haftmann
parents: 33963
diff changeset
   463
val _ =
33969
1e7ca47c6c3d dropped some unused bindings
haftmann
parents: 33968
diff changeset
   464
  OuterSyntax.command "rep_datatype" "represent existing types inductively" K.thy_goal
1e7ca47c6c3d dropped some unused bindings
haftmann
parents: 33968
diff changeset
   465
    (Scan.option (P.$$$ "(" |-- Scan.repeat1 P.name --| P.$$$ ")") -- Scan.repeat1 P.term
1e7ca47c6c3d dropped some unused bindings
haftmann
parents: 33968
diff changeset
   466
      >> (fn (alt_names, ts) => Toplevel.print
1e7ca47c6c3d dropped some unused bindings
haftmann
parents: 33968
diff changeset
   467
           o Toplevel.theory_to_proof (rep_datatype_cmd alt_names ts)));
6385
5a6570458d9e rep_datatype: '_i' version, attributes, outer syntax;
wenzelm
parents: 6360
diff changeset
   468
30391
d930432adb13 adapted to simplified ThyOutput.antiquotation interface;
wenzelm
parents: 30364
diff changeset
   469
end;
33968
f94fb13ecbb3 modernized structures and tuned headers of datatype package modules; joined former datatype.ML and datatype_rep_proofs.ML
haftmann
parents: 33963
diff changeset
   470
f94fb13ecbb3 modernized structures and tuned headers of datatype package modules; joined former datatype.ML and datatype_rep_proofs.ML
haftmann
parents: 33963
diff changeset
   471
end;