src/HOL/Nominal/nominal_package.ML
author wenzelm
Thu Jan 05 17:16:38 2006 +0100 (2006-01-05)
changeset 18582 4f4cc426b440
parent 18579 002d371401f5
child 18658 317a6f0ef8b9
permissions -rw-r--r--
provide projections of induct_weak, induct_unsafe;
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(* $Id$ *)
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signature NOMINAL_PACKAGE =
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sig
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  val add_nominal_datatype : bool -> string list -> (string list * bstring * mixfix *
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    (bstring * string list * mixfix) list) list -> theory -> theory
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end
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structure NominalPackage : NOMINAL_PACKAGE =
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struct
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open DatatypeAux;
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open NominalAtoms;
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(** FIXME: DatatypePackage should export this function **)
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local
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fun dt_recs (DtTFree _) = []
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  | dt_recs (DtType (_, dts)) = List.concat (map 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 = Sign.base_name (#1 (valOf (AList.lookup (op =) descr i)));
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    val bnames = map the_bname (distinct (List.concat (map dt_recs args)));
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  in map (fn (c, _) => space_implode "_" (Sign.base_name c :: bnames)) constrs end;
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fun induct_cases descr =
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  DatatypeProp.indexify_names (List.concat (map (dt_cases descr) (map #2 descr)));
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fun exhaust_cases descr i = dt_cases descr (valOf (AList.lookup (op =) descr i));
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in
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fun mk_case_names_induct descr = RuleCases.case_names (induct_cases descr);
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fun mk_case_names_exhausts descr new =
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  map (RuleCases.case_names o exhaust_cases descr o #1)
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    (List.filter (fn ((_, (name, _, _))) => name mem_string new) descr);
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end;
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(*******************************)
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val (_ $ (_ $ (_ $ (distinct_f $ _) $ _))) = hd (prems_of distinct_lemma);
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fun read_typ sign ((Ts, sorts), str) =
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  let
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    val T = Type.no_tvars (Sign.read_typ (sign, (AList.lookup op =)
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      (map (apfst (rpair ~1)) sorts)) str) handle TYPE (msg, _, _) => error msg
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  in (Ts @ [T], add_typ_tfrees (T, sorts)) end;
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(** taken from HOL/Tools/datatype_aux.ML **)
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fun indtac indrule indnames i st =
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  let
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    val ts = HOLogic.dest_conj (HOLogic.dest_Trueprop (concl_of indrule));
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    val ts' = HOLogic.dest_conj (HOLogic.dest_Trueprop
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      (Logic.strip_imp_concl (List.nth (prems_of st, i - 1))));
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    val getP = if can HOLogic.dest_imp (hd ts) then
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      (apfst SOME) o HOLogic.dest_imp else pair NONE;
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    fun abstr (t1, t2) = (case t1 of
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        NONE => (case filter (fn Free (s, _) => s mem indnames | _ => false)
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              (term_frees t2) of
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            [Free (s, T)] => absfree (s, T, t2)
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          | _ => sys_error "indtac")
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      | SOME (_ $ t' $ _) => Abs ("x", fastype_of t', abstract_over (t', t2)))
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    val cert = cterm_of (Thm.sign_of_thm st);
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    val Ps = map (cert o head_of o snd o getP) ts;
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    val indrule' = cterm_instantiate (Ps ~~
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      (map (cert o abstr o getP) ts')) indrule
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  in
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    rtac indrule' i st
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  end;
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fun projections rule =
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  ProjectRule.projections rule
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  |> map (standard #> RuleCases.save rule);
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fun gen_add_nominal_datatype prep_typ err flat_names new_type_names dts thy =
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  let
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    (* this theory is used just for parsing *)
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    val tmp_thy = thy |>
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      Theory.copy |>
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      Theory.add_types (map (fn (tvs, tname, mx, _) =>
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        (tname, length tvs, mx)) dts);
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    val sign = Theory.sign_of tmp_thy;
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    val atoms = atoms_of thy;
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    val classes = map (NameSpace.map_base (fn s => "pt_" ^ s)) atoms;
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    val cp_classes = List.concat (map (fn atom1 => map (fn atom2 =>
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      Sign.intern_class thy ("cp_" ^ Sign.base_name atom1 ^ "_" ^
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        Sign.base_name atom2)) atoms) atoms);
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    fun augment_sort S = S union classes;
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    val augment_sort_typ = map_type_tfree (fn (s, S) => TFree (s, augment_sort S));
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    fun prep_constr ((constrs, sorts), (cname, cargs, mx)) =
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      let val (cargs', sorts') = Library.foldl (prep_typ sign) (([], sorts), cargs)
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      in (constrs @ [(cname, cargs', mx)], sorts') end
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    fun prep_dt_spec ((dts, sorts), (tvs, tname, mx, constrs)) =
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      let val (constrs', sorts') = Library.foldl prep_constr (([], sorts), constrs)
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      in (dts @ [(tvs, tname, mx, constrs')], sorts') end
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    val (dts', sorts) = Library.foldl prep_dt_spec (([], []), dts);
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    val sorts' = map (apsnd augment_sort) sorts;
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    val tyvars = map #1 dts';
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    val types_syntax = map (fn (tvs, tname, mx, constrs) => (tname, mx)) dts';
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    val constr_syntax = map (fn (tvs, tname, mx, constrs) =>
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      map (fn (cname, cargs, mx) => (cname, mx)) constrs) dts';
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    val ps = map (fn (_, n, _, _) =>
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      (Sign.full_name sign n, Sign.full_name sign (n ^ "_Rep"))) dts;
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    val rps = map Library.swap ps;
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    fun replace_types (Type ("nominal.ABS", [T, U])) = 
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          Type ("fun", [T, Type ("nominal.noption", [replace_types U])])
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      | replace_types (Type (s, Ts)) =
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          Type (getOpt (AList.lookup op = ps s, s), map replace_types Ts)
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      | replace_types T = T;
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    fun replace_types' (Type (s, Ts)) =
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          Type (getOpt (AList.lookup op = rps s, s), map replace_types' Ts)
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      | replace_types' T = T;
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    val dts'' = map (fn (tvs, tname, mx, constrs) => (tvs, tname ^ "_Rep", NoSyn,
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      map (fn (cname, cargs, mx) => (cname,
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        map (augment_sort_typ o replace_types) cargs, NoSyn)) constrs)) dts';
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    val new_type_names' = map (fn n => n ^ "_Rep") new_type_names;
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    val full_new_type_names' = map (Sign.full_name (sign_of thy)) new_type_names';
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    val ({induction, ...},thy1) =
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      DatatypePackage.add_datatype_i err flat_names new_type_names' dts'' thy;
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    val SOME {descr, ...} = Symtab.lookup
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      (DatatypePackage.get_datatypes thy1) (hd full_new_type_names');
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    fun nth_dtyp i = typ_of_dtyp descr sorts' (DtRec i);
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    (**** define permutation functions ****)
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    val permT = mk_permT (TFree ("'x", HOLogic.typeS));
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    val pi = Free ("pi", permT);
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    val perm_types = map (fn (i, _) =>
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      let val T = nth_dtyp i
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      in permT --> T --> T end) descr;
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    val perm_names = replicate (length new_type_names) "nominal.perm" @
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      DatatypeProp.indexify_names (map (fn i => Sign.full_name (sign_of thy1)
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        ("perm_" ^ name_of_typ (nth_dtyp i)))
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          (length new_type_names upto length descr - 1));
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    val perm_names_types = perm_names ~~ perm_types;
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    val perm_eqs = List.concat (map (fn (i, (_, _, constrs)) =>
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      let val T = nth_dtyp i
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      in map (fn (cname, dts) => 
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        let
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          val Ts = map (typ_of_dtyp descr sorts') dts;
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          val names = DatatypeProp.make_tnames Ts;
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          val args = map Free (names ~~ Ts);
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          val c = Const (cname, Ts ---> T);
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          fun perm_arg (dt, x) =
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            let val T = type_of x
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            in if is_rec_type dt then
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                let val (Us, _) = strip_type T
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                in list_abs (map (pair "x") Us,
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                  Const (List.nth (perm_names_types, body_index dt)) $ pi $
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                    list_comb (x, map (fn (i, U) =>
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                      Const ("nominal.perm", permT --> U --> U) $
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                        (Const ("List.rev", permT --> permT) $ pi) $
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                        Bound i) ((length Us - 1 downto 0) ~~ Us)))
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                end
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              else Const ("nominal.perm", permT --> T --> T) $ pi $ x
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            end;  
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        in
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          (("", HOLogic.mk_Trueprop (HOLogic.mk_eq
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            (Const (List.nth (perm_names_types, i)) $
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               Free ("pi", mk_permT (TFree ("'x", HOLogic.typeS))) $
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               list_comb (c, args),
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             list_comb (c, map perm_arg (dts ~~ args))))), [])
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        end) constrs
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      end) descr);
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    val (thy2, perm_simps) = thy1 |>
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      Theory.add_consts_i (map (fn (s, T) => (Sign.base_name s, T, NoSyn))
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        (List.drop (perm_names_types, length new_type_names))) |>
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      PrimrecPackage.add_primrec_i "" perm_eqs;
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    (**** prove that permutation functions introduced by unfolding are ****)
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    (**** equivalent to already existing permutation functions         ****)
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    val _ = warning ("length descr: " ^ string_of_int (length descr));
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    val _ = warning ("length new_type_names: " ^ string_of_int (length new_type_names));
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    val perm_indnames = DatatypeProp.make_tnames (map body_type perm_types);
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    val perm_fun_def = PureThy.get_thm thy2 (Name "perm_fun_def");
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    val unfolded_perm_eq_thms =
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      if length descr = length new_type_names then []
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      else map standard (List.drop (split_conj_thm
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        (Goal.prove thy2 [] []
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          (HOLogic.mk_Trueprop (foldr1 HOLogic.mk_conj
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            (map (fn (c as (s, T), x) =>
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               let val [T1, T2] = binder_types T
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               in HOLogic.mk_eq (Const c $ pi $ Free (x, T2),
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                 Const ("nominal.perm", T) $ pi $ Free (x, T2))
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               end)
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             (perm_names_types ~~ perm_indnames))))
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          (fn _ => EVERY [indtac induction perm_indnames 1,
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            ALLGOALS (asm_full_simp_tac
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              (simpset_of thy2 addsimps [perm_fun_def]))])),
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        length new_type_names));
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    (**** prove [] \<bullet> t = t ****)
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    val _ = warning "perm_empty_thms";
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    val perm_empty_thms = List.concat (map (fn a =>
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      let val permT = mk_permT (Type (a, []))
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      in map standard (List.take (split_conj_thm
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        (Goal.prove thy2 [] []
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          (HOLogic.mk_Trueprop (foldr1 HOLogic.mk_conj
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            (map (fn ((s, T), x) => HOLogic.mk_eq
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                (Const (s, permT --> T --> T) $
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                   Const ("List.list.Nil", permT) $ Free (x, T),
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                 Free (x, T)))
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             (perm_names ~~
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              map body_type perm_types ~~ perm_indnames))))
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          (fn _ => EVERY [indtac induction perm_indnames 1,
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            ALLGOALS (asm_full_simp_tac (simpset_of thy2))])),
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        length new_type_names))
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      end)
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      atoms);
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    (**** prove (pi1 @ pi2) \<bullet> t = pi1 \<bullet> (pi2 \<bullet> t) ****)
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    val _ = warning "perm_append_thms";
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    (*FIXME: these should be looked up statically*)
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    val at_pt_inst = PureThy.get_thm thy2 (Name "at_pt_inst");
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    val pt2 = PureThy.get_thm thy2 (Name "pt2");
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    val perm_append_thms = List.concat (map (fn a =>
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      let
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        val permT = mk_permT (Type (a, []));
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        val pi1 = Free ("pi1", permT);
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        val pi2 = Free ("pi2", permT);
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        val pt_inst = PureThy.get_thm thy2 (Name ("pt_" ^ Sign.base_name a ^ "_inst"));
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        val pt2' = pt_inst RS pt2;
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        val pt2_ax = PureThy.get_thm thy2
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          (Name (NameSpace.map_base (fn s => "pt_" ^ s ^ "2") a));
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      in List.take (map standard (split_conj_thm
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        (Goal.prove thy2 [] []
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             (HOLogic.mk_Trueprop (foldr1 HOLogic.mk_conj
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                (map (fn ((s, T), x) =>
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                    let val perm = Const (s, permT --> T --> T)
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                    in HOLogic.mk_eq
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                      (perm $ (Const ("List.op @", permT --> permT --> permT) $
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                         pi1 $ pi2) $ Free (x, T),
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                       perm $ pi1 $ (perm $ pi2 $ Free (x, T)))
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                    end)
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                  (perm_names ~~
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                   map body_type perm_types ~~ perm_indnames))))
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           (fn _ => EVERY [indtac induction perm_indnames 1,
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              ALLGOALS (asm_full_simp_tac (simpset_of thy2 addsimps [pt2', pt2_ax]))]))),
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         length new_type_names)
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      end) atoms);
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    (**** prove pi1 ~ pi2 ==> pi1 \<bullet> t = pi2 \<bullet> t ****)
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    val _ = warning "perm_eq_thms";
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    val pt3 = PureThy.get_thm thy2 (Name "pt3");
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    val pt3_rev = PureThy.get_thm thy2 (Name "pt3_rev");
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    val perm_eq_thms = List.concat (map (fn a =>
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      let
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        val permT = mk_permT (Type (a, []));
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        val pi1 = Free ("pi1", permT);
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        val pi2 = Free ("pi2", permT);
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        (*FIXME: not robust - better access these theorems using NominalData?*)
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        val at_inst = PureThy.get_thm thy2 (Name ("at_" ^ Sign.base_name a ^ "_inst"));
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        val pt_inst = PureThy.get_thm thy2 (Name ("pt_" ^ Sign.base_name a ^ "_inst"));
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        val pt3' = pt_inst RS pt3;
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        val pt3_rev' = at_inst RS (pt_inst RS pt3_rev);
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        val pt3_ax = PureThy.get_thm thy2
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          (Name (NameSpace.map_base (fn s => "pt_" ^ s ^ "3") a));
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      in List.take (map standard (split_conj_thm
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        (Goal.prove thy2 [] [] (Logic.mk_implies
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             (HOLogic.mk_Trueprop (Const ("nominal.prm_eq",
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                permT --> permT --> HOLogic.boolT) $ pi1 $ pi2),
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              HOLogic.mk_Trueprop (foldr1 HOLogic.mk_conj
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                (map (fn ((s, T), x) =>
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   298
                    let val perm = Const (s, permT --> T --> T)
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   299
                    in HOLogic.mk_eq
berghofe@17870
   300
                      (perm $ pi1 $ Free (x, T),
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   301
                       perm $ pi2 $ Free (x, T))
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   302
                    end)
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   303
                  (perm_names ~~
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   304
                   map body_type perm_types ~~ perm_indnames)))))
berghofe@18010
   305
           (fn _ => EVERY [indtac induction perm_indnames 1,
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   306
              ALLGOALS (asm_full_simp_tac (simpset_of thy2 addsimps [pt3', pt3_rev', pt3_ax]))]))),
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   307
         length new_type_names)
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   308
      end) atoms);
berghofe@17870
   309
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   310
    (**** prove pi1 \<bullet> (pi2 \<bullet> t) = (pi1 \<bullet> pi2) \<bullet> (pi1 \<bullet> t) ****)
berghofe@17870
   311
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   312
    val cp1 = PureThy.get_thm thy2 (Name "cp1");
berghofe@17870
   313
    val dj_cp = PureThy.get_thm thy2 (Name "dj_cp");
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   314
    val pt_perm_compose = PureThy.get_thm thy2 (Name "pt_perm_compose");
berghofe@17870
   315
    val pt_perm_compose_rev = PureThy.get_thm thy2 (Name "pt_perm_compose_rev");
berghofe@17870
   316
    val dj_perm_perm_forget = PureThy.get_thm thy2 (Name "dj_perm_perm_forget");
berghofe@17870
   317
berghofe@17870
   318
    fun composition_instance name1 name2 thy =
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   319
      let
berghofe@17870
   320
        val name1' = Sign.base_name name1;
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   321
        val name2' = Sign.base_name name2;
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   322
        val cp_class = Sign.intern_class thy ("cp_" ^ name1' ^ "_" ^ name2');
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   323
        val permT1 = mk_permT (Type (name1, []));
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   324
        val permT2 = mk_permT (Type (name2, []));
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   325
        val augment = map_type_tfree
berghofe@17870
   326
          (fn (x, S) => TFree (x, cp_class :: S));
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   327
        val Ts = map (augment o body_type) perm_types;
berghofe@17870
   328
        val cp_inst = PureThy.get_thm thy
berghofe@17870
   329
          (Name ("cp_" ^ name1' ^ "_" ^ name2' ^ "_inst"));
berghofe@17870
   330
        val simps = simpset_of thy addsimps (perm_fun_def ::
berghofe@17870
   331
          (if name1 <> name2 then
berghofe@17870
   332
             let val dj = PureThy.get_thm thy (Name ("dj_" ^ name2' ^ "_" ^ name1'))
berghofe@17870
   333
             in [dj RS (cp_inst RS dj_cp), dj RS dj_perm_perm_forget] end
berghofe@17870
   334
           else
berghofe@17870
   335
             let
berghofe@17870
   336
               val at_inst = PureThy.get_thm thy (Name ("at_" ^ name1' ^ "_inst"));
berghofe@17870
   337
               val pt_inst = PureThy.get_thm thy (Name ("pt_" ^ name1' ^ "_inst"))
berghofe@17870
   338
             in
berghofe@17870
   339
               [cp_inst RS cp1 RS sym,
berghofe@17870
   340
                at_inst RS (pt_inst RS pt_perm_compose) RS sym,
berghofe@17870
   341
                at_inst RS (pt_inst RS pt_perm_compose_rev) RS sym]
berghofe@17870
   342
            end))
berghofe@18010
   343
        val thms = split_conj_thm (standard (Goal.prove thy [] []
berghofe@17870
   344
            (HOLogic.mk_Trueprop (foldr1 HOLogic.mk_conj
berghofe@17870
   345
              (map (fn ((s, T), x) =>
berghofe@17870
   346
                  let
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   347
                    val pi1 = Free ("pi1", permT1);
berghofe@17870
   348
                    val pi2 = Free ("pi2", permT2);
berghofe@17870
   349
                    val perm1 = Const (s, permT1 --> T --> T);
berghofe@17870
   350
                    val perm2 = Const (s, permT2 --> T --> T);
berghofe@17870
   351
                    val perm3 = Const ("nominal.perm", permT1 --> permT2 --> permT2)
berghofe@17870
   352
                  in HOLogic.mk_eq
berghofe@17870
   353
                    (perm1 $ pi1 $ (perm2 $ pi2 $ Free (x, T)),
berghofe@17870
   354
                     perm2 $ (perm3 $ pi1 $ pi2) $ (perm1 $ pi1 $ Free (x, T)))
berghofe@17870
   355
                  end)
berghofe@18010
   356
                (perm_names ~~ Ts ~~ perm_indnames))))
berghofe@18010
   357
          (fn _ => EVERY [indtac induction perm_indnames 1,
berghofe@18010
   358
             ALLGOALS (asm_full_simp_tac simps)])))
berghofe@17870
   359
      in
berghofe@17870
   360
        foldl (fn ((s, tvs), thy) => AxClass.add_inst_arity_i
berghofe@17870
   361
            (s, replicate (length tvs) (cp_class :: classes), [cp_class])
berghofe@17870
   362
            (AxClass.intro_classes_tac [] THEN ALLGOALS (resolve_tac thms)) thy)
berghofe@17870
   363
          thy (full_new_type_names' ~~ tyvars)
berghofe@17870
   364
      end;
berghofe@17870
   365
urbanc@18381
   366
    val (perm_thmss,thy3) = thy2 |>
berghofe@17870
   367
      fold (fn name1 => fold (composition_instance name1) atoms) atoms |>
berghofe@17870
   368
      curry (Library.foldr (fn ((i, (tyname, args, _)), thy) =>
berghofe@17870
   369
        AxClass.add_inst_arity_i (tyname, replicate (length args) classes, classes)
berghofe@17870
   370
        (AxClass.intro_classes_tac [] THEN REPEAT (EVERY
berghofe@17870
   371
           [resolve_tac perm_empty_thms 1,
berghofe@17870
   372
            resolve_tac perm_append_thms 1,
berghofe@17870
   373
            resolve_tac perm_eq_thms 1, assume_tac 1])) thy))
berghofe@17870
   374
        (List.take (descr, length new_type_names)) |>
berghofe@17870
   375
      PureThy.add_thmss
berghofe@17870
   376
        [((space_implode "_" new_type_names ^ "_unfolded_perm_eq",
berghofe@17870
   377
          unfolded_perm_eq_thms), [Simplifier.simp_add_global]),
berghofe@17870
   378
         ((space_implode "_" new_type_names ^ "_perm_empty",
berghofe@17870
   379
          perm_empty_thms), [Simplifier.simp_add_global]),
berghofe@17870
   380
         ((space_implode "_" new_type_names ^ "_perm_append",
berghofe@17870
   381
          perm_append_thms), [Simplifier.simp_add_global]),
berghofe@17870
   382
         ((space_implode "_" new_type_names ^ "_perm_eq",
berghofe@17870
   383
          perm_eq_thms), [Simplifier.simp_add_global])];
berghofe@17870
   384
  
berghofe@17870
   385
    (**** Define representing sets ****)
berghofe@17870
   386
berghofe@17870
   387
    val _ = warning "representing sets";
berghofe@17870
   388
berghofe@17870
   389
    val rep_set_names = map (Sign.full_name thy3) (DatatypeProp.indexify_names
berghofe@17870
   390
      (map (fn (i, _) => name_of_typ (nth_dtyp i) ^ "_set") descr));
berghofe@17870
   391
    val big_rep_name =
berghofe@17870
   392
      space_implode "_" (DatatypeProp.indexify_names (List.mapPartial
urbanc@18579
   393
        (fn (i, ("nominal.noption", _, _)) => NONE
berghofe@17870
   394
          | (i, _) => SOME (name_of_typ (nth_dtyp i))) descr)) ^ "_set";
berghofe@17870
   395
    val _ = warning ("big_rep_name: " ^ big_rep_name);
berghofe@17870
   396
berghofe@17870
   397
    fun strip_option (dtf as DtType ("fun", [dt, DtRec i])) =
berghofe@17870
   398
          (case AList.lookup op = descr i of
urbanc@18579
   399
             SOME ("nominal.noption", _, [(_, [dt']), _]) =>
berghofe@17870
   400
               apfst (cons dt) (strip_option dt')
berghofe@17870
   401
           | _ => ([], dtf))
urbanc@18579
   402
      | strip_option (DtType ("fun", [dt, DtType ("nominal.noption", [dt'])])) =
berghofe@18261
   403
          apfst (cons dt) (strip_option dt')
berghofe@17870
   404
      | strip_option dt = ([], dt);
berghofe@17870
   405
berghofe@18280
   406
    val dt_atomTs = distinct (map (typ_of_dtyp descr sorts')
berghofe@18280
   407
      (List.concat (map (fn (_, (_, _, cs)) => List.concat
berghofe@18280
   408
        (map (List.concat o map (fst o strip_option) o snd) cs)) descr)));
berghofe@18280
   409
berghofe@17870
   410
    fun make_intr s T (cname, cargs) =
berghofe@17870
   411
      let
berghofe@17870
   412
        fun mk_prem (dt, (j, j', prems, ts)) = 
berghofe@17870
   413
          let
berghofe@17870
   414
            val (dts, dt') = strip_option dt;
berghofe@17870
   415
            val (dts', dt'') = strip_dtyp dt';
berghofe@18107
   416
            val Ts = map (typ_of_dtyp descr sorts') dts;
berghofe@18107
   417
            val Us = map (typ_of_dtyp descr sorts') dts';
berghofe@18107
   418
            val T = typ_of_dtyp descr sorts' dt'';
berghofe@17870
   419
            val free = mk_Free "x" (Us ---> T) j;
berghofe@17870
   420
            val free' = app_bnds free (length Us);
berghofe@17870
   421
            fun mk_abs_fun (T, (i, t)) =
berghofe@17870
   422
              let val U = fastype_of t
berghofe@17870
   423
              in (i + 1, Const ("nominal.abs_fun", [T, U, T] --->
urbanc@18579
   424
                Type ("nominal.noption", [U])) $ mk_Free "y" T i $ t)
berghofe@17870
   425
              end
berghofe@17870
   426
          in (j + 1, j' + length Ts,
berghofe@17870
   427
            case dt'' of
berghofe@17870
   428
                DtRec k => list_all (map (pair "x") Us,
berghofe@17870
   429
                  HOLogic.mk_Trueprop (HOLogic.mk_mem (free',
berghofe@17870
   430
                    Const (List.nth (rep_set_names, k),
berghofe@17870
   431
                      HOLogic.mk_setT T)))) :: prems
berghofe@17870
   432
              | _ => prems,
berghofe@17870
   433
            snd (foldr mk_abs_fun (j', free) Ts) :: ts)
berghofe@17870
   434
          end;
berghofe@17870
   435
berghofe@17870
   436
        val (_, _, prems, ts) = foldr mk_prem (1, 1, [], []) cargs;
berghofe@17870
   437
        val concl = HOLogic.mk_Trueprop (HOLogic.mk_mem
berghofe@17870
   438
          (list_comb (Const (cname, map fastype_of ts ---> T), ts),
berghofe@17870
   439
           Const (s, HOLogic.mk_setT T)))
berghofe@17870
   440
      in Logic.list_implies (prems, concl)
berghofe@17870
   441
      end;
berghofe@17870
   442
berghofe@17870
   443
    val (intr_ts, ind_consts) =
berghofe@17870
   444
      apfst List.concat (ListPair.unzip (List.mapPartial
urbanc@18579
   445
        (fn ((_, ("nominal.noption", _, _)), _) => NONE
berghofe@17870
   446
          | ((i, (_, _, constrs)), rep_set_name) =>
berghofe@17870
   447
              let val T = nth_dtyp i
berghofe@17870
   448
              in SOME (map (make_intr rep_set_name T) constrs,
berghofe@17870
   449
                Const (rep_set_name, HOLogic.mk_setT T))
berghofe@17870
   450
              end)
berghofe@17870
   451
                (descr ~~ rep_set_names)));
berghofe@17870
   452
berghofe@17870
   453
    val (thy4, {raw_induct = rep_induct, intrs = rep_intrs, ...}) =
berghofe@17870
   454
      setmp InductivePackage.quiet_mode false
berghofe@17870
   455
        (InductivePackage.add_inductive_i false true big_rep_name false true false
berghofe@17870
   456
           ind_consts (map (fn x => (("", x), [])) intr_ts) []) thy3;
berghofe@17870
   457
berghofe@17870
   458
    (**** Prove that representing set is closed under permutation ****)
berghofe@17870
   459
berghofe@17870
   460
    val _ = warning "proving closure under permutation...";
berghofe@17870
   461
berghofe@17870
   462
    val perm_indnames' = List.mapPartial
urbanc@18579
   463
      (fn (x, (_, ("nominal.noption", _, _))) => NONE | (x, _) => SOME x)
berghofe@17870
   464
      (perm_indnames ~~ descr);
berghofe@17870
   465
berghofe@17870
   466
    fun mk_perm_closed name = map (fn th => standard (th RS mp))
berghofe@18010
   467
      (List.take (split_conj_thm (Goal.prove thy4 [] []
berghofe@17870
   468
        (HOLogic.mk_Trueprop (foldr1 HOLogic.mk_conj (map
berghofe@17870
   469
           (fn (S, x) =>
berghofe@17870
   470
              let
berghofe@17870
   471
                val S = map_term_types (map_type_tfree
berghofe@17870
   472
                  (fn (s, cs) => TFree (s, cs union cp_classes))) S;
berghofe@17870
   473
                val T = HOLogic.dest_setT (fastype_of S);
berghofe@17870
   474
                val permT = mk_permT (Type (name, []))
berghofe@17870
   475
              in HOLogic.mk_imp (HOLogic.mk_mem (Free (x, T), S),
berghofe@17870
   476
                HOLogic.mk_mem (Const ("nominal.perm", permT --> T --> T) $
berghofe@17870
   477
                  Free ("pi", permT) $ Free (x, T), S))
berghofe@18010
   478
              end) (ind_consts ~~ perm_indnames'))))
berghofe@18010
   479
        (fn _ => EVERY (* CU: added perm_fun_def in the final tactic in order to deal with funs *)
berghofe@17870
   480
           [indtac rep_induct [] 1,
berghofe@17870
   481
            ALLGOALS (simp_tac (simpset_of thy4 addsimps
berghofe@17870
   482
              (symmetric perm_fun_def :: PureThy.get_thms thy4 (Name ("abs_perm"))))),
berghofe@17870
   483
            ALLGOALS (resolve_tac rep_intrs 
berghofe@17870
   484
               THEN_ALL_NEW (asm_full_simp_tac (simpset_of thy4 addsimps [perm_fun_def])))])),
berghofe@17870
   485
        length new_type_names));
berghofe@17870
   486
berghofe@17870
   487
    (* FIXME: theorems are stored in database for testing only *)
berghofe@17870
   488
    val perm_closed_thmss = map mk_perm_closed atoms;
urbanc@18381
   489
    val (_,thy5) = PureThy.add_thmss [(("perm_closed", List.concat perm_closed_thmss), [])] thy4;
berghofe@17870
   490
berghofe@17870
   491
    (**** typedef ****)
berghofe@17870
   492
berghofe@17870
   493
    val _ = warning "defining type...";
berghofe@17870
   494
berghofe@18366
   495
    val (typedefs, thy6) =
berghofe@18366
   496
      fold_map (fn ((((name, mx), tvs), c), name') => fn thy =>
berghofe@17870
   497
        setmp TypedefPackage.quiet_mode true
berghofe@17870
   498
          (TypedefPackage.add_typedef_i false (SOME name') (name, tvs, mx) c NONE
berghofe@17870
   499
            (rtac exI 1 THEN
berghofe@17870
   500
              QUIET_BREADTH_FIRST (has_fewer_prems 1)
berghofe@17870
   501
              (resolve_tac rep_intrs 1))) thy |> (fn (thy, r) =>
berghofe@17870
   502
        let
berghofe@17870
   503
          val permT = mk_permT (TFree (variant tvs "'a", HOLogic.typeS));
berghofe@17870
   504
          val pi = Free ("pi", permT);
berghofe@17870
   505
          val tvs' = map (fn s => TFree (s, the (AList.lookup op = sorts' s))) tvs;
berghofe@17870
   506
          val T = Type (Sign.intern_type thy name, tvs');
berghofe@17870
   507
          val Const (_, Type (_, [U])) = c
berghofe@18366
   508
        in apfst (pair r o hd)
berghofe@17870
   509
          (PureThy.add_defs_i true [(("prm_" ^ name ^ "_def", Logic.mk_equals
berghofe@17870
   510
            (Const ("nominal.perm", permT --> T --> T) $ pi $ Free ("x", T),
berghofe@17870
   511
             Const (Sign.intern_const thy ("Abs_" ^ name), U --> T) $
berghofe@17870
   512
               (Const ("nominal.perm", permT --> U --> U) $ pi $
berghofe@17870
   513
                 (Const (Sign.intern_const thy ("Rep_" ^ name), T --> U) $
berghofe@17870
   514
                   Free ("x", T))))), [])] thy)
berghofe@17870
   515
        end))
berghofe@18366
   516
          (types_syntax ~~ tyvars ~~
berghofe@18366
   517
            (List.take (ind_consts, length new_type_names)) ~~ new_type_names) thy5;
berghofe@17870
   518
berghofe@17870
   519
    val perm_defs = map snd typedefs;
berghofe@17870
   520
    val Abs_inverse_thms = map (#Abs_inverse o fst) typedefs;
berghofe@18016
   521
    val Rep_inverse_thms = map (#Rep_inverse o fst) typedefs;
berghofe@17870
   522
    val Rep_thms = map (#Rep o fst) typedefs;
berghofe@17870
   523
berghofe@18016
   524
    val big_name = space_implode "_" new_type_names;
berghofe@18016
   525
berghofe@18016
   526
berghofe@17870
   527
    (** prove that new types are in class pt_<name> **)
berghofe@17870
   528
berghofe@17870
   529
    val _ = warning "prove that new types are in class pt_<name> ...";
berghofe@17870
   530
berghofe@17870
   531
    fun pt_instance ((class, atom), perm_closed_thms) =
berghofe@17870
   532
      fold (fn (((({Abs_inverse, Rep_inverse, Rep, ...},
berghofe@17870
   533
        perm_def), name), tvs), perm_closed) => fn thy =>
berghofe@17870
   534
          AxClass.add_inst_arity_i
berghofe@17870
   535
            (Sign.intern_type thy name,
berghofe@17870
   536
              replicate (length tvs) (classes @ cp_classes), [class])
berghofe@17870
   537
            (EVERY [AxClass.intro_classes_tac [],
berghofe@17870
   538
              rewrite_goals_tac [perm_def],
berghofe@17870
   539
              asm_full_simp_tac (simpset_of thy addsimps [Rep_inverse]) 1,
berghofe@17870
   540
              asm_full_simp_tac (simpset_of thy addsimps
berghofe@17870
   541
                [Rep RS perm_closed RS Abs_inverse]) 1,
berghofe@17870
   542
              asm_full_simp_tac (HOL_basic_ss addsimps [PureThy.get_thm thy
berghofe@17870
   543
                (Name ("pt_" ^ Sign.base_name atom ^ "3"))]) 1]) thy)
berghofe@17870
   544
        (typedefs ~~ new_type_names ~~ tyvars ~~ perm_closed_thms);
berghofe@17870
   545
berghofe@17870
   546
berghofe@17870
   547
    (** prove that new types are in class cp_<name1>_<name2> **)
berghofe@17870
   548
berghofe@17870
   549
    val _ = warning "prove that new types are in class cp_<name1>_<name2> ...";
berghofe@17870
   550
berghofe@17870
   551
    fun cp_instance (atom1, perm_closed_thms1) (atom2, perm_closed_thms2) thy =
berghofe@17870
   552
      let
berghofe@17870
   553
        val name = "cp_" ^ Sign.base_name atom1 ^ "_" ^ Sign.base_name atom2;
berghofe@17870
   554
        val class = Sign.intern_class thy name;
berghofe@17870
   555
        val cp1' = PureThy.get_thm thy (Name (name ^ "_inst")) RS cp1
berghofe@17870
   556
      in fold (fn ((((({Abs_inverse, Rep_inverse, Rep, ...},
berghofe@17870
   557
        perm_def), name), tvs), perm_closed1), perm_closed2) => fn thy =>
berghofe@17870
   558
          AxClass.add_inst_arity_i
berghofe@17870
   559
            (Sign.intern_type thy name,
berghofe@17870
   560
              replicate (length tvs) (classes @ cp_classes), [class])
berghofe@17870
   561
            (EVERY [AxClass.intro_classes_tac [],
berghofe@17870
   562
              rewrite_goals_tac [perm_def],
berghofe@17870
   563
              asm_full_simp_tac (simpset_of thy addsimps
berghofe@17870
   564
                ((Rep RS perm_closed1 RS Abs_inverse) ::
berghofe@17870
   565
                 (if atom1 = atom2 then []
berghofe@17870
   566
                  else [Rep RS perm_closed2 RS Abs_inverse]))) 1,
berghofe@18016
   567
              cong_tac 1,
berghofe@17870
   568
              rtac refl 1,
berghofe@17870
   569
              rtac cp1' 1]) thy)
berghofe@17870
   570
        (typedefs ~~ new_type_names ~~ tyvars ~~ perm_closed_thms1 ~~
berghofe@17870
   571
          perm_closed_thms2) thy
berghofe@17870
   572
      end;
berghofe@17870
   573
berghofe@17870
   574
    val thy7 = fold (fn x => fn thy => thy |>
berghofe@17870
   575
      pt_instance x |>
berghofe@17870
   576
      fold (cp_instance (apfst snd x)) (atoms ~~ perm_closed_thmss))
berghofe@17870
   577
        (classes ~~ atoms ~~ perm_closed_thmss) thy6;
berghofe@17870
   578
berghofe@17870
   579
    (**** constructors ****)
berghofe@17870
   580
berghofe@17870
   581
    fun mk_abs_fun (x, t) =
berghofe@17870
   582
      let
berghofe@17870
   583
        val T = fastype_of x;
berghofe@17870
   584
        val U = fastype_of t
berghofe@17870
   585
      in
berghofe@17870
   586
        Const ("nominal.abs_fun", T --> U --> T -->
urbanc@18579
   587
          Type ("nominal.noption", [U])) $ x $ t
berghofe@17870
   588
      end;
berghofe@17870
   589
berghofe@18016
   590
    val (ty_idxs, _) = foldl
urbanc@18579
   591
      (fn ((i, ("nominal.noption", _, _)), p) => p
berghofe@18016
   592
        | ((i, _), (ty_idxs, j)) => (ty_idxs @ [(i, j)], j + 1)) ([], 0) descr;
berghofe@18016
   593
berghofe@18016
   594
    fun reindex (DtType (s, dts)) = DtType (s, map reindex dts)
berghofe@18016
   595
      | reindex (DtRec i) = DtRec (the (AList.lookup op = ty_idxs i))
berghofe@18016
   596
      | reindex dt = dt;
berghofe@18016
   597
berghofe@18016
   598
    fun strip_suffix i s = implode (List.take (explode s, size s - i));
berghofe@18016
   599
berghofe@18016
   600
    (** strips the "_Rep" in type names *)
urbanc@18045
   601
    fun strip_nth_name i s = 
urbanc@18045
   602
      let val xs = NameSpace.unpack s; 
urbanc@18045
   603
      in NameSpace.pack (Library.nth_map (length xs - i) (strip_suffix 4) xs) end;
berghofe@18016
   604
berghofe@18107
   605
    val (descr'', ndescr) = ListPair.unzip (List.mapPartial
urbanc@18579
   606
      (fn (i, ("nominal.noption", _, _)) => NONE
berghofe@18107
   607
        | (i, (s, dts, constrs)) =>
berghofe@18107
   608
             let
berghofe@18107
   609
               val SOME index = AList.lookup op = ty_idxs i;
berghofe@18107
   610
               val (constrs1, constrs2) = ListPair.unzip
berghofe@18107
   611
                 (map (fn (cname, cargs) => apfst (pair (strip_nth_name 2 cname))
berghofe@18107
   612
                   (foldl_map (fn (dts, dt) =>
berghofe@18107
   613
                     let val (dts', dt') = strip_option dt
berghofe@18107
   614
                     in (dts @ dts' @ [reindex dt'], (length dts, length dts')) end)
berghofe@18107
   615
                       ([], cargs))) constrs)
berghofe@18107
   616
             in SOME ((index, (strip_nth_name 1 s,  map reindex dts, constrs1)),
berghofe@18107
   617
               (index, constrs2))
berghofe@18107
   618
             end) descr);
urbanc@18045
   619
berghofe@18016
   620
    val (descr1, descr2) = splitAt (length new_type_names, descr'');
berghofe@18016
   621
    val descr' = [descr1, descr2];
berghofe@18016
   622
berghofe@18107
   623
    val typ_of_dtyp' = replace_types' o typ_of_dtyp descr sorts';
berghofe@17870
   624
berghofe@17870
   625
    val rep_names = map (fn s =>
berghofe@17870
   626
      Sign.intern_const thy7 ("Rep_" ^ s)) new_type_names;
berghofe@17870
   627
    val abs_names = map (fn s =>
berghofe@17870
   628
      Sign.intern_const thy7 ("Abs_" ^ s)) new_type_names;
berghofe@17870
   629
berghofe@18016
   630
    val recTs' = List.mapPartial
urbanc@18579
   631
      (fn ((_, ("nominal.noption", _, _)), T) => NONE
berghofe@18016
   632
        | (_, T) => SOME T) (descr ~~ get_rec_types descr sorts');
berghofe@18107
   633
    val recTs = get_rec_types descr'' sorts';
berghofe@18016
   634
    val newTs' = Library.take (length new_type_names, recTs');
berghofe@18016
   635
    val newTs = Library.take (length new_type_names, recTs);
berghofe@17870
   636
berghofe@17870
   637
    val full_new_type_names = map (Sign.full_name (sign_of thy)) new_type_names;
berghofe@17870
   638
berghofe@17870
   639
    fun make_constr_def tname T T' ((thy, defs, eqns), ((cname, cargs), (cname', mx))) =
berghofe@17870
   640
      let
berghofe@17870
   641
        fun constr_arg (dt, (j, l_args, r_args)) =
berghofe@17870
   642
          let
berghofe@17870
   643
            val x' = mk_Free "x" (typ_of_dtyp' dt) j;
berghofe@17870
   644
            val (dts, dt') = strip_option dt;
berghofe@17870
   645
            val xs = map (fn (dt, i) => mk_Free "x" (typ_of_dtyp' dt) i)
berghofe@17870
   646
              (dts ~~ (j upto j + length dts - 1))
berghofe@17870
   647
            val x = mk_Free "x" (typ_of_dtyp' dt') (j + length dts)
berghofe@17870
   648
            val (dts', dt'') = strip_dtyp dt'
berghofe@18261
   649
          in
berghofe@18261
   650
            (j + length dts + 1,
berghofe@18261
   651
             xs @ x :: l_args,
berghofe@18261
   652
             foldr mk_abs_fun
berghofe@18261
   653
               (case dt'' of
berghofe@18261
   654
                  DtRec k => if k < length new_type_names then
berghofe@18261
   655
                      list_abs (map (pair "z" o typ_of_dtyp') dts',
berghofe@18261
   656
                        Const (List.nth (rep_names, k), typ_of_dtyp' dt'' -->
berghofe@18261
   657
                          typ_of_dtyp descr sorts' dt'') $ app_bnds x (length dts'))
berghofe@18261
   658
                    else error "nested recursion not (yet) supported"
berghofe@18261
   659
                | _ => x) xs :: r_args)
berghofe@17870
   660
          end
berghofe@17870
   661
berghofe@17870
   662
        val (_, l_args, r_args) = foldr constr_arg (1, [], []) cargs;
berghofe@17870
   663
        val abs_name = Sign.intern_const (Theory.sign_of thy) ("Abs_" ^ tname);
berghofe@17870
   664
        val rep_name = Sign.intern_const (Theory.sign_of thy) ("Rep_" ^ tname);
berghofe@17870
   665
        val constrT = map fastype_of l_args ---> T;
berghofe@17870
   666
        val lhs = list_comb (Const (Sign.full_name thy (Sign.base_name cname),
berghofe@17870
   667
          constrT), l_args);
berghofe@17870
   668
        val rhs = list_comb (Const (cname, map fastype_of r_args ---> T'), r_args);
berghofe@17870
   669
        val def = Logic.mk_equals (lhs, Const (abs_name, T' --> T) $ rhs);
berghofe@17870
   670
        val eqn = HOLogic.mk_Trueprop (HOLogic.mk_eq
berghofe@17870
   671
          (Const (rep_name, T --> T') $ lhs, rhs));
berghofe@17870
   672
        val def_name = (Sign.base_name cname) ^ "_def";
berghofe@18366
   673
        val ([def_thm], thy') = thy |>
berghofe@17870
   674
          Theory.add_consts_i [(cname', constrT, mx)] |>
berghofe@17870
   675
          (PureThy.add_defs_i false o map Thm.no_attributes) [(def_name, def)]
berghofe@17870
   676
      in (thy', defs @ [def_thm], eqns @ [eqn]) end;
berghofe@17870
   677
berghofe@17870
   678
    fun dt_constr_defs ((thy, defs, eqns, dist_lemmas),
berghofe@17870
   679
        (((((_, (_, _, constrs)), tname), T), T'), constr_syntax)) =
berghofe@17870
   680
      let
berghofe@17870
   681
        val rep_const = cterm_of thy
berghofe@17870
   682
          (Const (Sign.intern_const thy ("Rep_" ^ tname), T --> T'));
berghofe@17870
   683
        val dist = standard (cterm_instantiate [(cterm_of thy distinct_f, rep_const)] distinct_lemma);
berghofe@17870
   684
        val (thy', defs', eqns') = Library.foldl (make_constr_def tname T T')
berghofe@17870
   685
          ((Theory.add_path tname thy, defs, []), constrs ~~ constr_syntax)
berghofe@17870
   686
      in
berghofe@17870
   687
        (parent_path flat_names thy', defs', eqns @ [eqns'], dist_lemmas @ [dist])
berghofe@17870
   688
      end;
berghofe@17870
   689
berghofe@17870
   690
    val (thy8, constr_defs, constr_rep_eqns, dist_lemmas) = Library.foldl dt_constr_defs
berghofe@17870
   691
      ((thy7, [], [], []), List.take (descr, length new_type_names) ~~
berghofe@17870
   692
        new_type_names ~~ newTs ~~ newTs' ~~ constr_syntax);
berghofe@17870
   693
berghofe@17870
   694
    val abs_inject_thms = map (fn tname =>
berghofe@17870
   695
      PureThy.get_thm thy8 (Name ("Abs_" ^ tname ^ "_inject"))) new_type_names;
berghofe@17870
   696
berghofe@17870
   697
    val rep_inject_thms = map (fn tname =>
berghofe@17870
   698
      PureThy.get_thm thy8 (Name ("Rep_" ^ tname ^ "_inject"))) new_type_names;
berghofe@17870
   699
berghofe@17870
   700
    val rep_thms = map (fn tname =>
berghofe@17870
   701
      PureThy.get_thm thy8 (Name ("Rep_" ^ tname))) new_type_names;
berghofe@17870
   702
berghofe@17870
   703
    val rep_inverse_thms = map (fn tname =>
berghofe@17870
   704
      PureThy.get_thm thy8 (Name ("Rep_" ^ tname ^ "_inverse"))) new_type_names;
berghofe@17870
   705
berghofe@17870
   706
    (* prove theorem  Rep_i (Constr_j ...) = Constr'_j ...  *)
berghofe@17870
   707
    
berghofe@17870
   708
    fun prove_constr_rep_thm eqn =
berghofe@17870
   709
      let
berghofe@17870
   710
        val inj_thms = map (fn r => r RS iffD1) abs_inject_thms;
berghofe@17870
   711
        val rewrites = constr_defs @ map mk_meta_eq rep_inverse_thms
berghofe@18010
   712
      in standard (Goal.prove thy8 [] [] eqn (fn _ => EVERY
berghofe@17870
   713
        [resolve_tac inj_thms 1,
berghofe@17870
   714
         rewrite_goals_tac rewrites,
berghofe@17870
   715
         rtac refl 3,
berghofe@17870
   716
         resolve_tac rep_intrs 2,
berghofe@18010
   717
         REPEAT (resolve_tac rep_thms 1)]))
berghofe@17870
   718
      end;
berghofe@17870
   719
berghofe@17870
   720
    val constr_rep_thmss = map (map prove_constr_rep_thm) constr_rep_eqns;
berghofe@17870
   721
berghofe@17870
   722
    (* prove theorem  pi \<bullet> Rep_i x = Rep_i (pi \<bullet> x) *)
berghofe@17870
   723
berghofe@17870
   724
    fun prove_perm_rep_perm (atom, perm_closed_thms) = map (fn th =>
berghofe@17870
   725
      let
berghofe@17870
   726
        val _ $ (_ $ (Rep $ x) $ _) = Logic.unvarify (prop_of th);
berghofe@17870
   727
        val Type ("fun", [T, U]) = fastype_of Rep;
berghofe@17870
   728
        val permT = mk_permT (Type (atom, []));
berghofe@17870
   729
        val pi = Free ("pi", permT);
berghofe@17870
   730
      in
berghofe@18010
   731
        standard (Goal.prove thy8 [] [] (HOLogic.mk_Trueprop (HOLogic.mk_eq
berghofe@17870
   732
            (Const ("nominal.perm", permT --> U --> U) $ pi $ (Rep $ x),
berghofe@18010
   733
             Rep $ (Const ("nominal.perm", permT --> T --> T) $ pi $ x))))
berghofe@18010
   734
          (fn _ => simp_tac (HOL_basic_ss addsimps (perm_defs @ Abs_inverse_thms @
berghofe@18010
   735
            perm_closed_thms @ Rep_thms)) 1))
berghofe@17870
   736
      end) Rep_thms;
berghofe@17870
   737
berghofe@17870
   738
    val perm_rep_perm_thms = List.concat (map prove_perm_rep_perm
berghofe@17870
   739
      (atoms ~~ perm_closed_thmss));
berghofe@17870
   740
berghofe@17870
   741
    (* prove distinctness theorems *)
berghofe@17870
   742
berghofe@18016
   743
    val distinct_props = setmp DatatypeProp.dtK 1000
berghofe@18016
   744
      (DatatypeProp.make_distincts new_type_names descr' sorts') thy8;
berghofe@17870
   745
berghofe@17870
   746
    val dist_rewrites = map (fn (rep_thms, dist_lemma) =>
berghofe@17870
   747
      dist_lemma::(rep_thms @ [In0_eq, In1_eq, In0_not_In1, In1_not_In0]))
berghofe@17870
   748
        (constr_rep_thmss ~~ dist_lemmas);
berghofe@17870
   749
berghofe@17870
   750
    fun prove_distinct_thms (_, []) = []
berghofe@17870
   751
      | prove_distinct_thms (p as (rep_thms, dist_lemma), t::ts) =
berghofe@17870
   752
          let
berghofe@18010
   753
            val dist_thm = standard (Goal.prove thy8 [] [] t (fn _ =>
berghofe@18010
   754
              simp_tac (simpset_of thy8 addsimps (dist_lemma :: rep_thms)) 1))
berghofe@17870
   755
          in dist_thm::(standard (dist_thm RS not_sym))::
berghofe@17870
   756
            (prove_distinct_thms (p, ts))
berghofe@17870
   757
          end;
berghofe@17870
   758
berghofe@17870
   759
    val distinct_thms = map prove_distinct_thms
berghofe@17870
   760
      (constr_rep_thmss ~~ dist_lemmas ~~ distinct_props);
berghofe@17870
   761
berghofe@17870
   762
    (** prove equations for permutation functions **)
berghofe@17870
   763
berghofe@17870
   764
    val abs_perm = PureThy.get_thms thy8 (Name "abs_perm"); (* FIXME *)
berghofe@17870
   765
berghofe@17870
   766
    val perm_simps' = map (fn (((i, (_, _, constrs)), tname), constr_rep_thms) =>
berghofe@17870
   767
      let val T = replace_types' (nth_dtyp i)
berghofe@17870
   768
      in List.concat (map (fn (atom, perm_closed_thms) =>
berghofe@17870
   769
          map (fn ((cname, dts), constr_rep_thm) => 
berghofe@17870
   770
        let
berghofe@17870
   771
          val cname = Sign.intern_const thy8
berghofe@17870
   772
            (NameSpace.append tname (Sign.base_name cname));
berghofe@17870
   773
          val permT = mk_permT (Type (atom, []));
berghofe@17870
   774
          val pi = Free ("pi", permT);
berghofe@17870
   775
berghofe@17870
   776
          fun perm t =
berghofe@17870
   777
            let val T = fastype_of t
berghofe@17870
   778
            in Const ("nominal.perm", permT --> T --> T) $ pi $ t end;
berghofe@17870
   779
berghofe@17870
   780
          fun constr_arg (dt, (j, l_args, r_args)) =
berghofe@17870
   781
            let
berghofe@17870
   782
              val x' = mk_Free "x" (typ_of_dtyp' dt) j;
berghofe@17870
   783
              val (dts, dt') = strip_option dt;
berghofe@17870
   784
              val Ts = map typ_of_dtyp' dts;
berghofe@17870
   785
              val xs = map (fn (T, i) => mk_Free "x" T i)
berghofe@17870
   786
                (Ts ~~ (j upto j + length dts - 1))
berghofe@17870
   787
              val x = mk_Free "x" (typ_of_dtyp' dt') (j + length dts);
berghofe@17870
   788
              val (dts', dt'') = strip_dtyp dt';
berghofe@18261
   789
            in
berghofe@18261
   790
              (j + length dts + 1,
berghofe@18261
   791
               xs @ x :: l_args,
berghofe@18261
   792
               map perm (xs @ [x]) @ r_args)
berghofe@17870
   793
            end
berghofe@17870
   794
berghofe@17870
   795
          val (_, l_args, r_args) = foldr constr_arg (1, [], []) dts;
berghofe@17870
   796
          val c = Const (cname, map fastype_of l_args ---> T)
berghofe@17870
   797
        in
berghofe@18010
   798
          standard (Goal.prove thy8 [] []
berghofe@17870
   799
            (HOLogic.mk_Trueprop (HOLogic.mk_eq
berghofe@18010
   800
              (perm (list_comb (c, l_args)), list_comb (c, r_args))))
berghofe@18010
   801
            (fn _ => EVERY
berghofe@17870
   802
              [simp_tac (simpset_of thy8 addsimps (constr_rep_thm :: perm_defs)) 1,
berghofe@17870
   803
               simp_tac (HOL_basic_ss addsimps (Rep_thms @ Abs_inverse_thms @
berghofe@17870
   804
                 constr_defs @ perm_closed_thms)) 1,
berghofe@17870
   805
               TRY (simp_tac (HOL_basic_ss addsimps
berghofe@17870
   806
                 (symmetric perm_fun_def :: abs_perm)) 1),
berghofe@17870
   807
               TRY (simp_tac (HOL_basic_ss addsimps
berghofe@17870
   808
                 (perm_fun_def :: perm_defs @ Rep_thms @ Abs_inverse_thms @
berghofe@18010
   809
                    perm_closed_thms)) 1)]))
berghofe@17870
   810
        end) (constrs ~~ constr_rep_thms)) (atoms ~~ perm_closed_thmss))
berghofe@17870
   811
      end) (List.take (descr, length new_type_names) ~~ new_type_names ~~ constr_rep_thmss);
berghofe@17870
   812
berghofe@17870
   813
    (** prove injectivity of constructors **)
berghofe@17870
   814
berghofe@17870
   815
    val rep_inject_thms' = map (fn th => th RS sym) rep_inject_thms;
berghofe@17870
   816
    val alpha = PureThy.get_thms thy8 (Name "alpha");
berghofe@17870
   817
    val abs_fresh = PureThy.get_thms thy8 (Name "abs_fresh");
berghofe@17870
   818
    val fresh_def = PureThy.get_thm thy8 (Name "fresh_def");
berghofe@17870
   819
    val supp_def = PureThy.get_thm thy8 (Name "supp_def");
berghofe@17870
   820
berghofe@17870
   821
    val inject_thms = map (fn (((i, (_, _, constrs)), tname), constr_rep_thms) =>
berghofe@17870
   822
      let val T = replace_types' (nth_dtyp i)
berghofe@17870
   823
      in List.mapPartial (fn ((cname, dts), constr_rep_thm) =>
berghofe@17870
   824
        if null dts then NONE else SOME
berghofe@17870
   825
        let
berghofe@17870
   826
          val cname = Sign.intern_const thy8
berghofe@17870
   827
            (NameSpace.append tname (Sign.base_name cname));
berghofe@17870
   828
berghofe@17870
   829
          fun make_inj (dt, (j, args1, args2, eqs)) =
berghofe@17870
   830
            let
berghofe@17870
   831
              val x' = mk_Free "x" (typ_of_dtyp' dt) j;
berghofe@17870
   832
              val y' = mk_Free "y" (typ_of_dtyp' dt) j;
berghofe@17870
   833
              val (dts, dt') = strip_option dt;
berghofe@17870
   834
              val Ts_idx = map typ_of_dtyp' dts ~~ (j upto j + length dts - 1);
berghofe@17870
   835
              val xs = map (fn (T, i) => mk_Free "x" T i) Ts_idx;
berghofe@17870
   836
              val ys = map (fn (T, i) => mk_Free "y" T i) Ts_idx;
berghofe@17870
   837
              val x = mk_Free "x" (typ_of_dtyp' dt') (j + length dts);
berghofe@17870
   838
              val y = mk_Free "y" (typ_of_dtyp' dt') (j + length dts);
berghofe@17870
   839
              val (dts', dt'') = strip_dtyp dt';
berghofe@18261
   840
            in
berghofe@18261
   841
              (j + length dts + 1,
berghofe@18261
   842
               xs @ (x :: args1), ys @ (y :: args2),
berghofe@18261
   843
               HOLogic.mk_eq
berghofe@18261
   844
                 (foldr mk_abs_fun x xs, foldr mk_abs_fun y ys) :: eqs)
berghofe@17870
   845
            end;
berghofe@17870
   846
berghofe@17870
   847
          val (_, args1, args2, eqs) = foldr make_inj (1, [], [], []) dts;
berghofe@17870
   848
          val Ts = map fastype_of args1;
berghofe@17870
   849
          val c = Const (cname, Ts ---> T)
berghofe@17870
   850
        in
berghofe@18010
   851
          standard (Goal.prove thy8 [] [] (HOLogic.mk_Trueprop (HOLogic.mk_eq
berghofe@17870
   852
              (HOLogic.mk_eq (list_comb (c, args1), list_comb (c, args2)),
berghofe@18010
   853
               foldr1 HOLogic.mk_conj eqs)))
berghofe@18010
   854
            (fn _ => EVERY
berghofe@17870
   855
               [asm_full_simp_tac (simpset_of thy8 addsimps (constr_rep_thm ::
berghofe@17870
   856
                  rep_inject_thms')) 1,
berghofe@17870
   857
                TRY (asm_full_simp_tac (HOL_basic_ss addsimps (fresh_def :: supp_def ::
berghofe@17870
   858
                  alpha @ abs_perm @ abs_fresh @ rep_inject_thms @
berghofe@17874
   859
                  perm_rep_perm_thms)) 1),
berghofe@17874
   860
                TRY (asm_full_simp_tac (HOL_basic_ss addsimps (perm_fun_def ::
berghofe@18010
   861
                  expand_fun_eq :: rep_inject_thms @ perm_rep_perm_thms)) 1)]))
berghofe@17870
   862
        end) (constrs ~~ constr_rep_thms)
berghofe@17870
   863
      end) (List.take (descr, length new_type_names) ~~ new_type_names ~~ constr_rep_thmss);
berghofe@17870
   864
berghofe@17872
   865
    (** equations for support and freshness **)
berghofe@17872
   866
berghofe@17872
   867
    val Un_assoc = PureThy.get_thm thy8 (Name "Un_assoc");
berghofe@17872
   868
    val de_Morgan_conj = PureThy.get_thm thy8 (Name "de_Morgan_conj");
berghofe@17872
   869
    val Collect_disj_eq = PureThy.get_thm thy8 (Name "Collect_disj_eq");
berghofe@17872
   870
    val finite_Un = PureThy.get_thm thy8 (Name "finite_Un");
berghofe@17872
   871
berghofe@17872
   872
    val (supp_thms, fresh_thms) = ListPair.unzip (map ListPair.unzip
berghofe@17872
   873
      (map (fn ((((i, (_, _, constrs)), tname), inject_thms'), perm_thms') =>
berghofe@17872
   874
      let val T = replace_types' (nth_dtyp i)
berghofe@17872
   875
      in List.concat (map (fn (cname, dts) => map (fn atom =>
berghofe@17872
   876
        let
berghofe@17872
   877
          val cname = Sign.intern_const thy8
berghofe@17872
   878
            (NameSpace.append tname (Sign.base_name cname));
berghofe@17872
   879
          val atomT = Type (atom, []);
berghofe@17872
   880
berghofe@17872
   881
          fun process_constr (dt, (j, args1, args2)) =
berghofe@17872
   882
            let
berghofe@17872
   883
              val x' = mk_Free "x" (typ_of_dtyp' dt) j;
berghofe@17872
   884
              val (dts, dt') = strip_option dt;
berghofe@17872
   885
              val Ts_idx = map typ_of_dtyp' dts ~~ (j upto j + length dts - 1);
berghofe@17872
   886
              val xs = map (fn (T, i) => mk_Free "x" T i) Ts_idx;
berghofe@17872
   887
              val x = mk_Free "x" (typ_of_dtyp' dt') (j + length dts);
berghofe@17872
   888
              val (dts', dt'') = strip_dtyp dt';
berghofe@18261
   889
            in
berghofe@18261
   890
              (j + length dts + 1,
berghofe@18261
   891
               xs @ (x :: args1), foldr mk_abs_fun x xs :: args2)
berghofe@17872
   892
            end;
berghofe@17872
   893
berghofe@17872
   894
          val (_, args1, args2) = foldr process_constr (1, [], []) dts;
berghofe@17872
   895
          val Ts = map fastype_of args1;
berghofe@17872
   896
          val c = list_comb (Const (cname, Ts ---> T), args1);
berghofe@17872
   897
          fun supp t =
berghofe@17872
   898
            Const ("nominal.supp", fastype_of t --> HOLogic.mk_setT atomT) $ t;
berghofe@17872
   899
          fun fresh t =
berghofe@17872
   900
            Const ("nominal.fresh", atomT --> fastype_of t --> HOLogic.boolT) $
berghofe@17872
   901
              Free ("a", atomT) $ t;
berghofe@18010
   902
          val supp_thm = standard (Goal.prove thy8 [] []
berghofe@17872
   903
              (HOLogic.mk_Trueprop (HOLogic.mk_eq
berghofe@17872
   904
                (supp c,
berghofe@17872
   905
                 if null dts then Const ("{}", HOLogic.mk_setT atomT)
berghofe@18010
   906
                 else foldr1 (HOLogic.mk_binop "op Un") (map supp args2))))
berghofe@17872
   907
            (fn _ =>
berghofe@18010
   908
              simp_tac (HOL_basic_ss addsimps (supp_def ::
berghofe@17872
   909
                 Un_assoc :: de_Morgan_conj :: Collect_disj_eq :: finite_Un ::
berghofe@17874
   910
                 symmetric empty_def :: Finites.emptyI :: simp_thms @
berghofe@18010
   911
                 abs_perm @ abs_fresh @ inject_thms' @ perm_thms')) 1))
berghofe@17872
   912
        in
berghofe@17872
   913
          (supp_thm,
berghofe@18010
   914
           standard (Goal.prove thy8 [] [] (HOLogic.mk_Trueprop (HOLogic.mk_eq
berghofe@17872
   915
              (fresh c,
berghofe@17872
   916
               if null dts then HOLogic.true_const
berghofe@18010
   917
               else foldr1 HOLogic.mk_conj (map fresh args2))))
berghofe@17872
   918
             (fn _ =>
berghofe@18010
   919
               simp_tac (simpset_of thy8 addsimps [fresh_def, supp_thm]) 1)))
berghofe@17872
   920
        end) atoms) constrs)
berghofe@17872
   921
      end) (List.take (descr, length new_type_names) ~~ new_type_names ~~ inject_thms ~~ perm_simps')));
berghofe@17872
   922
berghofe@18107
   923
    (**** weak induction theorem ****)
berghofe@18016
   924
berghofe@18107
   925
    val arities = get_arities descr'';
berghofe@18016
   926
berghofe@18016
   927
    fun mk_funs_inv thm =
berghofe@18016
   928
      let
berghofe@18016
   929
        val {sign, prop, ...} = rep_thm thm;
berghofe@18016
   930
        val _ $ (_ $ (Const (_, Type (_, [U, _])) $ _ $ S)) $
berghofe@18016
   931
          (_ $ (_ $ (r $ (a $ _)) $ _)) = Type.freeze prop;
berghofe@18016
   932
        val used = add_term_tfree_names (a, []);
berghofe@18016
   933
berghofe@18016
   934
        fun mk_thm i =
berghofe@18016
   935
          let
berghofe@18016
   936
            val Ts = map (TFree o rpair HOLogic.typeS)
berghofe@18016
   937
              (variantlist (replicate i "'t", used));
berghofe@18016
   938
            val f = Free ("f", Ts ---> U)
berghofe@18016
   939
          in standard (Goal.prove sign [] [] (Logic.mk_implies
berghofe@18016
   940
            (HOLogic.mk_Trueprop (HOLogic.list_all
berghofe@18016
   941
               (map (pair "x") Ts, HOLogic.mk_mem (app_bnds f i, S))),
berghofe@18016
   942
             HOLogic.mk_Trueprop (HOLogic.mk_eq (list_abs (map (pair "x") Ts,
berghofe@18016
   943
               r $ (a $ app_bnds f i)), f))))
berghofe@18016
   944
            (fn _ => EVERY [REPEAT (rtac ext 1), REPEAT (etac allE 1), rtac thm 1, atac 1]))
berghofe@18016
   945
          end
berghofe@18016
   946
      in map (fn r => r RS subst) (thm :: map mk_thm arities) end;
berghofe@18016
   947
berghofe@18016
   948
    fun mk_indrule_lemma ((prems, concls), (((i, _), T), U)) =
berghofe@18016
   949
      let
berghofe@18016
   950
        val Rep_t = Const (List.nth (rep_names, i), T --> U) $
berghofe@18016
   951
          mk_Free "x" T i;
berghofe@18016
   952
berghofe@18016
   953
        val Abs_t =  Const (List.nth (abs_names, i), U --> T)
berghofe@18016
   954
berghofe@18016
   955
      in (prems @ [HOLogic.imp $ HOLogic.mk_mem (Rep_t,
berghofe@18016
   956
            Const (List.nth (rep_set_names, i), HOLogic.mk_setT U)) $
berghofe@18016
   957
              (mk_Free "P" (T --> HOLogic.boolT) (i + 1) $ (Abs_t $ Rep_t))],
berghofe@18016
   958
          concls @ [mk_Free "P" (T --> HOLogic.boolT) (i + 1) $ mk_Free "x" T i])
berghofe@18016
   959
      end;
berghofe@18016
   960
berghofe@18016
   961
    val (indrule_lemma_prems, indrule_lemma_concls) =
berghofe@18107
   962
      Library.foldl mk_indrule_lemma (([], []), (descr'' ~~ recTs ~~ recTs'));
berghofe@18016
   963
berghofe@18016
   964
    val indrule_lemma = standard (Goal.prove thy8 [] []
berghofe@18016
   965
      (Logic.mk_implies
berghofe@18016
   966
        (HOLogic.mk_Trueprop (mk_conj indrule_lemma_prems),
berghofe@18016
   967
         HOLogic.mk_Trueprop (mk_conj indrule_lemma_concls))) (fn _ => EVERY
berghofe@18016
   968
           [REPEAT (etac conjE 1),
berghofe@18016
   969
            REPEAT (EVERY
berghofe@18016
   970
              [TRY (rtac conjI 1), full_simp_tac (HOL_basic_ss addsimps Rep_inverse_thms) 1,
berghofe@18016
   971
               etac mp 1, resolve_tac Rep_thms 1])]));
berghofe@18016
   972
berghofe@18016
   973
    val Ps = map head_of (HOLogic.dest_conj (HOLogic.dest_Trueprop (concl_of indrule_lemma)));
berghofe@18016
   974
    val frees = if length Ps = 1 then [Free ("P", snd (dest_Var (hd Ps)))] else
berghofe@18016
   975
      map (Free o apfst fst o dest_Var) Ps;
berghofe@18016
   976
    val indrule_lemma' = cterm_instantiate
berghofe@18016
   977
      (map (cterm_of thy8) Ps ~~ map (cterm_of thy8) frees) indrule_lemma;
berghofe@18016
   978
berghofe@18016
   979
    val Abs_inverse_thms' = List.concat (map mk_funs_inv Abs_inverse_thms);
berghofe@18016
   980
berghofe@18016
   981
    val dt_induct_prop = DatatypeProp.make_ind descr' sorts';
berghofe@18016
   982
    val dt_induct = standard (Goal.prove thy8 []
berghofe@18016
   983
      (Logic.strip_imp_prems dt_induct_prop) (Logic.strip_imp_concl dt_induct_prop)
berghofe@18016
   984
      (fn prems => EVERY
berghofe@18016
   985
        [rtac indrule_lemma' 1,
berghofe@18016
   986
         (DatatypeAux.indtac rep_induct THEN_ALL_NEW ObjectLogic.atomize_tac) 1,
berghofe@18016
   987
         EVERY (map (fn (prem, r) => (EVERY
berghofe@18016
   988
           [REPEAT (eresolve_tac Abs_inverse_thms' 1),
berghofe@18016
   989
            simp_tac (HOL_basic_ss addsimps [symmetric r]) 1,
berghofe@18016
   990
            DEPTH_SOLVE_1 (ares_tac [prem] 1 ORELSE etac allE 1)]))
berghofe@18016
   991
                (prems ~~ constr_defs))]));
berghofe@18016
   992
berghofe@18107
   993
    val case_names_induct = mk_case_names_induct descr'';
berghofe@18016
   994
berghofe@18066
   995
    (**** prove that new datatypes have finite support ****)
berghofe@18066
   996
urbanc@18246
   997
    val _ = warning "proving finite support for the new datatype";
urbanc@18246
   998
berghofe@18066
   999
    val indnames = DatatypeProp.make_tnames recTs;
berghofe@18066
  1000
berghofe@18066
  1001
    val abs_supp = PureThy.get_thms thy8 (Name "abs_supp");
urbanc@18067
  1002
    val supp_atm = PureThy.get_thms thy8 (Name "supp_atm");
berghofe@18066
  1003
berghofe@18066
  1004
    val finite_supp_thms = map (fn atom =>
berghofe@18066
  1005
      let val atomT = Type (atom, [])
berghofe@18066
  1006
      in map standard (List.take
berghofe@18066
  1007
        (split_conj_thm (Goal.prove thy8 [] [] (HOLogic.mk_Trueprop
berghofe@18066
  1008
           (foldr1 HOLogic.mk_conj (map (fn (s, T) => HOLogic.mk_mem
berghofe@18066
  1009
             (Const ("nominal.supp", T --> HOLogic.mk_setT atomT) $ Free (s, T),
berghofe@18066
  1010
              Const ("Finite_Set.Finites", HOLogic.mk_setT (HOLogic.mk_setT atomT))))
berghofe@18066
  1011
               (indnames ~~ recTs))))
berghofe@18066
  1012
           (fn _ => indtac dt_induct indnames 1 THEN
berghofe@18066
  1013
            ALLGOALS (asm_full_simp_tac (simpset_of thy8 addsimps
urbanc@18067
  1014
              (abs_supp @ supp_atm @
berghofe@18066
  1015
               PureThy.get_thms thy8 (Name ("fs_" ^ Sign.base_name atom ^ "1")) @
berghofe@18066
  1016
               List.concat supp_thms))))),
berghofe@18066
  1017
         length new_type_names))
berghofe@18066
  1018
      end) atoms;
berghofe@18066
  1019
berghofe@18107
  1020
    (**** strong induction theorem ****)
berghofe@18107
  1021
berghofe@18107
  1022
    val pnames = if length descr'' = 1 then ["P"]
berghofe@18107
  1023
      else map (fn i => "P" ^ string_of_int i) (1 upto length descr'');
berghofe@18245
  1024
    val ind_sort = if null dt_atomTs then HOLogic.typeS
berghofe@18245
  1025
      else map (fn T => Sign.intern_class thy8 ("fs_" ^
berghofe@18245
  1026
        Sign.base_name (fst (dest_Type T)))) dt_atomTs;
berghofe@18107
  1027
    val fsT = TFree ("'n", ind_sort);
berghofe@18107
  1028
berghofe@18107
  1029
    fun make_pred i T =
berghofe@18302
  1030
      Free (List.nth (pnames, i), fsT --> T --> HOLogic.boolT);
berghofe@18107
  1031
berghofe@18107
  1032
    fun make_ind_prem k T ((cname, cargs), idxs) =
berghofe@18107
  1033
      let
berghofe@18107
  1034
        val recs = List.filter is_rec_type cargs;
berghofe@18107
  1035
        val Ts = map (typ_of_dtyp descr'' sorts') cargs;
berghofe@18107
  1036
        val recTs' = map (typ_of_dtyp descr'' sorts') recs;
berghofe@18107
  1037
        val tnames = variantlist (DatatypeProp.make_tnames Ts, pnames);
berghofe@18107
  1038
        val rec_tnames = map fst (List.filter (is_rec_type o snd) (tnames ~~ cargs));
berghofe@18107
  1039
        val frees = tnames ~~ Ts;
berghofe@18107
  1040
        val z = (variant tnames "z", fsT);
berghofe@18107
  1041
berghofe@18107
  1042
        fun mk_prem ((dt, s), T) =
berghofe@18107
  1043
          let
berghofe@18107
  1044
            val (Us, U) = strip_type T;
berghofe@18107
  1045
            val l = length Us
berghofe@18107
  1046
          in list_all (z :: map (pair "x") Us, HOLogic.mk_Trueprop
berghofe@18302
  1047
            (make_pred (body_index dt) U $ Bound l $ app_bnds (Free (s, T)) l))
berghofe@18107
  1048
          end;
berghofe@18107
  1049
berghofe@18107
  1050
        val prems = map mk_prem (recs ~~ rec_tnames ~~ recTs');
berghofe@18107
  1051
        val prems' = map (fn p as (_, T) => HOLogic.mk_Trueprop
berghofe@18107
  1052
            (Const ("nominal.fresh", T --> fsT --> HOLogic.boolT) $
berghofe@18107
  1053
              Free p $ Free z))
berghofe@18107
  1054
          (map (curry List.nth frees) (List.concat (map (fn (m, n) =>
berghofe@18107
  1055
             m upto m + n - 1) idxs)))
berghofe@18107
  1056
berghofe@18302
  1057
      in list_all_free (frees @ [z], Logic.list_implies (prems' @ prems,
berghofe@18302
  1058
        HOLogic.mk_Trueprop (make_pred k T $ Free z $
berghofe@18302
  1059
          list_comb (Const (cname, Ts ---> T), map Free frees))))
berghofe@18107
  1060
      end;
berghofe@18107
  1061
berghofe@18107
  1062
    val ind_prems = List.concat (map (fn (((i, (_, _, constrs)), (_, idxss)), T) =>
berghofe@18107
  1063
      map (make_ind_prem i T) (constrs ~~ idxss)) (descr'' ~~ ndescr ~~ recTs));
berghofe@18107
  1064
    val tnames = DatatypeProp.make_tnames recTs;
berghofe@18107
  1065
    val z = (variant tnames "z", fsT);
berghofe@18107
  1066
    val ind_concl = HOLogic.mk_Trueprop (foldr1 (HOLogic.mk_binop "op &")
berghofe@18302
  1067
      (map (fn (((i, _), T), tname) => make_pred i T $ Free z $ Free (tname, T))
berghofe@18107
  1068
        (descr'' ~~ recTs ~~ tnames)));
berghofe@18107
  1069
    val induct = Logic.list_implies (ind_prems, ind_concl);
berghofe@18107
  1070
urbanc@18104
  1071
    val simp_atts = replicate (length new_type_names) [Simplifier.simp_add_global];
urbanc@18104
  1072
wenzelm@18582
  1073
    val ((_, [induct_rule]), thy9) = thy8 |>
berghofe@18016
  1074
      Theory.add_path big_name |>
urbanc@18381
  1075
      PureThy.add_thms [(("induct_weak", dt_induct), [case_names_induct])] ||>
wenzelm@18582
  1076
      (PureThy.add_thmss [(("inducts_weak", projections dt_induct), [case_names_induct])] #> snd)
wenzelm@18582
  1077
      ||> Theory.parent_path ||>>
berghofe@18350
  1078
      DatatypeAux.store_thmss_atts "distinct" new_type_names simp_atts distinct_thms ||>>
berghofe@18350
  1079
      DatatypeAux.store_thmss "constr_rep" new_type_names constr_rep_thmss ||>>
berghofe@18350
  1080
      DatatypeAux.store_thmss_atts "perm" new_type_names simp_atts perm_simps' ||>>
berghofe@18350
  1081
      DatatypeAux.store_thmss "inject" new_type_names inject_thms ||>>
berghofe@18350
  1082
      DatatypeAux.store_thmss "supp" new_type_names supp_thms ||>>
berghofe@18350
  1083
      DatatypeAux.store_thmss_atts "fresh" new_type_names simp_atts fresh_thms ||>
berghofe@18261
  1084
      fold (fn (atom, ths) => fn thy =>
berghofe@18066
  1085
        let val class = Sign.intern_class thy ("fs_" ^ Sign.base_name atom)
berghofe@18066
  1086
        in fold (fn T => AxClass.add_inst_arity_i
berghofe@18066
  1087
            (fst (dest_Type T),
berghofe@18066
  1088
              replicate (length sorts) [class], [class])
berghofe@18066
  1089
            (AxClass.intro_classes_tac [] THEN resolve_tac ths 1)) newTs thy
berghofe@18350
  1090
        end) (atoms ~~ finite_supp_thms) ||>
berghofe@18350
  1091
      Theory.add_path big_name ||>>
wenzelm@18582
  1092
      PureThy.add_axioms_i [(("induct_unsafe", induct), [case_names_induct])]
wenzelm@18582
  1093
    val thy10 = thy9
wenzelm@18582
  1094
      |> PureThy.add_thmss [(("inducts_unsafe", projections induct_rule), [case_names_induct])]
wenzelm@18582
  1095
      |> snd
wenzelm@18582
  1096
      |> Theory.parent_path;
berghofe@17870
  1097
  in
wenzelm@18582
  1098
    thy10
berghofe@17870
  1099
  end;
berghofe@17870
  1100
berghofe@17870
  1101
val add_nominal_datatype = gen_add_nominal_datatype read_typ true;
berghofe@17870
  1102
berghofe@17870
  1103
berghofe@17870
  1104
(* FIXME: The following stuff should be exported by DatatypePackage *)
berghofe@17870
  1105
berghofe@17870
  1106
local structure P = OuterParse and K = OuterKeyword in
berghofe@17870
  1107
berghofe@17870
  1108
val datatype_decl =
berghofe@17870
  1109
  Scan.option (P.$$$ "(" |-- P.name --| P.$$$ ")") -- P.type_args -- P.name -- P.opt_infix --
berghofe@17870
  1110
    (P.$$$ "=" |-- P.enum1 "|" (P.name -- Scan.repeat P.typ -- P.opt_mixfix));
berghofe@17870
  1111
berghofe@17870
  1112
fun mk_datatype args =
berghofe@17870
  1113
  let
berghofe@17870
  1114
    val names = map (fn ((((NONE, _), t), _), _) => t | ((((SOME t, _), _), _), _) => t) args;
berghofe@17870
  1115
    val specs = map (fn ((((_, vs), t), mx), cons) =>
berghofe@17870
  1116
      (vs, t, mx, map (fn ((x, y), z) => (x, y, z)) cons)) args;
berghofe@18068
  1117
  in add_nominal_datatype false names specs end;
berghofe@17870
  1118
berghofe@17870
  1119
val nominal_datatypeP =
berghofe@17870
  1120
  OuterSyntax.command "nominal_datatype" "define inductive datatypes" K.thy_decl
berghofe@17870
  1121
    (P.and_list1 datatype_decl >> (Toplevel.theory o mk_datatype));
berghofe@17870
  1122
berghofe@17870
  1123
val _ = OuterSyntax.add_parsers [nominal_datatypeP];
berghofe@17870
  1124
berghofe@17870
  1125
end;
berghofe@17870
  1126
berghofe@18261
  1127
end
berghofe@18261
  1128