src/HOL/Nominal/nominal_package.ML
author berghofe
Wed Nov 02 16:37:39 2005 +0100 (2005-11-02)
changeset 18068 e8c3d371594e
parent 18067 8b9848d150ba
child 18104 dbe58b104cb9
permissions -rw-r--r--
Moved atom stuff to new file nominal_atoms.ML
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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 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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    val typ_of_dtyp = typ_of_dtyp descr sorts';
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    fun nth_dtyp i = typ_of_dtyp (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 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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                    let val perm = Const (s, permT --> T --> T)
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                    in HOLogic.mk_eq
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   297
                      (perm $ pi1 $ Free (x, T),
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   298
                       perm $ pi2 $ Free (x, T))
berghofe@17870
   299
                    end)
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   300
                  (perm_names ~~
berghofe@18010
   301
                   map body_type perm_types ~~ perm_indnames)))))
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   302
           (fn _ => EVERY [indtac induction perm_indnames 1,
berghofe@17870
   303
              ALLGOALS (asm_full_simp_tac (simpset_of thy2 addsimps [pt3', pt3_rev', pt3_ax]))]))),
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   304
         length new_type_names)
berghofe@17870
   305
      end) atoms);
berghofe@17870
   306
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   307
    (**** prove pi1 \<bullet> (pi2 \<bullet> t) = (pi1 \<bullet> pi2) \<bullet> (pi1 \<bullet> t) ****)
berghofe@17870
   308
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   309
    val cp1 = PureThy.get_thm thy2 (Name "cp1");
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   310
    val dj_cp = PureThy.get_thm thy2 (Name "dj_cp");
berghofe@17870
   311
    val pt_perm_compose = PureThy.get_thm thy2 (Name "pt_perm_compose");
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   312
    val pt_perm_compose_rev = PureThy.get_thm thy2 (Name "pt_perm_compose_rev");
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   313
    val dj_perm_perm_forget = PureThy.get_thm thy2 (Name "dj_perm_perm_forget");
berghofe@17870
   314
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   315
    fun composition_instance name1 name2 thy =
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   316
      let
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   317
        val name1' = Sign.base_name name1;
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   318
        val name2' = Sign.base_name name2;
berghofe@17870
   319
        val cp_class = Sign.intern_class thy ("cp_" ^ name1' ^ "_" ^ name2');
berghofe@17870
   320
        val permT1 = mk_permT (Type (name1, []));
berghofe@17870
   321
        val permT2 = mk_permT (Type (name2, []));
berghofe@17870
   322
        val augment = map_type_tfree
berghofe@17870
   323
          (fn (x, S) => TFree (x, cp_class :: S));
berghofe@17870
   324
        val Ts = map (augment o body_type) perm_types;
berghofe@17870
   325
        val cp_inst = PureThy.get_thm thy
berghofe@17870
   326
          (Name ("cp_" ^ name1' ^ "_" ^ name2' ^ "_inst"));
berghofe@17870
   327
        val simps = simpset_of thy addsimps (perm_fun_def ::
berghofe@17870
   328
          (if name1 <> name2 then
berghofe@17870
   329
             let val dj = PureThy.get_thm thy (Name ("dj_" ^ name2' ^ "_" ^ name1'))
berghofe@17870
   330
             in [dj RS (cp_inst RS dj_cp), dj RS dj_perm_perm_forget] end
berghofe@17870
   331
           else
berghofe@17870
   332
             let
berghofe@17870
   333
               val at_inst = PureThy.get_thm thy (Name ("at_" ^ name1' ^ "_inst"));
berghofe@17870
   334
               val pt_inst = PureThy.get_thm thy (Name ("pt_" ^ name1' ^ "_inst"))
berghofe@17870
   335
             in
berghofe@17870
   336
               [cp_inst RS cp1 RS sym,
berghofe@17870
   337
                at_inst RS (pt_inst RS pt_perm_compose) RS sym,
berghofe@17870
   338
                at_inst RS (pt_inst RS pt_perm_compose_rev) RS sym]
berghofe@17870
   339
            end))
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   340
        val thms = split_conj_thm (standard (Goal.prove thy [] []
berghofe@17870
   341
            (HOLogic.mk_Trueprop (foldr1 HOLogic.mk_conj
berghofe@17870
   342
              (map (fn ((s, T), x) =>
berghofe@17870
   343
                  let
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   344
                    val pi1 = Free ("pi1", permT1);
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   345
                    val pi2 = Free ("pi2", permT2);
berghofe@17870
   346
                    val perm1 = Const (s, permT1 --> T --> T);
berghofe@17870
   347
                    val perm2 = Const (s, permT2 --> T --> T);
berghofe@17870
   348
                    val perm3 = Const ("nominal.perm", permT1 --> permT2 --> permT2)
berghofe@17870
   349
                  in HOLogic.mk_eq
berghofe@17870
   350
                    (perm1 $ pi1 $ (perm2 $ pi2 $ Free (x, T)),
berghofe@17870
   351
                     perm2 $ (perm3 $ pi1 $ pi2) $ (perm1 $ pi1 $ Free (x, T)))
berghofe@17870
   352
                  end)
berghofe@18010
   353
                (perm_names ~~ Ts ~~ perm_indnames))))
berghofe@18010
   354
          (fn _ => EVERY [indtac induction perm_indnames 1,
berghofe@18010
   355
             ALLGOALS (asm_full_simp_tac simps)])))
berghofe@17870
   356
      in
berghofe@17870
   357
        foldl (fn ((s, tvs), thy) => AxClass.add_inst_arity_i
berghofe@17870
   358
            (s, replicate (length tvs) (cp_class :: classes), [cp_class])
berghofe@17870
   359
            (AxClass.intro_classes_tac [] THEN ALLGOALS (resolve_tac thms)) thy)
berghofe@17870
   360
          thy (full_new_type_names' ~~ tyvars)
berghofe@17870
   361
      end;
berghofe@17870
   362
berghofe@17870
   363
    val (thy3, perm_thmss) = thy2 |>
berghofe@17870
   364
      fold (fn name1 => fold (composition_instance name1) atoms) atoms |>
berghofe@17870
   365
      curry (Library.foldr (fn ((i, (tyname, args, _)), thy) =>
berghofe@17870
   366
        AxClass.add_inst_arity_i (tyname, replicate (length args) classes, classes)
berghofe@17870
   367
        (AxClass.intro_classes_tac [] THEN REPEAT (EVERY
berghofe@17870
   368
           [resolve_tac perm_empty_thms 1,
berghofe@17870
   369
            resolve_tac perm_append_thms 1,
berghofe@17870
   370
            resolve_tac perm_eq_thms 1, assume_tac 1])) thy))
berghofe@17870
   371
        (List.take (descr, length new_type_names)) |>
berghofe@17870
   372
      PureThy.add_thmss
berghofe@17870
   373
        [((space_implode "_" new_type_names ^ "_unfolded_perm_eq",
berghofe@17870
   374
          unfolded_perm_eq_thms), [Simplifier.simp_add_global]),
berghofe@17870
   375
         ((space_implode "_" new_type_names ^ "_perm_empty",
berghofe@17870
   376
          perm_empty_thms), [Simplifier.simp_add_global]),
berghofe@17870
   377
         ((space_implode "_" new_type_names ^ "_perm_append",
berghofe@17870
   378
          perm_append_thms), [Simplifier.simp_add_global]),
berghofe@17870
   379
         ((space_implode "_" new_type_names ^ "_perm_eq",
berghofe@17870
   380
          perm_eq_thms), [Simplifier.simp_add_global])];
berghofe@17870
   381
  
berghofe@17870
   382
    (**** Define representing sets ****)
berghofe@17870
   383
berghofe@17870
   384
    val _ = warning "representing sets";
berghofe@17870
   385
berghofe@17870
   386
    val rep_set_names = map (Sign.full_name thy3) (DatatypeProp.indexify_names
berghofe@17870
   387
      (map (fn (i, _) => name_of_typ (nth_dtyp i) ^ "_set") descr));
berghofe@17870
   388
    val big_rep_name =
berghofe@17870
   389
      space_implode "_" (DatatypeProp.indexify_names (List.mapPartial
berghofe@17870
   390
        (fn (i, ("nominal.nOption", _, _)) => NONE
berghofe@17870
   391
          | (i, _) => SOME (name_of_typ (nth_dtyp i))) descr)) ^ "_set";
berghofe@17870
   392
    val _ = warning ("big_rep_name: " ^ big_rep_name);
berghofe@17870
   393
berghofe@17870
   394
    fun strip_option (dtf as DtType ("fun", [dt, DtRec i])) =
berghofe@17870
   395
          (case AList.lookup op = descr i of
berghofe@17870
   396
             SOME ("nominal.nOption", _, [(_, [dt']), _]) =>
berghofe@17870
   397
               apfst (cons dt) (strip_option dt')
berghofe@17870
   398
           | _ => ([], dtf))
berghofe@17870
   399
      | strip_option dt = ([], dt);
berghofe@17870
   400
berghofe@17870
   401
    fun make_intr s T (cname, cargs) =
berghofe@17870
   402
      let
berghofe@17870
   403
        fun mk_prem (dt, (j, j', prems, ts)) = 
berghofe@17870
   404
          let
berghofe@17870
   405
            val (dts, dt') = strip_option dt;
berghofe@17870
   406
            val (dts', dt'') = strip_dtyp dt';
berghofe@17870
   407
            val Ts = map typ_of_dtyp dts;
berghofe@17870
   408
            val Us = map typ_of_dtyp dts';
berghofe@17870
   409
            val T = typ_of_dtyp dt'';
berghofe@17870
   410
            val free = mk_Free "x" (Us ---> T) j;
berghofe@17870
   411
            val free' = app_bnds free (length Us);
berghofe@17870
   412
            fun mk_abs_fun (T, (i, t)) =
berghofe@17870
   413
              let val U = fastype_of t
berghofe@17870
   414
              in (i + 1, Const ("nominal.abs_fun", [T, U, T] --->
berghofe@17870
   415
                Type ("nominal.nOption", [U])) $ mk_Free "y" T i $ t)
berghofe@17870
   416
              end
berghofe@17870
   417
          in (j + 1, j' + length Ts,
berghofe@17870
   418
            case dt'' of
berghofe@17870
   419
                DtRec k => list_all (map (pair "x") Us,
berghofe@17870
   420
                  HOLogic.mk_Trueprop (HOLogic.mk_mem (free',
berghofe@17870
   421
                    Const (List.nth (rep_set_names, k),
berghofe@17870
   422
                      HOLogic.mk_setT T)))) :: prems
berghofe@17870
   423
              | _ => prems,
berghofe@17870
   424
            snd (foldr mk_abs_fun (j', free) Ts) :: ts)
berghofe@17870
   425
          end;
berghofe@17870
   426
berghofe@17870
   427
        val (_, _, prems, ts) = foldr mk_prem (1, 1, [], []) cargs;
berghofe@17870
   428
        val concl = HOLogic.mk_Trueprop (HOLogic.mk_mem
berghofe@17870
   429
          (list_comb (Const (cname, map fastype_of ts ---> T), ts),
berghofe@17870
   430
           Const (s, HOLogic.mk_setT T)))
berghofe@17870
   431
      in Logic.list_implies (prems, concl)
berghofe@17870
   432
      end;
berghofe@17870
   433
berghofe@17870
   434
    val (intr_ts, ind_consts) =
berghofe@17870
   435
      apfst List.concat (ListPair.unzip (List.mapPartial
berghofe@17870
   436
        (fn ((_, ("nominal.nOption", _, _)), _) => NONE
berghofe@17870
   437
          | ((i, (_, _, constrs)), rep_set_name) =>
berghofe@17870
   438
              let val T = nth_dtyp i
berghofe@17870
   439
              in SOME (map (make_intr rep_set_name T) constrs,
berghofe@17870
   440
                Const (rep_set_name, HOLogic.mk_setT T))
berghofe@17870
   441
              end)
berghofe@17870
   442
                (descr ~~ rep_set_names)));
berghofe@17870
   443
berghofe@17870
   444
    val (thy4, {raw_induct = rep_induct, intrs = rep_intrs, ...}) =
berghofe@17870
   445
      setmp InductivePackage.quiet_mode false
berghofe@17870
   446
        (InductivePackage.add_inductive_i false true big_rep_name false true false
berghofe@17870
   447
           ind_consts (map (fn x => (("", x), [])) intr_ts) []) thy3;
berghofe@17870
   448
berghofe@17870
   449
    (**** Prove that representing set is closed under permutation ****)
berghofe@17870
   450
berghofe@17870
   451
    val _ = warning "proving closure under permutation...";
berghofe@17870
   452
berghofe@17870
   453
    val perm_indnames' = List.mapPartial
berghofe@17870
   454
      (fn (x, (_, ("nominal.nOption", _, _))) => NONE | (x, _) => SOME x)
berghofe@17870
   455
      (perm_indnames ~~ descr);
berghofe@17870
   456
berghofe@17870
   457
    fun mk_perm_closed name = map (fn th => standard (th RS mp))
berghofe@18010
   458
      (List.take (split_conj_thm (Goal.prove thy4 [] []
berghofe@17870
   459
        (HOLogic.mk_Trueprop (foldr1 HOLogic.mk_conj (map
berghofe@17870
   460
           (fn (S, x) =>
berghofe@17870
   461
              let
berghofe@17870
   462
                val S = map_term_types (map_type_tfree
berghofe@17870
   463
                  (fn (s, cs) => TFree (s, cs union cp_classes))) S;
berghofe@17870
   464
                val T = HOLogic.dest_setT (fastype_of S);
berghofe@17870
   465
                val permT = mk_permT (Type (name, []))
berghofe@17870
   466
              in HOLogic.mk_imp (HOLogic.mk_mem (Free (x, T), S),
berghofe@17870
   467
                HOLogic.mk_mem (Const ("nominal.perm", permT --> T --> T) $
berghofe@17870
   468
                  Free ("pi", permT) $ Free (x, T), S))
berghofe@18010
   469
              end) (ind_consts ~~ perm_indnames'))))
berghofe@18010
   470
        (fn _ => EVERY (* CU: added perm_fun_def in the final tactic in order to deal with funs *)
berghofe@17870
   471
           [indtac rep_induct [] 1,
berghofe@17870
   472
            ALLGOALS (simp_tac (simpset_of thy4 addsimps
berghofe@17870
   473
              (symmetric perm_fun_def :: PureThy.get_thms thy4 (Name ("abs_perm"))))),
berghofe@17870
   474
            ALLGOALS (resolve_tac rep_intrs 
berghofe@17870
   475
               THEN_ALL_NEW (asm_full_simp_tac (simpset_of thy4 addsimps [perm_fun_def])))])),
berghofe@17870
   476
        length new_type_names));
berghofe@17870
   477
berghofe@17870
   478
    (* FIXME: theorems are stored in database for testing only *)
berghofe@17870
   479
    val perm_closed_thmss = map mk_perm_closed atoms;
berghofe@17870
   480
    val (thy5, _) = PureThy.add_thmss [(("perm_closed",
berghofe@17870
   481
      List.concat perm_closed_thmss), [])] thy4;
berghofe@17870
   482
berghofe@17870
   483
    (**** typedef ****)
berghofe@17870
   484
berghofe@17870
   485
    val _ = warning "defining type...";
berghofe@17870
   486
berghofe@17870
   487
    val (thy6, typedefs) =
berghofe@17870
   488
      foldl_map (fn (thy, ((((name, mx), tvs), c), name')) =>
berghofe@17870
   489
        setmp TypedefPackage.quiet_mode true
berghofe@17870
   490
          (TypedefPackage.add_typedef_i false (SOME name') (name, tvs, mx) c NONE
berghofe@17870
   491
            (rtac exI 1 THEN
berghofe@17870
   492
              QUIET_BREADTH_FIRST (has_fewer_prems 1)
berghofe@17870
   493
              (resolve_tac rep_intrs 1))) thy |> (fn (thy, r) =>
berghofe@17870
   494
        let
berghofe@17870
   495
          val permT = mk_permT (TFree (variant tvs "'a", HOLogic.typeS));
berghofe@17870
   496
          val pi = Free ("pi", permT);
berghofe@17870
   497
          val tvs' = map (fn s => TFree (s, the (AList.lookup op = sorts' s))) tvs;
berghofe@17870
   498
          val T = Type (Sign.intern_type thy name, tvs');
berghofe@17870
   499
          val Const (_, Type (_, [U])) = c
berghofe@17870
   500
        in apsnd (pair r o hd)
berghofe@17870
   501
          (PureThy.add_defs_i true [(("prm_" ^ name ^ "_def", Logic.mk_equals
berghofe@17870
   502
            (Const ("nominal.perm", permT --> T --> T) $ pi $ Free ("x", T),
berghofe@17870
   503
             Const (Sign.intern_const thy ("Abs_" ^ name), U --> T) $
berghofe@17870
   504
               (Const ("nominal.perm", permT --> U --> U) $ pi $
berghofe@17870
   505
                 (Const (Sign.intern_const thy ("Rep_" ^ name), T --> U) $
berghofe@17870
   506
                   Free ("x", T))))), [])] thy)
berghofe@17870
   507
        end))
berghofe@17870
   508
          (thy5, types_syntax ~~ tyvars ~~
berghofe@17870
   509
            (List.take (ind_consts, length new_type_names)) ~~ new_type_names);
berghofe@17870
   510
berghofe@17870
   511
    val perm_defs = map snd typedefs;
berghofe@17870
   512
    val Abs_inverse_thms = map (#Abs_inverse o fst) typedefs;
berghofe@18016
   513
    val Rep_inverse_thms = map (#Rep_inverse o fst) typedefs;
berghofe@17870
   514
    val Rep_thms = map (#Rep o fst) typedefs;
berghofe@17870
   515
berghofe@18016
   516
    val big_name = space_implode "_" new_type_names;
berghofe@18016
   517
berghofe@18016
   518
berghofe@17870
   519
    (** prove that new types are in class pt_<name> **)
berghofe@17870
   520
berghofe@17870
   521
    val _ = warning "prove that new types are in class pt_<name> ...";
berghofe@17870
   522
berghofe@17870
   523
    fun pt_instance ((class, atom), perm_closed_thms) =
berghofe@17870
   524
      fold (fn (((({Abs_inverse, Rep_inverse, Rep, ...},
berghofe@17870
   525
        perm_def), name), tvs), perm_closed) => fn thy =>
berghofe@17870
   526
          AxClass.add_inst_arity_i
berghofe@17870
   527
            (Sign.intern_type thy name,
berghofe@17870
   528
              replicate (length tvs) (classes @ cp_classes), [class])
berghofe@17870
   529
            (EVERY [AxClass.intro_classes_tac [],
berghofe@17870
   530
              rewrite_goals_tac [perm_def],
berghofe@17870
   531
              asm_full_simp_tac (simpset_of thy addsimps [Rep_inverse]) 1,
berghofe@17870
   532
              asm_full_simp_tac (simpset_of thy addsimps
berghofe@17870
   533
                [Rep RS perm_closed RS Abs_inverse]) 1,
berghofe@17870
   534
              asm_full_simp_tac (HOL_basic_ss addsimps [PureThy.get_thm thy
berghofe@17870
   535
                (Name ("pt_" ^ Sign.base_name atom ^ "3"))]) 1]) thy)
berghofe@17870
   536
        (typedefs ~~ new_type_names ~~ tyvars ~~ perm_closed_thms);
berghofe@17870
   537
berghofe@17870
   538
berghofe@17870
   539
    (** prove that new types are in class cp_<name1>_<name2> **)
berghofe@17870
   540
berghofe@17870
   541
    val _ = warning "prove that new types are in class cp_<name1>_<name2> ...";
berghofe@17870
   542
berghofe@17870
   543
    fun cp_instance (atom1, perm_closed_thms1) (atom2, perm_closed_thms2) thy =
berghofe@17870
   544
      let
berghofe@17870
   545
        val name = "cp_" ^ Sign.base_name atom1 ^ "_" ^ Sign.base_name atom2;
berghofe@17870
   546
        val class = Sign.intern_class thy name;
berghofe@17870
   547
        val cp1' = PureThy.get_thm thy (Name (name ^ "_inst")) RS cp1
berghofe@17870
   548
      in fold (fn ((((({Abs_inverse, Rep_inverse, Rep, ...},
berghofe@17870
   549
        perm_def), name), tvs), perm_closed1), perm_closed2) => fn thy =>
berghofe@17870
   550
          AxClass.add_inst_arity_i
berghofe@17870
   551
            (Sign.intern_type thy name,
berghofe@17870
   552
              replicate (length tvs) (classes @ cp_classes), [class])
berghofe@17870
   553
            (EVERY [AxClass.intro_classes_tac [],
berghofe@17870
   554
              rewrite_goals_tac [perm_def],
berghofe@17870
   555
              asm_full_simp_tac (simpset_of thy addsimps
berghofe@17870
   556
                ((Rep RS perm_closed1 RS Abs_inverse) ::
berghofe@17870
   557
                 (if atom1 = atom2 then []
berghofe@17870
   558
                  else [Rep RS perm_closed2 RS Abs_inverse]))) 1,
berghofe@18016
   559
              cong_tac 1,
berghofe@17870
   560
              rtac refl 1,
berghofe@17870
   561
              rtac cp1' 1]) thy)
berghofe@17870
   562
        (typedefs ~~ new_type_names ~~ tyvars ~~ perm_closed_thms1 ~~
berghofe@17870
   563
          perm_closed_thms2) thy
berghofe@17870
   564
      end;
berghofe@17870
   565
berghofe@17870
   566
    val thy7 = fold (fn x => fn thy => thy |>
berghofe@17870
   567
      pt_instance x |>
berghofe@17870
   568
      fold (cp_instance (apfst snd x)) (atoms ~~ perm_closed_thmss))
berghofe@17870
   569
        (classes ~~ atoms ~~ perm_closed_thmss) thy6;
berghofe@17870
   570
berghofe@17870
   571
    (**** constructors ****)
berghofe@17870
   572
berghofe@17870
   573
    fun mk_abs_fun (x, t) =
berghofe@17870
   574
      let
berghofe@17870
   575
        val T = fastype_of x;
berghofe@17870
   576
        val U = fastype_of t
berghofe@17870
   577
      in
berghofe@17870
   578
        Const ("nominal.abs_fun", T --> U --> T -->
berghofe@17870
   579
          Type ("nominal.nOption", [U])) $ x $ t
berghofe@17870
   580
      end;
berghofe@17870
   581
berghofe@18016
   582
    val (ty_idxs, _) = foldl
berghofe@18016
   583
      (fn ((i, ("nominal.nOption", _, _)), p) => p
berghofe@18016
   584
        | ((i, _), (ty_idxs, j)) => (ty_idxs @ [(i, j)], j + 1)) ([], 0) descr;
berghofe@18016
   585
berghofe@18016
   586
    fun reindex (DtType (s, dts)) = DtType (s, map reindex dts)
berghofe@18016
   587
      | reindex (DtRec i) = DtRec (the (AList.lookup op = ty_idxs i))
berghofe@18016
   588
      | reindex dt = dt;
berghofe@18016
   589
berghofe@18016
   590
    fun strip_suffix i s = implode (List.take (explode s, size s - i));
berghofe@18016
   591
berghofe@18016
   592
    (** strips the "_Rep" in type names *)
urbanc@18045
   593
    fun strip_nth_name i s = 
urbanc@18045
   594
      let val xs = NameSpace.unpack s; 
urbanc@18045
   595
      in NameSpace.pack (Library.nth_map (length xs - i) (strip_suffix 4) xs) end;
berghofe@18016
   596
berghofe@18016
   597
    val descr'' = List.mapPartial
berghofe@18016
   598
      (fn (i, ("nominal.nOption", _, _)) => NONE
berghofe@18016
   599
        | (i, (s, dts, constrs)) => SOME (the (AList.lookup op = ty_idxs i),
berghofe@18016
   600
            (strip_nth_name 1 s,  map reindex dts,
berghofe@18016
   601
             map (fn (cname, cargs) =>
berghofe@18016
   602
               (strip_nth_name 2 cname,
berghofe@18016
   603
                foldl (fn (dt, dts) =>
berghofe@18016
   604
                  let val (dts', dt') = strip_option dt
berghofe@18016
   605
                  in (dts @ dts' @ [reindex dt']) end) [] cargs)) constrs))) descr;
urbanc@18045
   606
berghofe@18016
   607
    val (descr1, descr2) = splitAt (length new_type_names, descr'');
berghofe@18016
   608
    val descr' = [descr1, descr2];
berghofe@18016
   609
berghofe@17870
   610
    val typ_of_dtyp' = replace_types' o typ_of_dtyp;
berghofe@17870
   611
berghofe@17870
   612
    val rep_names = map (fn s =>
berghofe@17870
   613
      Sign.intern_const thy7 ("Rep_" ^ s)) new_type_names;
berghofe@17870
   614
    val abs_names = map (fn s =>
berghofe@17870
   615
      Sign.intern_const thy7 ("Abs_" ^ s)) new_type_names;
berghofe@17870
   616
berghofe@18016
   617
    val recTs' = List.mapPartial
berghofe@18016
   618
      (fn ((_, ("nominal.nOption", _, _)), T) => NONE
berghofe@18016
   619
        | (_, T) => SOME T) (descr ~~ get_rec_types descr sorts');
berghofe@18016
   620
    val recTs = get_rec_types (List.concat descr') sorts';
berghofe@18016
   621
    val newTs' = Library.take (length new_type_names, recTs');
berghofe@18016
   622
    val newTs = Library.take (length new_type_names, recTs);
berghofe@17870
   623
berghofe@17870
   624
    val full_new_type_names = map (Sign.full_name (sign_of thy)) new_type_names;
berghofe@17870
   625
berghofe@17870
   626
    fun make_constr_def tname T T' ((thy, defs, eqns), ((cname, cargs), (cname', mx))) =
berghofe@17870
   627
      let
berghofe@17870
   628
        fun constr_arg (dt, (j, l_args, r_args)) =
berghofe@17870
   629
          let
berghofe@17870
   630
            val x' = mk_Free "x" (typ_of_dtyp' dt) j;
berghofe@17870
   631
            val (dts, dt') = strip_option dt;
berghofe@17870
   632
            val xs = map (fn (dt, i) => mk_Free "x" (typ_of_dtyp' dt) i)
berghofe@17870
   633
              (dts ~~ (j upto j + length dts - 1))
berghofe@17870
   634
            val x = mk_Free "x" (typ_of_dtyp' dt') (j + length dts)
berghofe@17870
   635
            val (dts', dt'') = strip_dtyp dt'
berghofe@17870
   636
          in case dt'' of
berghofe@17870
   637
              DtRec k => if k < length new_type_names then
berghofe@17870
   638
                  (j + length dts + 1,
berghofe@17870
   639
                   xs @ x :: l_args,
berghofe@17870
   640
                   foldr mk_abs_fun
berghofe@17870
   641
                     (list_abs (map (pair "z" o typ_of_dtyp') dts',
berghofe@17870
   642
                       Const (List.nth (rep_names, k), typ_of_dtyp' dt'' -->
berghofe@17870
   643
                         typ_of_dtyp dt'') $ app_bnds x (length dts')))
berghofe@17870
   644
                     xs :: r_args)
berghofe@17870
   645
                else error "nested recursion not (yet) supported"
berghofe@17870
   646
            | _ => (j + 1, x' :: l_args, x' :: r_args)
berghofe@17870
   647
          end
berghofe@17870
   648
berghofe@17870
   649
        val (_, l_args, r_args) = foldr constr_arg (1, [], []) cargs;
berghofe@17870
   650
        val abs_name = Sign.intern_const (Theory.sign_of thy) ("Abs_" ^ tname);
berghofe@17870
   651
        val rep_name = Sign.intern_const (Theory.sign_of thy) ("Rep_" ^ tname);
berghofe@17870
   652
        val constrT = map fastype_of l_args ---> T;
berghofe@17870
   653
        val lhs = list_comb (Const (Sign.full_name thy (Sign.base_name cname),
berghofe@17870
   654
          constrT), l_args);
berghofe@17870
   655
        val rhs = list_comb (Const (cname, map fastype_of r_args ---> T'), r_args);
berghofe@17870
   656
        val def = Logic.mk_equals (lhs, Const (abs_name, T' --> T) $ rhs);
berghofe@17870
   657
        val eqn = HOLogic.mk_Trueprop (HOLogic.mk_eq
berghofe@17870
   658
          (Const (rep_name, T --> T') $ lhs, rhs));
berghofe@17870
   659
        val def_name = (Sign.base_name cname) ^ "_def";
berghofe@17870
   660
        val (thy', [def_thm]) = thy |>
berghofe@17870
   661
          Theory.add_consts_i [(cname', constrT, mx)] |>
berghofe@17870
   662
          (PureThy.add_defs_i false o map Thm.no_attributes) [(def_name, def)]
berghofe@17870
   663
      in (thy', defs @ [def_thm], eqns @ [eqn]) end;
berghofe@17870
   664
berghofe@17870
   665
    fun dt_constr_defs ((thy, defs, eqns, dist_lemmas),
berghofe@17870
   666
        (((((_, (_, _, constrs)), tname), T), T'), constr_syntax)) =
berghofe@17870
   667
      let
berghofe@17870
   668
        val rep_const = cterm_of thy
berghofe@17870
   669
          (Const (Sign.intern_const thy ("Rep_" ^ tname), T --> T'));
berghofe@17870
   670
        val dist = standard (cterm_instantiate [(cterm_of thy distinct_f, rep_const)] distinct_lemma);
berghofe@17870
   671
        val (thy', defs', eqns') = Library.foldl (make_constr_def tname T T')
berghofe@17870
   672
          ((Theory.add_path tname thy, defs, []), constrs ~~ constr_syntax)
berghofe@17870
   673
      in
berghofe@17870
   674
        (parent_path flat_names thy', defs', eqns @ [eqns'], dist_lemmas @ [dist])
berghofe@17870
   675
      end;
berghofe@17870
   676
berghofe@17870
   677
    val (thy8, constr_defs, constr_rep_eqns, dist_lemmas) = Library.foldl dt_constr_defs
berghofe@17870
   678
      ((thy7, [], [], []), List.take (descr, length new_type_names) ~~
berghofe@17870
   679
        new_type_names ~~ newTs ~~ newTs' ~~ constr_syntax);
berghofe@17870
   680
berghofe@17870
   681
    val abs_inject_thms = map (fn tname =>
berghofe@17870
   682
      PureThy.get_thm thy8 (Name ("Abs_" ^ tname ^ "_inject"))) new_type_names;
berghofe@17870
   683
berghofe@17870
   684
    val rep_inject_thms = map (fn tname =>
berghofe@17870
   685
      PureThy.get_thm thy8 (Name ("Rep_" ^ tname ^ "_inject"))) new_type_names;
berghofe@17870
   686
berghofe@17870
   687
    val rep_thms = map (fn tname =>
berghofe@17870
   688
      PureThy.get_thm thy8 (Name ("Rep_" ^ tname))) new_type_names;
berghofe@17870
   689
berghofe@17870
   690
    val rep_inverse_thms = map (fn tname =>
berghofe@17870
   691
      PureThy.get_thm thy8 (Name ("Rep_" ^ tname ^ "_inverse"))) new_type_names;
berghofe@17870
   692
berghofe@17870
   693
    (* prove theorem  Rep_i (Constr_j ...) = Constr'_j ...  *)
berghofe@17870
   694
    
berghofe@17870
   695
    fun prove_constr_rep_thm eqn =
berghofe@17870
   696
      let
berghofe@17870
   697
        val inj_thms = map (fn r => r RS iffD1) abs_inject_thms;
berghofe@17870
   698
        val rewrites = constr_defs @ map mk_meta_eq rep_inverse_thms
berghofe@18010
   699
      in standard (Goal.prove thy8 [] [] eqn (fn _ => EVERY
berghofe@17870
   700
        [resolve_tac inj_thms 1,
berghofe@17870
   701
         rewrite_goals_tac rewrites,
berghofe@17870
   702
         rtac refl 3,
berghofe@17870
   703
         resolve_tac rep_intrs 2,
berghofe@18010
   704
         REPEAT (resolve_tac rep_thms 1)]))
berghofe@17870
   705
      end;
berghofe@17870
   706
berghofe@17870
   707
    val constr_rep_thmss = map (map prove_constr_rep_thm) constr_rep_eqns;
berghofe@17870
   708
berghofe@17870
   709
    (* prove theorem  pi \<bullet> Rep_i x = Rep_i (pi \<bullet> x) *)
berghofe@17870
   710
berghofe@17870
   711
    fun prove_perm_rep_perm (atom, perm_closed_thms) = map (fn th =>
berghofe@17870
   712
      let
berghofe@17870
   713
        val _ $ (_ $ (Rep $ x) $ _) = Logic.unvarify (prop_of th);
berghofe@17870
   714
        val Type ("fun", [T, U]) = fastype_of Rep;
berghofe@17870
   715
        val permT = mk_permT (Type (atom, []));
berghofe@17870
   716
        val pi = Free ("pi", permT);
berghofe@17870
   717
      in
berghofe@18010
   718
        standard (Goal.prove thy8 [] [] (HOLogic.mk_Trueprop (HOLogic.mk_eq
berghofe@17870
   719
            (Const ("nominal.perm", permT --> U --> U) $ pi $ (Rep $ x),
berghofe@18010
   720
             Rep $ (Const ("nominal.perm", permT --> T --> T) $ pi $ x))))
berghofe@18010
   721
          (fn _ => simp_tac (HOL_basic_ss addsimps (perm_defs @ Abs_inverse_thms @
berghofe@18010
   722
            perm_closed_thms @ Rep_thms)) 1))
berghofe@17870
   723
      end) Rep_thms;
berghofe@17870
   724
berghofe@17870
   725
    val perm_rep_perm_thms = List.concat (map prove_perm_rep_perm
berghofe@17870
   726
      (atoms ~~ perm_closed_thmss));
berghofe@17870
   727
berghofe@17870
   728
    (* prove distinctness theorems *)
berghofe@17870
   729
berghofe@18016
   730
    val distinct_props = setmp DatatypeProp.dtK 1000
berghofe@18016
   731
      (DatatypeProp.make_distincts new_type_names descr' sorts') thy8;
berghofe@17870
   732
berghofe@17870
   733
    val dist_rewrites = map (fn (rep_thms, dist_lemma) =>
berghofe@17870
   734
      dist_lemma::(rep_thms @ [In0_eq, In1_eq, In0_not_In1, In1_not_In0]))
berghofe@17870
   735
        (constr_rep_thmss ~~ dist_lemmas);
berghofe@17870
   736
berghofe@17870
   737
    fun prove_distinct_thms (_, []) = []
berghofe@17870
   738
      | prove_distinct_thms (p as (rep_thms, dist_lemma), t::ts) =
berghofe@17870
   739
          let
berghofe@18010
   740
            val dist_thm = standard (Goal.prove thy8 [] [] t (fn _ =>
berghofe@18010
   741
              simp_tac (simpset_of thy8 addsimps (dist_lemma :: rep_thms)) 1))
berghofe@17870
   742
          in dist_thm::(standard (dist_thm RS not_sym))::
berghofe@17870
   743
            (prove_distinct_thms (p, ts))
berghofe@17870
   744
          end;
berghofe@17870
   745
berghofe@17870
   746
    val distinct_thms = map prove_distinct_thms
berghofe@17870
   747
      (constr_rep_thmss ~~ dist_lemmas ~~ distinct_props);
berghofe@17870
   748
berghofe@17870
   749
    (** prove equations for permutation functions **)
berghofe@17870
   750
berghofe@17870
   751
    val abs_perm = PureThy.get_thms thy8 (Name "abs_perm"); (* FIXME *)
berghofe@17870
   752
berghofe@17870
   753
    val perm_simps' = map (fn (((i, (_, _, constrs)), tname), constr_rep_thms) =>
berghofe@17870
   754
      let val T = replace_types' (nth_dtyp i)
berghofe@17870
   755
      in List.concat (map (fn (atom, perm_closed_thms) =>
berghofe@17870
   756
          map (fn ((cname, dts), constr_rep_thm) => 
berghofe@17870
   757
        let
berghofe@17870
   758
          val cname = Sign.intern_const thy8
berghofe@17870
   759
            (NameSpace.append tname (Sign.base_name cname));
berghofe@17870
   760
          val permT = mk_permT (Type (atom, []));
berghofe@17870
   761
          val pi = Free ("pi", permT);
berghofe@17870
   762
berghofe@17870
   763
          fun perm t =
berghofe@17870
   764
            let val T = fastype_of t
berghofe@17870
   765
            in Const ("nominal.perm", permT --> T --> T) $ pi $ t end;
berghofe@17870
   766
berghofe@17870
   767
          fun constr_arg (dt, (j, l_args, r_args)) =
berghofe@17870
   768
            let
berghofe@17870
   769
              val x' = mk_Free "x" (typ_of_dtyp' dt) j;
berghofe@17870
   770
              val (dts, dt') = strip_option dt;
berghofe@17870
   771
              val Ts = map typ_of_dtyp' dts;
berghofe@17870
   772
              val xs = map (fn (T, i) => mk_Free "x" T i)
berghofe@17870
   773
                (Ts ~~ (j upto j + length dts - 1))
berghofe@17870
   774
              val x = mk_Free "x" (typ_of_dtyp' dt') (j + length dts);
berghofe@17870
   775
              val (dts', dt'') = strip_dtyp dt';
berghofe@17870
   776
            in case dt'' of
berghofe@17870
   777
                DtRec k => if k < length new_type_names then
berghofe@17870
   778
                    (j + length dts + 1,
berghofe@17870
   779
                     xs @ x :: l_args,
berghofe@17870
   780
                     map perm (xs @ [x]) @ r_args)
berghofe@17870
   781
                  else error "nested recursion not (yet) supported"
berghofe@17870
   782
              | _ => (j + 1, x' :: l_args, perm x' :: r_args)
berghofe@17870
   783
            end
berghofe@17870
   784
berghofe@17870
   785
          val (_, l_args, r_args) = foldr constr_arg (1, [], []) dts;
berghofe@17870
   786
          val c = Const (cname, map fastype_of l_args ---> T)
berghofe@17870
   787
        in
berghofe@18010
   788
          standard (Goal.prove thy8 [] []
berghofe@17870
   789
            (HOLogic.mk_Trueprop (HOLogic.mk_eq
berghofe@18010
   790
              (perm (list_comb (c, l_args)), list_comb (c, r_args))))
berghofe@18010
   791
            (fn _ => EVERY
berghofe@17870
   792
              [simp_tac (simpset_of thy8 addsimps (constr_rep_thm :: perm_defs)) 1,
berghofe@17870
   793
               simp_tac (HOL_basic_ss addsimps (Rep_thms @ Abs_inverse_thms @
berghofe@17870
   794
                 constr_defs @ perm_closed_thms)) 1,
berghofe@17870
   795
               TRY (simp_tac (HOL_basic_ss addsimps
berghofe@17870
   796
                 (symmetric perm_fun_def :: abs_perm)) 1),
berghofe@17870
   797
               TRY (simp_tac (HOL_basic_ss addsimps
berghofe@17870
   798
                 (perm_fun_def :: perm_defs @ Rep_thms @ Abs_inverse_thms @
berghofe@18010
   799
                    perm_closed_thms)) 1)]))
berghofe@17870
   800
        end) (constrs ~~ constr_rep_thms)) (atoms ~~ perm_closed_thmss))
berghofe@17870
   801
      end) (List.take (descr, length new_type_names) ~~ new_type_names ~~ constr_rep_thmss);
berghofe@17870
   802
berghofe@17870
   803
    (** prove injectivity of constructors **)
berghofe@17870
   804
berghofe@17870
   805
    val rep_inject_thms' = map (fn th => th RS sym) rep_inject_thms;
berghofe@17870
   806
    val alpha = PureThy.get_thms thy8 (Name "alpha");
berghofe@17870
   807
    val abs_fresh = PureThy.get_thms thy8 (Name "abs_fresh");
berghofe@17870
   808
    val fresh_def = PureThy.get_thm thy8 (Name "fresh_def");
berghofe@17870
   809
    val supp_def = PureThy.get_thm thy8 (Name "supp_def");
berghofe@17870
   810
berghofe@17870
   811
    val inject_thms = map (fn (((i, (_, _, constrs)), tname), constr_rep_thms) =>
berghofe@17870
   812
      let val T = replace_types' (nth_dtyp i)
berghofe@17870
   813
      in List.mapPartial (fn ((cname, dts), constr_rep_thm) =>
berghofe@17870
   814
        if null dts then NONE else SOME
berghofe@17870
   815
        let
berghofe@17870
   816
          val cname = Sign.intern_const thy8
berghofe@17870
   817
            (NameSpace.append tname (Sign.base_name cname));
berghofe@17870
   818
berghofe@17870
   819
          fun make_inj (dt, (j, args1, args2, eqs)) =
berghofe@17870
   820
            let
berghofe@17870
   821
              val x' = mk_Free "x" (typ_of_dtyp' dt) j;
berghofe@17870
   822
              val y' = mk_Free "y" (typ_of_dtyp' dt) j;
berghofe@17870
   823
              val (dts, dt') = strip_option dt;
berghofe@17870
   824
              val Ts_idx = map typ_of_dtyp' dts ~~ (j upto j + length dts - 1);
berghofe@17870
   825
              val xs = map (fn (T, i) => mk_Free "x" T i) Ts_idx;
berghofe@17870
   826
              val ys = map (fn (T, i) => mk_Free "y" T i) Ts_idx;
berghofe@17870
   827
              val x = mk_Free "x" (typ_of_dtyp' dt') (j + length dts);
berghofe@17870
   828
              val y = mk_Free "y" (typ_of_dtyp' dt') (j + length dts);
berghofe@17870
   829
              val (dts', dt'') = strip_dtyp dt';
berghofe@17870
   830
            in case dt'' of
berghofe@17870
   831
                DtRec k => if k < length new_type_names then
berghofe@17870
   832
                    (j + length dts + 1,
berghofe@17870
   833
                     xs @ (x :: args1), ys @ (y :: args2),
berghofe@17870
   834
                     HOLogic.mk_eq
berghofe@17870
   835
                       (foldr mk_abs_fun x xs, foldr mk_abs_fun y ys) :: eqs)
berghofe@17870
   836
                  else error "nested recursion not (yet) supported"
berghofe@17870
   837
              | _ => (j + 1, x' :: args1, y' :: args2, HOLogic.mk_eq (x', y') :: eqs)
berghofe@17870
   838
            end;
berghofe@17870
   839
berghofe@17870
   840
          val (_, args1, args2, eqs) = foldr make_inj (1, [], [], []) dts;
berghofe@17870
   841
          val Ts = map fastype_of args1;
berghofe@17870
   842
          val c = Const (cname, Ts ---> T)
berghofe@17870
   843
        in
berghofe@18010
   844
          standard (Goal.prove thy8 [] [] (HOLogic.mk_Trueprop (HOLogic.mk_eq
berghofe@17870
   845
              (HOLogic.mk_eq (list_comb (c, args1), list_comb (c, args2)),
berghofe@18010
   846
               foldr1 HOLogic.mk_conj eqs)))
berghofe@18010
   847
            (fn _ => EVERY
berghofe@17870
   848
               [asm_full_simp_tac (simpset_of thy8 addsimps (constr_rep_thm ::
berghofe@17870
   849
                  rep_inject_thms')) 1,
berghofe@17870
   850
                TRY (asm_full_simp_tac (HOL_basic_ss addsimps (fresh_def :: supp_def ::
berghofe@17870
   851
                  alpha @ abs_perm @ abs_fresh @ rep_inject_thms @
berghofe@17874
   852
                  perm_rep_perm_thms)) 1),
berghofe@17874
   853
                TRY (asm_full_simp_tac (HOL_basic_ss addsimps (perm_fun_def ::
berghofe@18010
   854
                  expand_fun_eq :: rep_inject_thms @ perm_rep_perm_thms)) 1)]))
berghofe@17870
   855
        end) (constrs ~~ constr_rep_thms)
berghofe@17870
   856
      end) (List.take (descr, length new_type_names) ~~ new_type_names ~~ constr_rep_thmss);
berghofe@17870
   857
berghofe@17872
   858
    (** equations for support and freshness **)
berghofe@17872
   859
berghofe@17872
   860
    val Un_assoc = PureThy.get_thm thy8 (Name "Un_assoc");
berghofe@17872
   861
    val de_Morgan_conj = PureThy.get_thm thy8 (Name "de_Morgan_conj");
berghofe@17872
   862
    val Collect_disj_eq = PureThy.get_thm thy8 (Name "Collect_disj_eq");
berghofe@17872
   863
    val finite_Un = PureThy.get_thm thy8 (Name "finite_Un");
berghofe@17872
   864
berghofe@17872
   865
    val (supp_thms, fresh_thms) = ListPair.unzip (map ListPair.unzip
berghofe@17872
   866
      (map (fn ((((i, (_, _, constrs)), tname), inject_thms'), perm_thms') =>
berghofe@17872
   867
      let val T = replace_types' (nth_dtyp i)
berghofe@17872
   868
      in List.concat (map (fn (cname, dts) => map (fn atom =>
berghofe@17872
   869
        let
berghofe@17872
   870
          val cname = Sign.intern_const thy8
berghofe@17872
   871
            (NameSpace.append tname (Sign.base_name cname));
berghofe@17872
   872
          val atomT = Type (atom, []);
berghofe@17872
   873
berghofe@17872
   874
          fun process_constr (dt, (j, args1, args2)) =
berghofe@17872
   875
            let
berghofe@17872
   876
              val x' = mk_Free "x" (typ_of_dtyp' dt) j;
berghofe@17872
   877
              val (dts, dt') = strip_option dt;
berghofe@17872
   878
              val Ts_idx = map typ_of_dtyp' dts ~~ (j upto j + length dts - 1);
berghofe@17872
   879
              val xs = map (fn (T, i) => mk_Free "x" T i) Ts_idx;
berghofe@17872
   880
              val x = mk_Free "x" (typ_of_dtyp' dt') (j + length dts);
berghofe@17872
   881
              val (dts', dt'') = strip_dtyp dt';
berghofe@17872
   882
            in case dt'' of
berghofe@17872
   883
                DtRec k => if k < length new_type_names then
berghofe@17872
   884
                    (j + length dts + 1,
berghofe@17872
   885
                     xs @ (x :: args1), foldr mk_abs_fun x xs :: args2)
berghofe@17872
   886
                  else error "nested recursion not (yet) supported"
berghofe@17872
   887
              | _ => (j + 1, x' :: args1, x' :: args2)
berghofe@17872
   888
            end;
berghofe@17872
   889
berghofe@17872
   890
          val (_, args1, args2) = foldr process_constr (1, [], []) dts;
berghofe@17872
   891
          val Ts = map fastype_of args1;
berghofe@17872
   892
          val c = list_comb (Const (cname, Ts ---> T), args1);
berghofe@17872
   893
          fun supp t =
berghofe@17872
   894
            Const ("nominal.supp", fastype_of t --> HOLogic.mk_setT atomT) $ t;
berghofe@17872
   895
          fun fresh t =
berghofe@17872
   896
            Const ("nominal.fresh", atomT --> fastype_of t --> HOLogic.boolT) $
berghofe@17872
   897
              Free ("a", atomT) $ t;
berghofe@18010
   898
          val supp_thm = standard (Goal.prove thy8 [] []
berghofe@17872
   899
              (HOLogic.mk_Trueprop (HOLogic.mk_eq
berghofe@17872
   900
                (supp c,
berghofe@17872
   901
                 if null dts then Const ("{}", HOLogic.mk_setT atomT)
berghofe@18010
   902
                 else foldr1 (HOLogic.mk_binop "op Un") (map supp args2))))
berghofe@17872
   903
            (fn _ =>
berghofe@18010
   904
              simp_tac (HOL_basic_ss addsimps (supp_def ::
berghofe@17872
   905
                 Un_assoc :: de_Morgan_conj :: Collect_disj_eq :: finite_Un ::
berghofe@17874
   906
                 symmetric empty_def :: Finites.emptyI :: simp_thms @
berghofe@18010
   907
                 abs_perm @ abs_fresh @ inject_thms' @ perm_thms')) 1))
berghofe@17872
   908
        in
berghofe@17872
   909
          (supp_thm,
berghofe@18010
   910
           standard (Goal.prove thy8 [] [] (HOLogic.mk_Trueprop (HOLogic.mk_eq
berghofe@17872
   911
              (fresh c,
berghofe@17872
   912
               if null dts then HOLogic.true_const
berghofe@18010
   913
               else foldr1 HOLogic.mk_conj (map fresh args2))))
berghofe@17872
   914
             (fn _ =>
berghofe@18010
   915
               simp_tac (simpset_of thy8 addsimps [fresh_def, supp_thm]) 1)))
berghofe@17872
   916
        end) atoms) constrs)
berghofe@17872
   917
      end) (List.take (descr, length new_type_names) ~~ new_type_names ~~ inject_thms ~~ perm_simps')));
berghofe@17872
   918
berghofe@18016
   919
    (**** Induction theorem ****)
berghofe@18016
   920
berghofe@18016
   921
    val arities = get_arities (List.concat descr');
berghofe@18016
   922
berghofe@18016
   923
    fun mk_funs_inv thm =
berghofe@18016
   924
      let
berghofe@18016
   925
        val {sign, prop, ...} = rep_thm thm;
berghofe@18016
   926
        val _ $ (_ $ (Const (_, Type (_, [U, _])) $ _ $ S)) $
berghofe@18016
   927
          (_ $ (_ $ (r $ (a $ _)) $ _)) = Type.freeze prop;
berghofe@18016
   928
        val used = add_term_tfree_names (a, []);
berghofe@18016
   929
berghofe@18016
   930
        fun mk_thm i =
berghofe@18016
   931
          let
berghofe@18016
   932
            val Ts = map (TFree o rpair HOLogic.typeS)
berghofe@18016
   933
              (variantlist (replicate i "'t", used));
berghofe@18016
   934
            val f = Free ("f", Ts ---> U)
berghofe@18016
   935
          in standard (Goal.prove sign [] [] (Logic.mk_implies
berghofe@18016
   936
            (HOLogic.mk_Trueprop (HOLogic.list_all
berghofe@18016
   937
               (map (pair "x") Ts, HOLogic.mk_mem (app_bnds f i, S))),
berghofe@18016
   938
             HOLogic.mk_Trueprop (HOLogic.mk_eq (list_abs (map (pair "x") Ts,
berghofe@18016
   939
               r $ (a $ app_bnds f i)), f))))
berghofe@18016
   940
            (fn _ => EVERY [REPEAT (rtac ext 1), REPEAT (etac allE 1), rtac thm 1, atac 1]))
berghofe@18016
   941
          end
berghofe@18016
   942
      in map (fn r => r RS subst) (thm :: map mk_thm arities) end;
berghofe@18016
   943
berghofe@18016
   944
    fun mk_indrule_lemma ((prems, concls), (((i, _), T), U)) =
berghofe@18016
   945
      let
berghofe@18016
   946
        val Rep_t = Const (List.nth (rep_names, i), T --> U) $
berghofe@18016
   947
          mk_Free "x" T i;
berghofe@18016
   948
berghofe@18016
   949
        val Abs_t =  Const (List.nth (abs_names, i), U --> T)
berghofe@18016
   950
berghofe@18016
   951
      in (prems @ [HOLogic.imp $ HOLogic.mk_mem (Rep_t,
berghofe@18016
   952
            Const (List.nth (rep_set_names, i), HOLogic.mk_setT U)) $
berghofe@18016
   953
              (mk_Free "P" (T --> HOLogic.boolT) (i + 1) $ (Abs_t $ Rep_t))],
berghofe@18016
   954
          concls @ [mk_Free "P" (T --> HOLogic.boolT) (i + 1) $ mk_Free "x" T i])
berghofe@18016
   955
      end;
berghofe@18016
   956
berghofe@18016
   957
    val (indrule_lemma_prems, indrule_lemma_concls) =
berghofe@18016
   958
      Library.foldl mk_indrule_lemma (([], []), (List.concat descr' ~~ recTs ~~ recTs'));
berghofe@18016
   959
berghofe@18016
   960
    val indrule_lemma = standard (Goal.prove thy8 [] []
berghofe@18016
   961
      (Logic.mk_implies
berghofe@18016
   962
        (HOLogic.mk_Trueprop (mk_conj indrule_lemma_prems),
berghofe@18016
   963
         HOLogic.mk_Trueprop (mk_conj indrule_lemma_concls))) (fn _ => EVERY
berghofe@18016
   964
           [REPEAT (etac conjE 1),
berghofe@18016
   965
            REPEAT (EVERY
berghofe@18016
   966
              [TRY (rtac conjI 1), full_simp_tac (HOL_basic_ss addsimps Rep_inverse_thms) 1,
berghofe@18016
   967
               etac mp 1, resolve_tac Rep_thms 1])]));
berghofe@18016
   968
berghofe@18016
   969
    val Ps = map head_of (HOLogic.dest_conj (HOLogic.dest_Trueprop (concl_of indrule_lemma)));
berghofe@18016
   970
    val frees = if length Ps = 1 then [Free ("P", snd (dest_Var (hd Ps)))] else
berghofe@18016
   971
      map (Free o apfst fst o dest_Var) Ps;
berghofe@18016
   972
    val indrule_lemma' = cterm_instantiate
berghofe@18016
   973
      (map (cterm_of thy8) Ps ~~ map (cterm_of thy8) frees) indrule_lemma;
berghofe@18016
   974
berghofe@18016
   975
    val Abs_inverse_thms' = List.concat (map mk_funs_inv Abs_inverse_thms);
berghofe@18016
   976
berghofe@18016
   977
    val dt_induct_prop = DatatypeProp.make_ind descr' sorts';
berghofe@18016
   978
    val dt_induct = standard (Goal.prove thy8 []
berghofe@18016
   979
      (Logic.strip_imp_prems dt_induct_prop) (Logic.strip_imp_concl dt_induct_prop)
berghofe@18016
   980
      (fn prems => EVERY
berghofe@18016
   981
        [rtac indrule_lemma' 1,
berghofe@18016
   982
         (DatatypeAux.indtac rep_induct THEN_ALL_NEW ObjectLogic.atomize_tac) 1,
berghofe@18016
   983
         EVERY (map (fn (prem, r) => (EVERY
berghofe@18016
   984
           [REPEAT (eresolve_tac Abs_inverse_thms' 1),
berghofe@18016
   985
            simp_tac (HOL_basic_ss addsimps [symmetric r]) 1,
berghofe@18016
   986
            DEPTH_SOLVE_1 (ares_tac [prem] 1 ORELSE etac allE 1)]))
berghofe@18016
   987
                (prems ~~ constr_defs))]));
berghofe@18016
   988
urbanc@18017
   989
    val case_names_induct = mk_case_names_induct (List.concat descr');
berghofe@18016
   990
berghofe@18066
   991
    (**** prove that new datatypes have finite support ****)
berghofe@18066
   992
berghofe@18066
   993
    val indnames = DatatypeProp.make_tnames recTs;
berghofe@18066
   994
berghofe@18066
   995
    val abs_supp = PureThy.get_thms thy8 (Name "abs_supp");
urbanc@18067
   996
    val supp_atm = PureThy.get_thms thy8 (Name "supp_atm");
berghofe@18066
   997
berghofe@18066
   998
    val finite_supp_thms = map (fn atom =>
berghofe@18066
   999
      let val atomT = Type (atom, [])
berghofe@18066
  1000
      in map standard (List.take
berghofe@18066
  1001
        (split_conj_thm (Goal.prove thy8 [] [] (HOLogic.mk_Trueprop
berghofe@18066
  1002
           (foldr1 HOLogic.mk_conj (map (fn (s, T) => HOLogic.mk_mem
berghofe@18066
  1003
             (Const ("nominal.supp", T --> HOLogic.mk_setT atomT) $ Free (s, T),
berghofe@18066
  1004
              Const ("Finite_Set.Finites", HOLogic.mk_setT (HOLogic.mk_setT atomT))))
berghofe@18066
  1005
               (indnames ~~ recTs))))
berghofe@18066
  1006
           (fn _ => indtac dt_induct indnames 1 THEN
berghofe@18066
  1007
            ALLGOALS (asm_full_simp_tac (simpset_of thy8 addsimps
urbanc@18067
  1008
              (abs_supp @ supp_atm @
berghofe@18066
  1009
               PureThy.get_thms thy8 (Name ("fs_" ^ Sign.base_name atom ^ "1")) @
berghofe@18066
  1010
               List.concat supp_thms))))),
berghofe@18066
  1011
         length new_type_names))
berghofe@18066
  1012
      end) atoms;
berghofe@18066
  1013
berghofe@17870
  1014
    val (thy9, _) = thy8 |>
berghofe@18016
  1015
      Theory.add_path big_name |>
urbanc@18017
  1016
      PureThy.add_thms [(("induct_weak", dt_induct), [case_names_induct])] |>>
berghofe@18016
  1017
      Theory.parent_path |>>>
berghofe@17870
  1018
      DatatypeAux.store_thmss "distinct" new_type_names distinct_thms |>>>
berghofe@17870
  1019
      DatatypeAux.store_thmss "constr_rep" new_type_names constr_rep_thmss |>>>
berghofe@17870
  1020
      DatatypeAux.store_thmss "perm" new_type_names perm_simps' |>>>
berghofe@17872
  1021
      DatatypeAux.store_thmss "inject" new_type_names inject_thms |>>>
berghofe@17872
  1022
      DatatypeAux.store_thmss "supp" new_type_names supp_thms |>>>
berghofe@18066
  1023
      DatatypeAux.store_thmss "fresh" new_type_names fresh_thms |>>
berghofe@18066
  1024
      fold (fn (atom, ths) => fn thy =>
berghofe@18066
  1025
        let val class = Sign.intern_class thy ("fs_" ^ Sign.base_name atom)
berghofe@18066
  1026
        in fold (fn T => AxClass.add_inst_arity_i
berghofe@18066
  1027
            (fst (dest_Type T),
berghofe@18066
  1028
              replicate (length sorts) [class], [class])
berghofe@18066
  1029
            (AxClass.intro_classes_tac [] THEN resolve_tac ths 1)) newTs thy
berghofe@18066
  1030
        end) (atoms ~~ finite_supp_thms);
berghofe@17870
  1031
berghofe@17870
  1032
  in
berghofe@18068
  1033
    thy9
berghofe@17870
  1034
  end;
berghofe@17870
  1035
berghofe@17870
  1036
val add_nominal_datatype = gen_add_nominal_datatype read_typ true;
berghofe@17870
  1037
berghofe@17870
  1038
berghofe@17870
  1039
(* FIXME: The following stuff should be exported by DatatypePackage *)
berghofe@17870
  1040
berghofe@17870
  1041
local structure P = OuterParse and K = OuterKeyword in
berghofe@17870
  1042
berghofe@17870
  1043
val datatype_decl =
berghofe@17870
  1044
  Scan.option (P.$$$ "(" |-- P.name --| P.$$$ ")") -- P.type_args -- P.name -- P.opt_infix --
berghofe@17870
  1045
    (P.$$$ "=" |-- P.enum1 "|" (P.name -- Scan.repeat P.typ -- P.opt_mixfix));
berghofe@17870
  1046
berghofe@17870
  1047
fun mk_datatype args =
berghofe@17870
  1048
  let
berghofe@17870
  1049
    val names = map (fn ((((NONE, _), t), _), _) => t | ((((SOME t, _), _), _), _) => t) args;
berghofe@17870
  1050
    val specs = map (fn ((((_, vs), t), mx), cons) =>
berghofe@17870
  1051
      (vs, t, mx, map (fn ((x, y), z) => (x, y, z)) cons)) args;
berghofe@18068
  1052
  in add_nominal_datatype false names specs end;
berghofe@17870
  1053
berghofe@17870
  1054
val nominal_datatypeP =
berghofe@17870
  1055
  OuterSyntax.command "nominal_datatype" "define inductive datatypes" K.thy_decl
berghofe@17870
  1056
    (P.and_list1 datatype_decl >> (Toplevel.theory o mk_datatype));
berghofe@17870
  1057
berghofe@17870
  1058
val _ = OuterSyntax.add_parsers [nominal_datatypeP];
berghofe@17870
  1059
berghofe@17870
  1060
end;
berghofe@17870
  1061
berghofe@17870
  1062
end