src/HOL/Nominal/nominal_package.ML
author berghofe
Wed Jan 11 18:21:23 2006 +0100 (2006-01-11)
changeset 18658 317a6f0ef8b9
parent 18582 4f4cc426b440
child 18707 9d6154f76476
permissions -rw-r--r--
Implemented proof of (strong) induction rule.
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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 mk_subgoal i f st =
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  let
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    val cg = List.nth (cprems_of st, i - 1);
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    val g = term_of cg;
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    val revcut_rl' = Thm.lift_rule cg revcut_rl;
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    val v = head_of (Logic.strip_assums_concl (hd (prems_of revcut_rl')));
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    val ps = Logic.strip_params g;
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    val cert = cterm_of (sign_of_thm st);
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  in
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    compose_tac (false,
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      Thm.instantiate ([], [(cert v, cert (list_abs (ps,
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        f (rev ps) (Logic.strip_assums_hyp g) (Logic.strip_assums_concl g))))])
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      revcut_rl', 2) i st
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  end;
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(** simplification procedure for sorting permutations **)
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val dj_cp = thm "dj_cp";
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fun dest_permT (Type ("fun", [Type ("List.list", [Type ("*", [T, _])]),
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      Type ("fun", [_, U])])) = (T, U);
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fun permTs_of (Const ("nominal.perm", T) $ t $ u) = fst (dest_permT T) :: permTs_of u
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  | permTs_of _ = [];
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fun perm_simproc' thy ss (Const ("nominal.perm", T) $ t $ (u as Const ("nominal.perm", U) $ r $ s)) =
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      let
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        val (aT as Type (a, []), S) = dest_permT T;
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        val (bT as Type (b, []), _) = dest_permT U
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      in if aT mem permTs_of u andalso aT <> bT then
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          let
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            val a' = Sign.base_name a;
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            val b' = Sign.base_name b;
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            val cp = PureThy.get_thm thy (Name ("cp_" ^ a' ^ "_" ^ b' ^ "_inst"));
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            val dj = PureThy.get_thm thy (Name ("dj_" ^ b' ^ "_" ^ a'));
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            val dj_cp' = [cp, dj] MRS dj_cp;
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            val cert = SOME o cterm_of thy
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          in
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            SOME (mk_meta_eq (Drule.instantiate' [SOME (ctyp_of thy S)]
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              [cert t, cert r, cert s] dj_cp'))
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          end
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        else NONE
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      end
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  | perm_simproc' thy ss _ = NONE;
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val perm_simproc =
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  Simplifier.simproc (the_context ()) "perm_simp" ["pi1 \\<bullet> (pi2 \\<bullet> x)"] perm_simproc';
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val allE_Nil = read_instantiate_sg (the_context()) [("x", "[]")] allE;
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val meta_spec = thm "meta_spec";
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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 norm_sort thy = Sorts.norm_sort (snd (#classes (Type.rep_tsig (Sign.tsig_of thy))));
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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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   304
        val pi1 = Free ("pi1", permT);
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   305
        val pi2 = Free ("pi2", permT);
berghofe@17870
   306
        val pt_inst = PureThy.get_thm thy2 (Name ("pt_" ^ Sign.base_name a ^ "_inst"));
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   307
        val pt2' = pt_inst RS pt2;
berghofe@17870
   308
        val pt2_ax = PureThy.get_thm thy2
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   309
          (Name (NameSpace.map_base (fn s => "pt_" ^ s ^ "2") a));
berghofe@17870
   310
      in List.take (map standard (split_conj_thm
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   311
        (Goal.prove thy2 [] []
berghofe@17870
   312
             (HOLogic.mk_Trueprop (foldr1 HOLogic.mk_conj
berghofe@17870
   313
                (map (fn ((s, T), x) =>
berghofe@17870
   314
                    let val perm = Const (s, permT --> T --> T)
berghofe@17870
   315
                    in HOLogic.mk_eq
berghofe@17870
   316
                      (perm $ (Const ("List.op @", permT --> permT --> permT) $
berghofe@17870
   317
                         pi1 $ pi2) $ Free (x, T),
berghofe@17870
   318
                       perm $ pi1 $ (perm $ pi2 $ Free (x, T)))
berghofe@17870
   319
                    end)
berghofe@17870
   320
                  (perm_names ~~
berghofe@18010
   321
                   map body_type perm_types ~~ perm_indnames))))
berghofe@18010
   322
           (fn _ => EVERY [indtac induction perm_indnames 1,
berghofe@17870
   323
              ALLGOALS (asm_full_simp_tac (simpset_of thy2 addsimps [pt2', pt2_ax]))]))),
berghofe@17870
   324
         length new_type_names)
berghofe@17870
   325
      end) atoms);
berghofe@17870
   326
berghofe@17870
   327
    (**** prove pi1 ~ pi2 ==> pi1 \<bullet> t = pi2 \<bullet> t ****)
berghofe@17870
   328
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   329
    val _ = warning "perm_eq_thms";
berghofe@17870
   330
berghofe@17870
   331
    val pt3 = PureThy.get_thm thy2 (Name "pt3");
berghofe@17870
   332
    val pt3_rev = PureThy.get_thm thy2 (Name "pt3_rev");
berghofe@17870
   333
berghofe@17870
   334
    val perm_eq_thms = List.concat (map (fn a =>
berghofe@17870
   335
      let
berghofe@17870
   336
        val permT = mk_permT (Type (a, []));
berghofe@17870
   337
        val pi1 = Free ("pi1", permT);
berghofe@17870
   338
        val pi2 = Free ("pi2", permT);
berghofe@17870
   339
        (*FIXME: not robust - better access these theorems using NominalData?*)
berghofe@17870
   340
        val at_inst = PureThy.get_thm thy2 (Name ("at_" ^ Sign.base_name a ^ "_inst"));
berghofe@17870
   341
        val pt_inst = PureThy.get_thm thy2 (Name ("pt_" ^ Sign.base_name a ^ "_inst"));
berghofe@17870
   342
        val pt3' = pt_inst RS pt3;
berghofe@17870
   343
        val pt3_rev' = at_inst RS (pt_inst RS pt3_rev);
berghofe@17870
   344
        val pt3_ax = PureThy.get_thm thy2
berghofe@17870
   345
          (Name (NameSpace.map_base (fn s => "pt_" ^ s ^ "3") a));
berghofe@17870
   346
      in List.take (map standard (split_conj_thm
berghofe@18010
   347
        (Goal.prove thy2 [] [] (Logic.mk_implies
berghofe@17870
   348
             (HOLogic.mk_Trueprop (Const ("nominal.prm_eq",
berghofe@17870
   349
                permT --> permT --> HOLogic.boolT) $ pi1 $ pi2),
berghofe@17870
   350
              HOLogic.mk_Trueprop (foldr1 HOLogic.mk_conj
berghofe@17870
   351
                (map (fn ((s, T), x) =>
berghofe@17870
   352
                    let val perm = Const (s, permT --> T --> T)
berghofe@17870
   353
                    in HOLogic.mk_eq
berghofe@17870
   354
                      (perm $ pi1 $ Free (x, T),
berghofe@17870
   355
                       perm $ pi2 $ Free (x, T))
berghofe@17870
   356
                    end)
berghofe@17870
   357
                  (perm_names ~~
berghofe@18010
   358
                   map body_type perm_types ~~ perm_indnames)))))
berghofe@18010
   359
           (fn _ => EVERY [indtac induction perm_indnames 1,
berghofe@17870
   360
              ALLGOALS (asm_full_simp_tac (simpset_of thy2 addsimps [pt3', pt3_rev', pt3_ax]))]))),
berghofe@17870
   361
         length new_type_names)
berghofe@17870
   362
      end) atoms);
berghofe@17870
   363
berghofe@17870
   364
    (**** prove pi1 \<bullet> (pi2 \<bullet> t) = (pi1 \<bullet> pi2) \<bullet> (pi1 \<bullet> t) ****)
berghofe@17870
   365
berghofe@17870
   366
    val cp1 = PureThy.get_thm thy2 (Name "cp1");
berghofe@17870
   367
    val dj_cp = PureThy.get_thm thy2 (Name "dj_cp");
berghofe@17870
   368
    val pt_perm_compose = PureThy.get_thm thy2 (Name "pt_perm_compose");
berghofe@17870
   369
    val pt_perm_compose_rev = PureThy.get_thm thy2 (Name "pt_perm_compose_rev");
berghofe@17870
   370
    val dj_perm_perm_forget = PureThy.get_thm thy2 (Name "dj_perm_perm_forget");
berghofe@17870
   371
berghofe@17870
   372
    fun composition_instance name1 name2 thy =
berghofe@17870
   373
      let
berghofe@17870
   374
        val name1' = Sign.base_name name1;
berghofe@17870
   375
        val name2' = Sign.base_name name2;
berghofe@17870
   376
        val cp_class = Sign.intern_class thy ("cp_" ^ name1' ^ "_" ^ name2');
berghofe@17870
   377
        val permT1 = mk_permT (Type (name1, []));
berghofe@17870
   378
        val permT2 = mk_permT (Type (name2, []));
berghofe@17870
   379
        val augment = map_type_tfree
berghofe@17870
   380
          (fn (x, S) => TFree (x, cp_class :: S));
berghofe@17870
   381
        val Ts = map (augment o body_type) perm_types;
berghofe@17870
   382
        val cp_inst = PureThy.get_thm thy
berghofe@17870
   383
          (Name ("cp_" ^ name1' ^ "_" ^ name2' ^ "_inst"));
berghofe@17870
   384
        val simps = simpset_of thy addsimps (perm_fun_def ::
berghofe@17870
   385
          (if name1 <> name2 then
berghofe@17870
   386
             let val dj = PureThy.get_thm thy (Name ("dj_" ^ name2' ^ "_" ^ name1'))
berghofe@17870
   387
             in [dj RS (cp_inst RS dj_cp), dj RS dj_perm_perm_forget] end
berghofe@17870
   388
           else
berghofe@17870
   389
             let
berghofe@17870
   390
               val at_inst = PureThy.get_thm thy (Name ("at_" ^ name1' ^ "_inst"));
berghofe@17870
   391
               val pt_inst = PureThy.get_thm thy (Name ("pt_" ^ name1' ^ "_inst"))
berghofe@17870
   392
             in
berghofe@17870
   393
               [cp_inst RS cp1 RS sym,
berghofe@17870
   394
                at_inst RS (pt_inst RS pt_perm_compose) RS sym,
berghofe@17870
   395
                at_inst RS (pt_inst RS pt_perm_compose_rev) RS sym]
berghofe@17870
   396
            end))
berghofe@18010
   397
        val thms = split_conj_thm (standard (Goal.prove thy [] []
berghofe@17870
   398
            (HOLogic.mk_Trueprop (foldr1 HOLogic.mk_conj
berghofe@17870
   399
              (map (fn ((s, T), x) =>
berghofe@17870
   400
                  let
berghofe@17870
   401
                    val pi1 = Free ("pi1", permT1);
berghofe@17870
   402
                    val pi2 = Free ("pi2", permT2);
berghofe@17870
   403
                    val perm1 = Const (s, permT1 --> T --> T);
berghofe@17870
   404
                    val perm2 = Const (s, permT2 --> T --> T);
berghofe@17870
   405
                    val perm3 = Const ("nominal.perm", permT1 --> permT2 --> permT2)
berghofe@17870
   406
                  in HOLogic.mk_eq
berghofe@17870
   407
                    (perm1 $ pi1 $ (perm2 $ pi2 $ Free (x, T)),
berghofe@17870
   408
                     perm2 $ (perm3 $ pi1 $ pi2) $ (perm1 $ pi1 $ Free (x, T)))
berghofe@17870
   409
                  end)
berghofe@18010
   410
                (perm_names ~~ Ts ~~ perm_indnames))))
berghofe@18010
   411
          (fn _ => EVERY [indtac induction perm_indnames 1,
berghofe@18010
   412
             ALLGOALS (asm_full_simp_tac simps)])))
berghofe@17870
   413
      in
berghofe@17870
   414
        foldl (fn ((s, tvs), thy) => AxClass.add_inst_arity_i
berghofe@17870
   415
            (s, replicate (length tvs) (cp_class :: classes), [cp_class])
berghofe@17870
   416
            (AxClass.intro_classes_tac [] THEN ALLGOALS (resolve_tac thms)) thy)
berghofe@17870
   417
          thy (full_new_type_names' ~~ tyvars)
berghofe@17870
   418
      end;
berghofe@17870
   419
urbanc@18381
   420
    val (perm_thmss,thy3) = thy2 |>
berghofe@17870
   421
      fold (fn name1 => fold (composition_instance name1) atoms) atoms |>
berghofe@17870
   422
      curry (Library.foldr (fn ((i, (tyname, args, _)), thy) =>
berghofe@17870
   423
        AxClass.add_inst_arity_i (tyname, replicate (length args) classes, classes)
berghofe@17870
   424
        (AxClass.intro_classes_tac [] THEN REPEAT (EVERY
berghofe@17870
   425
           [resolve_tac perm_empty_thms 1,
berghofe@17870
   426
            resolve_tac perm_append_thms 1,
berghofe@17870
   427
            resolve_tac perm_eq_thms 1, assume_tac 1])) thy))
berghofe@17870
   428
        (List.take (descr, length new_type_names)) |>
berghofe@17870
   429
      PureThy.add_thmss
berghofe@17870
   430
        [((space_implode "_" new_type_names ^ "_unfolded_perm_eq",
berghofe@17870
   431
          unfolded_perm_eq_thms), [Simplifier.simp_add_global]),
berghofe@17870
   432
         ((space_implode "_" new_type_names ^ "_perm_empty",
berghofe@17870
   433
          perm_empty_thms), [Simplifier.simp_add_global]),
berghofe@17870
   434
         ((space_implode "_" new_type_names ^ "_perm_append",
berghofe@17870
   435
          perm_append_thms), [Simplifier.simp_add_global]),
berghofe@17870
   436
         ((space_implode "_" new_type_names ^ "_perm_eq",
berghofe@17870
   437
          perm_eq_thms), [Simplifier.simp_add_global])];
berghofe@17870
   438
  
berghofe@17870
   439
    (**** Define representing sets ****)
berghofe@17870
   440
berghofe@17870
   441
    val _ = warning "representing sets";
berghofe@17870
   442
berghofe@17870
   443
    val rep_set_names = map (Sign.full_name thy3) (DatatypeProp.indexify_names
berghofe@17870
   444
      (map (fn (i, _) => name_of_typ (nth_dtyp i) ^ "_set") descr));
berghofe@17870
   445
    val big_rep_name =
berghofe@17870
   446
      space_implode "_" (DatatypeProp.indexify_names (List.mapPartial
urbanc@18579
   447
        (fn (i, ("nominal.noption", _, _)) => NONE
berghofe@17870
   448
          | (i, _) => SOME (name_of_typ (nth_dtyp i))) descr)) ^ "_set";
berghofe@17870
   449
    val _ = warning ("big_rep_name: " ^ big_rep_name);
berghofe@17870
   450
berghofe@17870
   451
    fun strip_option (dtf as DtType ("fun", [dt, DtRec i])) =
berghofe@17870
   452
          (case AList.lookup op = descr i of
urbanc@18579
   453
             SOME ("nominal.noption", _, [(_, [dt']), _]) =>
berghofe@17870
   454
               apfst (cons dt) (strip_option dt')
berghofe@17870
   455
           | _ => ([], dtf))
urbanc@18579
   456
      | strip_option (DtType ("fun", [dt, DtType ("nominal.noption", [dt'])])) =
berghofe@18261
   457
          apfst (cons dt) (strip_option dt')
berghofe@17870
   458
      | strip_option dt = ([], dt);
berghofe@17870
   459
berghofe@18280
   460
    val dt_atomTs = distinct (map (typ_of_dtyp descr sorts')
berghofe@18280
   461
      (List.concat (map (fn (_, (_, _, cs)) => List.concat
berghofe@18280
   462
        (map (List.concat o map (fst o strip_option) o snd) cs)) descr)));
berghofe@18280
   463
berghofe@17870
   464
    fun make_intr s T (cname, cargs) =
berghofe@17870
   465
      let
berghofe@17870
   466
        fun mk_prem (dt, (j, j', prems, ts)) = 
berghofe@17870
   467
          let
berghofe@17870
   468
            val (dts, dt') = strip_option dt;
berghofe@17870
   469
            val (dts', dt'') = strip_dtyp dt';
berghofe@18107
   470
            val Ts = map (typ_of_dtyp descr sorts') dts;
berghofe@18107
   471
            val Us = map (typ_of_dtyp descr sorts') dts';
berghofe@18107
   472
            val T = typ_of_dtyp descr sorts' dt'';
berghofe@17870
   473
            val free = mk_Free "x" (Us ---> T) j;
berghofe@17870
   474
            val free' = app_bnds free (length Us);
berghofe@17870
   475
            fun mk_abs_fun (T, (i, t)) =
berghofe@17870
   476
              let val U = fastype_of t
berghofe@17870
   477
              in (i + 1, Const ("nominal.abs_fun", [T, U, T] --->
urbanc@18579
   478
                Type ("nominal.noption", [U])) $ mk_Free "y" T i $ t)
berghofe@17870
   479
              end
berghofe@17870
   480
          in (j + 1, j' + length Ts,
berghofe@17870
   481
            case dt'' of
berghofe@17870
   482
                DtRec k => list_all (map (pair "x") Us,
berghofe@17870
   483
                  HOLogic.mk_Trueprop (HOLogic.mk_mem (free',
berghofe@17870
   484
                    Const (List.nth (rep_set_names, k),
berghofe@17870
   485
                      HOLogic.mk_setT T)))) :: prems
berghofe@17870
   486
              | _ => prems,
berghofe@17870
   487
            snd (foldr mk_abs_fun (j', free) Ts) :: ts)
berghofe@17870
   488
          end;
berghofe@17870
   489
berghofe@17870
   490
        val (_, _, prems, ts) = foldr mk_prem (1, 1, [], []) cargs;
berghofe@17870
   491
        val concl = HOLogic.mk_Trueprop (HOLogic.mk_mem
berghofe@17870
   492
          (list_comb (Const (cname, map fastype_of ts ---> T), ts),
berghofe@17870
   493
           Const (s, HOLogic.mk_setT T)))
berghofe@17870
   494
      in Logic.list_implies (prems, concl)
berghofe@17870
   495
      end;
berghofe@17870
   496
berghofe@17870
   497
    val (intr_ts, ind_consts) =
berghofe@17870
   498
      apfst List.concat (ListPair.unzip (List.mapPartial
urbanc@18579
   499
        (fn ((_, ("nominal.noption", _, _)), _) => NONE
berghofe@17870
   500
          | ((i, (_, _, constrs)), rep_set_name) =>
berghofe@17870
   501
              let val T = nth_dtyp i
berghofe@17870
   502
              in SOME (map (make_intr rep_set_name T) constrs,
berghofe@17870
   503
                Const (rep_set_name, HOLogic.mk_setT T))
berghofe@17870
   504
              end)
berghofe@17870
   505
                (descr ~~ rep_set_names)));
berghofe@17870
   506
berghofe@17870
   507
    val (thy4, {raw_induct = rep_induct, intrs = rep_intrs, ...}) =
berghofe@17870
   508
      setmp InductivePackage.quiet_mode false
berghofe@17870
   509
        (InductivePackage.add_inductive_i false true big_rep_name false true false
berghofe@17870
   510
           ind_consts (map (fn x => (("", x), [])) intr_ts) []) thy3;
berghofe@17870
   511
berghofe@17870
   512
    (**** Prove that representing set is closed under permutation ****)
berghofe@17870
   513
berghofe@17870
   514
    val _ = warning "proving closure under permutation...";
berghofe@17870
   515
berghofe@17870
   516
    val perm_indnames' = List.mapPartial
urbanc@18579
   517
      (fn (x, (_, ("nominal.noption", _, _))) => NONE | (x, _) => SOME x)
berghofe@17870
   518
      (perm_indnames ~~ descr);
berghofe@17870
   519
berghofe@17870
   520
    fun mk_perm_closed name = map (fn th => standard (th RS mp))
berghofe@18010
   521
      (List.take (split_conj_thm (Goal.prove thy4 [] []
berghofe@17870
   522
        (HOLogic.mk_Trueprop (foldr1 HOLogic.mk_conj (map
berghofe@17870
   523
           (fn (S, x) =>
berghofe@17870
   524
              let
berghofe@17870
   525
                val S = map_term_types (map_type_tfree
berghofe@17870
   526
                  (fn (s, cs) => TFree (s, cs union cp_classes))) S;
berghofe@17870
   527
                val T = HOLogic.dest_setT (fastype_of S);
berghofe@17870
   528
                val permT = mk_permT (Type (name, []))
berghofe@17870
   529
              in HOLogic.mk_imp (HOLogic.mk_mem (Free (x, T), S),
berghofe@17870
   530
                HOLogic.mk_mem (Const ("nominal.perm", permT --> T --> T) $
berghofe@17870
   531
                  Free ("pi", permT) $ Free (x, T), S))
berghofe@18010
   532
              end) (ind_consts ~~ perm_indnames'))))
berghofe@18010
   533
        (fn _ => EVERY (* CU: added perm_fun_def in the final tactic in order to deal with funs *)
berghofe@17870
   534
           [indtac rep_induct [] 1,
berghofe@17870
   535
            ALLGOALS (simp_tac (simpset_of thy4 addsimps
berghofe@17870
   536
              (symmetric perm_fun_def :: PureThy.get_thms thy4 (Name ("abs_perm"))))),
berghofe@17870
   537
            ALLGOALS (resolve_tac rep_intrs 
berghofe@17870
   538
               THEN_ALL_NEW (asm_full_simp_tac (simpset_of thy4 addsimps [perm_fun_def])))])),
berghofe@17870
   539
        length new_type_names));
berghofe@17870
   540
berghofe@17870
   541
    (* FIXME: theorems are stored in database for testing only *)
berghofe@17870
   542
    val perm_closed_thmss = map mk_perm_closed atoms;
urbanc@18381
   543
    val (_,thy5) = PureThy.add_thmss [(("perm_closed", List.concat perm_closed_thmss), [])] thy4;
berghofe@17870
   544
berghofe@17870
   545
    (**** typedef ****)
berghofe@17870
   546
berghofe@17870
   547
    val _ = warning "defining type...";
berghofe@17870
   548
berghofe@18366
   549
    val (typedefs, thy6) =
berghofe@18366
   550
      fold_map (fn ((((name, mx), tvs), c), name') => fn thy =>
berghofe@17870
   551
        setmp TypedefPackage.quiet_mode true
berghofe@17870
   552
          (TypedefPackage.add_typedef_i false (SOME name') (name, tvs, mx) c NONE
berghofe@17870
   553
            (rtac exI 1 THEN
berghofe@17870
   554
              QUIET_BREADTH_FIRST (has_fewer_prems 1)
berghofe@17870
   555
              (resolve_tac rep_intrs 1))) thy |> (fn (thy, r) =>
berghofe@17870
   556
        let
berghofe@17870
   557
          val permT = mk_permT (TFree (variant tvs "'a", HOLogic.typeS));
berghofe@17870
   558
          val pi = Free ("pi", permT);
berghofe@17870
   559
          val tvs' = map (fn s => TFree (s, the (AList.lookup op = sorts' s))) tvs;
berghofe@17870
   560
          val T = Type (Sign.intern_type thy name, tvs');
berghofe@17870
   561
          val Const (_, Type (_, [U])) = c
berghofe@18366
   562
        in apfst (pair r o hd)
berghofe@17870
   563
          (PureThy.add_defs_i true [(("prm_" ^ name ^ "_def", Logic.mk_equals
berghofe@17870
   564
            (Const ("nominal.perm", permT --> T --> T) $ pi $ Free ("x", T),
berghofe@17870
   565
             Const (Sign.intern_const thy ("Abs_" ^ name), U --> T) $
berghofe@17870
   566
               (Const ("nominal.perm", permT --> U --> U) $ pi $
berghofe@17870
   567
                 (Const (Sign.intern_const thy ("Rep_" ^ name), T --> U) $
berghofe@17870
   568
                   Free ("x", T))))), [])] thy)
berghofe@17870
   569
        end))
berghofe@18366
   570
          (types_syntax ~~ tyvars ~~
berghofe@18366
   571
            (List.take (ind_consts, length new_type_names)) ~~ new_type_names) thy5;
berghofe@17870
   572
berghofe@17870
   573
    val perm_defs = map snd typedefs;
berghofe@17870
   574
    val Abs_inverse_thms = map (#Abs_inverse o fst) typedefs;
berghofe@18016
   575
    val Rep_inverse_thms = map (#Rep_inverse o fst) typedefs;
berghofe@17870
   576
    val Rep_thms = map (#Rep o fst) typedefs;
berghofe@17870
   577
berghofe@18016
   578
    val big_name = space_implode "_" new_type_names;
berghofe@18016
   579
berghofe@18016
   580
berghofe@17870
   581
    (** prove that new types are in class pt_<name> **)
berghofe@17870
   582
berghofe@17870
   583
    val _ = warning "prove that new types are in class pt_<name> ...";
berghofe@17870
   584
berghofe@17870
   585
    fun pt_instance ((class, atom), perm_closed_thms) =
berghofe@17870
   586
      fold (fn (((({Abs_inverse, Rep_inverse, Rep, ...},
berghofe@17870
   587
        perm_def), name), tvs), perm_closed) => fn thy =>
berghofe@17870
   588
          AxClass.add_inst_arity_i
berghofe@17870
   589
            (Sign.intern_type thy name,
berghofe@17870
   590
              replicate (length tvs) (classes @ cp_classes), [class])
berghofe@17870
   591
            (EVERY [AxClass.intro_classes_tac [],
berghofe@17870
   592
              rewrite_goals_tac [perm_def],
berghofe@17870
   593
              asm_full_simp_tac (simpset_of thy addsimps [Rep_inverse]) 1,
berghofe@17870
   594
              asm_full_simp_tac (simpset_of thy addsimps
berghofe@17870
   595
                [Rep RS perm_closed RS Abs_inverse]) 1,
berghofe@17870
   596
              asm_full_simp_tac (HOL_basic_ss addsimps [PureThy.get_thm thy
berghofe@17870
   597
                (Name ("pt_" ^ Sign.base_name atom ^ "3"))]) 1]) thy)
berghofe@17870
   598
        (typedefs ~~ new_type_names ~~ tyvars ~~ perm_closed_thms);
berghofe@17870
   599
berghofe@17870
   600
berghofe@17870
   601
    (** prove that new types are in class cp_<name1>_<name2> **)
berghofe@17870
   602
berghofe@17870
   603
    val _ = warning "prove that new types are in class cp_<name1>_<name2> ...";
berghofe@17870
   604
berghofe@17870
   605
    fun cp_instance (atom1, perm_closed_thms1) (atom2, perm_closed_thms2) thy =
berghofe@17870
   606
      let
berghofe@17870
   607
        val name = "cp_" ^ Sign.base_name atom1 ^ "_" ^ Sign.base_name atom2;
berghofe@17870
   608
        val class = Sign.intern_class thy name;
berghofe@17870
   609
        val cp1' = PureThy.get_thm thy (Name (name ^ "_inst")) RS cp1
berghofe@17870
   610
      in fold (fn ((((({Abs_inverse, Rep_inverse, Rep, ...},
berghofe@17870
   611
        perm_def), name), tvs), perm_closed1), perm_closed2) => fn thy =>
berghofe@17870
   612
          AxClass.add_inst_arity_i
berghofe@17870
   613
            (Sign.intern_type thy name,
berghofe@17870
   614
              replicate (length tvs) (classes @ cp_classes), [class])
berghofe@17870
   615
            (EVERY [AxClass.intro_classes_tac [],
berghofe@17870
   616
              rewrite_goals_tac [perm_def],
berghofe@17870
   617
              asm_full_simp_tac (simpset_of thy addsimps
berghofe@17870
   618
                ((Rep RS perm_closed1 RS Abs_inverse) ::
berghofe@17870
   619
                 (if atom1 = atom2 then []
berghofe@17870
   620
                  else [Rep RS perm_closed2 RS Abs_inverse]))) 1,
berghofe@18016
   621
              cong_tac 1,
berghofe@17870
   622
              rtac refl 1,
berghofe@17870
   623
              rtac cp1' 1]) thy)
berghofe@17870
   624
        (typedefs ~~ new_type_names ~~ tyvars ~~ perm_closed_thms1 ~~
berghofe@17870
   625
          perm_closed_thms2) thy
berghofe@17870
   626
      end;
berghofe@17870
   627
berghofe@17870
   628
    val thy7 = fold (fn x => fn thy => thy |>
berghofe@17870
   629
      pt_instance x |>
berghofe@17870
   630
      fold (cp_instance (apfst snd x)) (atoms ~~ perm_closed_thmss))
berghofe@17870
   631
        (classes ~~ atoms ~~ perm_closed_thmss) thy6;
berghofe@17870
   632
berghofe@17870
   633
    (**** constructors ****)
berghofe@17870
   634
berghofe@17870
   635
    fun mk_abs_fun (x, t) =
berghofe@17870
   636
      let
berghofe@17870
   637
        val T = fastype_of x;
berghofe@17870
   638
        val U = fastype_of t
berghofe@17870
   639
      in
berghofe@17870
   640
        Const ("nominal.abs_fun", T --> U --> T -->
urbanc@18579
   641
          Type ("nominal.noption", [U])) $ x $ t
berghofe@17870
   642
      end;
berghofe@17870
   643
berghofe@18016
   644
    val (ty_idxs, _) = foldl
urbanc@18579
   645
      (fn ((i, ("nominal.noption", _, _)), p) => p
berghofe@18016
   646
        | ((i, _), (ty_idxs, j)) => (ty_idxs @ [(i, j)], j + 1)) ([], 0) descr;
berghofe@18016
   647
berghofe@18016
   648
    fun reindex (DtType (s, dts)) = DtType (s, map reindex dts)
berghofe@18016
   649
      | reindex (DtRec i) = DtRec (the (AList.lookup op = ty_idxs i))
berghofe@18016
   650
      | reindex dt = dt;
berghofe@18016
   651
berghofe@18016
   652
    fun strip_suffix i s = implode (List.take (explode s, size s - i));
berghofe@18016
   653
berghofe@18016
   654
    (** strips the "_Rep" in type names *)
urbanc@18045
   655
    fun strip_nth_name i s = 
urbanc@18045
   656
      let val xs = NameSpace.unpack s; 
urbanc@18045
   657
      in NameSpace.pack (Library.nth_map (length xs - i) (strip_suffix 4) xs) end;
berghofe@18016
   658
berghofe@18107
   659
    val (descr'', ndescr) = ListPair.unzip (List.mapPartial
urbanc@18579
   660
      (fn (i, ("nominal.noption", _, _)) => NONE
berghofe@18107
   661
        | (i, (s, dts, constrs)) =>
berghofe@18107
   662
             let
berghofe@18107
   663
               val SOME index = AList.lookup op = ty_idxs i;
berghofe@18107
   664
               val (constrs1, constrs2) = ListPair.unzip
berghofe@18107
   665
                 (map (fn (cname, cargs) => apfst (pair (strip_nth_name 2 cname))
berghofe@18107
   666
                   (foldl_map (fn (dts, dt) =>
berghofe@18107
   667
                     let val (dts', dt') = strip_option dt
berghofe@18107
   668
                     in (dts @ dts' @ [reindex dt'], (length dts, length dts')) end)
berghofe@18107
   669
                       ([], cargs))) constrs)
berghofe@18107
   670
             in SOME ((index, (strip_nth_name 1 s,  map reindex dts, constrs1)),
berghofe@18107
   671
               (index, constrs2))
berghofe@18107
   672
             end) descr);
urbanc@18045
   673
berghofe@18016
   674
    val (descr1, descr2) = splitAt (length new_type_names, descr'');
berghofe@18016
   675
    val descr' = [descr1, descr2];
berghofe@18016
   676
berghofe@18107
   677
    val typ_of_dtyp' = replace_types' o typ_of_dtyp descr sorts';
berghofe@17870
   678
berghofe@17870
   679
    val rep_names = map (fn s =>
berghofe@17870
   680
      Sign.intern_const thy7 ("Rep_" ^ s)) new_type_names;
berghofe@17870
   681
    val abs_names = map (fn s =>
berghofe@17870
   682
      Sign.intern_const thy7 ("Abs_" ^ s)) new_type_names;
berghofe@17870
   683
berghofe@18016
   684
    val recTs' = List.mapPartial
urbanc@18579
   685
      (fn ((_, ("nominal.noption", _, _)), T) => NONE
berghofe@18016
   686
        | (_, T) => SOME T) (descr ~~ get_rec_types descr sorts');
berghofe@18107
   687
    val recTs = get_rec_types descr'' sorts';
berghofe@18016
   688
    val newTs' = Library.take (length new_type_names, recTs');
berghofe@18016
   689
    val newTs = Library.take (length new_type_names, recTs);
berghofe@17870
   690
berghofe@17870
   691
    val full_new_type_names = map (Sign.full_name (sign_of thy)) new_type_names;
berghofe@17870
   692
berghofe@17870
   693
    fun make_constr_def tname T T' ((thy, defs, eqns), ((cname, cargs), (cname', mx))) =
berghofe@17870
   694
      let
berghofe@17870
   695
        fun constr_arg (dt, (j, l_args, r_args)) =
berghofe@17870
   696
          let
berghofe@17870
   697
            val x' = mk_Free "x" (typ_of_dtyp' dt) j;
berghofe@17870
   698
            val (dts, dt') = strip_option dt;
berghofe@17870
   699
            val xs = map (fn (dt, i) => mk_Free "x" (typ_of_dtyp' dt) i)
berghofe@17870
   700
              (dts ~~ (j upto j + length dts - 1))
berghofe@17870
   701
            val x = mk_Free "x" (typ_of_dtyp' dt') (j + length dts)
berghofe@17870
   702
            val (dts', dt'') = strip_dtyp dt'
berghofe@18261
   703
          in
berghofe@18261
   704
            (j + length dts + 1,
berghofe@18261
   705
             xs @ x :: l_args,
berghofe@18261
   706
             foldr mk_abs_fun
berghofe@18261
   707
               (case dt'' of
berghofe@18261
   708
                  DtRec k => if k < length new_type_names then
berghofe@18261
   709
                      list_abs (map (pair "z" o typ_of_dtyp') dts',
berghofe@18261
   710
                        Const (List.nth (rep_names, k), typ_of_dtyp' dt'' -->
berghofe@18261
   711
                          typ_of_dtyp descr sorts' dt'') $ app_bnds x (length dts'))
berghofe@18261
   712
                    else error "nested recursion not (yet) supported"
berghofe@18261
   713
                | _ => x) xs :: r_args)
berghofe@17870
   714
          end
berghofe@17870
   715
berghofe@17870
   716
        val (_, l_args, r_args) = foldr constr_arg (1, [], []) cargs;
berghofe@17870
   717
        val abs_name = Sign.intern_const (Theory.sign_of thy) ("Abs_" ^ tname);
berghofe@17870
   718
        val rep_name = Sign.intern_const (Theory.sign_of thy) ("Rep_" ^ tname);
berghofe@17870
   719
        val constrT = map fastype_of l_args ---> T;
berghofe@17870
   720
        val lhs = list_comb (Const (Sign.full_name thy (Sign.base_name cname),
berghofe@17870
   721
          constrT), l_args);
berghofe@17870
   722
        val rhs = list_comb (Const (cname, map fastype_of r_args ---> T'), r_args);
berghofe@17870
   723
        val def = Logic.mk_equals (lhs, Const (abs_name, T' --> T) $ rhs);
berghofe@17870
   724
        val eqn = HOLogic.mk_Trueprop (HOLogic.mk_eq
berghofe@17870
   725
          (Const (rep_name, T --> T') $ lhs, rhs));
berghofe@17870
   726
        val def_name = (Sign.base_name cname) ^ "_def";
berghofe@18366
   727
        val ([def_thm], thy') = thy |>
berghofe@17870
   728
          Theory.add_consts_i [(cname', constrT, mx)] |>
berghofe@17870
   729
          (PureThy.add_defs_i false o map Thm.no_attributes) [(def_name, def)]
berghofe@17870
   730
      in (thy', defs @ [def_thm], eqns @ [eqn]) end;
berghofe@17870
   731
berghofe@17870
   732
    fun dt_constr_defs ((thy, defs, eqns, dist_lemmas),
berghofe@17870
   733
        (((((_, (_, _, constrs)), tname), T), T'), constr_syntax)) =
berghofe@17870
   734
      let
berghofe@17870
   735
        val rep_const = cterm_of thy
berghofe@17870
   736
          (Const (Sign.intern_const thy ("Rep_" ^ tname), T --> T'));
berghofe@17870
   737
        val dist = standard (cterm_instantiate [(cterm_of thy distinct_f, rep_const)] distinct_lemma);
berghofe@17870
   738
        val (thy', defs', eqns') = Library.foldl (make_constr_def tname T T')
berghofe@17870
   739
          ((Theory.add_path tname thy, defs, []), constrs ~~ constr_syntax)
berghofe@17870
   740
      in
berghofe@17870
   741
        (parent_path flat_names thy', defs', eqns @ [eqns'], dist_lemmas @ [dist])
berghofe@17870
   742
      end;
berghofe@17870
   743
berghofe@17870
   744
    val (thy8, constr_defs, constr_rep_eqns, dist_lemmas) = Library.foldl dt_constr_defs
berghofe@17870
   745
      ((thy7, [], [], []), List.take (descr, length new_type_names) ~~
berghofe@17870
   746
        new_type_names ~~ newTs ~~ newTs' ~~ constr_syntax);
berghofe@17870
   747
berghofe@17870
   748
    val abs_inject_thms = map (fn tname =>
berghofe@17870
   749
      PureThy.get_thm thy8 (Name ("Abs_" ^ tname ^ "_inject"))) new_type_names;
berghofe@17870
   750
berghofe@17870
   751
    val rep_inject_thms = map (fn tname =>
berghofe@17870
   752
      PureThy.get_thm thy8 (Name ("Rep_" ^ tname ^ "_inject"))) new_type_names;
berghofe@17870
   753
berghofe@17870
   754
    val rep_thms = map (fn tname =>
berghofe@17870
   755
      PureThy.get_thm thy8 (Name ("Rep_" ^ tname))) new_type_names;
berghofe@17870
   756
berghofe@17870
   757
    val rep_inverse_thms = map (fn tname =>
berghofe@17870
   758
      PureThy.get_thm thy8 (Name ("Rep_" ^ tname ^ "_inverse"))) new_type_names;
berghofe@17870
   759
berghofe@17870
   760
    (* prove theorem  Rep_i (Constr_j ...) = Constr'_j ...  *)
berghofe@17870
   761
    
berghofe@17870
   762
    fun prove_constr_rep_thm eqn =
berghofe@17870
   763
      let
berghofe@17870
   764
        val inj_thms = map (fn r => r RS iffD1) abs_inject_thms;
berghofe@17870
   765
        val rewrites = constr_defs @ map mk_meta_eq rep_inverse_thms
berghofe@18010
   766
      in standard (Goal.prove thy8 [] [] eqn (fn _ => EVERY
berghofe@17870
   767
        [resolve_tac inj_thms 1,
berghofe@17870
   768
         rewrite_goals_tac rewrites,
berghofe@17870
   769
         rtac refl 3,
berghofe@17870
   770
         resolve_tac rep_intrs 2,
berghofe@18010
   771
         REPEAT (resolve_tac rep_thms 1)]))
berghofe@17870
   772
      end;
berghofe@17870
   773
berghofe@17870
   774
    val constr_rep_thmss = map (map prove_constr_rep_thm) constr_rep_eqns;
berghofe@17870
   775
berghofe@17870
   776
    (* prove theorem  pi \<bullet> Rep_i x = Rep_i (pi \<bullet> x) *)
berghofe@17870
   777
berghofe@17870
   778
    fun prove_perm_rep_perm (atom, perm_closed_thms) = map (fn th =>
berghofe@17870
   779
      let
berghofe@17870
   780
        val _ $ (_ $ (Rep $ x) $ _) = Logic.unvarify (prop_of th);
berghofe@17870
   781
        val Type ("fun", [T, U]) = fastype_of Rep;
berghofe@17870
   782
        val permT = mk_permT (Type (atom, []));
berghofe@17870
   783
        val pi = Free ("pi", permT);
berghofe@17870
   784
      in
berghofe@18010
   785
        standard (Goal.prove thy8 [] [] (HOLogic.mk_Trueprop (HOLogic.mk_eq
berghofe@17870
   786
            (Const ("nominal.perm", permT --> U --> U) $ pi $ (Rep $ x),
berghofe@18010
   787
             Rep $ (Const ("nominal.perm", permT --> T --> T) $ pi $ x))))
berghofe@18010
   788
          (fn _ => simp_tac (HOL_basic_ss addsimps (perm_defs @ Abs_inverse_thms @
berghofe@18010
   789
            perm_closed_thms @ Rep_thms)) 1))
berghofe@17870
   790
      end) Rep_thms;
berghofe@17870
   791
berghofe@17870
   792
    val perm_rep_perm_thms = List.concat (map prove_perm_rep_perm
berghofe@17870
   793
      (atoms ~~ perm_closed_thmss));
berghofe@17870
   794
berghofe@17870
   795
    (* prove distinctness theorems *)
berghofe@17870
   796
berghofe@18016
   797
    val distinct_props = setmp DatatypeProp.dtK 1000
berghofe@18016
   798
      (DatatypeProp.make_distincts new_type_names descr' sorts') thy8;
berghofe@17870
   799
berghofe@17870
   800
    val dist_rewrites = map (fn (rep_thms, dist_lemma) =>
berghofe@17870
   801
      dist_lemma::(rep_thms @ [In0_eq, In1_eq, In0_not_In1, In1_not_In0]))
berghofe@17870
   802
        (constr_rep_thmss ~~ dist_lemmas);
berghofe@17870
   803
berghofe@17870
   804
    fun prove_distinct_thms (_, []) = []
berghofe@17870
   805
      | prove_distinct_thms (p as (rep_thms, dist_lemma), t::ts) =
berghofe@17870
   806
          let
berghofe@18010
   807
            val dist_thm = standard (Goal.prove thy8 [] [] t (fn _ =>
berghofe@18010
   808
              simp_tac (simpset_of thy8 addsimps (dist_lemma :: rep_thms)) 1))
berghofe@17870
   809
          in dist_thm::(standard (dist_thm RS not_sym))::
berghofe@17870
   810
            (prove_distinct_thms (p, ts))
berghofe@17870
   811
          end;
berghofe@17870
   812
berghofe@17870
   813
    val distinct_thms = map prove_distinct_thms
berghofe@17870
   814
      (constr_rep_thmss ~~ dist_lemmas ~~ distinct_props);
berghofe@17870
   815
berghofe@17870
   816
    (** prove equations for permutation functions **)
berghofe@17870
   817
berghofe@17870
   818
    val abs_perm = PureThy.get_thms thy8 (Name "abs_perm"); (* FIXME *)
berghofe@17870
   819
berghofe@17870
   820
    val perm_simps' = map (fn (((i, (_, _, constrs)), tname), constr_rep_thms) =>
berghofe@17870
   821
      let val T = replace_types' (nth_dtyp i)
berghofe@17870
   822
      in List.concat (map (fn (atom, perm_closed_thms) =>
berghofe@17870
   823
          map (fn ((cname, dts), constr_rep_thm) => 
berghofe@17870
   824
        let
berghofe@17870
   825
          val cname = Sign.intern_const thy8
berghofe@17870
   826
            (NameSpace.append tname (Sign.base_name cname));
berghofe@17870
   827
          val permT = mk_permT (Type (atom, []));
berghofe@17870
   828
          val pi = Free ("pi", permT);
berghofe@17870
   829
berghofe@17870
   830
          fun perm t =
berghofe@17870
   831
            let val T = fastype_of t
berghofe@17870
   832
            in Const ("nominal.perm", permT --> T --> T) $ pi $ t end;
berghofe@17870
   833
berghofe@17870
   834
          fun constr_arg (dt, (j, l_args, r_args)) =
berghofe@17870
   835
            let
berghofe@17870
   836
              val x' = mk_Free "x" (typ_of_dtyp' dt) j;
berghofe@17870
   837
              val (dts, dt') = strip_option dt;
berghofe@17870
   838
              val Ts = map typ_of_dtyp' dts;
berghofe@17870
   839
              val xs = map (fn (T, i) => mk_Free "x" T i)
berghofe@17870
   840
                (Ts ~~ (j upto j + length dts - 1))
berghofe@17870
   841
              val x = mk_Free "x" (typ_of_dtyp' dt') (j + length dts);
berghofe@17870
   842
              val (dts', dt'') = strip_dtyp dt';
berghofe@18261
   843
            in
berghofe@18261
   844
              (j + length dts + 1,
berghofe@18261
   845
               xs @ x :: l_args,
berghofe@18261
   846
               map perm (xs @ [x]) @ r_args)
berghofe@17870
   847
            end
berghofe@17870
   848
berghofe@17870
   849
          val (_, l_args, r_args) = foldr constr_arg (1, [], []) dts;
berghofe@17870
   850
          val c = Const (cname, map fastype_of l_args ---> T)
berghofe@17870
   851
        in
berghofe@18010
   852
          standard (Goal.prove thy8 [] []
berghofe@17870
   853
            (HOLogic.mk_Trueprop (HOLogic.mk_eq
berghofe@18010
   854
              (perm (list_comb (c, l_args)), list_comb (c, r_args))))
berghofe@18010
   855
            (fn _ => EVERY
berghofe@17870
   856
              [simp_tac (simpset_of thy8 addsimps (constr_rep_thm :: perm_defs)) 1,
berghofe@17870
   857
               simp_tac (HOL_basic_ss addsimps (Rep_thms @ Abs_inverse_thms @
berghofe@17870
   858
                 constr_defs @ perm_closed_thms)) 1,
berghofe@17870
   859
               TRY (simp_tac (HOL_basic_ss addsimps
berghofe@17870
   860
                 (symmetric perm_fun_def :: abs_perm)) 1),
berghofe@17870
   861
               TRY (simp_tac (HOL_basic_ss addsimps
berghofe@17870
   862
                 (perm_fun_def :: perm_defs @ Rep_thms @ Abs_inverse_thms @
berghofe@18010
   863
                    perm_closed_thms)) 1)]))
berghofe@17870
   864
        end) (constrs ~~ constr_rep_thms)) (atoms ~~ perm_closed_thmss))
berghofe@17870
   865
      end) (List.take (descr, length new_type_names) ~~ new_type_names ~~ constr_rep_thmss);
berghofe@17870
   866
berghofe@17870
   867
    (** prove injectivity of constructors **)
berghofe@17870
   868
berghofe@17870
   869
    val rep_inject_thms' = map (fn th => th RS sym) rep_inject_thms;
berghofe@17870
   870
    val alpha = PureThy.get_thms thy8 (Name "alpha");
berghofe@17870
   871
    val abs_fresh = PureThy.get_thms thy8 (Name "abs_fresh");
berghofe@17870
   872
    val fresh_def = PureThy.get_thm thy8 (Name "fresh_def");
berghofe@17870
   873
    val supp_def = PureThy.get_thm thy8 (Name "supp_def");
berghofe@17870
   874
berghofe@17870
   875
    val inject_thms = map (fn (((i, (_, _, constrs)), tname), constr_rep_thms) =>
berghofe@17870
   876
      let val T = replace_types' (nth_dtyp i)
berghofe@17870
   877
      in List.mapPartial (fn ((cname, dts), constr_rep_thm) =>
berghofe@17870
   878
        if null dts then NONE else SOME
berghofe@17870
   879
        let
berghofe@17870
   880
          val cname = Sign.intern_const thy8
berghofe@17870
   881
            (NameSpace.append tname (Sign.base_name cname));
berghofe@17870
   882
berghofe@17870
   883
          fun make_inj (dt, (j, args1, args2, eqs)) =
berghofe@17870
   884
            let
berghofe@17870
   885
              val x' = mk_Free "x" (typ_of_dtyp' dt) j;
berghofe@17870
   886
              val y' = mk_Free "y" (typ_of_dtyp' dt) j;
berghofe@17870
   887
              val (dts, dt') = strip_option dt;
berghofe@17870
   888
              val Ts_idx = map typ_of_dtyp' dts ~~ (j upto j + length dts - 1);
berghofe@17870
   889
              val xs = map (fn (T, i) => mk_Free "x" T i) Ts_idx;
berghofe@17870
   890
              val ys = map (fn (T, i) => mk_Free "y" T i) Ts_idx;
berghofe@17870
   891
              val x = mk_Free "x" (typ_of_dtyp' dt') (j + length dts);
berghofe@17870
   892
              val y = mk_Free "y" (typ_of_dtyp' dt') (j + length dts);
berghofe@17870
   893
              val (dts', dt'') = strip_dtyp dt';
berghofe@18261
   894
            in
berghofe@18261
   895
              (j + length dts + 1,
berghofe@18261
   896
               xs @ (x :: args1), ys @ (y :: args2),
berghofe@18261
   897
               HOLogic.mk_eq
berghofe@18261
   898
                 (foldr mk_abs_fun x xs, foldr mk_abs_fun y ys) :: eqs)
berghofe@17870
   899
            end;
berghofe@17870
   900
berghofe@17870
   901
          val (_, args1, args2, eqs) = foldr make_inj (1, [], [], []) dts;
berghofe@17870
   902
          val Ts = map fastype_of args1;
berghofe@17870
   903
          val c = Const (cname, Ts ---> T)
berghofe@17870
   904
        in
berghofe@18010
   905
          standard (Goal.prove thy8 [] [] (HOLogic.mk_Trueprop (HOLogic.mk_eq
berghofe@17870
   906
              (HOLogic.mk_eq (list_comb (c, args1), list_comb (c, args2)),
berghofe@18010
   907
               foldr1 HOLogic.mk_conj eqs)))
berghofe@18010
   908
            (fn _ => EVERY
berghofe@17870
   909
               [asm_full_simp_tac (simpset_of thy8 addsimps (constr_rep_thm ::
berghofe@17870
   910
                  rep_inject_thms')) 1,
berghofe@17870
   911
                TRY (asm_full_simp_tac (HOL_basic_ss addsimps (fresh_def :: supp_def ::
berghofe@17870
   912
                  alpha @ abs_perm @ abs_fresh @ rep_inject_thms @
berghofe@17874
   913
                  perm_rep_perm_thms)) 1),
berghofe@17874
   914
                TRY (asm_full_simp_tac (HOL_basic_ss addsimps (perm_fun_def ::
berghofe@18010
   915
                  expand_fun_eq :: rep_inject_thms @ perm_rep_perm_thms)) 1)]))
berghofe@17870
   916
        end) (constrs ~~ constr_rep_thms)
berghofe@17870
   917
      end) (List.take (descr, length new_type_names) ~~ new_type_names ~~ constr_rep_thmss);
berghofe@17870
   918
berghofe@17872
   919
    (** equations for support and freshness **)
berghofe@17872
   920
berghofe@17872
   921
    val Un_assoc = PureThy.get_thm thy8 (Name "Un_assoc");
berghofe@17872
   922
    val de_Morgan_conj = PureThy.get_thm thy8 (Name "de_Morgan_conj");
berghofe@17872
   923
    val Collect_disj_eq = PureThy.get_thm thy8 (Name "Collect_disj_eq");
berghofe@17872
   924
    val finite_Un = PureThy.get_thm thy8 (Name "finite_Un");
berghofe@17872
   925
berghofe@17872
   926
    val (supp_thms, fresh_thms) = ListPair.unzip (map ListPair.unzip
berghofe@17872
   927
      (map (fn ((((i, (_, _, constrs)), tname), inject_thms'), perm_thms') =>
berghofe@17872
   928
      let val T = replace_types' (nth_dtyp i)
berghofe@17872
   929
      in List.concat (map (fn (cname, dts) => map (fn atom =>
berghofe@17872
   930
        let
berghofe@17872
   931
          val cname = Sign.intern_const thy8
berghofe@17872
   932
            (NameSpace.append tname (Sign.base_name cname));
berghofe@17872
   933
          val atomT = Type (atom, []);
berghofe@17872
   934
berghofe@17872
   935
          fun process_constr (dt, (j, args1, args2)) =
berghofe@17872
   936
            let
berghofe@17872
   937
              val x' = mk_Free "x" (typ_of_dtyp' dt) j;
berghofe@17872
   938
              val (dts, dt') = strip_option dt;
berghofe@17872
   939
              val Ts_idx = map typ_of_dtyp' dts ~~ (j upto j + length dts - 1);
berghofe@17872
   940
              val xs = map (fn (T, i) => mk_Free "x" T i) Ts_idx;
berghofe@17872
   941
              val x = mk_Free "x" (typ_of_dtyp' dt') (j + length dts);
berghofe@17872
   942
              val (dts', dt'') = strip_dtyp dt';
berghofe@18261
   943
            in
berghofe@18261
   944
              (j + length dts + 1,
berghofe@18261
   945
               xs @ (x :: args1), foldr mk_abs_fun x xs :: args2)
berghofe@17872
   946
            end;
berghofe@17872
   947
berghofe@17872
   948
          val (_, args1, args2) = foldr process_constr (1, [], []) dts;
berghofe@17872
   949
          val Ts = map fastype_of args1;
berghofe@17872
   950
          val c = list_comb (Const (cname, Ts ---> T), args1);
berghofe@17872
   951
          fun supp t =
berghofe@17872
   952
            Const ("nominal.supp", fastype_of t --> HOLogic.mk_setT atomT) $ t;
berghofe@17872
   953
          fun fresh t =
berghofe@17872
   954
            Const ("nominal.fresh", atomT --> fastype_of t --> HOLogic.boolT) $
berghofe@17872
   955
              Free ("a", atomT) $ t;
berghofe@18010
   956
          val supp_thm = standard (Goal.prove thy8 [] []
berghofe@17872
   957
              (HOLogic.mk_Trueprop (HOLogic.mk_eq
berghofe@17872
   958
                (supp c,
berghofe@17872
   959
                 if null dts then Const ("{}", HOLogic.mk_setT atomT)
berghofe@18010
   960
                 else foldr1 (HOLogic.mk_binop "op Un") (map supp args2))))
berghofe@17872
   961
            (fn _ =>
berghofe@18010
   962
              simp_tac (HOL_basic_ss addsimps (supp_def ::
berghofe@17872
   963
                 Un_assoc :: de_Morgan_conj :: Collect_disj_eq :: finite_Un ::
berghofe@17874
   964
                 symmetric empty_def :: Finites.emptyI :: simp_thms @
berghofe@18010
   965
                 abs_perm @ abs_fresh @ inject_thms' @ perm_thms')) 1))
berghofe@17872
   966
        in
berghofe@17872
   967
          (supp_thm,
berghofe@18010
   968
           standard (Goal.prove thy8 [] [] (HOLogic.mk_Trueprop (HOLogic.mk_eq
berghofe@17872
   969
              (fresh c,
berghofe@17872
   970
               if null dts then HOLogic.true_const
berghofe@18010
   971
               else foldr1 HOLogic.mk_conj (map fresh args2))))
berghofe@17872
   972
             (fn _ =>
berghofe@18010
   973
               simp_tac (simpset_of thy8 addsimps [fresh_def, supp_thm]) 1)))
berghofe@17872
   974
        end) atoms) constrs)
berghofe@17872
   975
      end) (List.take (descr, length new_type_names) ~~ new_type_names ~~ inject_thms ~~ perm_simps')));
berghofe@17872
   976
berghofe@18107
   977
    (**** weak induction theorem ****)
berghofe@18016
   978
berghofe@18107
   979
    val arities = get_arities descr'';
berghofe@18016
   980
berghofe@18016
   981
    fun mk_funs_inv thm =
berghofe@18016
   982
      let
berghofe@18016
   983
        val {sign, prop, ...} = rep_thm thm;
berghofe@18016
   984
        val _ $ (_ $ (Const (_, Type (_, [U, _])) $ _ $ S)) $
berghofe@18016
   985
          (_ $ (_ $ (r $ (a $ _)) $ _)) = Type.freeze prop;
berghofe@18016
   986
        val used = add_term_tfree_names (a, []);
berghofe@18016
   987
berghofe@18016
   988
        fun mk_thm i =
berghofe@18016
   989
          let
berghofe@18016
   990
            val Ts = map (TFree o rpair HOLogic.typeS)
berghofe@18016
   991
              (variantlist (replicate i "'t", used));
berghofe@18016
   992
            val f = Free ("f", Ts ---> U)
berghofe@18016
   993
          in standard (Goal.prove sign [] [] (Logic.mk_implies
berghofe@18016
   994
            (HOLogic.mk_Trueprop (HOLogic.list_all
berghofe@18016
   995
               (map (pair "x") Ts, HOLogic.mk_mem (app_bnds f i, S))),
berghofe@18016
   996
             HOLogic.mk_Trueprop (HOLogic.mk_eq (list_abs (map (pair "x") Ts,
berghofe@18016
   997
               r $ (a $ app_bnds f i)), f))))
berghofe@18016
   998
            (fn _ => EVERY [REPEAT (rtac ext 1), REPEAT (etac allE 1), rtac thm 1, atac 1]))
berghofe@18016
   999
          end
berghofe@18016
  1000
      in map (fn r => r RS subst) (thm :: map mk_thm arities) end;
berghofe@18016
  1001
berghofe@18016
  1002
    fun mk_indrule_lemma ((prems, concls), (((i, _), T), U)) =
berghofe@18016
  1003
      let
berghofe@18016
  1004
        val Rep_t = Const (List.nth (rep_names, i), T --> U) $
berghofe@18016
  1005
          mk_Free "x" T i;
berghofe@18016
  1006
berghofe@18016
  1007
        val Abs_t =  Const (List.nth (abs_names, i), U --> T)
berghofe@18016
  1008
berghofe@18016
  1009
      in (prems @ [HOLogic.imp $ HOLogic.mk_mem (Rep_t,
berghofe@18016
  1010
            Const (List.nth (rep_set_names, i), HOLogic.mk_setT U)) $
berghofe@18016
  1011
              (mk_Free "P" (T --> HOLogic.boolT) (i + 1) $ (Abs_t $ Rep_t))],
berghofe@18016
  1012
          concls @ [mk_Free "P" (T --> HOLogic.boolT) (i + 1) $ mk_Free "x" T i])
berghofe@18016
  1013
      end;
berghofe@18016
  1014
berghofe@18016
  1015
    val (indrule_lemma_prems, indrule_lemma_concls) =
berghofe@18107
  1016
      Library.foldl mk_indrule_lemma (([], []), (descr'' ~~ recTs ~~ recTs'));
berghofe@18016
  1017
berghofe@18016
  1018
    val indrule_lemma = standard (Goal.prove thy8 [] []
berghofe@18016
  1019
      (Logic.mk_implies
berghofe@18016
  1020
        (HOLogic.mk_Trueprop (mk_conj indrule_lemma_prems),
berghofe@18016
  1021
         HOLogic.mk_Trueprop (mk_conj indrule_lemma_concls))) (fn _ => EVERY
berghofe@18016
  1022
           [REPEAT (etac conjE 1),
berghofe@18016
  1023
            REPEAT (EVERY
berghofe@18016
  1024
              [TRY (rtac conjI 1), full_simp_tac (HOL_basic_ss addsimps Rep_inverse_thms) 1,
berghofe@18016
  1025
               etac mp 1, resolve_tac Rep_thms 1])]));
berghofe@18016
  1026
berghofe@18016
  1027
    val Ps = map head_of (HOLogic.dest_conj (HOLogic.dest_Trueprop (concl_of indrule_lemma)));
berghofe@18016
  1028
    val frees = if length Ps = 1 then [Free ("P", snd (dest_Var (hd Ps)))] else
berghofe@18016
  1029
      map (Free o apfst fst o dest_Var) Ps;
berghofe@18016
  1030
    val indrule_lemma' = cterm_instantiate
berghofe@18016
  1031
      (map (cterm_of thy8) Ps ~~ map (cterm_of thy8) frees) indrule_lemma;
berghofe@18016
  1032
berghofe@18016
  1033
    val Abs_inverse_thms' = List.concat (map mk_funs_inv Abs_inverse_thms);
berghofe@18016
  1034
berghofe@18016
  1035
    val dt_induct_prop = DatatypeProp.make_ind descr' sorts';
berghofe@18016
  1036
    val dt_induct = standard (Goal.prove thy8 []
berghofe@18016
  1037
      (Logic.strip_imp_prems dt_induct_prop) (Logic.strip_imp_concl dt_induct_prop)
berghofe@18016
  1038
      (fn prems => EVERY
berghofe@18016
  1039
        [rtac indrule_lemma' 1,
berghofe@18016
  1040
         (DatatypeAux.indtac rep_induct THEN_ALL_NEW ObjectLogic.atomize_tac) 1,
berghofe@18016
  1041
         EVERY (map (fn (prem, r) => (EVERY
berghofe@18016
  1042
           [REPEAT (eresolve_tac Abs_inverse_thms' 1),
berghofe@18016
  1043
            simp_tac (HOL_basic_ss addsimps [symmetric r]) 1,
berghofe@18016
  1044
            DEPTH_SOLVE_1 (ares_tac [prem] 1 ORELSE etac allE 1)]))
berghofe@18016
  1045
                (prems ~~ constr_defs))]));
berghofe@18016
  1046
berghofe@18107
  1047
    val case_names_induct = mk_case_names_induct descr'';
berghofe@18016
  1048
berghofe@18066
  1049
    (**** prove that new datatypes have finite support ****)
berghofe@18066
  1050
urbanc@18246
  1051
    val _ = warning "proving finite support for the new datatype";
urbanc@18246
  1052
berghofe@18066
  1053
    val indnames = DatatypeProp.make_tnames recTs;
berghofe@18066
  1054
berghofe@18066
  1055
    val abs_supp = PureThy.get_thms thy8 (Name "abs_supp");
urbanc@18067
  1056
    val supp_atm = PureThy.get_thms thy8 (Name "supp_atm");
berghofe@18066
  1057
berghofe@18066
  1058
    val finite_supp_thms = map (fn atom =>
berghofe@18066
  1059
      let val atomT = Type (atom, [])
berghofe@18066
  1060
      in map standard (List.take
berghofe@18066
  1061
        (split_conj_thm (Goal.prove thy8 [] [] (HOLogic.mk_Trueprop
berghofe@18066
  1062
           (foldr1 HOLogic.mk_conj (map (fn (s, T) => HOLogic.mk_mem
berghofe@18066
  1063
             (Const ("nominal.supp", T --> HOLogic.mk_setT atomT) $ Free (s, T),
berghofe@18066
  1064
              Const ("Finite_Set.Finites", HOLogic.mk_setT (HOLogic.mk_setT atomT))))
berghofe@18066
  1065
               (indnames ~~ recTs))))
berghofe@18066
  1066
           (fn _ => indtac dt_induct indnames 1 THEN
berghofe@18066
  1067
            ALLGOALS (asm_full_simp_tac (simpset_of thy8 addsimps
urbanc@18067
  1068
              (abs_supp @ supp_atm @
berghofe@18066
  1069
               PureThy.get_thms thy8 (Name ("fs_" ^ Sign.base_name atom ^ "1")) @
berghofe@18066
  1070
               List.concat supp_thms))))),
berghofe@18066
  1071
         length new_type_names))
berghofe@18066
  1072
      end) atoms;
berghofe@18066
  1073
berghofe@18658
  1074
    val simp_atts = replicate (length new_type_names) [Simplifier.simp_add_global];
berghofe@18658
  1075
berghofe@18658
  1076
    val (_, thy9) = thy8 |>
berghofe@18658
  1077
      Theory.add_path big_name |>
berghofe@18658
  1078
      PureThy.add_thms [(("induct_weak", dt_induct), [case_names_induct])] ||>>
berghofe@18658
  1079
      PureThy.add_thmss [(("inducts_weak", projections dt_induct), [case_names_induct])] ||>
berghofe@18658
  1080
      Theory.parent_path ||>>
berghofe@18658
  1081
      DatatypeAux.store_thmss_atts "distinct" new_type_names simp_atts distinct_thms ||>>
berghofe@18658
  1082
      DatatypeAux.store_thmss "constr_rep" new_type_names constr_rep_thmss ||>>
berghofe@18658
  1083
      DatatypeAux.store_thmss_atts "perm" new_type_names simp_atts perm_simps' ||>>
berghofe@18658
  1084
      DatatypeAux.store_thmss "inject" new_type_names inject_thms ||>>
berghofe@18658
  1085
      DatatypeAux.store_thmss "supp" new_type_names supp_thms ||>>
berghofe@18658
  1086
      DatatypeAux.store_thmss_atts "fresh" new_type_names simp_atts fresh_thms ||>
berghofe@18658
  1087
      fold (fn (atom, ths) => fn thy =>
berghofe@18658
  1088
        let val class = Sign.intern_class thy ("fs_" ^ Sign.base_name atom)
berghofe@18658
  1089
        in fold (fn T => AxClass.add_inst_arity_i
berghofe@18658
  1090
            (fst (dest_Type T),
berghofe@18658
  1091
              replicate (length sorts) [class], [class])
berghofe@18658
  1092
            (AxClass.intro_classes_tac [] THEN resolve_tac ths 1)) newTs thy
berghofe@18658
  1093
        end) (atoms ~~ finite_supp_thms);
berghofe@18658
  1094
berghofe@18107
  1095
    (**** strong induction theorem ****)
berghofe@18107
  1096
berghofe@18107
  1097
    val pnames = if length descr'' = 1 then ["P"]
berghofe@18107
  1098
      else map (fn i => "P" ^ string_of_int i) (1 upto length descr'');
berghofe@18245
  1099
    val ind_sort = if null dt_atomTs then HOLogic.typeS
berghofe@18658
  1100
      else norm_sort thy9 (map (fn T => Sign.intern_class thy9 ("fs_" ^
berghofe@18658
  1101
        Sign.base_name (fst (dest_Type T)))) dt_atomTs);
berghofe@18107
  1102
    val fsT = TFree ("'n", ind_sort);
berghofe@18658
  1103
    val fsT' = TFree ("'n", HOLogic.typeS);
berghofe@18107
  1104
berghofe@18658
  1105
    val fresh_fs = map (fn (s, T) => (T, Free (s, fsT' --> HOLogic.mk_setT T)))
berghofe@18658
  1106
      (DatatypeProp.indexify_names (replicate (length dt_atomTs) "f") ~~ dt_atomTs);
berghofe@18658
  1107
berghofe@18658
  1108
    fun make_pred fsT i T =
berghofe@18302
  1109
      Free (List.nth (pnames, i), fsT --> T --> HOLogic.boolT);
berghofe@18107
  1110
berghofe@18658
  1111
    fun make_ind_prem fsT f k T ((cname, cargs), idxs) =
berghofe@18107
  1112
      let
berghofe@18107
  1113
        val recs = List.filter is_rec_type cargs;
berghofe@18107
  1114
        val Ts = map (typ_of_dtyp descr'' sorts') cargs;
berghofe@18107
  1115
        val recTs' = map (typ_of_dtyp descr'' sorts') recs;
berghofe@18107
  1116
        val tnames = variantlist (DatatypeProp.make_tnames Ts, pnames);
berghofe@18107
  1117
        val rec_tnames = map fst (List.filter (is_rec_type o snd) (tnames ~~ cargs));
berghofe@18107
  1118
        val frees = tnames ~~ Ts;
berghofe@18107
  1119
        val z = (variant tnames "z", fsT);
berghofe@18107
  1120
berghofe@18107
  1121
        fun mk_prem ((dt, s), T) =
berghofe@18107
  1122
          let
berghofe@18107
  1123
            val (Us, U) = strip_type T;
berghofe@18107
  1124
            val l = length Us
berghofe@18107
  1125
          in list_all (z :: map (pair "x") Us, HOLogic.mk_Trueprop
berghofe@18658
  1126
            (make_pred fsT (body_index dt) U $ Bound l $ app_bnds (Free (s, T)) l))
berghofe@18107
  1127
          end;
berghofe@18107
  1128
berghofe@18107
  1129
        val prems = map mk_prem (recs ~~ rec_tnames ~~ recTs');
berghofe@18107
  1130
        val prems' = map (fn p as (_, T) => HOLogic.mk_Trueprop
berghofe@18658
  1131
            (f T (Free p) (Free z)))
berghofe@18107
  1132
          (map (curry List.nth frees) (List.concat (map (fn (m, n) =>
berghofe@18107
  1133
             m upto m + n - 1) idxs)))
berghofe@18107
  1134
berghofe@18302
  1135
      in list_all_free (frees @ [z], Logic.list_implies (prems' @ prems,
berghofe@18658
  1136
        HOLogic.mk_Trueprop (make_pred fsT k T $ Free z $
berghofe@18302
  1137
          list_comb (Const (cname, Ts ---> T), map Free frees))))
berghofe@18107
  1138
      end;
berghofe@18107
  1139
berghofe@18107
  1140
    val ind_prems = List.concat (map (fn (((i, (_, _, constrs)), (_, idxss)), T) =>
berghofe@18658
  1141
      map (make_ind_prem fsT (fn T => fn t => fn u =>
berghofe@18658
  1142
        Const ("nominal.fresh", T --> fsT --> HOLogic.boolT) $ t $ u) i T)
berghofe@18658
  1143
          (constrs ~~ idxss)) (descr'' ~~ ndescr ~~ recTs));
berghofe@18107
  1144
    val tnames = DatatypeProp.make_tnames recTs;
berghofe@18658
  1145
    val zs = variantlist (replicate (length descr'') "z", tnames);
berghofe@18107
  1146
    val ind_concl = HOLogic.mk_Trueprop (foldr1 (HOLogic.mk_binop "op &")
berghofe@18658
  1147
      (map (fn ((((i, _), T), tname), z) =>
berghofe@18658
  1148
        make_pred fsT i T $ Free (z, fsT) $ Free (tname, T))
berghofe@18658
  1149
        (descr'' ~~ recTs ~~ tnames ~~ zs)));
berghofe@18107
  1150
    val induct = Logic.list_implies (ind_prems, ind_concl);
berghofe@18107
  1151
berghofe@18658
  1152
    val ind_prems' =
berghofe@18658
  1153
      map (fn (_, f as Free (_, T)) => list_all_free ([("x", fsT')],
berghofe@18658
  1154
        HOLogic.mk_Trueprop (HOLogic.mk_mem (f $ Free ("x", fsT'),
berghofe@18658
  1155
          Const ("Finite_Set.Finites", HOLogic.mk_setT (body_type T)))))) fresh_fs @
berghofe@18658
  1156
      List.concat (map (fn (((i, (_, _, constrs)), (_, idxss)), T) =>
berghofe@18658
  1157
        map (make_ind_prem fsT' (fn T => fn t => fn u => HOLogic.Not $
berghofe@18658
  1158
          HOLogic.mk_mem (t, the (AList.lookup op = fresh_fs T) $ u)) i T)
berghofe@18658
  1159
            (constrs ~~ idxss)) (descr'' ~~ ndescr ~~ recTs));
berghofe@18658
  1160
    val ind_concl' = HOLogic.mk_Trueprop (foldr1 (HOLogic.mk_binop "op &")
berghofe@18658
  1161
      (map (fn ((((i, _), T), tname), z) =>
berghofe@18658
  1162
        make_pred fsT' i T $ Free (z, fsT') $ Free (tname, T))
berghofe@18658
  1163
        (descr'' ~~ recTs ~~ tnames ~~ zs)));
berghofe@18658
  1164
    val induct' = Logic.list_implies (ind_prems', ind_concl');
berghofe@18658
  1165
berghofe@18658
  1166
    fun mk_perm Ts (t, u) =
berghofe@18658
  1167
      let
berghofe@18658
  1168
        val T = fastype_of1 (Ts, t);
berghofe@18658
  1169
        val U = fastype_of1 (Ts, u)
berghofe@18658
  1170
      in Const ("nominal.perm", T --> U --> U) $ t $ u end;
berghofe@18658
  1171
berghofe@18658
  1172
    val aux_ind_vars =
berghofe@18658
  1173
      (DatatypeProp.indexify_names (replicate (length dt_atomTs) "pi") ~~
berghofe@18658
  1174
       map mk_permT dt_atomTs) @ [("z", fsT')];
berghofe@18658
  1175
    val aux_ind_Ts = rev (map snd aux_ind_vars);
berghofe@18658
  1176
    val aux_ind_concl = HOLogic.mk_Trueprop (foldr1 (HOLogic.mk_binop "op &")
berghofe@18658
  1177
      (map (fn (((i, _), T), tname) =>
berghofe@18658
  1178
        HOLogic.list_all (aux_ind_vars, make_pred fsT' i T $ Bound 0 $
berghofe@18658
  1179
          foldr (mk_perm aux_ind_Ts) (Free (tname, T))
berghofe@18658
  1180
            (map Bound (length dt_atomTs downto 1))))
berghofe@18658
  1181
        (descr'' ~~ recTs ~~ tnames)));
berghofe@18658
  1182
berghofe@18658
  1183
    fun mk_ind_perm i k p l vs j =
berghofe@18658
  1184
      let
berghofe@18658
  1185
        val n = length vs;
berghofe@18658
  1186
        val Ts = map snd vs;
berghofe@18658
  1187
        val T = List.nth (Ts, i - j);
berghofe@18658
  1188
        val pT = NominalAtoms.mk_permT T
berghofe@18658
  1189
      in
berghofe@18658
  1190
        Const ("List.list.Cons", HOLogic.mk_prodT (T, T) --> pT --> pT) $
berghofe@18658
  1191
          (HOLogic.pair_const T T $ Bound (l - j) $ foldr (mk_perm Ts)
berghofe@18658
  1192
            (Bound (i - j))
berghofe@18658
  1193
            (map (mk_ind_perm i k p l vs) (j - 1 downto 0) @
berghofe@18658
  1194
             map Bound (n - k - 1 downto n - k - p))) $
berghofe@18658
  1195
          Const ("List.list.Nil", pT)
berghofe@18658
  1196
      end;
berghofe@18658
  1197
berghofe@18658
  1198
    fun mk_fresh i i' j k p l vs _ _ =
berghofe@18658
  1199
      let
berghofe@18658
  1200
        val n = length vs;
berghofe@18658
  1201
        val Ts = map snd vs;
berghofe@18658
  1202
        val T = List.nth (Ts, n - i - 1 - j);
berghofe@18658
  1203
        val f = the (AList.lookup op = fresh_fs T);
berghofe@18658
  1204
        val U = List.nth (Ts, n - i' - 1);
berghofe@18658
  1205
        val S = HOLogic.mk_setT T;
berghofe@18658
  1206
        val prms = map (mk_ind_perm (n - i) k p (n - l) (("a", T) :: vs))
berghofe@18658
  1207
            (j - 1 downto 0) @
berghofe@18658
  1208
          map Bound (n - k downto n - k - p + 1)
berghofe@18658
  1209
      in
berghofe@18658
  1210
        HOLogic.mk_Trueprop (Const ("Ex", (T --> HOLogic.boolT) --> HOLogic.boolT) $
berghofe@18658
  1211
          Abs ("a", T, HOLogic.Not $
berghofe@18658
  1212
            (Const ("op :", T --> S --> HOLogic.boolT) $ Bound 0 $
berghofe@18658
  1213
              (Const ("insert", T --> S --> S) $
berghofe@18658
  1214
                (foldr (mk_perm (T :: Ts)) (Bound (n - i - j)) prms) $
berghofe@18658
  1215
                (Const ("op Un", S --> S --> S) $ (f $ Bound (n - k - p)) $
berghofe@18658
  1216
                   (Const ("nominal.supp", U --> S) $
berghofe@18658
  1217
                     foldr (mk_perm (T :: Ts)) (Bound (n - i')) prms))))))
berghofe@18658
  1218
      end;
urbanc@18104
  1219
berghofe@18658
  1220
    fun mk_fresh_constr is p vs _ concl =
berghofe@18658
  1221
      let
berghofe@18658
  1222
        val n = length vs;
berghofe@18658
  1223
        val Ts = map snd vs;
berghofe@18658
  1224
        val _ $ (_ $ _ $ t) = concl;
berghofe@18658
  1225
        val c = head_of t;
berghofe@18658
  1226
        val T = body_type (fastype_of c);
berghofe@18658
  1227
        val k = foldr op + 0 (map (fn (_, i) => i + 1) is);
berghofe@18658
  1228
        val ps = map Bound (n - k - 1 downto n - k - p);
berghofe@18658
  1229
        val (_, _, ts, us) = foldl (fn ((_, i), (m, n, ts, us)) =>
berghofe@18658
  1230
          (m - i - 1, n - i,
berghofe@18658
  1231
           ts @ map Bound (n downto n - i + 1) @
berghofe@18658
  1232
             [foldr (mk_perm Ts) (Bound (m - i))
berghofe@18658
  1233
                (map (mk_ind_perm m k p n vs) (i - 1 downto 0) @ ps)],
berghofe@18658
  1234
           us @ map (fn j => foldr (mk_perm Ts) (Bound j) ps) (m downto m - i)))
berghofe@18658
  1235
          (n - 1, n - k - p - 2, [], []) is
berghofe@18658
  1236
      in
berghofe@18658
  1237
        HOLogic.mk_Trueprop (HOLogic.eq_const T $ list_comb (c, ts) $ list_comb (c, us))
berghofe@18658
  1238
      end;
berghofe@18658
  1239
berghofe@18658
  1240
    val abs_fun_finite_supp = PureThy.get_thm thy9 (Name "abs_fun_finite_supp");
berghofe@18658
  1241
berghofe@18658
  1242
    val at_finite_select = PureThy.get_thm thy9 (Name "at_finite_select");
berghofe@18658
  1243
berghofe@18658
  1244
    val induct_aux_lemmas = List.concat (map (fn Type (s, _) =>
berghofe@18658
  1245
      [PureThy.get_thm thy9 (Name ("pt_" ^ Sign.base_name s ^ "_inst")),
berghofe@18658
  1246
       PureThy.get_thm thy9 (Name ("fs_" ^ Sign.base_name s ^ "1")),
berghofe@18658
  1247
       PureThy.get_thm thy9 (Name ("at_" ^ Sign.base_name s ^ "_inst"))]) dt_atomTs);
berghofe@18658
  1248
berghofe@18658
  1249
    val induct_aux_lemmas' = map (fn Type (s, _) =>
berghofe@18658
  1250
      PureThy.get_thm thy9 (Name ("pt_" ^ Sign.base_name s ^ "2")) RS sym) dt_atomTs;
berghofe@18658
  1251
berghofe@18658
  1252
    val induct_aux = standard (Goal.prove thy9 [] ind_prems' ind_concl'
berghofe@18658
  1253
      (fn prems => EVERY
berghofe@18658
  1254
        ([mk_subgoal 1 (K (K (K aux_ind_concl))),
berghofe@18658
  1255
          indtac dt_induct tnames 1] @
berghofe@18658
  1256
         List.concat (map (fn ((_, (_, _, constrs)), (_, constrs')) =>
berghofe@18658
  1257
           List.concat (map (fn ((cname, cargs), is) =>
berghofe@18658
  1258
             [simp_tac (HOL_basic_ss addsimps List.concat perm_simps') 1,
berghofe@18658
  1259
              REPEAT (rtac allI 1)] @
berghofe@18658
  1260
             List.concat (map
berghofe@18658
  1261
               (fn ((_, 0), _) => []
berghofe@18658
  1262
                 | ((i, j), k) => List.concat (map (fn j' =>
berghofe@18658
  1263
                     let
berghofe@18658
  1264
                       val DtType (tname, _) = List.nth (cargs, i + j');
berghofe@18658
  1265
                       val atom = Sign.base_name tname
berghofe@18658
  1266
                     in
berghofe@18658
  1267
                       [mk_subgoal 1 (mk_fresh i (i + j) j'
berghofe@18658
  1268
                          (length cargs) (length dt_atomTs)
berghofe@18658
  1269
                          (length cargs + length dt_atomTs + 1 + i - k)),
berghofe@18658
  1270
                        rtac at_finite_select 1,
berghofe@18658
  1271
                        rtac (PureThy.get_thm thy9 (Name ("at_" ^ atom ^ "_inst"))) 1,
berghofe@18658
  1272
                        asm_full_simp_tac (simpset_of thy9 addsimps
berghofe@18658
  1273
                          [PureThy.get_thm thy9 (Name ("fs_" ^ atom ^ "1"))]) 1,
berghofe@18658
  1274
                        resolve_tac prems 1,
berghofe@18658
  1275
                        etac exE 1,
berghofe@18658
  1276
                        asm_full_simp_tac (simpset_of thy9 addsimps
berghofe@18658
  1277
                          [symmetric fresh_def]) 1]
berghofe@18658
  1278
                     end) (0 upto j - 1))) (is ~~ (0 upto length is - 1))) @
berghofe@18658
  1279
             (if exists (not o equal 0 o snd) is then
berghofe@18658
  1280
                [mk_subgoal 1 (mk_fresh_constr is (length dt_atomTs)),
berghofe@18658
  1281
                 asm_full_simp_tac (simpset_of thy9 addsimps
berghofe@18658
  1282
                   (List.concat inject_thms @
berghofe@18658
  1283
                    alpha @ abs_perm @ abs_fresh @ [abs_fun_finite_supp] @
berghofe@18658
  1284
                    induct_aux_lemmas)) 1,
berghofe@18658
  1285
                 dtac sym 1,
berghofe@18658
  1286
                 asm_full_simp_tac (simpset_of thy9
berghofe@18658
  1287
                   addsimps induct_aux_lemmas'
berghofe@18658
  1288
                   addsimprocs [perm_simproc]) 1,
berghofe@18658
  1289
                 REPEAT (etac conjE 1)]
berghofe@18658
  1290
              else
berghofe@18658
  1291
                []) @
berghofe@18658
  1292
             [(resolve_tac prems THEN_ALL_NEW
berghofe@18658
  1293
                (atac ORELSE' ((REPEAT o etac allE) THEN' atac))) 1])
berghofe@18658
  1294
               (constrs ~~ constrs'))) (descr'' ~~ ndescr)) @
berghofe@18658
  1295
         [REPEAT (eresolve_tac [conjE, allE_Nil] 1),
berghofe@18658
  1296
          REPEAT (etac allE 1),
berghofe@18658
  1297
          REPEAT (TRY (rtac conjI 1) THEN asm_full_simp_tac (simpset_of thy9) 1)])));
berghofe@18658
  1298
berghofe@18658
  1299
    val induct_aux' = Thm.instantiate ([],
berghofe@18658
  1300
      map (fn (s, T) =>
berghofe@18658
  1301
        let val pT = TVar (("'n", 0), HOLogic.typeS) --> T --> HOLogic.boolT
berghofe@18658
  1302
        in (cterm_of thy9 (Var ((s, 0), pT)), cterm_of thy9 (Free (s, pT))) end)
berghofe@18658
  1303
          (pnames ~~ recTs) @
berghofe@18658
  1304
      map (fn (_, f) =>
berghofe@18658
  1305
        let val f' = Logic.varify f
berghofe@18658
  1306
        in (cterm_of thy9 f',
berghofe@18658
  1307
          cterm_of thy9 (Const ("nominal.supp", fastype_of f')))
berghofe@18658
  1308
        end) fresh_fs) induct_aux;
berghofe@18658
  1309
berghofe@18658
  1310
    val induct = standard (Goal.prove thy9 [] ind_prems ind_concl
berghofe@18658
  1311
      (fn prems => EVERY
berghofe@18658
  1312
         [rtac induct_aux' 1,
berghofe@18658
  1313
          REPEAT (resolve_tac induct_aux_lemmas 1),
berghofe@18658
  1314
          REPEAT ((resolve_tac prems THEN_ALL_NEW
berghofe@18658
  1315
            (etac meta_spec ORELSE' full_simp_tac (HOL_basic_ss addsimps [fresh_def]))) 1)]))
berghofe@18658
  1316
berghofe@18658
  1317
    val (_, thy10) = thy9 |>
berghofe@18016
  1318
      Theory.add_path big_name |>
berghofe@18658
  1319
      PureThy.add_thms [(("induct'", induct_aux), [])] ||>>
berghofe@18658
  1320
      PureThy.add_thms [(("induct", induct), [case_names_induct])] ||>>
berghofe@18658
  1321
      PureThy.add_thmss [(("inducts", projections induct), [case_names_induct])] ||>
berghofe@18658
  1322
      Theory.parent_path;
berghofe@18658
  1323
berghofe@17870
  1324
  in
wenzelm@18582
  1325
    thy10
berghofe@17870
  1326
  end;
berghofe@17870
  1327
berghofe@17870
  1328
val add_nominal_datatype = gen_add_nominal_datatype read_typ true;
berghofe@17870
  1329
berghofe@17870
  1330
berghofe@17870
  1331
(* FIXME: The following stuff should be exported by DatatypePackage *)
berghofe@17870
  1332
berghofe@17870
  1333
local structure P = OuterParse and K = OuterKeyword in
berghofe@17870
  1334
berghofe@17870
  1335
val datatype_decl =
berghofe@17870
  1336
  Scan.option (P.$$$ "(" |-- P.name --| P.$$$ ")") -- P.type_args -- P.name -- P.opt_infix --
berghofe@17870
  1337
    (P.$$$ "=" |-- P.enum1 "|" (P.name -- Scan.repeat P.typ -- P.opt_mixfix));
berghofe@17870
  1338
berghofe@17870
  1339
fun mk_datatype args =
berghofe@17870
  1340
  let
berghofe@17870
  1341
    val names = map (fn ((((NONE, _), t), _), _) => t | ((((SOME t, _), _), _), _) => t) args;
berghofe@17870
  1342
    val specs = map (fn ((((_, vs), t), mx), cons) =>
berghofe@17870
  1343
      (vs, t, mx, map (fn ((x, y), z) => (x, y, z)) cons)) args;
berghofe@18068
  1344
  in add_nominal_datatype false names specs end;
berghofe@17870
  1345
berghofe@17870
  1346
val nominal_datatypeP =
berghofe@17870
  1347
  OuterSyntax.command "nominal_datatype" "define inductive datatypes" K.thy_decl
berghofe@17870
  1348
    (P.and_list1 datatype_decl >> (Toplevel.theory o mk_datatype));
berghofe@17870
  1349
berghofe@17870
  1350
val _ = OuterSyntax.add_parsers [nominal_datatypeP];
berghofe@17870
  1351
berghofe@17870
  1352
end;
berghofe@17870
  1353
berghofe@18261
  1354
end
berghofe@18261
  1355