diff -r 8aff3f3ce47f -r 45a69c9cc4cc Nominal/NewAlpha.thy
--- a/Nominal/NewAlpha.thy	Sun May 23 02:15:24 2010 +0100
+++ b/Nominal/NewAlpha.thy	Mon May 24 20:02:37 2010 +0100
@@ -1,236 +1,231 @@
 theory NewAlpha
-imports "Abs" "Perm" "Nominal2_FSet"
-uses ("nominal_dt_rawperm.ML")
-     ("nominal_dt_rawfuns.ML")
+imports "Abs" "Perm"
 begin
 
-use "nominal_dt_rawperm.ML"
-use "nominal_dt_rawfuns.ML"
-
 ML {*
-open Nominal_Dt_RawPerm
-open Nominal_Dt_RawFuns
-*}
-
-
-ML {*
-fun mk_binop2 ctxt s (l, r) =
-  Syntax.check_term ctxt (Const (s, dummyT) $ l $ r)
+fun mk_prod_fv (t1, t2) =
+let
+  val ty1 = fastype_of t1
+  val ty2 = fastype_of t2 
+  val resT = HOLogic.mk_prodT (domain_type ty1, domain_type ty2) --> @{typ "atom set"}
+in
+  Const (@{const_name "prod_fv"}, [ty1, ty2] ---> resT) $ t1 $ t2
+end
 *}
 
 ML {*
-fun mk_compound_fv' ctxt = foldr1 (mk_binop2 ctxt @{const_name prod_fv})
-fun mk_compound_alpha' ctxt = foldr1 (mk_binop2 ctxt @{const_name prod_rel})
+fun mk_prod_alpha (t1, t2) =
+let
+  val ty1 = fastype_of t1
+  val ty2 = fastype_of t2 
+  val prodT = HOLogic.mk_prodT (domain_type ty1, domain_type ty2)
+  val resT = [prodT, prodT] ---> @{typ "bool"}
+in
+  Const (@{const_name "prod_alpha"}, [ty1, ty2] ---> resT) $ t1 $ t2
+end
 *}
 
 ML {*
-fun alpha_bm_lsts lthy dt_descr sorts dts args args2 alpha_frees fv_frees
-  bn_alphabn alpha_const binds bodys =
+fun mk_binders lthy bmode args bodies = 
+let  
+  fun bind_set lthy args (NONE, i) = setify lthy (nth args i)
+    | bind_set _ args (SOME bn, i) = bn $ (nth args i)
+  fun bind_lst lthy args (NONE, i) = listify lthy (nth args i)
+    | bind_lst _ args (SOME bn, i) = bn $ (nth args i)
+
+  val (connect_fn, bind_fn) =
+    case bmode of
+      Lst => (mk_append, bind_lst) 
+    | Set => (mk_union,  bind_set)
+    | Res => (mk_union,  bind_set)
+in
+  foldl1 connect_fn (map (bind_fn lthy args) bodies)
+end
+*}
+
+ML {* 
+fun mk_alpha_prem bmode fv alpha args args' binders binders' =
 let
-  fun bind_set args (NONE, no) = setify lthy (nth args no)
-    | bind_set args (SOME f, no) = f $ (nth args no)
-  fun bind_lst args (NONE, no) = listify lthy (nth args no)
-    | bind_lst args (SOME f, no) = f $ (nth args no)
-  fun append (t1, t2) =
-    Const(@{const_name append}, @{typ "atom list \<Rightarrow> atom list \<Rightarrow> atom list"}) $ t1 $ t2;
-  fun binds_fn args nos =
-    if alpha_const = @{const_name alpha_lst}
-    then foldr1 append (map (bind_lst args) nos)
-    else fold_union (map (bind_set args) nos);
-  val lhs_binds = binds_fn args binds;
-  val rhs_binds = binds_fn args2 binds;
-  val lhs_bodys = foldr1 HOLogic.mk_prod (map (nth args) bodys);
-  val rhs_bodys = foldr1 HOLogic.mk_prod (map (nth args2) bodys);
-  val lhs = HOLogic.mk_prod (lhs_binds, lhs_bodys);
-  val rhs = HOLogic.mk_prod (rhs_binds, rhs_bodys);
-  val body_dts = map (nth dts) bodys;
-  fun fv_for_dt dt =
-    if Datatype_Aux.is_rec_type dt
-    then nth fv_frees (Datatype_Aux.body_index dt)
-    else Const (@{const_name supp},
-      Datatype_Aux.typ_of_dtyp dt_descr sorts dt --> @{typ "atom set"})
-  val fvs = map fv_for_dt body_dts;
-  val fv = mk_compound_fv' lthy fvs;
-  fun alpha_for_dt dt =
-    if Datatype_Aux.is_rec_type dt
-    then nth alpha_frees (Datatype_Aux.body_index dt)
-    else Const (@{const_name "op ="},
-      Datatype_Aux.typ_of_dtyp dt_descr sorts dt -->
-      Datatype_Aux.typ_of_dtyp dt_descr sorts dt --> @{typ bool})
-  val alphas = map alpha_for_dt body_dts;
-  val alpha = mk_compound_alpha' lthy alphas;
-  val alpha_gen_pre = Const (alpha_const, dummyT) $ lhs $ alpha $ fv $ (Bound 0) $ rhs
-  val alpha_gen_ex = HOLogic.exists_const @{typ perm} $ Abs ("p", @{typ perm}, alpha_gen_pre)
-  val t = Syntax.check_term lthy alpha_gen_ex
-  fun alpha_bn_bind (SOME bn, i) =
-      if member (op =) bodys i then NONE
-      else SOME ((the (AList.lookup (op=) bn_alphabn bn)) $ nth args i $ nth args2 i)
-    | alpha_bn_bind (NONE, _) = NONE
+  val (alpha_name, binder_ty) = 
+    case bmode of
+      Lst => (@{const_name "alpha_lst"}, @{typ "atom list"})
+    | Set => (@{const_name "alpha_gen"}, @{typ "atom set"})
+    | Res => (@{const_name "alpha_res"}, @{typ "atom set"})
+  val ty = fastype_of args
+  val pair_ty = HOLogic.mk_prodT (binder_ty, ty)
+  val alpha_ty = [ty, ty] ---> @{typ "bool"}
+  val fv_ty = ty --> @{typ "atom set"}
 in
-  t :: (map_filter alpha_bn_bind binds)
+  HOLogic.exists_const @{typ perm} $ Abs ("p", @{typ perm},
+    Const (alpha_name, [pair_ty, alpha_ty, fv_ty, @{typ "perm"}, pair_ty] ---> @{typ bool}) 
+      $ HOLogic.mk_prod (binders, args) $ alpha $ fv $ (Bound 0) $ HOLogic.mk_prod (binders', args'))
 end
 *}
 
 ML {*
-fun alpha_bn_bm lthy dt_descr sorts dts args args2 alpha_frees fv_frees bn_alphabn args_in_bn bm =
-case bm of
-  BC (_, [], [i]) =>
-    let
-      val arg = nth args i;
-      val arg2 = nth args2 i;
-      val dt = nth dts i;
-    in
-      case AList.lookup (op=) args_in_bn i of
-        NONE => if Datatype_Aux.is_rec_type dt
-                then [(nth alpha_frees (Datatype_Aux.body_index dt)) $ arg $ arg2]
-                else [HOLogic.mk_eq (arg, arg2)]
-      | SOME (SOME (f : term)) => [(the (AList.lookup (op=) bn_alphabn f)) $ arg $ arg2]
-      | SOME NONE => []
-    end
-| BC (Lst, x, y) => alpha_bm_lsts lthy dt_descr sorts dts args args2 alpha_frees
-    fv_frees bn_alphabn @{const_name alpha_lst} x y
-| BC (Set, x, y) => alpha_bm_lsts lthy dt_descr sorts dts args args2 alpha_frees
-    fv_frees bn_alphabn @{const_name alpha_gen} x y
-| BC (Res, x, y) => alpha_bm_lsts lthy dt_descr sorts dts args args2 alpha_frees
-    fv_frees bn_alphabn @{const_name alpha_res} x y
+fun mk_alpha_bn_prem alpha_bn_map args args' bodies binder = 
+  case binder of
+    (NONE, i) => []
+  | (SOME bn, i) =>
+     if member (op=) bodies i
+     then [] 
+     else [the (AList.lookup (op=) alpha_bn_map bn) $ (nth args i) $ (nth args' i)]
 *}
 
-
 ML {*
-fun alpha_bn lthy dt_descr sorts alpha_frees fv_frees bn_alphabn bclausess
-  (alphabn, (_, ith_dtyp, args_in_bns)) =
+fun mk_alpha_prems lthy alpha_map alpha_bn_map is_rec (args, args') bclause =
 let
-  fun alpha_bn_constr (cname, dts) (args_in_bn, bclauses) =
-  let
-    val Ts = map (Datatype_Aux.typ_of_dtyp dt_descr sorts) dts;
-    val names = Datatype_Prop.make_tnames Ts;
-    val names2 = Name.variant_list names (Datatype_Prop.make_tnames Ts);
-    val args = map Free (names ~~ Ts);
-    val args2 = map Free (names2 ~~ Ts);
-    val c = Const (cname, Ts ---> (nth_dtyp dt_descr sorts ith_dtyp));
-    val alpha_bn_bm = alpha_bn_bm lthy dt_descr sorts dts args args2 alpha_frees
-      fv_frees bn_alphabn args_in_bn;
-    val rhs = HOLogic.mk_Trueprop
-      (alphabn $ (list_comb (c, args)) $ (list_comb (c, args2)));
-    val lhss = map HOLogic.mk_Trueprop (flat (map alpha_bn_bm bclauses))
-  in
-    Library.foldr Logic.mk_implies (lhss, rhs)
-  end;
-  val (_, (_, _, constrs)) = nth dt_descr ith_dtyp;
+  fun mk_frees i =
+    let
+      val arg = nth args i
+      val arg' = nth args' i
+      val ty = fastype_of arg
+    in
+      if nth is_rec i
+      then fst (the (AList.lookup (op=) alpha_map ty)) $ arg $ arg'
+      else HOLogic.mk_eq (arg, arg')
+    end
+  fun mk_alpha_fv i = 
+    let
+      val ty = fastype_of (nth args i)
+    in
+      case AList.lookup (op=) alpha_map ty of
+        NONE => (HOLogic.eq_const ty, supp_const ty) 
+      | SOME (alpha, fv) => (alpha, fv) 
+    end
+  
 in
-  map2 alpha_bn_constr constrs (args_in_bns ~~ bclausess)
+  case bclause of
+    BC (_, [], bodies) => map (HOLogic.mk_Trueprop o mk_frees) bodies 
+  | BC (bmode, binders, bodies) => 
+    let
+      val (alphas, fvs) = split_list (map mk_alpha_fv bodies)
+      val comp_fv = foldl1 mk_prod_fv fvs
+      val comp_alpha = foldl1 mk_prod_alpha alphas
+      val comp_args = foldl1 HOLogic.mk_prod (map (nth args) bodies)
+      val comp_args' = foldl1 HOLogic.mk_prod (map (nth args') bodies)
+      val comp_binders = mk_binders lthy bmode args binders
+      val comp_binders' = mk_binders lthy bmode args' binders
+      val alpha_prem = 
+        mk_alpha_prem bmode comp_fv comp_alpha comp_args comp_args' comp_binders comp_binders'
+      val alpha_bn_prems = flat (map (mk_alpha_bn_prem alpha_bn_map args args' bodies) binders)
+    in
+      map HOLogic.mk_Trueprop (alpha_prem::alpha_bn_prems)
+    end
 end
 *}
 
 ML {*
-fun alpha_bns lthy dt_descr sorts alpha_frees fv_frees bn_funs bclausesss =
+fun mk_alpha_intros lthy alpha_map alpha_bn_map (constr, ty, arg_tys, is_rec) bclauses = 
 let
-  fun mk_alphabn_free (bn, ith, _) =
-    let
-      val alphabn_name = "alpha_" ^ (Long_Name.base_name (fst (dest_Const bn)));
-      val ty = nth_dtyp dt_descr sorts ith;
-      val alphabn_type = ty --> ty --> @{typ bool};
-      val alphabn_free = Free(alphabn_name, alphabn_type);
-    in
-      (alphabn_name, alphabn_free)
-    end;
-  val (alphabn_names, alphabn_frees) = split_list (map mk_alphabn_free bn_funs);
-  val bn_alphabn = (map (fn (bn, _, _) => bn) bn_funs) ~~ alphabn_frees
-  val bclausessl = map (fn (_, i, _) => nth bclausesss i) bn_funs;
-  val eqs = map2 (alpha_bn lthy dt_descr sorts alpha_frees fv_frees bn_alphabn) bclausessl
-    (alphabn_frees ~~ bn_funs);
+  val arg_names = Datatype_Prop.make_tnames arg_tys
+  val arg_names' = Name.variant_list arg_names arg_names
+  val args = map Free (arg_names ~~ arg_tys)
+  val args' = map Free (arg_names' ~~ arg_tys)
+  val alpha = fst (the (AList.lookup (op=) alpha_map ty))
+  val concl = HOLogic.mk_Trueprop (alpha $ list_comb (constr, args) $ list_comb (constr, args'))
+  val prems = map (mk_alpha_prems lthy alpha_map alpha_bn_map is_rec (args, args')) bclauses
 in
-  (bn_alphabn, alphabn_names, eqs)
+  Library.foldr Logic.mk_implies (flat prems, concl)
 end
 *}
 
 ML {*
-fun alpha_bm lthy dt_descr sorts dts args args2 alpha_frees fv_frees bn_alphabn bm =
-case bm of
-  BC (_, [], [i]) =>
-    let
-      val arg = nth args i;
-      val arg2 = nth args2 i;
-      val dt = nth dts i;
-    in
-      if Datatype_Aux.is_rec_type dt
-      then [(nth alpha_frees (Datatype_Aux.body_index dt)) $ arg $ arg2]
-      else [HOLogic.mk_eq (arg, arg2)]
-    end
-| BC (Lst, x, y) => alpha_bm_lsts lthy dt_descr sorts dts args args2 alpha_frees
-    fv_frees bn_alphabn @{const_name alpha_lst} x y
-| BC (Set, x, y) => alpha_bm_lsts lthy dt_descr sorts dts args args2 alpha_frees
-    fv_frees bn_alphabn @{const_name alpha_gen} x y
-| BC (Res, x, y) => alpha_bm_lsts lthy dt_descr sorts dts args args2 alpha_frees
-    fv_frees bn_alphabn @{const_name alpha_res} x y
+fun mk_alpha_bn lthy alpha_map alpha_bn_map bn_args is_rec (args, args') bclause =
+let
+  fun mk_alpha_bn_prem alpha_map alpha_bn_map bn_args (args, args') i = 
+  let
+    val arg = nth args i
+    val arg' = nth args' i
+    val ty = fastype_of arg
+  in
+    case AList.lookup (op=) bn_args i of
+      NONE => (case (AList.lookup (op=) alpha_map ty) of
+                 NONE =>  [HOLogic.mk_eq (arg, arg')]
+               | SOME (alpha, _) => [alpha $ arg $ arg'])
+    | SOME (NONE) => []
+    | SOME (SOME bn) => [the (AList.lookup (op=) alpha_bn_map bn) $ arg $ arg']
+  end  
+in
+  case bclause of
+    BC (_, [], bodies) => 
+      map HOLogic.mk_Trueprop 
+        (flat (map (mk_alpha_bn_prem alpha_map alpha_bn_map bn_args (args, args')) bodies))
+  | _ => mk_alpha_prems lthy alpha_map alpha_bn_map is_rec (args, args') bclause
+end
 *}
 
 ML {*
-fun alpha lthy dt_descr sorts alpha_frees fv_frees bn_alphabn bclausess (alpha_free, ith_dtyp) =
+fun mk_alpha_bn_intro lthy bn_trm alpha_map alpha_bn_map (bn_args, (constr, _, arg_tys, is_rec)) bclauses =
 let
-  fun alpha_constr (cname, dts) bclauses =
-  let
-    val Ts = map (Datatype_Aux.typ_of_dtyp dt_descr sorts) dts;
-    val names = Datatype_Prop.make_tnames Ts;
-    val names2 = Name.variant_list names (Datatype_Prop.make_tnames Ts);
-    val args = map Free (names ~~ Ts);
-    val args2 = map Free (names2 ~~ Ts);
-    val c = Const (cname, Ts ---> (nth_dtyp dt_descr sorts ith_dtyp));
-    val alpha_bm = alpha_bm lthy dt_descr sorts dts args args2 alpha_frees fv_frees bn_alphabn
-    val rhs = HOLogic.mk_Trueprop
-      (alpha_free $ (list_comb (c, args)) $ (list_comb (c, args2)));
-    val lhss = map HOLogic.mk_Trueprop (flat (map alpha_bm bclauses))
-  in
-    Library.foldr Logic.mk_implies (lhss, rhs)
-  end;
-  val (_, (_, _, constrs)) = nth dt_descr ith_dtyp;
+  val arg_names = Datatype_Prop.make_tnames arg_tys
+  val arg_names' = Name.variant_list arg_names arg_names
+  val args = map Free (arg_names ~~ arg_tys)
+  val args' = map Free (arg_names' ~~ arg_tys)
+  val alpha_bn = the (AList.lookup (op=) alpha_bn_map bn_trm)
+  val concl = HOLogic.mk_Trueprop (alpha_bn $ list_comb (constr, args) $ list_comb (constr, args'))
+  val prems = map (mk_alpha_bn lthy alpha_map alpha_bn_map bn_args is_rec (args, args')) bclauses
 in
-  map2 alpha_constr constrs bclausess
+  Library.foldr Logic.mk_implies (flat prems, concl)
 end
 *}
 
 ML {*
-fun define_raw_alpha dt_descr sorts bn_funs bclausesss fv_frees lthy =
+fun mk_alpha_bn_intros lthy alpha_map alpha_bn_map constrs_info bclausesss (bn_trm, bn_n, bn_argss) = 
 let
-  val alpha_names = prefix_dt_names dt_descr sorts "alpha_";
-  val alpha_types = map (fn (i, _) =>
-    nth_dtyp dt_descr sorts i --> nth_dtyp dt_descr sorts i --> @{typ bool}) dt_descr;
-  val alpha_frees = map Free (alpha_names ~~ alpha_types);
+  val nth_constrs_info = nth constrs_info bn_n
+  val nth_bclausess = nth bclausesss bn_n
+in
+  map2 (mk_alpha_bn_intro lthy bn_trm alpha_map alpha_bn_map) (bn_argss ~~ nth_constrs_info) nth_bclausess
+end
+*}
 
-  val (bn_alphabn, alpha_bn_names, alpha_bn_eqs) =
-    alpha_bns lthy dt_descr sorts alpha_frees fv_frees bn_funs bclausesss
+ML {*
+fun define_raw_alpha descr sorts bn_info bclausesss fvs fv_bns lthy =
+let
+  val alpha_names = prefix_dt_names descr sorts "alpha_"
+  val alpha_arg_tys = all_dtyps descr sorts
+  val alpha_tys = map (fn ty => [ty, ty] ---> @{typ bool}) alpha_arg_tys
+  val alpha_frees = map Free (alpha_names ~~ alpha_tys)
+  val alpha_map = alpha_arg_tys ~~ (alpha_frees ~~ fvs)
 
-  val alpha_bns = map snd bn_alphabn;
-  val alpha_bn_types = map fastype_of alpha_bns;
+  val (bns, bn_tys) = split_list (map (fn (bn, i, _) => (bn, i)) bn_info)
+  val bn_names = map (fn bn => Long_Name.base_name (fst (dest_Const bn))) bns
+  val alpha_bn_names = map (prefix "alpha_") bn_names
+  val alpha_bn_arg_tys = map (fn i => nth_dtyp descr sorts i) bn_tys
+  val alpha_bn_tys = map (fn ty => [ty, ty] ---> @{typ "bool"}) alpha_bn_arg_tys
+  val alpha_bn_frees = map Free (alpha_bn_names ~~ alpha_bn_tys)
+  val alpha_bn_map = bns ~~ alpha_bn_frees
 
-  val alpha_nums = 0 upto (length alpha_frees - 1)
+  val constrs_info = all_dtyp_constrs_types descr sorts
 
-  val alpha_eqs = map2 (alpha lthy dt_descr sorts alpha_frees fv_frees bn_alphabn) bclausesss
-    (alpha_frees ~~ alpha_nums);
+  val alpha_intros = map2 (map2 (mk_alpha_intros lthy alpha_map alpha_bn_map)) constrs_info bclausesss 
+  val alpha_bn_intros = map (mk_alpha_bn_intros lthy alpha_map alpha_bn_map constrs_info bclausesss) bn_info
 
   val all_alpha_names = map2 (fn s => fn ty => ((Binding.name s, ty), NoSyn))
-    (alpha_names @ alpha_bn_names) (alpha_types @ alpha_bn_types)
-  val all_alpha_eqs = map (pair Attrib.empty_binding) (flat alpha_eqs @ flat alpha_bn_eqs)
-
+    (alpha_names @ alpha_bn_names) (alpha_tys @ alpha_bn_tys)
+  val all_alpha_intros = map (pair Attrib.empty_binding) (flat alpha_intros @ flat alpha_bn_intros)
+  
   val (alphas, lthy') = Inductive.add_inductive_i
      {quiet_mode = true, verbose = false, alt_name = Binding.empty,
       coind = false, no_elim = false, no_ind = false, skip_mono = true, fork_mono = false}
-     all_alpha_names [] all_alpha_eqs [] lthy
+     all_alpha_names [] all_alpha_intros [] lthy
 
-  val alpha_ts_loc = #preds alphas;
+  val alpha_trms_loc = #preds alphas;
   val alpha_induct_loc = #raw_induct alphas;
   val alpha_intros_loc = #intrs alphas;
   val alpha_cases_loc = #elims alphas;
-  val morphism = ProofContext.export_morphism lthy' lthy;
+  val phi = ProofContext.export_morphism lthy' lthy;
 
-  val alpha_ts = map (Morphism.term morphism) alpha_ts_loc;
-  val alpha_induct = Morphism.thm morphism alpha_induct_loc;
-  val alpha_intros = Morphism.fact morphism alpha_intros_loc
-  val alpha_cases = Morphism.fact morphism alpha_cases_loc
+  val alpha_trms = map (Morphism.term phi) alpha_trms_loc;
+  val alpha_induct = Morphism.thm phi alpha_induct_loc;
+  val alpha_intros = map (Morphism.thm phi) alpha_intros_loc
+  val alpha_cases = map (Morphism.thm phi) alpha_cases_loc
 in
-  (alpha_ts, alpha_intros, alpha_cases, alpha_induct, lthy')
+  (alpha_trms, alpha_intros, alpha_cases, alpha_induct, lthy')
 end
-handle UnequalLengths => error "Main"
 *}
 
+ML {* ProofContext.export_morphism *}
+
 end