--- /dev/null	Thu Jan 01 00:00:00 1970 +0000
+++ b/Nominal/nominal_dt_rawperm.ML	Thu May 20 21:23:53 2010 +0100
@@ -0,0 +1,150 @@
+(*  Title:      nominal_dt_rawperm.ML
+    Author:     Cezary Kaliszyk
+    Author:     Christian Urban
+
+  Definitions of the raw permutations and
+  proof that the raw datatypes are in the
+  pt-class.
+*)
+
+signature NOMINAL_DT_RAWPERM =
+sig
+  val define_raw_perms: Datatype.descr -> (string * sort) list -> thm -> int -> theory -> 
+    (term list * thm list * thm list) * theory
+end
+
+
+structure Nominal_Dt_RawPerm: NOMINAL_DT_RAWPERM =
+struct
+
+
+(* permutation function for one argument 
+   
+    - in case the argument is recursive it returns 
+
+         permute_fn p arg
+
+    - in case the argument is non-recursive it will return
+
+         p o arg
+
+*)
+fun perm_arg permute_fn_frees p (arg_dty, arg) =
+  if Datatype_Aux.is_rec_type arg_dty 
+  then (nth permute_fn_frees (Datatype_Aux.body_index arg_dty)) $ p $ arg
+  else mk_perm p arg
+
+
+(* generates the equation for the permutation function for one constructor;
+   i is the index of the corresponding datatype *)
+fun perm_eq_constr dt_descr sorts permute_fn_frees i (cnstr_name, dts) =
+let
+  val p = Free ("p", @{typ perm})
+  val arg_tys = map (Datatype_Aux.typ_of_dtyp dt_descr sorts) dts
+  val arg_names = Name.variant_list ["p"] (Datatype_Prop.make_tnames arg_tys)
+  val args = map Free (arg_names ~~ arg_tys)
+  val cnstr = Const (cnstr_name, arg_tys ---> (nth_dtyp dt_descr sorts i))
+  val lhs = (nth permute_fn_frees i) $ p $ list_comb (cnstr, args)
+  val rhs = list_comb (cnstr, map (perm_arg permute_fn_frees p) (dts ~~ args))
+  val eq = HOLogic.mk_Trueprop (HOLogic.mk_eq (lhs, rhs))
+in
+  (Attrib.empty_binding, eq)
+end
+
+
+(** proves the two pt-type class properties **)
+
+fun prove_permute_zero lthy induct perm_defs perm_fns =
+let
+  val perm_types = map (body_type o fastype_of) perm_fns
+  val perm_indnames = Datatype_Prop.make_tnames perm_types
+  
+  fun single_goal ((perm_fn, T), x) =
+    HOLogic.mk_eq (perm_fn $ @{term "0::perm"} $ Free (x, T), Free (x, T))
+
+  val goals =
+    HOLogic.mk_Trueprop (foldr1 HOLogic.mk_conj
+      (map single_goal (perm_fns ~~ perm_types ~~ perm_indnames)))
+
+  val simps = HOL_basic_ss addsimps (@{thm permute_zero} :: perm_defs)
+
+  val tac = (Datatype_Aux.indtac induct perm_indnames 
+             THEN_ALL_NEW asm_simp_tac simps) 1
+in
+  Goal.prove lthy perm_indnames [] goals (K tac)
+  |> Datatype_Aux.split_conj_thm
+end
+
+
+fun prove_permute_plus lthy induct perm_defs perm_fns =
+let
+  val p = Free ("p", @{typ perm})
+  val q = Free ("q", @{typ perm})
+  val perm_types = map (body_type o fastype_of) perm_fns
+  val perm_indnames = Datatype_Prop.make_tnames perm_types
+  
+  fun single_goal ((perm_fn, T), x) = HOLogic.mk_eq 
+      (perm_fn $ (mk_plus p q) $ Free (x, T), perm_fn $ p $ (perm_fn $ q $ Free (x, T)))
+
+  val goals =
+    HOLogic.mk_Trueprop (foldr1 HOLogic.mk_conj
+      (map single_goal (perm_fns ~~ perm_types ~~ perm_indnames)))
+
+  val simps = HOL_basic_ss addsimps (@{thm permute_plus} :: perm_defs)
+
+  val tac = (Datatype_Aux.indtac induct perm_indnames
+             THEN_ALL_NEW asm_simp_tac simps) 1
+in
+  Goal.prove lthy ("p" :: "q" :: perm_indnames) [] goals (K tac)
+  |> Datatype_Aux.split_conj_thm 
+end
+
+
+(* user_dt_nos refers to the number of "un-unfolded" datatypes
+   given by the user
+*)
+fun define_raw_perms (dt_descr:Datatype.descr) sorts induct_thm user_dt_nos thy =
+let
+  val all_full_tnames = map (fn (_, (n, _, _)) => n) dt_descr;
+  val user_full_tnames = List.take (all_full_tnames, user_dt_nos);
+
+  val perm_fn_names = prefix_dt_names dt_descr sorts "permute_"
+  val perm_fn_types = map (fn (i, _) => perm_ty (nth_dtyp dt_descr sorts i)) dt_descr
+  val perm_fn_frees = map Free (perm_fn_names ~~ perm_fn_types)
+
+  fun perm_eq (i, (_, _, constrs)) = 
+    map (perm_eq_constr dt_descr sorts perm_fn_frees i) constrs;
+
+  val perm_eqs = maps perm_eq dt_descr;
+
+  val lthy =
+    Theory_Target.instantiation (user_full_tnames, [], @{sort pt}) thy;
+   
+  val ((perm_funs, perm_eq_thms), lthy') =
+    Primrec.add_primrec
+      (map (fn s => (Binding.name s, NONE, NoSyn)) perm_fn_names) perm_eqs lthy;
+    
+  val perm_zero_thms = prove_permute_zero lthy' induct_thm perm_eq_thms perm_funs
+  val perm_plus_thms = prove_permute_plus lthy' induct_thm perm_eq_thms perm_funs
+  val perm_zero_thms' = List.take (perm_zero_thms, user_dt_nos);
+  val perm_plus_thms' = List.take (perm_plus_thms, user_dt_nos)
+  val perms_name = space_implode "_" perm_fn_names
+  val perms_zero_bind = Binding.name (perms_name ^ "_zero")
+  val perms_plus_bind = Binding.name (perms_name ^ "_plus")
+  
+  fun tac _ (_, _, simps) =
+    Class.intro_classes_tac [] THEN ALLGOALS (resolve_tac simps)
+  
+  fun morphism phi (fvs, dfs, simps) =
+    (map (Morphism.term phi) fvs, map (Morphism.thm phi) dfs, map (Morphism.thm phi) simps);
+in
+  lthy'
+  |> snd o (Local_Theory.note ((perms_zero_bind, []), perm_zero_thms'))
+  |> snd o (Local_Theory.note ((perms_plus_bind, []), perm_plus_thms'))
+  |> Class_Target.prove_instantiation_exit_result morphism tac 
+       (perm_funs, perm_eq_thms, perm_zero_thms' @ perm_plus_thms')
+end
+
+
+end (* structure *)
+