src/HOLCF/Tools/repdef.ML

--- a/src/HOLCF/Tools/repdef.ML	Tue Nov 09 08:41:36 2010 -0800
+++ b/src/HOLCF/Tools/repdef.ML	Tue Nov 09 16:37:13 2010 -0800
@@ -7,7 +7,16 @@
 signature REPDEF =
 sig
   type rep_info =
-    { emb_def: thm, prj_def: thm, defl_def: thm, DEFL: thm }
+    {
+      emb_def : thm,
+      prj_def : thm,
+      defl_def : thm,
+      liftemb_def : thm,
+      liftprj_def : thm,
+      liftdefl_def : thm,
+      DEFL : thm,
+      LIFTDEFL : thm
+    }
 
   val add_repdef: bool -> binding option -> binding * (string * sort) list * mixfix ->
     term -> (binding * binding) option -> theory ->
@@ -28,7 +37,16 @@
 (** type definitions **)
 
 type rep_info =
-  { emb_def: thm, prj_def: thm, defl_def: thm, DEFL: thm };
+  {
+    emb_def : thm,
+    prj_def : thm,
+    defl_def : thm,
+    liftemb_def : thm,
+    liftprj_def : thm,
+    liftdefl_def : thm,
+    DEFL : thm,
+    LIFTDEFL : thm
+  };
 
 (* building types and terms *)
 
@@ -37,6 +55,18 @@
 fun emb_const T = Const (@{const_name emb}, T ->> udomT);
 fun prj_const T = Const (@{const_name prj}, udomT ->> T);
 fun defl_const T = Const (@{const_name defl}, Term.itselfT T --> deflT);
+fun liftemb_const T = Const (@{const_name liftemb}, mk_upT T ->> udomT);
+fun liftprj_const T = Const (@{const_name liftprj}, udomT ->> mk_upT T);
+fun liftdefl_const T = Const (@{const_name liftdefl}, Term.itselfT T --> deflT);
+
+fun mk_u_map t =
+  let
+    val (T, U) = dest_cfunT (fastype_of t);
+    val u_map_type = (T ->> U) ->> (mk_upT T ->> mk_upT U);
+    val u_map_const = Const (@{const_name u_map}, u_map_type);
+  in
+    mk_capply (u_map_const, t)
+  end;
 
 fun mk_cast (t, x) =
   capply_const (udomT, udomT)
@@ -100,10 +130,24 @@
       Abs ("x", udomT, Abs_const $ mk_cast (defl, Bound 0)));
     val defl_eqn = Logic.mk_equals (defl_const newT,
       Abs ("x", Term.itselfT newT, defl));
+    val liftemb_eqn =
+      Logic.mk_equals (liftemb_const newT,
+      mk_cfcomp (@{term "udom_emb u_approx"}, mk_u_map (emb_const newT)));
+    val liftprj_eqn =
+      Logic.mk_equals (liftprj_const newT,
+      mk_cfcomp (mk_u_map (prj_const newT), @{term "udom_prj u_approx"}));
+    val liftdefl_eqn =
+      Logic.mk_equals (liftdefl_const newT,
+        Abs ("t", Term.itselfT newT,
+          mk_capply (@{const u_defl}, defl_const newT $ Logic.mk_type newT)));
+
     val name_def = Binding.suffix_name "_def" name;
     val emb_bind = (Binding.prefix_name "emb_" name_def, []);
     val prj_bind = (Binding.prefix_name "prj_" name_def, []);
     val defl_bind = (Binding.prefix_name "defl_" name_def, []);
+    val liftemb_bind = (Binding.prefix_name "liftemb_" name_def, []);
+    val liftprj_bind = (Binding.prefix_name "liftprj_" name_def, []);
+    val liftdefl_bind = (Binding.prefix_name "liftdefl_" name_def, []);
 
     (*instantiate class rep*)
     val lthy = thy
@@ -114,16 +158,26 @@
         Specification.definition (NONE, (prj_bind, prj_eqn)) lthy;
     val ((_, (_, defl_ldef)), lthy) =
         Specification.definition (NONE, (defl_bind, defl_eqn)) lthy;
+    val ((_, (_, liftemb_ldef)), lthy) =
+        Specification.definition (NONE, (liftemb_bind, liftemb_eqn)) lthy;
+    val ((_, (_, liftprj_ldef)), lthy) =
+        Specification.definition (NONE, (liftprj_bind, liftprj_eqn)) lthy;
+    val ((_, (_, liftdefl_ldef)), lthy) =
+        Specification.definition (NONE, (liftdefl_bind, liftdefl_eqn)) lthy;
     val ctxt_thy = ProofContext.init_global (ProofContext.theory_of lthy);
     val emb_def = singleton (ProofContext.export lthy ctxt_thy) emb_ldef;
     val prj_def = singleton (ProofContext.export lthy ctxt_thy) prj_ldef;
     val defl_def = singleton (ProofContext.export lthy ctxt_thy) defl_ldef;
+    val liftemb_def = singleton (ProofContext.export lthy ctxt_thy) liftemb_ldef;
+    val liftprj_def = singleton (ProofContext.export lthy ctxt_thy) liftprj_ldef;
+    val liftdefl_def = singleton (ProofContext.export lthy ctxt_thy) liftdefl_ldef;
     val type_definition_thm =
       MetaSimplifier.rewrite_rule
         (the_list (#set_def (#2 info)))
         (#type_definition (#2 info));
     val typedef_thms =
-      [type_definition_thm, #below_def cpo_info, emb_def, prj_def, defl_def];
+      [type_definition_thm, #below_def cpo_info, emb_def, prj_def, defl_def,
+      liftemb_def, liftprj_def, liftdefl_def];
     val thy = lthy
       |> Class.prove_instantiation_instance
           (K (Tactic.rtac (@{thm typedef_rep_class} OF typedef_thms) 1))
@@ -131,15 +185,25 @@
 
     (*other theorems*)
     val defl_thm' = Thm.transfer thy defl_def;
+    val liftdefl_thm' = Thm.transfer thy liftdefl_def;
     val (DEFL_thm, thy) = thy
       |> Sign.add_path (Binding.name_of name)
       |> Global_Theory.add_thm
          ((Binding.prefix_name "DEFL_" name,
           Drule.zero_var_indexes (@{thm typedef_DEFL} OF [defl_thm'])), [])
       ||> Sign.restore_naming thy;
+    val (LIFTDEFL_thm, thy) = thy
+      |> Sign.add_path (Binding.name_of name)
+      |> Global_Theory.add_thm
+         ((Binding.prefix_name "LIFTDEFL_" name,
+          Drule.zero_var_indexes (@{thm typedef_LIFTDEFL} OF [liftdefl_thm'])), [])
+      ||> Sign.restore_naming thy;
 
     val rep_info =
-      { emb_def = emb_def, prj_def = prj_def, defl_def = defl_def, DEFL = DEFL_thm };
+      { emb_def = emb_def, prj_def = prj_def, defl_def = defl_def,
+        liftemb_def = liftemb_def, liftprj_def = liftprj_def,
+        liftdefl_def = liftdefl_def,
+        DEFL = DEFL_thm, LIFTDEFL = LIFTDEFL_thm };
   in
     ((info, cpo_info, pcpo_info, rep_info), thy)
   end