First steps towards strengthening of induction rules for
inductively defined predicates involving nominal datatypes.

--- /dev/null	Thu Jan 01 00:00:00 1970 +0000
+++ b/src/HOL/Nominal/nominal_inductive.ML	Tue Feb 13 18:18:45 2007 +0100
@@ -0,0 +1,74 @@
+(*  Title:      HOL/Nominal/nominal_inductive.ML
+    ID:         $Id$
+    Author:     Stefan Berghofer, TU Muenchen
+
+Infrastructure for proving additional properties of inductive predicates
+involving nominal datatypes
+*)
+
+signature NOMINAL_INDUCTIVE =
+sig
+  val nominal_inductive: string -> theory -> theory
+end
+
+structure NominalInductive : NOMINAL_INDUCTIVE =
+struct
+
+val perm_boolI = thm "perm_boolI";
+val (_, [perm_boolI_pi, _]) = Drule.strip_comb (snd (Thm.dest_comb
+  (Drule.strip_imp_concl (cprop_of perm_boolI))));
+
+fun transp ([] :: _) = []
+  | transp xs = map hd xs :: transp (map tl xs);
+
+fun nominal_inductive s thy =
+  let
+    val ctxt = ProofContext.init thy;
+    val ({names, ...}, {raw_induct, intrs, ...}) =
+      InductivePackage.the_inductive ctxt (Sign.intern_const thy s);
+    val atoms = NominalAtoms.atoms_of thy;
+    val eqvt_ss = HOL_basic_ss addsimps NominalThmDecls.get_eqvt_thms thy;
+    val t = Logic.unvarify (concl_of raw_induct);
+    val pi = Name.variant (add_term_names (t, [])) "pi";
+    val ps = map (fst o HOLogic.dest_imp)
+      (HOLogic.dest_conj (HOLogic.dest_Trueprop t));
+    fun eqvt_tac th intr = SUBPROOF (fn {prems, ...} =>
+      let val prems' = map (fn th' => th' RS th) prems
+      in (rtac intr THEN_ALL_NEW
+        (resolve_tac prems ORELSE'
+          (cut_facts_tac prems' THEN' full_simp_tac eqvt_ss))) 1
+      end) ctxt;
+    val thss = map (fn atom =>
+      let
+        val pi' = Free (pi, NominalAtoms.mk_permT (Type (atom, [])));
+        val perm_boolI' = Drule.cterm_instantiate
+          [(perm_boolI_pi, cterm_of thy pi')] perm_boolI
+      in map (fn th => standard (th RS mp))
+        (DatatypeAux.split_conj_thm (Goal.prove_global thy [] []
+          (HOLogic.mk_Trueprop (foldr1 HOLogic.mk_conj (map (fn p =>
+            HOLogic.mk_imp (p, list_comb
+             (apsnd (map (NominalPackage.mk_perm [] pi')) (strip_comb p)))) ps)))
+          (fn _ => EVERY (rtac raw_induct 1 :: map (fn (intr, i) =>
+              full_simp_tac eqvt_ss i THEN TRY (eqvt_tac perm_boolI' intr i))
+            (rev intrs ~~ (length intrs downto 1))))))
+      end) atoms;
+    val (_, thy') = PureThy.add_thmss (map (fn (name, ths) =>
+        ((Sign.base_name name ^ "_eqvt", ths), [NominalThmDecls.eqvt_add]))
+      (names ~~ transp thss)) thy;
+  in thy' end;
+
+
+(* outer syntax *)
+
+local structure P = OuterParse and K = OuterKeyword in
+
+val nominal_inductiveP =
+  OuterSyntax.command "nominal_inductive"
+    "prove additional properties of inductive predicate involving nominal datatypes" K.thy_decl
+    (P.name >> (Toplevel.theory o nominal_inductive));
+
+val _ = OuterSyntax.add_parsers [nominal_inductiveP];
+
+end;
+
+end