
diff -r f2e806570e83 -r 973672495414 src/HOL/Numeral.thy
--- a/src/HOL/Numeral.thy	Sun Jul 16 20:50:48 2000 +0200
+++ b/src/HOL/Numeral.thy	Sun Jul 16 20:51:19 2000 +0200
@@ -2,16 +2,20 @@
     ID:         $Id$
     Author:     Larry Paulson and Markus Wenzel
 
-Generic numerals represented as twos-complement bitstrings.
+Generic numerals represented as twos-complement bit strings, and
+selector function as ones-complement unit strings.
 *)
 
 theory Numeral = Datatype
 files "Tools/numeral_syntax.ML":
 
+
+(* numerals *)
+
 datatype
   bin = Pls
       | Min
-      | Bit bin bool	(infixl "BIT" 90)
+      | Bit bin bool    (infixl "BIT" 90)
 
 axclass
   number < "term"      (*for numeric types: nat, int, real, ...*)
@@ -20,9 +24,77 @@
   number_of :: "bin => 'a::number"
 
 syntax
-  "_Numeral" :: "xnum => 'a"	("_")
+  "_Numeral" :: "xnum => 'a"    ("_")
 
 setup NumeralSyntax.setup
 
 
+(* selector functions *)
+
+(*Note that type constraints on selector functons are not handled
+  properly here*)
+
+syntax
+  "_selector" :: 'a
+  "_op_selector" :: "xnum => 'a"            ("op _" [0] 1000)
+
+translations
+  "(_Numeral i) x" => "_selector i x"
+
+parse_translation {*
+  let
+    val fstC = Syntax.const "fst";
+    val sndC = Syntax.const "snd";
+    fun ap_snd t = sndC $ t;
+    fun comp_snd t = Syntax.const "op o" $ t $ sndC;
+
+    fun selector_tr [Free (x, _), t] =
+          let val i = Syntax.read_xnum x in
+            if i = 0 orelse i = ~1 then t
+            else if i > 0 then fstC $ funpow (i - 1) ap_snd t
+            else funpow (~i - 1) ap_snd t
+          end
+      | selector_tr ts = raise TERM ("selector_tr", ts);
+
+    fun op_selector_tr [Free (x, _)] =
+          let val i = Syntax.read_xnum x in
+            if i = 0 orelse i = ~1 then Abs ("x", dummyT, Bound 0)
+            else if i > 0 then funpow (i - 1) comp_snd fstC
+            else funpow (~i - 2) comp_snd sndC
+          end
+      | op_selector_tr ts = raise TERM ("op_selector_tr", ts);
+  in [("_selector", selector_tr), ("_op_selector", op_selector_tr)] end
+*}
+
+print_translation {*
+  let
+    fun mk_xnum i =
+      Syntax.free ("#" ^ (if i < 0 then "-" else "") ^ (string_of_int (abs i)));
+
+
+    fun snds_tr' (i, Const ("snd", _) $ t) = snds_tr' (i + 1, t)
+      | snds_tr' x = x;
+
+    fun fst_tr' t = let val (i, t') = snds_tr' (0, t) in (i + 1, t') end;
+    fun snd_tr' t = let val (i, t') = snds_tr' (0, t) in (~ (i + 2), t') end;
+
+    fun selector_tr' f (t :: ts) =
+          let val (i, u) = f t in
+            if ~2 <= i andalso i <= 1 then raise Match
+            else Term.list_comb (mk_xnum i $ u, ts) end
+      | selector_tr' _ [] = raise Match;
+
+
+    fun o_snd_tr' i (Const ("op o", _) $ t $ Const ("snd", _)) = o_snd_tr' (i + 1) t
+      | o_snd_tr' i (Const ("fst", _)) = i + 1
+      | o_snd_tr' i (Const ("snd", _)) = ~ (i + 2)
+      | o_snd_tr' _ _ = raise Match;
+
+    fun comp_tr' (t :: u :: ts) =
+          Term.list_comb (Syntax.const "_op_selector" $
+            mk_xnum (o_snd_tr' 0 (Syntax.const "op o" $ t $ u)), ts)
+      | comp_tr' _ = raise Match;
+  in [("fst", selector_tr' fst_tr'), ("snd", selector_tr' snd_tr'), ("op o", comp_tr')] end
+*}
+
 end




