src/HOL/Tools/numeral_syntax.ML

--- /dev/null	Thu Jan 01 00:00:00 1970 +0000
+++ b/src/HOL/Tools/numeral_syntax.ML	Tue Jul 06 21:08:30 1999 +0200
@@ -0,0 +1,103 @@
+(*  Title:      HOL/Tools/numeral_syntax.ML
+    ID:         $Id$
+    Author:     Markus Wenzel, TU Muenchen
+
+Concrete syntax for generic numerals.  Assumes consts and syntax of
+theory HOL/Numeral.
+*)
+
+signature NUMERAL_SYNTAX =
+sig
+  val dest_bin: term -> int
+  val setup: (theory -> theory) list
+end;
+
+structure NumeralSyntax: NUMERAL_SYNTAX =
+struct
+
+
+(* bits *)
+
+fun mk_bit 0 = Syntax.const "False"
+  | mk_bit 1 = Syntax.const "True"
+  | mk_bit _ = sys_error "mk_bit";
+
+fun dest_bit (Const ("False", _)) = 0
+  | dest_bit (Const ("True", _)) = 1
+  | dest_bit _ = raise Match;
+
+
+(* bit strings *)   (*we try to handle superfluous leading digits nicely*)
+
+fun prefix_len _ [] = 0
+  | prefix_len pred (x :: xs) =
+      if pred x then 1 + prefix_len pred xs else 0;
+
+fun mk_bin str =
+  let
+    val (sign, digs) =
+      (case Symbol.explode str of
+        "#" :: "-" :: cs => (~1, cs)
+      | "#" :: cs => (1, cs)
+      | _ => raise ERROR);
+
+    fun bin_of 0  = []
+      | bin_of ~1 = [~1]
+      | bin_of n  = (n mod 2) :: bin_of (n div 2);
+
+    fun term_of []   = Syntax.const "Numeral.bin.Pls"
+      | term_of [~1] = Syntax.const "Numeral.bin.Min"
+      | term_of (b :: bs) = Syntax.const "Numeral.bin.Bit" $ term_of bs $ mk_bit b;
+    in term_of (bin_of (sign * (#1 (Term.read_int digs)))) end;
+
+(*we consider all "spellings"; Min is likely to be declared elsewhere*)
+fun bin_of (Const ("Pls", _)) = []
+  | bin_of (Const ("bin.Pls", _)) = []
+  | bin_of (Const ("Numeral.bin.Pls", _)) = []
+  | bin_of (Const ("Min", _)) = [~1]
+  | bin_of (Const ("bin.Min", _)) = [~1]
+  | bin_of (Const ("Numeral.bin.Min", _)) = [~1]
+  | bin_of (Const ("Bit", _) $ bs $ b) = dest_bit b :: bin_of bs
+  | bin_of (Const ("bin.Bit", _) $ bs $ b) = dest_bit b :: bin_of bs
+  | bin_of (Const ("Numeral.bin.Bit", _) $ bs $ b) = dest_bit b :: bin_of bs
+  | bin_of _ = raise Match;
+
+fun int_of [] = 0
+  | int_of (b :: bs) = b + 2 * int_of bs;
+
+val dest_bin = int_of o bin_of;
+
+fun dest_bin_str tm =
+  let
+    val rev_digs = bin_of tm;
+    val (sign, zs) =
+      (case rev rev_digs of
+        ~1 :: bs => ("-", prefix_len (equal 1) bs)
+      | bs => ("", prefix_len (equal 0) bs));
+    val num = string_of_int (abs (int_of rev_digs));
+  in "#" ^ sign ^ implode (replicate zs "0") ^ num end;
+
+
+(* translation of integer numeral tokens to and from bitstrings *)
+
+fun numeral_tr (*"_Numeral"*) [t as Free (str, _)] =
+      (Syntax.const "Numeral.number_of" $
+        (mk_bin str handle ERROR => raise TERM ("numeral_tr", [t])))
+  | numeral_tr (*"_Numeral"*) ts = raise TERM ("numeral_tr", ts);
+
+fun numeral_tr' show_sorts (*"number_of"*) (Type ("fun", [_, T])) (t :: ts) =
+      let val t' = Syntax.const "_Numeral" $ (Syntax.const "_xnum" $ Syntax.free (dest_bin_str t)) in
+        if can Term.dest_Type T then t'
+        else Syntax.const Syntax.constrainC $ t' $ Syntax.term_of_typ show_sorts T
+      end
+  | numeral_tr' _ (*"number_of"*) _ _ = raise Match;
+
+
+(* theory setup *)
+
+val setup =
+ [Theory.add_trfuns ([], [("_Numeral", numeral_tr)], [], []),
+  Theory.add_trfunsT [("number_of", numeral_tr'), ("Numeral.number_of", numeral_tr')]];
+
+
+end;