src/HOL/Word/BitSyntax.thy

--- a/src/HOL/Word/BitSyntax.thy	Fri Apr 04 13:40:25 2008 +0200
+++ b/src/HOL/Word/BitSyntax.thy	Fri Apr 04 13:40:26 2008 +0200
@@ -6,17 +6,17 @@
 *)
 
 
-header {* Syntactic class for bitwise operations *}
+header {* Syntactic classes for bitwise operations *}
 
 theory BitSyntax
-imports Main Num_Lemmas
+imports BinGeneral
 begin
 
 class bit = type +
-  fixes bitNOT :: "'a \<Rightarrow> 'a"
-    and bitAND :: "'a \<Rightarrow> 'a \<Rightarrow> 'a"
-    and bitOR  :: "'a \<Rightarrow> 'a \<Rightarrow> 'a"
-    and bitXOR :: "'a \<Rightarrow> 'a \<Rightarrow> 'a"
+  fixes bitNOT :: "'a \<Rightarrow> 'a"       ("NOT _" [70] 71)
+    and bitAND :: "'a \<Rightarrow> 'a \<Rightarrow> 'a" (infixr "AND" 64)
+    and bitOR  :: "'a \<Rightarrow> 'a \<Rightarrow> 'a" (infixr "OR"  59)
+    and bitXOR :: "'a \<Rightarrow> 'a \<Rightarrow> 'a" (infixr "XOR" 59)
 
 text {*
   We want the bitwise operations to bind slightly weaker
@@ -24,23 +24,20 @@
   bind slightly stronger than @{text "*"}.
 *}
 
-notation
-  bitNOT  ("NOT _" [70] 71) and
-  bitAND  (infixr "AND" 64) and
-  bitOR   (infixr "OR"  59) and
-  bitXOR  (infixr "XOR" 59)
-
 text {*
   Testing and shifting operations.
 *}
-consts
-  test_bit :: "'a::bit \<Rightarrow> nat \<Rightarrow> bool" (infixl "!!" 100)
-  lsb      :: "'a::bit \<Rightarrow> bool"
-  msb      :: "'a::bit \<Rightarrow> bool"
-  set_bit  :: "'a::bit \<Rightarrow> nat \<Rightarrow> bool \<Rightarrow> 'a"
-  set_bits :: "(nat \<Rightarrow> bool) \<Rightarrow> 'a::bit" (binder "BITS " 10)
-  shiftl   :: "'a::bit \<Rightarrow> nat \<Rightarrow> 'a" (infixl "<<" 55)
-  shiftr   :: "'a::bit \<Rightarrow> nat \<Rightarrow> 'a" (infixl ">>" 55)
+
+class bits = bit +
+  fixes test_bit :: "'a \<Rightarrow> nat \<Rightarrow> bool" (infixl "!!" 100)
+    and lsb      :: "'a \<Rightarrow> bool"
+    and set_bit  :: "'a \<Rightarrow> nat \<Rightarrow> bool \<Rightarrow> 'a"
+    and set_bits :: "(nat \<Rightarrow> bool) \<Rightarrow> 'a" (binder "BITS " 10)
+    and shiftl   :: "'a \<Rightarrow> nat \<Rightarrow> 'a" (infixl "<<" 55)
+    and shiftr   :: "'a \<Rightarrow> nat \<Rightarrow> 'a" (infixl ">>" 55)
+
+class bitss = bits +
+  fixes msb      :: "'a \<Rightarrow> bool"
 
 
 subsection {* Bitwise operations on @{typ bit} *}
@@ -48,33 +45,28 @@
 instantiation bit :: bit
 begin
 
-definition
-  NOT_bit_def: "NOT x = (case x of bit.B0 \<Rightarrow> bit.B1 | bit.B1 \<Rightarrow> bit.B0)"
+primrec bitNOT_bit where
+  "NOT bit.B0 = bit.B1"
+  | "NOT bit.B1 = bit.B0"
 
-definition
-  AND_bit_def: "x AND y = (case x of bit.B0 \<Rightarrow> bit.B0 | bit.B1 \<Rightarrow> y)"
+primrec bitAND_bit where
+  "bit.B0 AND y = bit.B0"
+  | "bit.B1 AND y = y"
 
-definition
-  OR_bit_def: "(x OR y \<Colon> bit) = NOT (NOT x AND NOT y)"
+primrec bitOR_bit where
+  "bit.B0 OR y = y"
+  | "bit.B1 OR y = bit.B1"
 
-definition
-  XOR_bit_def: "(x XOR y \<Colon> bit) = (x AND NOT y) OR (NOT x AND y)"
+primrec bitXOR_bit where
+  "bit.B0 XOR y = y"
+  | "bit.B1 XOR y = NOT y"
 
 instance  ..
 
 end
 
-lemma bit_simps [simp]:
-  "NOT bit.B0 = bit.B1"
-  "NOT bit.B1 = bit.B0"
-  "bit.B0 AND y = bit.B0"
-  "bit.B1 AND y = y"
-  "bit.B0 OR y = y"
-  "bit.B1 OR y = bit.B1"
-  "bit.B0 XOR y = y"
-  "bit.B1 XOR y = NOT y"
-  by (simp_all add: NOT_bit_def AND_bit_def OR_bit_def
-                    XOR_bit_def split: bit.split)
+lemmas bit_simps =
+  bitNOT_bit.simps bitAND_bit.simps bitOR_bit.simps bitXOR_bit.simps
 
 lemma bit_extra_simps [simp]: 
   "x AND bit.B0 = bit.B0"