# HG changeset patch
# User haftmann
# Date 1383216260 -3600
# Node ID 9fda41a04c32e2df1f26783683c7017215e17b12
# Parent  85705ba18addac951ff4c0ccbede8d685f65df77
separated bit operations on type bit from generic syntactic bit operations

diff -r 85705ba18add -r 9fda41a04c32 src/HOL/Word/Bit_Bit.thy
--- /dev/null	Thu Jan 01 00:00:00 1970 +0000
+++ b/src/HOL/Word/Bit_Bit.thy	Thu Oct 31 11:44:20 2013 +0100
@@ -0,0 +1,73 @@
+(*  Title:      HOL/Word/Bit_Bit.thy
+    Author:     Author: Brian Huffman, PSU and Gerwin Klein, NICTA
+*)
+
+header {* Bit operations in \<Z>\<^sub>2*}
+
+theory Bit_Bit
+imports Bit_Operations "~~/src/HOL/Library/Bit"
+begin
+
+instantiation bit :: bit
+begin
+
+primrec bitNOT_bit where
+  "NOT 0 = (1::bit)"
+  | "NOT 1 = (0::bit)"
+
+primrec bitAND_bit where
+  "0 AND y = (0::bit)"
+  | "1 AND y = (y::bit)"
+
+primrec bitOR_bit where
+  "0 OR y = (y::bit)"
+  | "1 OR y = (1::bit)"
+
+primrec bitXOR_bit where
+  "0 XOR y = (y::bit)"
+  | "1 XOR y = (NOT y :: bit)"
+
+instance  ..
+
+end
+
+lemmas bit_simps =
+  bitNOT_bit.simps bitAND_bit.simps bitOR_bit.simps bitXOR_bit.simps
+
+lemma bit_extra_simps [simp]: 
+  "x AND 0 = (0::bit)"
+  "x AND 1 = (x::bit)"
+  "x OR 1 = (1::bit)"
+  "x OR 0 = (x::bit)"
+  "x XOR 1 = NOT (x::bit)"
+  "x XOR 0 = (x::bit)"
+  by (cases x, auto)+
+
+lemma bit_ops_comm: 
+  "(x::bit) AND y = y AND x"
+  "(x::bit) OR y = y OR x"
+  "(x::bit) XOR y = y XOR x"
+  by (cases y, auto)+
+
+lemma bit_ops_same [simp]: 
+  "(x::bit) AND x = x"
+  "(x::bit) OR x = x"
+  "(x::bit) XOR x = 0"
+  by (cases x, auto)+
+
+lemma bit_not_not [simp]: "NOT (NOT (x::bit)) = x"
+  by (cases x) auto
+
+lemma bit_or_def: "(b::bit) OR c = NOT (NOT b AND NOT c)"
+  by (induct b, simp_all)
+
+lemma bit_xor_def: "(b::bit) XOR c = (b AND NOT c) OR (NOT b AND c)"
+  by (induct b, simp_all)
+
+lemma bit_NOT_eq_1_iff [simp]: "NOT (b::bit) = 1 \<longleftrightarrow> b = 0"
+  by (induct b, simp_all)
+
+lemma bit_AND_eq_1_iff [simp]: "(a::bit) AND b = 1 \<longleftrightarrow> a = 1 \<and> b = 1"
+  by (induct a, simp_all)
+
+end
diff -r 85705ba18add -r 9fda41a04c32 src/HOL/Word/Bit_Int.thy
--- a/src/HOL/Word/Bit_Int.thy	Thu Oct 31 11:44:20 2013 +0100
+++ b/src/HOL/Word/Bit_Int.thy	Thu Oct 31 11:44:20 2013 +0100
@@ -9,7 +9,7 @@
 header {* Bitwise Operations on Binary Integers *}
 
 theory Bit_Int
-imports Bit_Representation Bit_Operations
+imports Bit_Representation Bit_Bit
 begin
 
 subsection {* Logical operations *}
diff -r 85705ba18add -r 9fda41a04c32 src/HOL/Word/Bit_Operations.thy
--- a/src/HOL/Word/Bit_Operations.thy	Thu Oct 31 11:44:20 2013 +0100
+++ b/src/HOL/Word/Bit_Operations.thy	Thu Oct 31 11:44:20 2013 +0100
@@ -8,8 +8,6 @@
 imports "~~/src/HOL/Library/Bit"
 begin
 
-subsection {* Abstract syntactic bit operations *}
-
 class bit =
   fixes bitNOT :: "'a \<Rightarrow> 'a"       ("NOT _" [70] 71)
     and bitAND :: "'a \<Rightarrow> 'a \<Rightarrow> 'a" (infixr "AND" 64)
@@ -37,69 +35,5 @@
 class bitss = bits +
   fixes msb      :: "'a \<Rightarrow> bool"
 
-  
-subsection {* Bitwise operations on @{typ bit} *}
-
-instantiation bit :: bit
-begin
-
-primrec bitNOT_bit where
-  "NOT 0 = (1::bit)"
-  | "NOT 1 = (0::bit)"
-
-primrec bitAND_bit where
-  "0 AND y = (0::bit)"
-  | "1 AND y = (y::bit)"
-
-primrec bitOR_bit where
-  "0 OR y = (y::bit)"
-  | "1 OR y = (1::bit)"
-
-primrec bitXOR_bit where
-  "0 XOR y = (y::bit)"
-  | "1 XOR y = (NOT y :: bit)"
-
-instance  ..
-
 end
 
-lemmas bit_simps =
-  bitNOT_bit.simps bitAND_bit.simps bitOR_bit.simps bitXOR_bit.simps
-
-lemma bit_extra_simps [simp]: 
-  "x AND 0 = (0::bit)"
-  "x AND 1 = (x::bit)"
-  "x OR 1 = (1::bit)"
-  "x OR 0 = (x::bit)"
-  "x XOR 1 = NOT (x::bit)"
-  "x XOR 0 = (x::bit)"
-  by (cases x, auto)+
-
-lemma bit_ops_comm: 
-  "(x::bit) AND y = y AND x"
-  "(x::bit) OR y = y OR x"
-  "(x::bit) XOR y = y XOR x"
-  by (cases y, auto)+
-
-lemma bit_ops_same [simp]: 
-  "(x::bit) AND x = x"
-  "(x::bit) OR x = x"
-  "(x::bit) XOR x = 0"
-  by (cases x, auto)+
-
-lemma bit_not_not [simp]: "NOT (NOT (x::bit)) = x"
-  by (cases x) auto
-
-lemma bit_or_def: "(b::bit) OR c = NOT (NOT b AND NOT c)"
-  by (induct b, simp_all)
-
-lemma bit_xor_def: "(b::bit) XOR c = (b AND NOT c) OR (NOT b AND c)"
-  by (induct b, simp_all)
-
-lemma bit_NOT_eq_1_iff [simp]: "NOT (b::bit) = 1 \<longleftrightarrow> b = 0"
-  by (induct b, simp_all)
-
-lemma bit_AND_eq_1_iff [simp]: "(a::bit) AND b = 1 \<longleftrightarrow> a = 1 \<and> b = 1"
-  by (induct a, simp_all)
-
-end
diff -r 85705ba18add -r 9fda41a04c32 src/HOL/Word/Word.thy
--- a/src/HOL/Word/Word.thy	Thu Oct 31 11:44:20 2013 +0100
+++ b/src/HOL/Word/Word.thy	Thu Oct 31 11:44:20 2013 +0100
@@ -8,6 +8,7 @@
 imports
   Type_Length
   "~~/src/HOL/Library/Boolean_Algebra"
+  Bit_Bit
   Bool_List_Representation
   Misc_Typedef
   Word_Miscellaneous