# HG changeset patch
# User haftmann
# Date 1207309226 -7200
# Node ID 799983936aad1c33affb97a379e54df36487b0d5
# Parent  7fcc10088e727533714e906d529b9fe88856cb94
syntactic classes for bit operations

diff -r 7fcc10088e72 -r 799983936aad 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"
diff -r 7fcc10088e72 -r 799983936aad src/HOL/Word/WordDefinition.thy
--- a/src/HOL/Word/WordDefinition.thy	Fri Apr 04 13:40:25 2008 +0200
+++ b/src/HOL/Word/WordDefinition.thy	Fri Apr 04 13:40:26 2008 +0200
@@ -8,7 +8,9 @@
 
 header {* Definition of Word Type *}
 
-theory WordDefinition imports Size BinBoolList TdThs begin
+theory WordDefinition
+imports Size BinBoolList TdThs
+begin
 
 typedef (open word) 'a word
   = "{(0::int) ..< 2^len_of TYPE('a::len0)}" by auto
@@ -97,9 +99,8 @@
 declare uint_def [code func del]
 
 lemma [code func]: "uint (word_of_int w \<Colon> 'a\<Colon>len0 word) = bintrunc (len_of TYPE('a)) w"
-  unfolding uint_def word_of_int_def
-  apply (rule Abs_word_inverse)
-  using range_bintrunc by auto
+  by (auto simp add: uint_def word_of_int_def intro!: Abs_word_inverse)
+    (insert range_bintrunc, auto)
 
 instantiation word :: (len0) "{number, uminus, minus, plus, one, zero, times, Divides.div, power, ord, bit}"
 begin
@@ -187,25 +188,54 @@
   "(x <s y) == (x <=s y & x ~= y)"
 
 
+
 subsection "Bit-wise operations"
 
-defs (overloaded)
-  word_test_bit_def: 
-  "test_bit (a::'a::len0 word) == bin_nth (uint a)"
+
+
+instantiation word :: (len0) bits
+begin
 
-  word_set_bit_def: 
-  "set_bit (a::'a::len0 word) n x == 
+definition
+  word_test_bit_def: "test_bit a = bin_nth (uint a)"
+
+definition
+  word_set_bit_def: "set_bit a n x =
    word_of_int (bin_sc n (If x bit.B1 bit.B0) (uint a))"
 
-  word_set_bits_def:  
-  "(BITS n. f n)::'a::len0 word == of_bl (bl_of_nth (len_of TYPE ('a)) f)"
+definition
+  word_set_bits_def: "(BITS n. f n) = of_bl (bl_of_nth (len_of TYPE ('a)) f)"
+
+definition
+  word_lsb_def: "lsb a \<longleftrightarrow> bin_last (uint a) = bit.B1"
+
+definition shiftl1 :: "'a word \<Rightarrow> 'a word" where
+  "shiftl1 w = word_of_int (uint w BIT bit.B0)"
+
+definition shiftr1 :: "'a word \<Rightarrow> 'a word" where
+  -- "shift right as unsigned or as signed, ie logical or arithmetic"
+  "shiftr1 w = word_of_int (bin_rest (uint w))"
+
+definition
+  shiftl_def: "w << n = (shiftl1 ^ n) w"
 
-  word_lsb_def: 
-  "lsb (a::'a::len0 word) == bin_last (uint a) = bit.B1"
+definition
+  shiftr_def: "w >> n = (shiftr1 ^ n) w"
+
+instance ..
+
+end
 
+instantiation word :: (len) bitss
+begin
+
+definition
   word_msb_def: 
-  "msb (a::'a::len word) == bin_sign (sint a) = Int.Min"
+  "msb a \<longleftrightarrow> bin_sign (sint a) = Int.Min"
 
+instance ..
+
+end
 
 constdefs
   setBit :: "'a :: len0 word => nat => 'a word" 
@@ -218,13 +248,6 @@
 subsection "Shift operations"
 
 constdefs
-  shiftl1 :: "'a :: len0 word => 'a word"
-  "shiftl1 w == word_of_int (uint w BIT bit.B0)"
-
-  -- "shift right as unsigned or as signed, ie logical or arithmetic"
-  shiftr1 :: "'a :: len0 word => 'a word"
-  "shiftr1 w == word_of_int (bin_rest (uint w))"
-
   sshiftr1 :: "'a :: len word => 'a word" 
   "sshiftr1 w == word_of_int (bin_rest (sint w))"
 
@@ -247,11 +270,6 @@
   "slice n w == slice1 (size w - n) w"
 
 
-defs (overloaded)
-  shiftl_def: "(w::'a::len0 word) << n == (shiftl1 ^ n) w"
-  shiftr_def: "(w::'a::len0 word) >> n == (shiftr1 ^ n) w"
-
-
 subsection "Rotation"
 
 constdefs
@@ -304,7 +322,6 @@
   "of_bool True = 1"
 
 
-
 lemmas of_nth_def = word_set_bits_def
 
 lemmas word_size_gt_0 [iff] = 
@@ -936,7 +953,7 @@
 lemmas ucast_down_bl = ucast_down_bl' [OF refl]
 
 lemmas slice_def' = slice_def [unfolded word_size]
-lemmas test_bit_def' = word_test_bit_def [THEN meta_eq_to_obj_eq, THEN fun_cong]
+lemmas test_bit_def' = word_test_bit_def [THEN fun_cong]
 
 lemmas word_log_defs = word_and_def word_or_def word_xor_def word_not_def
 lemmas word_log_bin_defs = word_log_defs