--- 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"
--- 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