--- a/src/HOL/Word/WordShift.thy Tue Aug 21 00:24:10 2007 +0200
+++ b/src/HOL/Word/WordShift.thy Tue Aug 21 01:07:05 2007 +0200
@@ -11,6 +11,41 @@
subsection "Bit shifting"
+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))"
+
+ bshiftr1 :: "bool => 'a :: len word => 'a word"
+ "bshiftr1 b w == of_bl (b # butlast (to_bl w))"
+
+ sshiftr :: "'a :: len word => nat => 'a word" (infixl ">>>" 55)
+ "w >>> n == (sshiftr1 ^ n) w"
+
+ mask :: "nat => 'a::len word"
+ "mask n == (1 << n) - 1"
+
+ revcast :: "'a :: len0 word => 'b :: len0 word"
+ "revcast w == of_bl (takefill False (len_of TYPE('b)) (to_bl w))"
+
+ slice1 :: "nat => 'a :: len0 word => 'b :: len0 word"
+ "slice1 n w == of_bl (takefill False n (to_bl w))"
+
+ slice :: "nat => 'a :: len0 word => 'b :: len0 word"
+ "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"
+
+lemmas slice_def' = slice_def [unfolded word_size]
+
lemma shiftl1_number [simp] :
"shiftl1 (number_of w) = number_of (w BIT bit.B0)"
apply (unfold shiftl1_def word_number_of_def)
@@ -862,6 +897,23 @@
subsection "Split and cat"
+constdefs
+ word_cat :: "'a :: len0 word => 'b :: len0 word => 'c :: len0 word"
+ "word_cat a b == word_of_int (bin_cat (uint a) (len_of TYPE ('b)) (uint b))"
+
+ word_split :: "'a :: len0 word => ('b :: len0 word) * ('c :: len0 word)"
+ "word_split a ==
+ case bin_split (len_of TYPE ('c)) (uint a) of
+ (u, v) => (word_of_int u, word_of_int v)"
+
+ word_rcat :: "'a :: len0 word list => 'b :: len0 word"
+ "word_rcat ws ==
+ word_of_int (bin_rcat (len_of TYPE ('a)) (map uint ws))"
+
+ word_rsplit :: "'a :: len0 word => 'b :: len word list"
+ "word_rsplit w ==
+ map word_of_int (bin_rsplit (len_of TYPE ('b)) (len_of TYPE ('a), uint w))"
+
lemmas word_split_bin' = word_split_def [THEN meta_eq_to_obj_eq, standard]
lemmas word_cat_bin' = word_cat_def [THEN meta_eq_to_obj_eq, standard]
@@ -1244,6 +1296,24 @@
subsection "Rotation"
+constdefs
+ rotater1 :: "'a list => 'a list"
+ "rotater1 ys ==
+ case ys of [] => [] | x # xs => last ys # butlast ys"
+
+ rotater :: "nat => 'a list => 'a list"
+ "rotater n == rotater1 ^ n"
+
+ word_rotr :: "nat => 'a :: len0 word => 'a :: len0 word"
+ "word_rotr n w == of_bl (rotater n (to_bl w))"
+
+ word_rotl :: "nat => 'a :: len0 word => 'a :: len0 word"
+ "word_rotl n w == of_bl (rotate n (to_bl w))"
+
+ word_roti :: "int => 'a :: len0 word => 'a :: len0 word"
+ "word_roti i w == if i >= 0 then word_rotr (nat i) w
+ else word_rotl (nat (- i)) w"
+
lemmas rotater_0' [simp] = rotater_def [where n = "0", simplified]
lemmas word_rot_defs = word_roti_def word_rotr_def word_rotl_def