--- a/src/HOL/Word/Examples/WordExamples.thy Wed Dec 28 12:55:37 2011 +0100
+++ b/src/HOL/Word/Examples/WordExamples.thy Wed Dec 28 13:20:46 2011 +0100
@@ -14,7 +14,7 @@
type_synonym word8 = "8 word"
type_synonym byte = word8
--- "modulus"
+text "modulus"
lemma "(27 :: 4 word) = -5" by simp
@@ -22,10 +22,12 @@
lemma "27 \<noteq> (11 :: 6 word)" by simp
--- "signed"
+text "signed"
+
lemma "(127 :: 6 word) = -1" by simp
--- "number ring simps"
+text "number ring simps"
+
lemma
"27 + 11 = (38::'a::len word)"
"27 + 11 = (6::5 word)"
@@ -43,57 +45,70 @@
lemma "23 \<le> (27::8 word)" by simp
lemma "\<not> 23 < (27::2 word)" by simp
lemma "0 < (4::3 word)" by simp
+lemma "1 < (4::3 word)" by simp
+lemma "0 < (1::3 word)" by simp
--- "ring operations"
+text "ring operations"
lemma "a + 2 * b + c - b = (b + c) + (a :: 32 word)" by simp
--- "casting"
+text "casting"
lemma "uint (234567 :: 10 word) = 71" by simp
lemma "uint (-234567 :: 10 word) = 953" by simp
lemma "sint (234567 :: 10 word) = 71" by simp
lemma "sint (-234567 :: 10 word) = -71" by simp
+lemma "uint (1 :: 10 word) = 1" by simp
lemma "unat (-234567 :: 10 word) = 953" by simp
+lemma "unat (1 :: 10 word) = 1" by simp
lemma "ucast (0b1010 :: 4 word) = (0b10 :: 2 word)" by simp
lemma "ucast (0b1010 :: 4 word) = (0b1010 :: 10 word)" by simp
lemma "scast (0b1010 :: 4 word) = (0b111010 :: 6 word)" by simp
+lemma "ucast (1 :: 4 word) = (1 :: 2 word)" by simp
--- "reducing goals to nat or int and arith:"
+text "reducing goals to nat or int and arith:"
lemma "i < x ==> i < (i + 1 :: 'a :: len word)" by unat_arith
lemma "i < x ==> i < (i + 1 :: 'a :: len word)" by uint_arith
--- "bool lists"
+text "bool lists"
lemma "of_bl [True, False, True, True] = (0b1011::'a::len word)" by simp
lemma "to_bl (0b110::4 word) = [False, True, True, False]" by simp
--- "this is not exactly fast, but bearable"
+text "this is not exactly fast, but bearable"
lemma "of_bl (replicate 32 True) = (0xFFFFFFFF::32 word)" by simp
--- "this works only for replicate n True"
+text "this works only for replicate n True"
lemma "of_bl (replicate 32 True) = (0xFFFFFFFF::32 word)"
by (unfold mask_bl [symmetric]) (simp add: mask_def)
--- "bit operations"
+text "bit operations"
lemma "0b110 AND 0b101 = (0b100 :: 32 word)" by simp
-
lemma "0b110 OR 0b011 = (0b111 :: 8 word)" by simp
-
lemma "0xF0 XOR 0xFF = (0x0F :: byte)" by simp
-
lemma "NOT (0xF0 :: 16 word) = 0xFF0F" by simp
+lemma "0 AND 5 = (0 :: byte)" by simp
+lemma "1 AND 1 = (1 :: byte)" by simp
+lemma "1 AND 0 = (0 :: byte)" by simp
+lemma "1 AND 5 = (1 :: byte)" apply simp? oops
+lemma "1 OR 6 = (7 :: byte)" apply simp? oops
+lemma "1 OR 1 = (1 :: byte)" by simp
+lemma "1 XOR 7 = (6 :: byte)" apply simp? oops
+lemma "1 XOR 1 = (0 :: byte)" by simp
+lemma "NOT 1 = (254 :: byte)" apply simp? oops
+lemma "NOT 0 = (255 :: byte)" apply simp oops
lemma "(-1 :: 32 word) = 0xFFFFFFFF" by simp
lemma "(0b0010 :: 4 word) !! 1" by simp
lemma "\<not> (0b0010 :: 4 word) !! 0" by simp
lemma "\<not> (0b1000 :: 3 word) !! 4" by simp
+lemma "\<not> (1 :: 3 word) !! 2" apply simp? oops
lemma "(0b11000 :: 10 word) !! n = (n = 4 \<or> n = 3)"
by (auto simp add: bin_nth_Bit0 bin_nth_Bit1)
@@ -101,12 +116,18 @@
lemma "set_bit 55 7 True = (183::'a::len0 word)" by simp
lemma "set_bit 0b0010 7 True = (0b10000010::'a::len0 word)" by simp
lemma "set_bit 0b0010 1 False = (0::'a::len0 word)" by simp
+lemma "set_bit 1 3 True = (0b1001::'a::len0 word)" apply simp? oops
+lemma "set_bit 1 0 False = (0::'a::len0 word)" apply simp? oops
lemma "lsb (0b0101::'a::len word)" by simp
lemma "\<not> lsb (0b1000::'a::len word)" by simp
+lemma "lsb (1::'a::len word)" by simp
+lemma "\<not> lsb (0::'a::len word)" by simp
lemma "\<not> msb (0b0101::4 word)" by simp
lemma "msb (0b1000::4 word)" by simp
+lemma "\<not> msb (1::4 word)" apply simp? oops
+lemma "\<not> msb (0::4 word)" apply simp? oops
lemma "word_cat (27::4 word) (27::8 word) = (2843::'a::len word)" by simp
lemma "word_cat (0b0011::4 word) (0b1111::6word) = (0b0011001111 :: 10 word)"
@@ -115,13 +136,19 @@
lemma "0b1011 << 2 = (0b101100::'a::len0 word)" by simp
lemma "0b1011 >> 2 = (0b10::8 word)" by simp
lemma "0b1011 >>> 2 = (0b10::8 word)" by simp
+lemma "1 << 2 = (0b100::'a::len0 word)" apply simp? oops
lemma "slice 3 (0b101111::6 word) = (0b101::3 word)" by simp
+lemma "slice 3 (1::6 word) = (0::3 word)" apply simp? oops
lemma "word_rotr 2 0b0110 = (0b1001::4 word)" by simp
lemma "word_rotl 1 0b1110 = (0b1101::4 word)" by simp
lemma "word_roti 2 0b1110 = (0b1011::4 word)" by simp
lemma "word_roti -2 0b0110 = (0b1001::4 word)" by simp
+lemma "word_rotr 2 0 = (0::4 word)" by simp
+lemma "word_rotr 2 1 = (0b0100::4 word)" apply simp? oops
+lemma "word_rotl 2 1 = (0b0100::4 word)" apply simp? oops
+lemma "word_roti -2 1 = (0b0100::4 word)" apply simp? oops
lemma "(x AND 0xff00) OR (x AND 0x00ff) = (x::16 word)"
proof -