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src/HOL/Word/Examples/WordExamples.thy

author | haftmann |

Mon, 26 Jan 2009 22:14:17 +0100 | |

changeset 29629 | 5111ce425e7a |

parent 26086 | 3c243098b64a |

child 29640 | 741f26190c96 |

permissions | -rw-r--r-- |

tuned header

(* Author: Gerwin Klein, NICTA Examples demonstrating and testing various word operations. *) header "Examples of word operations" theory WordExamples imports Word begin -- "modulus" lemma "(27 :: 4 word) = -5" by simp lemma "(27 :: 4 word) = 11" by simp lemma "27 \<noteq> (11 :: 6 word)" by simp -- "signed" lemma "(127 :: 6 word) = -1" by simp -- "number ring simps" lemma "27 + 11 = (38::'a::len word)" "27 + 11 = (6::5 word)" "7 * 3 = (21::'a::len word)" "11 - 27 = (-16::'a::len word)" "- -11 = (11::'a::len word)" "-40 + 1 = (-39::'a::len word)" by simp_all lemma "word_pred 2 = 1" by simp lemma "word_succ -3 = -2" by simp lemma "23 < (27::8 word)" by simp lemma "23 \<le> (27::8 word)" by simp lemma "\<not> 23 < (27::2 word)" by simp lemma "0 < (4::3 word)" by simp -- "ring operations" lemma "a + 2 * b + c - b = (b + c) + (a :: 32 word)" by simp -- "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 "unat (-234567 :: 10 word) = 953" 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 -- "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" 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" lemma "of_bl (replicate 32 True) = (0xFFFFFFFF::32 word)" by simp -- "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" 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 "(-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 "(0b11000 :: 10 word) !! n = (n = 4 \<or> n = 3)" by (auto simp add: bin_nth_Bit0 bin_nth_Bit1) 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 "lsb (0b0101::'a::len word)" by simp lemma "\<not> lsb (0b1000::'a::len word)" by simp lemma "\<not> msb (0b0101::4 word)" by simp lemma "msb (0b1000::4 word)" by simp 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)" by simp 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 "slice 3 (0b101111::6 word) = (0b101::3 word)" by simp 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 "(x AND 0xff00) OR (x AND 0x00ff) = (x::16 word)" proof - have "(x AND 0xff00) OR (x AND 0x00ff) = x AND (0xff00 OR 0x00ff)" by (simp only: word_ao_dist2) also have "0xff00 OR 0x00ff = (-1::16 word)" by simp also have "x AND -1 = x" by simp finally show ?thesis . qed end