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author | huffman |

Tue, 28 Aug 2007 03:49:18 +0200 | |

changeset 24441 | d2a5295570d0 |

parent 24440 | 27dcdcff5ce4 |

child 24442 | 39e29972cb96 |

Word Examples directory

src/HOL/Word/Examples/ROOT.ML | file | annotate | diff | comparison | revisions | |

src/HOL/Word/Examples/WordExamples.thy | file | annotate | diff | comparison | revisions |

--- /dev/null Thu Jan 01 00:00:00 1970 +0000 +++ b/src/HOL/Word/Examples/ROOT.ML Tue Aug 28 03:49:18 2007 +0200 @@ -0,0 +1,1 @@ +use_thy "WordExamples";

--- /dev/null Thu Jan 01 00:00:00 1970 +0000 +++ b/src/HOL/Word/Examples/WordExamples.thy Tue Aug 28 03:49:18 2007 +0200 @@ -0,0 +1,131 @@ +(* + ID: $Id$ + Author: Gerwin Klein, NICTA + + Examples demonstrating and testing various word operations. +*) + +theory WordExamples imports WordMain +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::finite word)" + "27 + 11 = (6::5 word)" + "7 * 3 = (21::'a::finite word)" + "11 - 27 = (-16::'a::finite word)" + "- -11 = (11::'a::finite word)" + "-40 + 1 = (-39::'a::finite 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 :: finite word)" by unat_arith +lemma "i < x ==> i < (i + 1 :: 'a :: finite word)" by uint_arith + +-- "bool lists" + +lemma "of_bl [True, False, True, True] = (0b1011::'a::finite 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_Bit) + +lemma "set_bit 55 7 True = (183::'a word)" by simp +lemma "set_bit 0b0010 7 True = (0b10000010::'a word)" by simp +lemma "set_bit 0b0010 1 False = (0::'a word)" by simp + +lemma "lsb (0b0101::'a::finite word)" by simp +lemma "\<not> lsb (0b1000::'a::finite 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::finite word)" by simp +lemma "word_cat (0b0011::4 word) (0b1111::6word) = (0b0011001111 :: 10 word)" + by simp + +lemma "0b1011 << 2 = (0b101100::'a 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