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3. Arithmetic omega - Presburger arithmetic (propositional formulas, with equalities, inequalities, for nat and Z) auto with arith - ring - associative commutative rewriting field - equalities in commutative fields (like ring, but with division) fourier - linear inequations with propositional structure, on real numbers 4. Induction Introduction (prove inductive facts) apply - treat each constructo
Coqã®å…¥é–€è¨˜äº‹ã‚’書ã会 (1) - ã²ã¨ã‚Šå‹‰å¼·ä¼š
証明支æ´ç³»Coqã®éŠã³æ–¹ã®å…¥é–€ã‚’書ã„ã¦ã¿ã‚‹ã‚ˆã€‚ã™ã§ã«ä¸–ã®ä¸ã«ä½•å€‹ã‚‚入門記事ã‚ã‚Šã¾ã™ã‘ã©ã€å¢—ãˆã¦å›°ã‚‹ã“ã¨ã¯ãªã‹ã‚ã†â€¦ã¨ã„ã†ã“ã¨ã§ã€‚ã¾ãšã€ã‚¤ãƒ³ã‚¹ãƒˆãƒ¼ãƒ«æ–¹æ³•ã«ã¤ã„ã¦ã¯ã€id:yoshihiro503 ã«ã‚ˆã‚‹ç´¹ä»‹è¨˜äº‹ http://d.hatena.ne.jp/yoshihiro503/20070706#p1 最近パソコンを買ã£ãŸã‚“ã ã‘ã©ã€ä½¿ã„æ–¹ãŒã‚ˆã解らãªã„。ã¨ã„ã†äººã®ãŸã‚ã«ã€ä»Šæ—¥ã¯Coqã®ã‚¤ãƒ³ã‚¹ãƒˆãƒ¼ãƒ«ã®æ–¹æ³•ã‚’紹介ã—よã†ã€‚ ã‚’å‚ç…§ã®ã“ã¨ã€‚ç¾æ™‚点ã§ã¯æœ€æ–°ã®å®‰å®šç‰ˆã® Coq 8.2 ãŒãŠã™ã™ã‚。
Coqã§ä¾å˜åž‹ - ã«ã‚ã¨ã‚Šå°å±‹ã§ã®ãƒ—ãƒã‚°ãƒ©ãƒŸãƒ³ã‚°
最近AgdaãŒã¯ã‚„ã£ã¦ã„ã‚‹ã¿ãŸã„ãªã®ã§ã€Coqã§ã‚‚ä¾å˜åž‹ï¼ˆdependent type）を使ã£ã¦ã¿ãŸã€‚ 実装ã—ãŸã®ã¯é•·ã• n ã®ãƒ™ã‚¯ãƒˆãƒ«åž‹ã 。ã“ã®ãƒ™ã‚¯ãƒˆãƒ«åž‹ã‚’使ã†ã¨ã€ç©ºã§ãªã„ã¨ã‹ã€é•·ã•ãŒç‰ã—ã„ã¨ã‹ã‚’åž‹ã®æ®µéšŽã§ä¿è¨¼ã§ãã‚‹ã®ã§ã€ã‚ˆã‚Šå®‰å…¨ãªãƒ—ãƒã‚°ãƒ©ãƒ を書ãã“ã¨ãŒã§ãã‚‹ã®ã 。 Variable A:Set. Inductive Vec : nat -> Set := | VNil : Vec O | VCons : forall n, A -> Vec n -> Vec (S n). ã“ã®ãƒ™ã‚¯ãƒˆãƒ«åž‹ã‚’使ãˆã°ã€ã‚³ãƒ³ãƒ‘イル時ã«é•·ã•ã®æ•´åˆæ€§ã‚‚ãƒã‚§ãƒƒã‚¯ã—ã¦ãã‚Œã¦ã€é–“é•ã„ãŒã‚ã‚‹å ´æ‰€ã‚’æ•™ãˆã¦ãれる。コンパイルã•ãˆé€šã‚Œã°ã€OutOfBoundsExceptionã®ã‚ˆã†ãªå®Ÿè¡Œæ™‚エラーã¯èµ·ã“ã‚Šãˆãªã„ã“ã¨ãŒä¿è¨¼ã•ã‚Œã‚‹ã€‚ 例ãˆã°ã€ä¸€èˆ¬çš„ã«ãƒªã‚¹ãƒˆã®head関数ã¯ã€å¼•æ•°ãŒ1以上ã®é•·ã•ã®ã¨ãã®ã¿å®šç¾©ã§ãã€ç©ºãƒªã‚¹ãƒˆã®å ´åˆã«ã¯å€¤
Gallina ã®æ§‹æ–‡ã¨ Vernacular コマンド
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CoqUn2010
- The document discusses garbage collection (GC) in Coq, including defining GC as a function that takes an initial and final memory state (m1 and m2) and exists an intermediate state (m) where the mark phase is applied to m1 and m and the sweep phase is applied from m to m2. - Safety properties are defined for memory states including disjointness of free and closed elements, and lemmas are proved
Coq Tutorial
eq_nat is recursively defined to test equality of two natural numbers n and m by pattern matching on their constructions. It returns true if both are 0, or if their successors S n' and S m' are recursively equal; otherwise it returns false. Evaluating eq_nat 3 3 returns true since 3 is constructed by applying S twice to 0, and both arguments have the same construction.Read less
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IIJ Research Laboratory
ãƒãƒƒãƒˆãƒ¯ãƒ¼ã‚¯ã®è¨ˆæ¸¬ã¨è§£æž インターãƒãƒƒãƒˆã®ä½¿ã‚れ方やãƒãƒƒãƒˆãƒ¯ãƒ¼ã‚¯ã®æŒ™å‹•ã‚’把æ¡ã™ã‚‹äº‹ã¯ã€ãƒãƒƒãƒˆãƒ¯ãƒ¼ã‚¯ã‚’é‹ç”¨ã—ã€ãã®æŠ€è¡“開発を行ㆠãŸã‚ã«æ¬ ã‹ã›ã¾ã›ã‚“。ã—ã‹ã—ã€è¦³æ¸¬ã§å¾—られるデータé‡ã¯è†¨å¤§ã§ã™ãŒãƒŽã‚¤ã‚ºãŒå¤šãã€ã¾ãŸã€è¦³æ¸¬ã§ãã‚‹ã®ã¯æ¥µã‚ã¦é™ã‚‰ã‚ŒãŸéƒ¨åˆ†ã§ã—ã‹ã‚ã‚Šã¾ã›ã‚“。ãã“ã§ã€è†¨å¤§ãªãƒ‡ãƒ¼ã‚¿ã‹ã‚‰æ„味ã®ã‚ã‚‹æƒ…å ±ã‚’æŠ½å‡ºã—ãŸã‚Šã€éƒ¨åˆ†çš„ãªè¦³æ¸¬ã‹ã‚‰ã‚ˆã‚Šä¸€èˆ¬çš„ãªå‚¾å‘を推測ã™ã‚‹äº‹ãŒå¿…è¦ã¨ãªã‚Šã¾ã™ã€‚... インターãƒãƒƒãƒˆåŸºç›¤æŠ€è¡“ 速ãã¦ã€å®‰å…¨ã§ã€ä¿¡é ¼æ€§ãŒé«˜ãã€ä½¿ã„ã‚„ã™ãã€ãªã©ã€ã‚¤ãƒ³ã‚¿ãƒ¼ãƒãƒƒãƒˆã‚µãƒ¼ãƒ“スã¸ã®è¦æ±‚ã¯ã¾ã™ã¾ã™é«˜ã¾ã£ã¦ã„ã¾ã™ã€‚ã“れらã®è¦æ±‚ã«å¿œãˆã‚‹ãŸã‚ã«ã€ã‚¤ãƒ³ã‚¿ãƒ¼ãƒãƒƒãƒˆã® 基盤技術も日々進æ©ã—ã¦ã„ã¾ã™ã€‚ã„ã¾ã‚„インターãƒãƒƒãƒˆã¯ã¤ãªãŒã‚‹ã ã‘ã®ã‚µãƒ¼ãƒ“スã§ã¯ãªãã€é«˜åº¦ã§è¤‡é›‘ãªæ©Ÿèƒ½ã‚’å‚™ãˆãŸç¤¾ä¼šåŸºç›¤ã¨ãªã‚Šã¾ã—ãŸã€‚IIJæŠ€è¡“ç ”ç©¶æ‰€ã¯ã€ã‚¤ãƒ³ã‚¿ãƒ¼ãƒãƒƒãƒˆã®åŸºç›¤ã¨ã—ã¦å®Ÿç¾ãŒæœŸå¾…ã•ã‚Œã‚‹æ©Ÿèƒ½ã‚’æä¾›ã™ã‚‹ãŸã‚ã«ã€ã•ã¾ã–ã¾ãªæŠ€è¡“課題ã«å–り組んã§
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GitHub - mzp/GC: Proof of Garbage Collector
Proof General: 1. Introducing Proof General
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