[B! coq] taraoã®ãƒ–ãƒƒã‚¯ãƒžãƒ¼ã‚¯

tarao id:tarao

coqã«é–¢ã™ã‚‹taraoã®ãƒ–ãƒƒã‚¯ãƒžãƒ¼ã‚¯ (8)

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ã€Žã‚½ãƒ•ãƒˆã‚¦ã‚§ã‚¢ã®åŸºç¤Žã€ã®ePubç‰ˆã‚’å…¬é–‹ã—ã¾ã—ãŸã€‚ - ã¿ãšã´ãƒ¼æ—¥è¨˜
ã€ŒSoftware Foundations(å’Œè¨³: ã‚½ãƒ•ãƒˆã‚¦ã‚§ã‚¢ã®åŸºç¤Ž)ã€ã¯Benjamin Pierceæ°ã‚‰ã«ã‚ˆã£ã¦æ›¸ã‹ã‚ŒãŸãƒ‰ã‚ãƒ¥ãƒ¡ãƒ³ãƒˆã§ã‚ã‚Šã€Coqã«ã‚ˆã‚Šãƒ—ãƒã‚°ãƒ©ãƒŸãƒ³ã‚°ã‚„ãƒ—ãƒã‚°ãƒ©ãƒŸãƒ³ã‚°è¨€èªžã®ç†è«–ãŒè§£èª¬ã•ã‚Œã¦ã„ã¾ã™ã€‚åŸºæœ¬çš„ãªéƒ¨åˆ†ã‹ã‚‰ä¸å¯§ã«è§£èª¬ã•ã‚Œã¦ã„ã‚‹ãŸã‚ã€Coqã®å…¥é–€æ›¸ã¨ã—ã¦ã‚‚ãƒ—ãƒã‚°ãƒ©ãƒŸãƒ³ã‚°è¨€èªžç†è«–ã®å…¥é–€æ›¸ã¨ã—ã¦ã‚‚ã€éžå¸¸ã«å„ªã‚ŒãŸå†…å®¹ã¨ãªã£ã¦ã„ã¾ã™ã€‚ ä»Šå›žã¯ã€ãã®ã€Œã‚½ãƒ•ãƒˆã‚¦ã‚§ã‚¢ã®åŸºç¤Žã€ã®ePubç‰ˆã‚’å…¬é–‹ã—ã¾ã—ãŸã€‚ å¯¾å¿œã—ãŸãƒªãƒ¼ãƒ€ã‚’ç”¨ã„ã‚‹ã“ã¨ã§ã€iPhoneã‚„iPadã€Androidã§æœ¬ãƒ‰ã‚ãƒ¥ãƒ¡ãƒ³ãƒˆã‚’èªã‚€ã“ã¨ãŒã§ãã¾ã™ã€‚ ãƒ€ã‚¦ãƒ³ãƒãƒ¼ãƒ‰ http://proofcafe.org/sf-beta/ ã‹ã‚‰ãƒ€ã‚¦ãƒ³ãƒãƒ¼ãƒ‰ã§ãã¾ã™ã€‚ ã¾ãŸmobiç‰ˆã‚‚ã‚ã‚Šã¾ã™ãŒã€Kindleã‚’æŒã£ã¦ãªã„ã®ã§ã€å‹•ä½œç¢ºèªã¯ã—ã¦ã„ã¾ã›ã‚“ã€‚ ãƒã‚°å ±å‘Š http://github.com/sfja/sfja ã¸ã®issuesç™»éŒ²
tarao 2012/07/16
coq
ãƒªãƒ³ã‚¯
Software Foundations æ—¥æœ¬èªžç‰ˆWiki
Software Foundationsæ—¥æœ¬èªžç‰ˆWikiã¸ã‚ˆã†ã“ã Software Foundationsã¯ã€ç±³å›½ãƒšãƒ³ã‚·ãƒ«ãƒãƒ‹ã‚¢å¤§ã®Benjamin Pierceå…ˆç”Ÿã®ã‚°ãƒ«ãƒ¼ãƒ—ã«ã‚ˆã£ã¦ä½œæˆãƒ»å…¬é–‹ã•ã‚Œã¦ã„ã‚‹ã€ãƒ—ãƒã‚°ãƒ©ãƒŸãƒ³ã‚°è¨€èªžCoqã«æ²¿ã£ãŸã‚½ãƒ•ãƒˆã‚¦ã‚§ã‚¢ä½œæˆã«ã¤ã„ã¦ã®ãƒ‰ã‚ãƒ¥ãƒ¡ãƒ³ãƒˆã§ã™ã€‚ ã“ã“ã¯ãã®æ—¥æœ¬èªžç‰ˆä½œæˆã«é›†ã¾ã£ãŸæœ‰å¿—ãŒæƒ…å ±ã‚’äº¤æ›ã™ã‚‹å ´ã§ã™ã€‚ æ—¥æœ¬èªžç‰ˆã®å…¬é–‹ã«ã‚ãŸã£ã¦ã€Pierceå…ˆç”Ÿã®ã”äº†è§£ã‚’ã„ãŸã ã„ã¦ã„ã¾ã™ã€‚
tarao 2012/02/23
coq
ãƒªãƒ³ã‚¯
OCamlã‚³ãƒ¼ãƒ‰ã‚’Coqã§æ¤œè¨¼ã§ãã‚‹ "CFML" ã§ è¨¼æ˜Žã‚³ãƒ³ãƒšã«æŒ‘æˆ¦ (æœªå®Œ) - keigoiã®æ—¥è¨˜
VSTTE 2012 Software Verification Competition ã¨ã„ã†ã‚½ãƒ•ãƒˆã‚¦ã‚§ã‚¢æ¤œè¨¼ã®ã‚³ãƒ³ãƒšãŒã‚ã£ãŸã€‚å‚åŠ ã¯ã‚ªãƒ¼ãƒ—ãƒ³ã§ã€å•é¡Œæ–‡ã‚‚PDFã§é…å¸ƒã•ã‚Œã¦ã„ã‚‹ã€‚ id:yoshihiro503 ãŒãƒãƒ¼ãƒ tebasakiã¨ã„ã†ãƒãƒ¼ãƒ ã§ãŒã‚“ã°ã£ã¦ã„ãŸã€‚åƒ•ã¯Coqã«æ…£ã‚Œã¦ã„ãªã‹ã£ãŸã®ã§ãƒãƒ¼ãƒ ã«å…¥ã‚‹ã®ã¯è¦‹é€ã£ãŸï¼ˆã¨ã„ã†ã‹ãƒãƒ¼ãƒ ã®äººæ•°ä¸Šé™4äººã§å…¥ã‚Œãªã‹ã£ãŸï¼‰ã€‚ ä»•äº‹ã‚„å‡ºå¼µã®ç‰‡æ‰‹é–“ã§ã‚„ã£ã¦ã„ãŸã®ã§ã€çµå±€ä¸€å•ã‚‚æ¤œè¨¼ã§ããªã‹ã£ãŸã‘ã©ã€æ¥½ã—ã‹ã£ãŸã€‚ æ¤œè¨¼ã«ã¯CFMLã¨ã„ã†ãƒ„ãƒ¼ãƒ«ã‚’å‹‰å¼·ã—ãªãŒã‚‰ä½¿ã£ãŸã€‚ ã“ã‚Œã‚’ä½¿ãˆã° OCaml ã®ã‚½ãƒ¼ã‚¹ã‚³ãƒ¼ãƒ‰ã‚’ Coq ã§æ¤œè¨¼ã§ãã‚‹ã€‚ ãã‚Œã‚‚ refåž‹ã«ã‚ˆã‚‹ç ´å£Šçš„ä»£å…¥ã¤ãã®æ‰‹ç¶šãçš„ãªOCamlã‚’å«ã‚€ã€‚ ãã—ã¦ Coqã¨é•ã„ã€ãƒ—ãƒã‚°ãƒ©ãƒ ã¯åœæ¢ã—ãªãã¦ã‚‚ã„ã„ã€‚ ã¤ã¾ã‚Šã€CFMLã‚’ä½¿ãˆã°ã€ æ‰‹ç¶šãåž‹ãƒ—ãƒã‚°ãƒ©ãƒ ã‚’ã€ãƒ›ãƒ¼ã‚¢è«–ç†+åˆ†é›¢è«–ç†(ã®ã‚ˆã†ãªã‚‚ã®;å¾Œè¿°)ã‚’ä½¿ã£ã¦
tarao 2011/11/12
proof

ocaml

coq
ãƒªãƒ³ã‚¯
è¿·è·¯ã®è©¦é¨“å•é¡Œã‚’è§£ã„ã¦ã¿ãŸ - ã«ã‚ã¨ã‚Šå°å±‹ã§ã®ãƒ—ãƒã‚°ãƒ©ãƒŸãƒ³ã‚°
å‚è€ƒï¼šäººæç²å¾—ä½œæˆ¦ãƒ»ï¼” è©¦é¨“å•é¡Œã»ã‹: äººç”Ÿã‚’æ›¸ãæ›ãˆã‚‹è€…ã™ã‚‰ã„ãŸã€‚ Lv4ã«è©•ä¾¡ã•ã‚Œã‚‹ãŸã‚ã«ã¯ã€æœ€çŸæ€§ã®å®Œå…¨ãªãƒã‚§ãƒƒã‚¯ãŒå¿…è¦ã ã£ãŸã®ã§Coqã§è¨¼æ˜Žã—ã¦ã¿ãŸã€‚ ã¾ãšã€accessiblesã¨ã„ã†é–¢æ•°ã‚’å®šç¾©ã—ã€ä»¥ä¸‹ã®æ€§è³ªã‚’è¨¼æ˜Žã—ãŸã€‚ ã“ã“ã§plengthã¯ãƒ‘ã‚¹ã®é•·ã•ã‚’è¨ˆã‚‹é–¢æ•°ã§ã€Path x pã¯pãŒxã‚’èµ·ç‚¹ã¨ã—ãŸãƒ‘ã‚¹ã§ã‚ã‚‹ã¨ã„ã†è¿°èªžã€‚endofã¯ãƒ‘ã‚¹ã®çµ‚ç‚¹ã‚’æ±‚ã‚ã‚‹é–¢æ•°ã€‚ Fixpoint accessibles (start : node) (len : nat) : list path := match len with | O => (PUnit start) :: nil | S n' => div_equiv path_equiv_dec @@ (flat_map expand @@ accessibles start n') end. ã“ã®é–¢æ•°ã¯startã‹ã‚‰å§‹ã¾ã£ã¦lenã®é•·ã•
tarao 2010/01/20
ã“ã‚ŒãŒçœŸã®Lv4 ã™ã°ã‚‰ã—ã„ï¼

coq

ocaml
ãƒªãƒ³ã‚¯
Coqã§ãƒ©ãƒ ãƒ€è¨ˆç®—ã‚’è¨¼æ˜Žã—ã¦ã¿ãŸ - ã¿ãšã´ãƒ¼æ—¥è¨˜
å‰ã‹ã‚‰ãšã£ã¨å–ã‚Šçµ„ã‚“ã§ã„ãŸã€ŒCoqã§å˜ç´”åž‹ä»˜ããƒ©ãƒ ãƒ€è¨ˆç®—ã‚’è¨¼æ˜Žã—ã¦ã¿ã‚ˆã†ã€ãŒä¸€æ®µè½ã—ã¾ã—ãŸã€‚ å‹•æ©Ÿ letå¤šç›¸ã®å®Ÿè£…ã¯ã—ãŸã‹ã‚‰ã€æ¬¡ã¯è¨¼æ˜Žã ã‚ æœ€è¿‘ã€æµè¡Œã£ã¦ã„ã‚‹Coqã‚’è¦šãˆãŸã„ æ‰±ãˆã‚‹ãƒ©ãƒ ãƒ€å¼ åž‹ã¯ã€Boolåž‹ã¨é–¢æ•°åž‹ã®ã¿ã€‚ Inductive type : Set := | BoolT : type | FunT : type -> type -> type. å¼ã¯ã€å¤‰æ•°å‚ç…§ã€çœŸå½å€¤ã€ãƒ©ãƒ ãƒ€(é–¢æ•°æŠ½è±¡)ã€é–¢æ•°é©ç”¨ã€ifå¼ã€‚ Inductive term : Set := Var : string -> term | Bool : bool -> term | Lambda : string -> type -> term -> term | Apply : term -> term -> term | If : term -> term -> term -> term. è¨¼æ˜Žã—ãŸå®šç† åž‹
tarao 2009/11/23
lambda

logic

coq
ãƒªãƒ³ã‚¯
Coqã®ãŠã‹ã’ã§è¦‹ã¤ã‘ã‚ŒãŸãƒã‚° - ã¿ãšã´ãƒ¼æ—¥è¨˜
æœ€è¿‘ã€Coqã§åž‹ä»˜ããƒ©ãƒ ãƒ€è¨ˆç®—ã‚’å®šç¾©ã—ã¦ã€Progressã‚„Preservationã‚’è¨¼æ˜Žã™ã‚‹ã¨ã„ã†éŠã³ã«ã¯ã¾ã£ã¦ã„ã¾ã™ã€‚ã¨ã¦ã‚‚ãŠã‚‚ã—ã‚ã„ã®ã§ã€ã¿ã‚“ãªã‚‚ã‚„ã‚‹ã¨ã„ã„ã¨æ€ã†ã‚ˆã€‚ ã§ã€æœ€è¿‘ã€substitution lemmaã®è¨¼æ˜Žã«ãƒãƒ£ãƒ¬ãƒ³ã‚¸ã—ã¦ã€ã‚‚ã‚ãã‚‚æ•—ã‚ŒåŽ»ã‚Šã¾ã—ãŸã€‚ã‚ˆãã‚ˆãè¦‹ç›´ã—ã¦ã¿ã‚‹ã¨ã€ãã‚‚ãã‚‚substitutionã®å®šç¾©ãŒé–“é•ã£ã¦ã„ã¾ã—ãŸã€‚ã“ã®ãƒã‚°ã¯ãªã‹ãªã‹æ ¹ãŒæ·±ãã¦ã€å‰ã«ä½œã£ãŸãƒˆã‚¤ãƒ»ã‚³ãƒ³ãƒ‘ã‚¤ãƒ©(scalet)ã§ã‚‚åŒã˜é–“é•ã„ã‚’ã—ã¦ã¾ã—ãŸã€‚ ã¨ã„ã†ã‚ã‘ã§ã€ã“ã‚Œã¯Coqã®ãŠã‹ã’ã§è¦‹ã¤ã‘ã‚ŒãŸãƒã‚°ã ã—ã€äººæ‰‹ã¯è¦‹ä»˜ã‘ã¥ã‚‰ã„ãƒã‚°ã¨è¨€ãˆãªã„ã“ã¨ã‚‚ãªã„ã®ã§è¨˜éŒ²ã—ã¦ãŠãã¾ã™ã€‚ ãƒã‚°ã‚’å«ã‚“ã Substitution ã¾ãšã¯ãƒã‚°ã‚’å«ã‚“ã Substitutionã§ã™ã€‚ã©ã“ãŒé–“é•ã£ã¦ã„ã‚‹ã‹åˆ†ã‹ã‚Šã¾ã™ã‹? ãƒœã‚¯ã¯åˆ†ã‹ã‚Šã¾ã›ã‚“ã§ã—ãŸã€‚ (* subst *) Inductive Subst : term ->
tarao 2009/11/08
substitution lemma in lambda calculus

coq
ãƒªãƒ³ã‚¯
ProofWeb
What is ProofWeb? ProofWeb is both a system for teaching logic and for using proof assistants through the web. ProofWeb can be used in three ways. First, one can use the guest login, for which one does not even need to register. Secondly, a user can be a student in a logic or proof assistants course. We are hosting courses free of charge. If you are a teacher and would like to host your course on
tarao 2009/03/16
proof

coq
ãƒªãƒ³ã‚¯
ãƒã‚±ãƒƒãƒˆã‚µãƒ¼ãƒãƒ¼ æ ¼å®‰ãƒ¬ãƒ³ã‚¿ãƒ«ã‚µãƒ¼ãƒãƒ¼
ãƒã‚±ãƒƒãƒˆã‚µãƒ¼ãƒãƒ¼ ãŠæŽ¢ã—ã®ãƒšãƒ¼ã‚¸ãŒè¦‹ã¤ã‹ã‚Šã¾ã›ã‚“ã€‚ è²´æ–¹ãŒã‚¢ã‚¯ã‚»ã‚¹ã—ã‚ˆã†ã¨ã—ãŸãƒšãƒ¼ã‚¸ã¯è¦‹ã¤ã‹ã‚Šã¾ã›ã‚“ã€‚ãƒšãƒ¼ã‚¸ã¯å‰Šé™¤ã•ã‚ŒãŸã‹ã€ã‚¢ã‚¯ã‚»ã‚¹å…ˆURLã®é–“é•ã„ã§ã‚ã‚‹å ´åˆãŒè€ƒãˆã‚‰ã‚Œã¾ã™ã€‚ æ£ã—ã„URLã‚’ã”ç¢ºèªãã ã•ã„ã€‚ ã“ã®ãƒšãƒ¼ã‚¸ã®ç®¡ç†è€…ã®æ–¹ã§ã€äºˆæœŸã›ãšã“ã®ãƒšãƒ¼ã‚¸ãŒè¡¨ç¤ºã•ã‚Œã¦ã„ã‚‹å ´åˆã¯ã€äº‹å‹™å±€ã¾ã§ãŠå•ã„åˆã‚ã›ãã ã•ã„ã€‚ ãƒ—ãƒãƒã‚±ã‚µãƒ¼ãƒãƒ¼ã®ãƒšãƒ¼ã‚¸ã¯ã“ã¡ã‚‰ã€‚ 5ç§’å¾Œã«è‡ªå‹•çš„ã«ç§»å‹•ã—ã¾ã™ã€‚
tarao 2009/01/29
ocaml

coq
ãƒªãƒ³ã‚¯
1