GitHub - bacam/coqjvm: Coq executable semantics and resource verifier
This repository contains: An executable semantics for a substantial fragment of the JVM in Coq [1]; a verifier for simple resource properties where the specifications and proofs are embedded in class files, written in Coq; an OCaml library for dealing with JVM classfiles; and a slightly modified copy of extlib 1.5 (see below). At the time of writing, I was able to build it with OCaml 4.02.3 and Co
Extensible core Featherweight Java
Core Featherweight Java (cFJ) is a variant of Featherweight Java without casts. This Coq development is meant to demonstrate how to design mechanized metatheory definitions and proofs in an extensible way. There are a number of different features that can be added to uFJ to build new variants of the language. These proofs were checked with Coq version version 8.3pl2. Earlier versions of Coq might
ProofSummit 2011 ã§ã€ŽCoqã«ã‚ˆã‚‹MsgPackシリアライザã®è¨¼æ˜Žã¨å®Ÿè£…ã€ã¨ã„ã†è©±ã‚’ã—ã¾ã—ãŸã€‚ - ã¿ãšã´ãƒ¼æ—¥è¨˜
ProofSummit2011ã§MsgPackを証明ã—ãŸã¨ãã®è©±ã‚’ã—ã¦ãã¾ã—ãŸã€‚内容ã¯åå¤å±‹Reject会è°ã§è©±ã—ãŸã“ã¨ã‚’膨らã¾ã›ãŸæ„Ÿã˜ã«ãªã£ã¦ã„ã¾ã™ã€‚ 話ã®è¶£æ—¨ã¨ã—ã¦ã¯ã€Œãƒã‚°ã£ã¦æ€–ã„ã˜ã‚ƒã‚“ → ã˜ã‚ƒã‚証明ã—よã†ãœ → ã‚„ã£ã¦ã¿ãŸã€ã¿ãŸã„ãªæ„Ÿã˜ã§ã™ã€‚ スライド Coqã«ã‚ˆã‚‹MsgPackã®è¨¼æ˜Ž View more presentations from Hiroki Mizuno ustream http://www.ustream.tv/recorded/17493318 感想 新宿ダンジョンã“ã‚ã„ [twitter:@ikegami__]ã•ã‚“ã¨[twitter:@masahiro_sakai]ã•ã‚“ã«Agdaã‚’æ•™ãˆã¦ã‚‚らãˆãŸã®ã§ã€ã¨ã¦ã‚‚よã‹ã£ãŸ Software Foundationsã®å’Œè¨³ãƒ—ãƒã‚¸ã‚§ã‚¯ãƒˆã€æ°—ã«ãªã‚Šã¾ã™
Proviola
The Proviola is a tool set for generating a dynamic (HTML + JavaScript) page out of a Coq proof script. The generated page can be used to display proof states without having the reader load the script into a proof assistant instance, giving a considerable advantage over browsing a repository of static files.The script below is a minimal example of a movie generated using the Proviola. Point to the
applpi
Applpi is a library in the Coq proof assistant that enables concurrent programs to be modeled and verified in Coq, and the models to be run as OCaml programs. It contains a formalization of a concurrent language based on the pi-calculus, a formalization of a specification language based on spatial logic and lemmas for formal verification. Applpi has been applied to the verification of an HTTP serv
Coqã§åˆ†é›¢è«–ç†(separation logic) - keigoiã®æ—¥è¨˜
分離論ç†ã¯ã€ãƒ’ãƒ¼ãƒ—é ˜åŸŸã«é–¢ã™ã‚‹è«–ç†çµåˆåã‚’ã‚‚ã¤è«–ç†ä½“ç³»ã 。ホーア論ç†ã®æ‹¡å¼µã§ã‚ã‚Šã€ãƒ’ープを使ã†ãƒ—ãƒã‚°ãƒ©ãƒ ã®ä»•æ§˜ã‚’書ã„ãŸã‚Šæ¤œè¨¼ã—ãŸã‚Šã¨ã„ã£ãŸã“ã¨ã«ä½¿ãˆã‚‹ã€‚ 具体的ã«ã¯ã€ A ∧ B (Aã‹ã¤B) ã«ã‚ˆãä¼¼ãŸã€ A ** B ã¨ã„ã†è«–ç†çµåˆåãŒè¿½åŠ ã•ã‚Œã¦ã„る。ã“れ㯠Aã§è¨€åŠã—ã¦ã„ã‚‹ãƒã‚¤ãƒ³ã‚¿ã¨ã€ Bã§è¨€åŠã—ã¦ã„ã‚‹ãƒã‚¤ãƒ³ã‚¿ãŒæŒ‡ã—ã¦ã„ã‚‹ãƒ’ãƒ¼ãƒ—é ˜åŸŸãŒã€åˆ†é›¢ã•ã‚Œã¦ã„ã‚‹(≒エイリアシングãŒãªã„)ã“ã¨ã‚’ã„ã£ã¦ã„る。 Affeldtã•ã‚“ãŒã€Coqã§åˆ†é›¢è«–ç†ã‚’書ã„ã¦ã€ã—ã‹ã‚‚ãれを公開ã—ã¦ãã ã•ã£ã¦ã„る。 http://staff.aist.go.jp/reynald.affeldt/seplog/ C言語ã§æ›¸ã‹ã‚ŒãŸOSã®ãƒ’ープマãƒãƒ¼ã‚¸ãƒ£ã‚„ã€SmartMIPSã®ã‚¢ã‚»ãƒ³ãƒ–ラã§æ›¸ã‹ã‚ŒãŸæš—å·ãƒ—リミティブã®æ¤œè¨¼ã‚’Coqã§ã‚„ã£ã¦ã„る。 ã“ã†ã„ã£ãŸã“ã¨ã‚’自分ã§ã‚‚触れるよã†ã«ãªã‚ŠãŸã„ã®ã§ã€ICFEM2006ã®ã‚½ãƒ¼ã‚¹ã‚’写経ã—ã¦
Formal Verification of Memory Properties
We are interested in the formal verification of low-level software. For this purpose, we have developed in the Coq proof assistant formalizations of Separation logic (as presented in the survey by John C. Reynolds). We have applied these formalizations to several use-cases, including: the verification of the heap manager of the Topsy operating system (paper) the verification of arithmetic function
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§
Coqã®Sortã«ã¤ã„ã¦
山本和彦 @kazu_yamamoto sort ã®è¨³èªžã‚’募集ã—ã¾ã™ã€‚ 「型ã®åž‹ã€ãらã„ã§ã™ã‹ï¼Ÿ Haskell ã® kind ã¨åŒºåˆ¥ãŒã¤ãã“ã¨ã‚’希望。 #coqt 2011-02-28 10:13:49
CoqPratyã§ã€ŽCoqã‹ã‚‰Rubyã¸ã€ã¨ã„ã†ç™ºè¡¨ã‚’ã—ã¦ã㟠- ã¿ãšã´ãƒ¼æ—¥è¨˜
CoqPartyã«å‚åŠ ã—ã¦ãã¾ã—ãŸã€‚ã™ã£ã’ー楽ã—ã‹ã£ãŸã€‚ 発表ã—ãŸã“㨠From Coq to Ruby / Coqã‹ã‚‰Rubyã¸View more presentations from mzpi. Coqã®Ruby Extractionを書ã„ãŸã¨ãã®è©±ã‚’ã—ã¦ãã¾ã—ãŸã€‚ Extractionを書ã‘ã°ã€ã©ã®å‹‰å¼·ä¼šã«ã‚‚Coqã®è©±ã§ä¹—ã‚Šè¾¼ã‚るよ! 内容ãŒid:yoshihiro503ã•ã‚“ã¨ã‹ã¶ã£ã¦ãŸã®ã§ã€ç”Ÿæˆã•ã‚ŒãŸã‚³ãƒ¼ãƒ‰ã®è§£èª¬ã‚’メインã§ã—ã¦ã¾ã—ãŸã€‚ 感想 Macã®ãƒ‡ã‚£ã‚¹ãƒ—レイアダプタをã¾ãŸå¤±ãã—ãŸorz。 Coqã®è©±ãŒã„ã£ã±ã„èžã‘ã¦ãŸã®ã—ã‹ã£ãŸã§ã™ã€‚ [twitter:@maeda_]ã®ã€Œã‚ãªãŸã®å¥½ããªtacticsã¯ï¼Ÿã€ãŒã‚¹ãƒ†ã‚ã™ãŽã‚‹ã€‚派生ã—ã¦ã‚ãªã·ã‚‹ã§äººæ°—ã®tacticsã¨ã‹ãŒã§ããŸã‚Šã—ãŸã€‚ Redmine/Backlogã«ã‚¤ã‚«å¨˜ã‚’表示ã•ã›ã‚‹ã®ã¯å¸¸è˜ by [twitter:@otf]。 懇
Coqã§å¤šé‡å†å¸°ã®ãƒ‡ãƒ¼ã‚¿æ§‹é€ を証明ã™ã‚‹ - ã«ã‚ã¨ã‚Šå°å±‹ã§ã®ãƒ—ãƒã‚°ãƒ©ãƒŸãƒ³ã‚°
Coqã§ã¯ä¸€é‡ã®å†å¸°çš„ãªãƒ‡ãƒ¼ã‚¿ã¯ä¾‹ãˆã°æ¬¡ã®æ§˜ã«å®šç¾©ã§ãる。 Inductive list (A: Set) : Set := Nil | Cons (x: A) (xs: list A). Coqã§ã¯å†å¸°çš„データ型をInductiveコマンドã§å®šç¾©ã—ãŸå ´åˆã€ãã®åž‹ã®ä»–ã« list_ind ã¨ã„ã†ã‚‚ã®ãŒã¤ã„ã§ã«å®šç¾©ã•ã‚Œã‚‹ã€‚ list_indã¯æ¬¡ã®æ§˜ãªåž‹ã‚’æŒã£ã¦ã„る。 Coq < Check list_ind. list_ind : forall (A : Set) (P : list A -> Prop), P (Nil A) -> (forall (x : A) (xs : list A), P xs -> P (Cons A x xs)) -> forall l : list A, P l ã“ã®list_indã¯å¸°ç´æ³•ã«é–¢ã—ã¦éžå¸¸ã«å¼·åŠ›ã§ã‚る。 リストを引数ã«æŒã¤ã‚ˆã†ãªä»»æ„ã®è¿°èªžPã«å¯¾ã—
Formalizing 100 Theorems
Theorems in the list which have not been formalized yet are in italics. Formalizations of constructive proofs are in italics too. The difficult proofs in the list (according to John all the others are not a serious challenge "given a week or two") have been underlined. The formalizations under a theorem are in the order of the list of systems, and not in chronological order. The List The Irrationa
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refineタクティックã§ã‚‰ãらãä¾å˜åž‹ãƒ—ãƒã‚°ãƒ©ãƒŸãƒ³ã‚°(?) - keigoiã®æ—¥è¨˜
下ã®è¨˜äº‹ã§ã¯ï¼Œ Definition dual_dec : forall (u1:sesstyp) (u2:sesstyp), {dual u1 u2}+{~dual u1 u2}. ã¨ã„ã†é–¢æ•°ã‚’，Coqã®è¨¼æ˜Žãƒ¢ãƒ¼ãƒ‰ã§ä½œã‚Šã¾ã—ãŸï¼Žã¨ã“ã‚ãŒè¨¼æ˜Žãƒ¢ãƒ¼ãƒ‰ã§ä½œã£ãŸãƒ—ãƒã‚°ãƒ©ãƒ ã¯æ¥µã‚ã¦è¤‡é›‘ã§ã‚¤ãƒžã‚¤ãƒåŠ¹çŽ‡ã®ã»ã©ãŒã‚ˆãã‚ã‹ã‚Šã¾ã›ã‚“ (Coq㧠Print dual_dec. ã™ã‚‹ã¨ã‚ã‹ã‚Šã¾ã™)． ソートSetã®éƒ¨åˆ†ã ã‘を見れã°dual_decã¯éžå¸¸ã«ç°¡å˜ãªé–¢æ•°ã§ï¼Œdual_boolã§è¦‹ãŸã‚ˆã†ã«é«˜ã€…é …ã®æ·±ã•å›žæ•°*2ã®ãƒ‘ターンマッãƒã§æ›¸ã‘ã‚‹ã¯ãšã§ã™ï¼Ž ã¨ã„ã†ã‚ã‘ã§ï¼Œdual_dec ã‚’ 直接 Î»é …ã§æ›¸ã下ã—ã¦ã¿ã¾ã—ょã†ï¼ŽãŸã ã—，ã›ã£ã‹ãCoqを使ã†ã®ã§ï¼Œè¨¼æ˜ŽãŒå¿…è¦ãªéƒ¨åˆ†ã¯æ¥µåŠ› 証明モードを使ã„ã¾ã™ï¼Ž ãã†ã„ã†ç”¨é€”ã«ã¯ refineタクティックを使ã„ã¾ã™ï¼Žã©ã†ã‚„ã£ã¦è¨¼æ˜Žã—ã¦ã„ã„ã‹ã‚ã‹ã‚‰ãªã„部分を _ ã«ã—ã¦ãŠã
Coq Tips
以下ã€Parameters A B C P Q R : Prop. を仮定。 目次 å‰ä»¶ (仮定) ãŒâ€¦â€¦ã®å ´åˆ 仮定㌠False ã®å ´åˆãƒ»ä»®å®šã«çŸ›ç›¾ãŒã‚ã‚‹å ´åˆ ä»®å®šãŒå¦å®šã®å ´åˆ (~A ã®å½¢) 仮定ãŒå«æ„ã®å ´åˆ (A -> B ã®å½¢) 仮定ãŒé€£è¨€ã®å ´åˆ (A /\ B ã®å½¢) 仮定ãŒé¸è¨€ã®å ´åˆ (A \/ B ã®å½¢) 仮定ãŒå…¨ç§°é‡åŒ–å (forall) ã®å ´åˆ 仮定ãŒå˜åœ¨é‡åŒ–å (exists) ã®å ´åˆ 後件 (ゴール) ãŒâ€¦â€¦ã®å ´åˆ ゴール㌠True ã®å ´åˆ ゴール㌠False・å¦å®šã®å ´åˆ ゴールãŒå«æ„ã®å ´åˆ (A -> B ã®å½¢) ゴールãŒé€£è¨€ã®å ´åˆ (A /\ B ã®å½¢) ゴールãŒé¸è¨€ã®å ´åˆ (A \/ B ã®å½¢) ゴールãŒå…¨ç§°é‡åŒ–å (forall) ã®å ´åˆ ゴールãŒå˜åœ¨é‡åŒ–å (exists) ã®å ´åˆ ゴールãŒæ’真命題 (トートãƒã‚¸ãƒ¼)
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https://dl.acm.org/citation.cfm?id=1786136
CiteSeerX
Separation Logic: A Logic for Shared Mutable Data Structures
Announcing Ssreflect 1.1 | The Coq Proof Assistant
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