[B! coq] eagletmtã®ãƒ–ãƒƒã‚¯ãƒžãƒ¼ã‚¯

eagletmt id:eagletmt

coqã«é–¢ã™ã‚‹eagletmtã®ãƒ–ãƒƒã‚¯ãƒžãƒ¼ã‚¯ (14)

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Basics_J
ãƒ—ãƒã‚°ãƒ©ãƒŸãƒ³ã‚°è¨€èªžCoqã«ã¯ã€ã»ã¨ã‚“ã©ä½•ã‚‚ï¼ˆãƒ–ãƒ¼ãƒ«åž‹ã‚„æ•°å€¤åž‹ã™ã‚‰ï¼‰ãƒ“ãƒ«ãƒˆã‚¤ãƒ³ã•ã‚Œã¦ã„ã¾ã›ã‚“ã€‚ãã®ä»£ã‚ã‚ŠCoqã«ã¯ã€æ–°ã—ã„åž‹ã‚„ãã‚Œã‚’å‡¦ç†ã™ã‚‹ãŸã‚ã®å¼·åŠ›ãªãƒ„ãƒ¼ãƒ«ãŒç”¨æ„ã•ã‚Œã¦ã„ã¾ã™ã€‚ ã¾ãšæœ€åˆã¯ã¨ã¦ã‚‚ç°¡å˜ãªã‚µãƒ³ãƒ—ãƒ«ã‹ã‚‰å§‹ã‚ã¾ã—ã‚‡ã†ã€‚æ¬¡ã®å®šç¾©ã¯ã€Coqã«å¯¾ã—ã¦ã€æ–°ã—ã„ãƒ‡ãƒ¼ã‚¿åž‹ã®ã‚»ãƒƒãƒˆï¼ˆé›†åˆï¼‰ã§ã‚ã‚‹'åž‹'ã‚’å®šç¾©ã—ã¦ã„ã¾ã™ã€‚ãã®åž‹ã¯æ—¥ã§ã€è¦ç´ ã¯æœˆæ›œæ—¥ã€ç«æ›œæ—¥...ãªã©ã§ã™ã€‚ãã®å®šç¾©ã®1è¡Œã¯ä»¥ä¸‹ã®ã‚ˆã†ã«ã‚‚èªã‚ã¾ã™ã€‚"æœˆæ›œæ—¥ã¯æ—¥ã€‚ç«æ›œæ—¥ã¯æ—¥"ã¨ã„ã£ãŸå…·åˆã§ã™ã€‚ Inductive day : Type := | monday : day | tuesday : day | wednesday : day | thursday : day | friday : day | saturday : day | sunday : day.
eagletmt 2011/07/31
coq
ãƒªãƒ³ã‚¯
Coqã®å…¥é–€è¨˜äº‹ã‚’æ›¸ãä¼š (4) - ã²ã¨ã‚Šå‹‰å¼·ä¼š
ä»Šå›žã¯ã€å…¥é–€è¨˜äº‹æ›¸ãã¯ã¡ã‚‡ã£ã¨ä¼‘æ†©ã—ã¦ã€Coqã®è§£èª¬è¨˜äº‹ãªã©ã‚’é›†ã‚ã‚‹ä¼šã§ã™ã€‚ è‹±èªž è¨€èªžãã®ã‚‚ã®ã‚’æµ…ã/æ·±ãçœºã‚ã¦ã„ãã€ã¨ã„ã†æ–¹å‘ã®ãƒ†ã‚ã‚¹ãƒˆï¼“ã¤ï¼š Coq in a Hurry ã€Œå¿™ã—ã„äººã®ãŸã‚ã®Coqå…¥é–€ã€ã€‚æ¯”è¼ƒçš„ã‚ˆãã¾ã¨ã¾ã£ã¦ã„ã‚‹æ°—ãŒã—ã¾ã—ãŸã€‚ Coq Proof Assistantï¼š A Tutorial æœ¬å®¶ã®ãƒãƒ¥ãƒ¼ãƒˆãƒªã‚¢ãƒ« Interactive Theorem Proving and Program Development (Coq'Art) Amazon å®šç•ªã®ä¸€å†Š è¬›ç¾©ã®ç´ æã¨ã—ã¦ä½œã‚‰ã‚ŒãŸãƒãƒ¥ãƒ¼ãƒˆãƒªã‚¢ãƒ«é”ã€‚ã‚ˆã‚Šå…·ä½“çš„ãªé¡Œæã§ã®æ¼”ç¿’ä»˜ããªã®ã§é¢ç™½ã„ã‹ã‚‚ï¼š 2nd Asian-Pacific Summer School on Formal Methods Using Proof Assistants for Programming Language Research or, H
eagletmt 2010/10/13
coq
ãƒªãƒ³ã‚¯
ãƒ¡ãƒ¢æ™’ã— - rfãªãƒ–ãƒã‚°
è‡ªåˆ†ã® Coq ãƒ¡ãƒ¢ã‚’æ™’ã—ã¦ã¿ã‚‹ã€‚ â– ; ã«ã¤ã„ã¦ T1 ; T2 T1 é©ç”¨å¾Œã€T1 ã«ã‚ˆã£ã¦å‡ºæ¥ãŸå…¨ã¦ã®ã‚µãƒ–ã‚´ãƒ¼ãƒ«ã«å¯¾ã—ã¦ T2 ã‚’é©ç”¨ T1 ; [T2 | T3] T1 é©ç”¨å¾Œã€T1 ã«ã‚ˆã£ã¦å‡ºæ¥ãŸã‚µãƒ–ã‚´ãƒ¼ãƒ« a, b ã«å¯¾ã—ã¦ã€a ã« T2ã€b ã« T3 ã‚’é©ç”¨ (ä¸è¦ãªã‚‰ T2, T3 ã‚’çœç•¥å¯(ä½•ã‚‚ã—ãªã„)) â– tacticã«ã¤ã„ã¦ intro / intros å‰æã®å°Žå…¥ ã‚´ãƒ¼ãƒ«ã® forall ã‚„ -> ã§æ‹¬ã‚‰ã‚ŒãŸéƒ¨åˆ†ã‚’å‰æã¸ intros ã§åå‰ã‚’ä»˜ã‘ã‚‹ã¨ãã¯å·¦ã‹ã‚‰ å‰æã«æŒã£ã¦è¡Œã‹ãªã„å ´åˆã¯ã€åå‰ã‚’ _ ã«ã™ã‚‹ (intros ã®ã¿) apply å‰æ A -> Bã€ã‚´ãƒ¼ãƒ« B ãŒã‚ã‚‹ã¨ãã€ã‚´ãƒ¼ãƒ«ã‚’ A ã«ã™ã‚‹ ã‚´ãƒ¼ãƒ«ã«é©ç”¨ã§ãã‚‹é–¢æ•°ãŒã‚ã‚‹ã¨ãã€apply é–¢æ•° ã§ã‚´ãƒ¼ãƒ«ã«é–¢æ•°ã‚’é©ç”¨ã™ã‚‹ assert assert (å‰æã®åå‰ := å¼) ã§ã€å¼ã«ã‚ˆã£ã¦è¨¼æ˜Žã•ã›ã‚‹
eagletmt 2010/09/03
coq
ãƒªãƒ³ã‚¯
è¨¼æ˜Žã—ã¦ã¿ãŸã€‚ - èŠã‚„ã‚“ã®é›‘è¨˜å¸³
http://d.hatena.ne.jp/m-hiyama/20100629/1277774676 ã‚’è¨¼æ˜Žã—ã¦ã¿ãŸã€‚ ã¨ã‚Šã‚ãˆãšã€å•é¡Œè¨å®š Axiom A : Set. Axiom A_eq_dec: forall a b: A, { a = b } + { a <> b }. Axiom A_mul : A -> A -> A. Axiom A_zero: A. Axiom A_one: A. Infix "*" := A_mul. Notation "0" := A_zero. Notation "1" := A_one. Axiom A_mul_assoc: forall a b c, (a * b) * c = a * (b * c). Axiom A_mul_comm: forall a b, a * b = b * a. Axiom A_mul_1_r: forall a,
eagletmt 2010/06/30
Coq
ãƒªãƒ³ã‚¯
Program Verification Through Characteristic Formulae
This paper describes CFML, the first program verification tool based on characteristic formulae. Given the source code of a pure Caml program, this tool generates a logical formula that implies any valid post-condition for that program. One can then prove that the program satisfies a given specification by reasoning interactively about the characteristic formula using a proof assistant such as Coq
eagletmt 2010/06/25
proof

coq

pfds
ãƒªãƒ³ã‚¯
ãƒ’ãƒ“ãƒ«ãƒ†(2010-06-17)
Î». Whyã§ãƒãƒ–ãƒ«ã‚½ãƒ¼ãƒˆã®æ£å½“æ€§ã‚’ç¤ºã™ è¨ˆç®—æ©Ÿè¨€èªžã§å®šç†è¨¼æ˜Ž (Proof Party.JP)ã®ã¨ãã«ã¯ã€Jahobã¨ã„ã†ãƒ„ãƒ¼ãƒ«ã‚’ä½¿ã£ã¦è‰²ã€…ã‚„ã£ã¦ã¿ãŸãŒã€æœ€è¿‘Whyã¨ã„ã†ä¼¼ãŸãƒ„ãƒ¼ãƒ«ã‚’çŸ¥ã£ãŸã®ã§ã€ã“ã£ã¡ã§ã‚‚åŒã˜ã‚ˆã†ãªã“ã¨ã‚’ã‚„ã£ã¦ã¿ã‚‹ã€‚ ã¾ãšã¯ã€Jahobã§ã‚‚è©¦ã—ãŸãƒãƒ–ãƒ«ã‚½ãƒ¼ãƒˆã®ä¾‹*1ã€‚ BubbleSort.java ã“ã‚Œã‚’ gwhy BubbleSort.java ã¨ã—ã¦gwhyã‚’èµ·å‹•ã™ã‚‹ã¨ã€Proof Obligation ãŒæŠ½å‡ºã•ã‚Œã¦ä¸€è¦§ã•ã‚Œã‚‹ã®ã§ã€ã‚ã¨ã¯ãƒ¡ãƒ‹ãƒ¥ãƒ¼ã‹ã‚‰ã€ŒProofã€ã€ŒProve all obligationsã€ã¨ã‹ã‚’é¸ã¹ã°å®šç†è¨¼æ˜Žå™¨ãªã©ãŒèµ°ã£ã¦è¨¼æ˜Žã‚’ã—ã¦ãã‚Œã‚‹ã€‚ å®šç†ç…§æ˜Žå™¨ã¨ã—ã¦ã¯ã€Alt-Ergoã—ã‹ã‚¤ãƒ³ã‚¹ãƒˆãƒ¼ãƒ«ã—ã¦ã„ãªã‹ã£ãŸã‘ã‚Œã©ã€ã“ã®ä¾‹ã§ã¯ã‚ã£ã•ã‚Šå…¨ Proof Obligation ãŒè¨¼æ˜Žã•ã‚ŒãŸã€‚ ä»¥ä¸‹ãŒçµæžœã®ç”»é¢ã€‚ gwhyã®ã“ã®ã‚¤ãƒ³ã‚¿ãƒ¼ãƒ•ã‚§ãƒ¼ã‚¹ã¯ãƒ†ã‚¹ãƒˆãƒ„ãƒ¼
eagletmt 2010/06/18
proof

Coq

java
ãƒªãƒ³ã‚¯
Whyã‚¤ãƒ³ã‚¹ãƒˆãƒ¼ãƒ«ãƒ¡ãƒ¢ - kencobaã®æ—¥è¨˜
Whyãƒ„ãƒ¼ãƒ«ã®ç¿’å¾—ã«ã¤ã„ã¦( http://groups.google.co.jp/group/fm-forum/browse_thread/thread/6fbd1bc05aa8f999) ã¨ã„ã†ã“ã¨ã§ã€ ç§ã‚‚ã‚„ã£ã¦ã¿ãŸã€‚ Whyã¨ã„ã†ã®ã¯ãƒ—ãƒã‚°ãƒ©ãƒ ã®æ¤œè¨¼ç”¨ãƒ„ãƒ¼ãƒ«ãªã®ã ãŒã€ ãƒ—ãƒã‚°ãƒ©ãƒ ã‚³ãƒ¼ãƒ‰ã«ã‚¢ã‚µãƒ¼ã‚·ãƒ§ãƒ³ã®ã‚ˆã†ã«æŒ¿å…¥ã—ãŸWhyã®ã‚³ãƒ¼ãƒ‰ã‚’ ã‚‚ã¨ã«ã€ãƒ—ãƒã‚°ãƒ©ãƒ ã‚’è‡ªå‹•çš„ã«æ¤œè¨¼ã—ã¦ãã‚Œã‚‹ã¨ã„ã†ã€ ãªã‚“ã ã‹ç´ æ™´ã‚‰ã—ã„ä»•çµ„ã¿ã‚’æŒã£ã¦ã„ã‚‹ã®ã ã€‚ ç§ã®ç’°å¢ƒã¯Ubuntuã€‚ 1.ã‚¤ãƒ³ã‚¹ãƒˆãƒ¼ãƒ« Coq(apt-getã§ã‚¤ãƒ³ã‚¹ãƒˆãƒ¼ãƒ«ã§ãã‚‹)ä»¥å¤–ã«å¿…è¦ãªã‚‚ã®ã¯ã€ why-2.24.tar.gz(http://why.lri.fr/) ã„ãã¤ã‹è¿½åŠ ã§ãƒ‘ãƒƒã‚±ãƒ¼ã‚¸ãŒå¿…è¦ã€‚ å…¨éƒ¨sudo apt-get installã§ã‚¤ãƒ³ã‚¹ãƒˆãƒ¼ãƒ«ã—ã¦ãŠãã€‚ libocamlgraph-ocaml-dev(ã“ã‚ŒãŒãªã„ã¨configur
eagletmt 2010/06/18
proof

Coq

java
ãƒªãƒ³ã‚¯
http://adam.chlipala.net/cpdt/cpdt.pdf
eagletmt 2010/05/26
dependent type

coq
ãƒªãƒ³ã‚¯
OCamlerã®ãŸã‚ã®Coqä¾¿åˆ©ãƒ¢ã‚¸ãƒ¥ãƒ¼ãƒ«ã‚’å…¬é–‹ã—ã¦ã¿ãŸ - ã«ã‚ã¨ã‚Šå°å±‹ã§ã®ãƒ—ãƒã‚°ãƒ©ãƒŸãƒ³ã‚°
ã“ã®Baseãƒ¢ã‚¸ãƒ¥ãƒ¼ãƒ«ã‚’ã‚¤ãƒ³ã‚¹ãƒˆãƒ¼ãƒ«ã™ã‚Œã°ã€å†™çœŸã®ç”¨ãªã‚³ãƒ¼ãƒ‰ã‚’æ›¸ãã“ã¨ãŒå‡ºæ¥ã‚‹ã€‚ ãƒ€ã‚¦ãƒ³ãƒãƒ¼ãƒ‰: http://sourceforge.jp/projects/coqbase/ å…·ä½“çš„ã«ã¯ä»¥ä¸‹ã®ã“ã¨ã‚’å®šç¾©ã—ãŸã€‚ æ¨™æº–å‡ºåŠ›ã¸å‡ºåŠ›ã™ã‚‹print, printlné–¢æ•° å‘½ä»¤ã‚’ã¤ãªã’ã‚‹ã‚»ãƒŸã‚³ãƒãƒ³æ¼”ç®—å ä¾å˜åž‹ã‚’ä½¿ã£ãŸåž‹å®‰å…¨ãªprintfé–¢æ•° natã‹ã‚‰OCamlã®intã€stringã‹ã‚‰OCamlã®stringã¸ã®ç›¸äº’å¤‰æ›é–¢æ•° Coqã§ã®boolã€sumboolã€listã€optionåž‹ã‚’ãã®ã¾ã¾OCamlã®åž‹ã¨ã—ã¦ä½¿ã†ãŸã‚ã®é€£æº
eagletmt 2010/01/26
Coq

OCaml
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•
eagletmt 2010/01/19
Coq
ãƒªãƒ³ã‚¯
Certified Programming with Dependent Types
This is the web site for a textbook about practical engineering with the Coq proof assistant. The focus is on building programs with proofs of correctness, using dependent types and scripted proof automation. I'm following an unusual philosophy in this book, so it may be of interest even to long-time Coq users. At the same time, I hope that it provides an easier introduction for newcomers, since s
eagletmt 2010/01/10
Coq
ãƒªãƒ³ã‚¯
Coq Tips
ä»¥ä¸‹ã€Parameters A B C P Q R : Prop. ã‚’ä»®å®šã€‚ ç›®æ¬¡ å‰ä»¶ (ä»®å®š) ãŒâ€¦â€¦ã®å ´åˆ ä»®å®šãŒ False ã®å ´åˆãƒ»ä»®å®šã«çŸ›ç›¾ãŒã‚ã‚‹å ´åˆ ä»®å®šãŒå¦å®šã®å ´åˆ (~A ã®å½¢) ä»®å®šãŒå«æ„ã®å ´åˆ (A -> B ã®å½¢) ä»®å®šãŒé€£è¨€ã®å ´åˆ (A /\ B ã®å½¢) ä»®å®šãŒé¸è¨€ã®å ´åˆ (A \/ B ã®å½¢) ä»®å®šãŒå…¨ç§°é‡åŒ–å (forall) ã®å ´åˆ ä»®å®šãŒå˜åœ¨é‡åŒ–å (exists) ã®å ´åˆ å¾Œä»¶ (ã‚´ãƒ¼ãƒ«) ãŒâ€¦â€¦ã®å ´åˆ ã‚´ãƒ¼ãƒ«ãŒ True ã®å ´åˆ ã‚´ãƒ¼ãƒ«ãŒ Falseãƒ»å¦å®šã®å ´åˆ ã‚´ãƒ¼ãƒ«ãŒå«æ„ã®å ´åˆ (A -> B ã®å½¢) ã‚´ãƒ¼ãƒ«ãŒé€£è¨€ã®å ´åˆ (A /\ B ã®å½¢) ã‚´ãƒ¼ãƒ«ãŒé¸è¨€ã®å ´åˆ (A \/ B ã®å½¢) ã‚´ãƒ¼ãƒ«ãŒå…¨ç§°é‡åŒ–å (forall) ã®å ´åˆ ã‚´ãƒ¼ãƒ«ãŒå˜åœ¨é‡åŒ–å (exists) ã®å ´åˆ ã‚´ãƒ¼ãƒ«ãŒæ’çœŸå‘½é¡Œ (ãƒˆãƒ¼ãƒˆãƒã‚¸ãƒ¼)
eagletmt 2010/01/01
Coq
ãƒªãƒ³ã‚¯
2009-10-23
Proof Party ã«è¡Œã‘ãªã„ã‘ã©ã€å‚åŠ ã—ã¦ã‚‹ã¤ã‚‚ã‚Šã§å•é¡Œã«æŒ‘æˆ¦ã—ã¦ã¿ãŸã€‚ä»Šæ—¥ã¯åå¤å±‹ã§ä¸€äººè¨¼æ˜Žãƒ‘ãƒ¼ãƒ†ã‚£ã€‚ãƒ‘ã‚ºãƒ«ã¨å¿œç”¨å•é¡Œã¯è§£ã„ã¦ã„ãªã„ã€‚ æ±äº¬ã¯é ã„ã®ã§ã€Proof Partyã®æ¬¡å›žãŒã‚‚ã—ã‚ã‚Œã° åå¤å±‹ã‹é–¢è¥¿ã§é–‹å‚¬ã—ã¦ã„ãŸã ã‘ã‚Œã°ã‚ã‚ŠãŒãŸã„ã§ã™ã€‚> ranhaã•ã‚“ è‡ªç„¶æ•°ã®æ§˜ã€…ãªæ€§è³ªã¯æ—¢ã«Coqã®æ¨™æº–ãƒ©ã‚¤ãƒ–ãƒ©ãƒªã«è±Šå¯Œã«æƒã£ã¦ã„ã‚‹ãŒã€ã“ã‚Œã‚‰ã®æ€§è³ªã¯éžå¸¸ã«ãƒ™ãƒ¼ã‚·ãƒƒã‚¯ãªã®ã§ã€ä¸€ã‹ã‚‰å®šç¾©ã—ã¦è¨¼æ˜Žã—ã¦ã¿ãŸã€‚ä»¥ä¸‹ã¯Coqã®Arithãƒ©ã‚¤ãƒ–ãƒ©ãƒªã‚‚ç‰¹åˆ¥ãªã‚¿ã‚¯ãƒ†ã‚£ãƒƒã‚¯ã‚‚ä½¿ã‚ãšã«å®Ÿè£…ã—ãŸã€‚ ã¾ãšã€è‡ªç„¶æ•°å…¨ä½“ã®åž‹ nat ã‚’å®šç¾©ã™ã‚‹ã€‚ Inductive nat : Set := | O : nat | S : nat -> nat. æ¬¡ã«ã“ã®è‡ªç„¶æ•°ä¸Šã§ã®è¶³ã—ç®—ã‚’è¨ˆç®—ã™ã‚‹ plus é–¢æ•°ã‚’å®šç¾©ã™ã‚‹ã€‚ Fixpoint plus x y := match x with | O => y | S x => S
eagletmt 2009/10/24
Coq
ãƒªãƒ³ã‚¯
ãƒãƒŽã‚¤ã®å¡” - èŠã‚„ã‚“ã®é›‘è¨˜å¸³
ä¹…ã—ã¶ã‚Šã«Coqã§éŠã¼ã†ã‹ã¨æ€ã£ã¦ã€ã„ã„å•é¡Œã¯ãªã„ã‹ã¨è€ƒãˆãŸã¨ã“ã‚ã€ãƒãƒŽã‚¤ã®å¡”ã‚ãŸã‚ŠãŒé¢ç™½ã„ã‚“ã˜ã‚ƒãªã‹ã‚ã†ã‹ã¨ã„ã†ã“ã¨ã§è¨¼æ˜Žã—ã¦ã¿ãŸã€‚ è¨¼æ˜Žã—ãŸã„ã“ã¨ã¯ãƒãƒŽã‚¤ã®å¡”ã‚’å®Œæˆã•ã›ã‚‹æœ€çŸæ‰‹æ•°ã¯2^n-1ã§ã‚ã‚‹ã“ã¨â€¦ ã¨æ€ã£ã¦å°‘ã—æ›¸ã„ã¦ã¿ãŸã‚“ã ã‘ã©ã€ã“ã‚Œã¯ã‹ãªã‚Šå¤§å¤‰ã ã¨ã„ã†ã“ã¨ã«ãªã£ã¦ã€ãƒãƒŽã‚¤ã®å¡”ã®è§£ç‰ã‚’è¨ˆç®—ã™ã‚‹é–¢æ•°ãŒæ£ã—ãè§£ã«ãªã£ã¦ã„ã‚‹ã“ã¨ã‚’è¨¼æ˜Žã™ã‚‹ã“ã¨ã‚’æœ€åˆã®ç›®æ¨™ã¨ã—ã¦ã¿ãŸã€‚ å•é¡Œè¨å®šã¯ä»¥ä¸‹ã®é€šã‚Š Inductive pos : Set := pos1 | pos2 | pos3. Inductive move : Set := | from_to (from to: pos): move. Definition tower := list pos. Definition moves := list move. Fixpoint single_tower (t: tower) (p: pos)
eagletmt 2009/09/27
Coq
ãƒªãƒ³ã‚¯
1