Type Equalities, Disequalities and obsoleting of Overlapping Instances
Type equality predicates: from OverlappingInstances to overcoming them Type equality predicates decide if two types are equal and return the result of the comparison as a type-level boolean. A type equality predicate ought to be total for ground types, that is, types with no free type variables. A more general type matching predicate compares the shape of two types, their top-level type constructo
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Mark P Jones: Typing Haskell in Haskell
REVISED VERSION Last updated: Thanksgiving day, November 23, 2000 Abstract Haskell benefits from a sophisticated type system, but implementors, programmers, and researchers suffer because it has no formal description. To remedy this shortcoming, we present a Haskell program that implements a Haskell typechecker, thus providing a mathematically rigorous specification in a notation that is familiar
Code reuse through polymorphic variants
Jacques Garrigue. In Workshop on Foundations of Software Engineering. Sasaguri, Japan, November 2000. Abstract. Their support for code reuse has made object-oriented languages popular. However, they do not succeed equally in all areas, particularly when data has a complex structure, making hard to keep the parallel between data and code. On the other hand, functional programming languages, which s
Inemuri nezumi diary(2009-04-18)
_ 型レベルプãƒã‚°ãƒ©ãƒŸãƒ³ã‚°ã®ä¼š ã«å‚åŠ ã—ã¾ã—ãŸã€‚感想や説明ã®è£œè¶³ã€ç™ºè¡¨è³‡æ–™ãªã©ã¯ã™ã¹ã¦ã“ã®æ—¥ä»˜ã®ãƒã‚°ã«ã¤ã‘ã‚‹ã“ã¨ã«ã—ã¾ã™ã€‚今週以é™ã€æ™‚é–“ã‚’ã‹ã‘ã¦ã®ã‚“ã³ã‚Šè¿½åŠ ã™ã‚‹äºˆå®šã§ã™ã€‚よã‚ã—ããŠé¡˜ã„ã—ã¾ã™ã€‚内容ã®æ¿ƒã„話を沢山èžã‘ãŸã®ã§ã€æ•´ç†ã™ã‚‹å¿…è¦ãŒã‚ã‚Šã¾ã™ã€‚主催ã—ã¦ãã ã•ã£ãŸã„ãªã°ã•ã‚“ã€ä¼šå ´ã‚’æä¾›ã—ã¦ãã ã•ã£ãŸã‚µã‚¤ãƒœã‚¦ã‚ºãƒ»ãƒ©ãƒœæ§˜ã€ã‚ã‚ŠãŒã¨ã†ã”ã–ã„ã¾ã—ãŸã€‚ [2009-04-28:追記]428ã®æ—¥ã«ã‚ˆã†ã‚„ã下書ãを清書ã™ã‚‹ã“ã¨ãŒã§ãã¾ã—ãŸã€‚ãµã„ー。 _ 型レベルプãƒã‚°ãƒ©ãƒŸãƒ³ã‚°ã®ä¼š 予告(注:2009-04-18ã«è¡Œã‚ã‚Œã€ç„¡äº‹æ¥½ã—ã終了ã—ã¾ã—ãŸ) 申ã—訳ã‚ã‚Šã¾ã›ã‚“ãŒã€ã“ã“ã«ã¯ SWF (Adobe Systems Flash) ãŒç½®ã„ã¦ã‚ã‚Šã¾ã™ã€‚ãŠè¦‹ã›ã™ã‚‹ã“ã¨ãŒã§ããªãã¦ã™ã¿ã¾ã›ã‚“。 ustreamé…ä¿¡ã‚ã‚‹ãã†ã§ã™ã€‚発表プãƒã‚°ãƒ©ãƒ ã¯ã€åž‹ãƒ¬ãƒ™ãƒ«ãƒ—ãƒã‚°ãƒ©ãƒŸãƒ³ã‚°ã®ä¼šã®ãƒšãƒ¼ã‚¸ã‚’ã”確èªä¸‹ã•ã„。 ã¿ã‚“ãªã‚‚ Wii ã®
Type Inference, Haskell and Dependent Types
Adam Gundry This thesis studies questions of type inference, unification and elaboration for languages that combine dependent type theory and functional programming. Languages such as modern Haskell have very expressive type systems, allowing the programmer a great deal of freedom. These require advanced type inference and unification algorithms to reconstruct details that were left implicit, and
ML多相ã®ç¶šã - sumiiã®ãƒ–ãƒã‚°
ã•ã¦ã€Wrightã®è«–æ–‡ã®å½“時ã¯ã€value restrictionã¯å¦¥å½“ãªåˆ¶é™ã ã£ãŸã€‚ãªãœãªã‚‰ã°ã€value restrictionã®ã›ã„ã§åž‹ä»˜ã‘ã§ããªããªã‚‹ä¸»ãªã‚±ãƒ¼ã‚¹ã¯ã€å¤šç›¸é–¢æ•°ã®éƒ¨åˆ†é©ç”¨ãŒã¾ãŸå¤šç›¸é–¢æ•°ã«ãªã‚‹ï¼ˆã¯ãšã®ï¼‰å ´åˆãらã„ã§ã€ãã‚Œã¯let x = eã®eã‚’fun y -> e yã®ã‚ˆã†ã«æ›¸ãæ›ãˆã‚‹ã“ã¨ï¼ˆÎ·å±•é–‹ï¼‰ã§å›žé¿ã§ããŸã‹ã‚‰ã§ã‚る。 ã¨ã“ã‚ãŒã€SML#ã®ã‚ˆã†ãªå¤šç›¸ãƒ¬ã‚³ãƒ¼ãƒ‰ã€OCamlã®ã‚ˆã†ãªå¤šç›¸ã‚ªãƒ–ジェクトãªã„ã—多相ãƒãƒªã‚¢ãƒ³ãƒˆã‚’利用ã™ã‚‹ã¨ã€value restrictionãŒæœ¬å½“ã«å•é¡Œã«ãªã£ã¦ãる。ãŸã¨ãˆã° # let f x = `V x ;; val f : 'a -> [> `V of 'a ] = <fun> # let v = f 1 ;;ãªã©ã§ã€vãŒpolymorphicã«ãªã‚‰ãªã„ã¨ã—ãŸã‚‰ã€ã€Œï¼ˆå®Ÿè³ªçš„ã«ï¼‰å¤šç›¸ãƒãƒªã‚¢ãƒ³ãƒˆã‚’è¿”ã™é–¢æ•°ã¯æ›¸ã‘ãªã„ã€ã“ã¨ã«ï¼ˆäº‹å®Ÿä¸Šï¼‰ãªã£ã¦ã—ã¾
ML多相 - sumiiã®ãƒ–ãƒã‚°
ã¨ã„ã†ã‚ã‘ã§å¤§ä½“ã®è§£èª¬ã€‚ MLã®å¤šç›¸åž‹æŽ¨è«–ã¯ã€let x = eã®ã‚ˆã†ãªå®£è¨€ãŒã‚ã£ãŸã‚‰ã€eã®åž‹ã‚’推論ã—ã¦ã€ã€Œæ±ºã¾ã‚‰ãªã‹ã£ãŸã€éƒ¨åˆ†ã¯ã€Œä½•ã§ã‚‚よã„ã€ã¨è§£é‡ˆã—ã€å…·ä½“化ã•ã‚Œãªã‹ã£ãŸåž‹å¤‰æ•°ã«ã¤ã„ã¦âˆ€ã‚’å…ˆé ã‚’è¿½åŠ ã™ã‚‹ã€‚ãŸã¨ãˆã°ã€ let id = fun y -> yã ã£ãŸã‚‰ã€fun y -> yã®åž‹ãŒÎ±â†’αã®ã‚ˆã†ã«æŽ¨è«–ã•ã‚Œã‚‹ã®ã§ã€idã®åž‹ã¯âˆ€Î±.α→αã«ãªã‚‹ã€‚ãŸã ã—ã€OCamlã‚„SML/NJã§ã¯ã€âˆ€Î±.ã¯çœç•¥ã•ã‚Œã€è¡¨ç¤ºã•ã‚Œãªã„。 ã¨ã“ã‚ãŒã€ç ´å£Šçš„代入やcall-with-current-continuationãªã©ã€Œå‰¯ä½œç”¨ã€ã®ã‚る言語ã§ã¯ã€ä¸Šè¿°ã®åž‹æŽ¨è«–ã¯ä¸å¥å…¨ã«ãªã‚‹ã€‚ãŸã¨ãˆã° let polyref = ref []ã«ãŠã„ã¦polyrefã®åž‹ãŒâˆ€Î±.α list refã¨æŽ¨è«–ã•ã‚Œã¦ã—ã¾ã£ãŸã‚‰ã€ polyref := [true]㨠123 + List.hd !polyrefãŒä¸¡æ–¹ã¨ã‚‚型付ã‘ã§ãã¦ã—
安全ã‹ã¤æŸ”軟ãªä¾å˜åž‹ -
ã“ã®è¨˜äº‹ã¯Theorem Proving Advent Calendar 2011ã®1日目ã®è¨˜äº‹ã§ã™ã€‚ 今日㯠Agda2 ã¨ã„ã†ãƒ—ãƒã‚°ãƒ©ãƒŸãƒ³ã‚°è¨€èªžã‚’用ã„ã¦ã€ä¾å˜åž‹ã‚’用ã„ã‚‹ã“ã¨ã§çµ¶å¯¾çš„ãªå®‰å…¨æ€§ã¨ Haskell ã‚„ OCaml ãªã©ã§ã¯(通常ã®æ–¹æ³•ã§ã¯)実ç¾ã§ããªã„柔軟ã•ã®ã©ã¡ã‚‰ã‚‚æŒã¤ãƒ—ãƒã‚°ãƒ©ãƒ を記述ã§ãã‚‹ã¨ã„ã†ã“ã¨ã«ã¤ã„ã¦æ›¸ãã¾ã™ã€‚ ã“ã®è¨˜äº‹ã¯ä¸»ã«ã€æ™®æ®µå‹•çš„型付ã‘ã®ãƒ—ãƒã‚°ãƒ©ãƒŸãƒ³ã‚°è¨€èªžã‚’使ã£ã¦ã„ã¦ã€é™çš„型付ãã®è¨€èªžã§ã¯è‡ªåˆ†ã®æ„図ã—ãŸã‚‚ã®ã‚’å分ã«è¡¨ç¾ã§ããªã„ã¨è€ƒãˆã¦ã„る人を対象èªè€…ã¨ã—ã¦ã„ã¾ã™ã€‚ ä¾å˜åž‹ã¨ã¯ åž‹ã«ä¾å˜ã™ã‚‹åž‹ã‚„ã€å€¤ã«ä¾å˜ã™ã‚‹åž‹ã‚’作れる型ã®ã“ã¨ã§ã™ã€‚ 例ãˆã°ã€å€¤ã«ä¾å˜ã™ã‚‹åž‹ã‚’用ã„ã‚‹ã“ã¨ã§åž‹ãƒ¬ãƒ™ãƒ«ã§ã‚µã‚¤ã‚ºãŒä¸Žãˆã‚‰ã‚Œã¦ã„るリストを作るã“ã¨ãŒå¯èƒ½ã§ã™ã€‚ ã¾ãŸã€ãƒªã‚¹ãƒˆã®çµåˆé–¢æ•°ã¯é•·ã• a ã®ãƒªã‚¹ãƒˆã¨é•·ã• b ã®ãƒªã‚¹ãƒˆã‚’å–ã‚Šã€ãƒªã‚¹ãƒˆ a+b ã®ãƒªã‚¹ãƒˆã‚’è¿”ã™ã¨ã„ã†ã‚ˆã†ãªåž‹ã‚’æŒã¤ã“ã¨ã«ãªã‚Šã¾ã™
OCaml 標準ライブラリ探訪 #3.0: Printf: 便利ã ã‘ã©ã„ã‚ã„ã‚謎ã®ã‚る奴 - camlspotter’s blog
関連リンク: OCaml 標準ライブラリ探訪 第0回 ãã®ä»–ã®å›žã¯ç¬¬0回ã®ãƒˆãƒ©ãƒƒã‚¯ãƒãƒƒã‚¯ã‚ˆã‚Šã”覧ãã ã•ã„。 printf ã£ã¦ OCaml ã§ã‚‚便利ã§ã™ã‚ˆã。C ã‹ã‚‰é€£ç¶¿ã¨ç¶šã„ã¦ã„ã‚‹åŠã°å¸¸è˜ã® % インターフェースã«åŠ ãˆã€ã¡ã‚‡ã£ã¨ä¸æ€è°ãªåž‹æŽ¨è«–ã®ãŠã‹ã’ã§åž‹å®‰å…¨æ€§ã‚‚ä¿è¨¼ã•ã‚Œã¦ã¾ã™ã€‚printf 使ã£ã¦ã¦åž‹ã‚¨ãƒ©ãƒ¼ãŒè¦‹ã¤ã‹ã‚‹ãŸã³ã«ã€ã‚ー C ã ã£ãŸã‚‰ seg fault ã—ã¦ãŸã‹ã‚‚ã—れんãªã€ã€ã€è‰¯ã‹ã£ãŸè‰¯ã‹ã£ãŸã€ã¨æ€ã„ã¾ã™ã€‚今日ã¯ãん㪠printf ç³»ã®é–¢æ•°ã‚’æä¾›ã™ã‚‹ Printf モジュールã®ãŠè©±ã€‚ OCaml ã§ã¯ printfç³»ã®é–¢æ•°ã¯ã€ä½•ã‹çŸ¥ã‚‰ã‚“ã‘ã©æ›¸ã„ãŸã‚‰å‹•ãã€ã ã‹ã‚‰æ·±ã詮索ã™ã‚‹ãªã€ã¨ã„ã†ä¸æ€è°(é©å½“) API ã¨ã—ã¦æä¾›ã•ã‚Œã¦ã„ã¾ã™ã€‚ç§ã¯ã“ã®æ¸…æ¿ä½µã›å‘‘ã‚€ OCaml ã®å§¿å‹¢ãŒå¥½ããªã‚“ã§ã™ãŒã€ã€ã€ã¾ã‚人ãã‚Œãžã‚Œã§ã™ãªã€‚ ãŠå“書ã Printf ã®ç‰¹æ®Šãªåž‹ä»˜ã‘ã«ã¤ã„㦠/ format
Monad ã«ã—ã¡ã‚ƒã† functor を通ã—ã¦ä»Šæ™‚ã® OCaml モジュールプãƒã‚°ãƒ©ãƒŸãƒ³ã‚°ã‚’俯瞰 - camlspotter’s blog
ã“ã‚Œã¯ç§ç”¨ã®è¦šãˆæ›¸ãã‚’é©å½“ã«æ•´å½¢ã—ãŸã‚‚ã®(ã¨ã„ã†ã‹ Sphinx 㧠hatena 記法ã«ã—ãŸã ã‘ã ã‘ã©)。ã ã‹ã‚‰ä»–ã®äººãŒèªã‚“ã§åˆ¤ã‚‹ã‚ˆã†ã«å…¨ã書ã„ã¦ã„ãªã„。OCaml ã‚„ ML ã®ãƒ¢ã‚¸ãƒ¥ãƒ¼ãƒ«ã‚·ã‚¹ãƒ†ãƒ 〠value polymorphismã€ã•ã‚‰ã«ã¯ relaxed value polymorphismã€ãã—ã¦æ—¥æœ¬èªžã‚’知ã£ã¦ã„る人ã«ã€ãªã‚‰ã°ä½•ã‹å½¹ã«ç«‹ã¤ã‹ã‚‚ã—ã‚Œãªã„。多分地çƒä¸Šã§æ•°å人もã„ãªã„。ã¾ã‚ã„ã„や。ã“れ見ã¦ã‚¦ãƒ˜ã‚§ã€ã¨æ€ã†ãªã‚‰ä¾‹ãˆã° F# ã¿ãŸã„㪠ML モジュールシステムを放棄ã—㦠class 階層を採用ã—ãŸè¨€èªžã¨ã‹ã€ Haskell ã¿ãŸã„㪠type class ã§ãƒ¢ã‚¸ãƒ¥ãƒ¼ãƒ«ã‚’実ç¾ã—ãŸã®ã¨ã‹ã‚’使ã†ã‹ã€ãã‚Œã¨ã‚‚ã‚‚ã£ã¨è¶…カッコã„ã„ナントナクヒューリスティックã§ä¾¿åˆ©ã‚ワマルãªåž‹æŽ¨è«–補助ã®ã¤ã„ãŸãƒ¢ã‚¸ãƒ¥ãƒ¼ãƒ«ã‚·ã‚¹ãƒ†ãƒ を考ãˆã¦ OCaml ã«è¶³ã—ã¦å…¬é–‹ã™ã‚Œã°ã„ã„。æ£ç›´ç§ã‚‚ã“ã“ã¾ã§æ¥ã‚‹ã¨ ML モ
Simonpj/Talk:FunWithTypeFuns - HaskellWiki
Fun with Type Functions Here is Version 3 of our paper (May 2010): Fun With Type Functions (version 3), Oleg Kiselyov, Ken Shan, and Simon Peyton Jones. This online version includes an Appendix that does not appear in the printed version. Slides (PDF) Source code which will appear in the proceedings of Tony Hoare's 75th birthday celebration. Abstract. Tony Hoare has always been a leader in writing
Efficient and Insightful Generalization
How OCaml type checker works -- or what polymorphism and garbage collection have in common There is more to Hindley-Milner type inference than the Algorithm W. In 1988, Didier Rémy was looking to speed up the type inference in Caml and discovered an elegant method of type generalization. Not only it is fast, avoiding scanning the type environment. It smoothly extends to catching of locally-declare
Simonpj/Talk:OutsideIn - HaskellWiki
Modular type inference with local assumptions: OutsideIn(X) This epic 73-page paper (JFP style) brings together our work on type inference for type functions, GADTS, and the like, in a single uniform framework. Version 3 (camera ready copy for JFP) is very substantially revised compared to the May 2010 version. OutsideIn(X) - Modular type inference with local assumptions: PDF Related papers (const
reflection
reflection: Reifies arbitrary terms into types that can be reflected back into terms This package addresses the configuration problem which is propagating configurations that are available at run-time, allowing multiple configurations to coexist without resorting to mutable global variables or System.IO.Unsafe.unsafePerformIO. That package is an implementation of the ideas presented in the paper "
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GitHub - goldfirere/singletons: Fake dependent types in Haskell using singletons
é¾ç”° 真 | CiNii Research
GADT based type classes and auto-reification in jhc
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