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1. Curry–Howard - Wikipedia, The Free Encyclopedia The Curry–Howard correspondence is the close relationship between computer More recently, extensions of the CurryHoward correspondence have been http://en.wikipedia.org/wiki/Curry-Howard_isomorphism

var wgNotice = ""; var wgNoticeLocal = ""; var wgNoticeLang = "en"; var wgNoticeProject = "wikipedia"; Curry–Howard From Wikipedia, the free encyclopedia (Redirected from Curry-Howard isomorphism Jump to: navigation search The Curry–Howard correspondence is the close relationship between computer programs and mathematical proofs; the correspondence is also known as the Curry–Howard isomorphism , or the formulae-as-types correspondence . A number of different formulations have been used, for a principle now identified as the independent discovery of the American mathematician Haskell Curry and logician William Alvin Howard The correspondence can be seen at two levels: firstly, that of an analogy , which states that the return type of a function (i.e., the type of values returned by a function) is analogous to a logical theorem, subject to hypotheses corresponding to the types of the argument values passed to the function; and that the program to compute that function is analogous to a proof of that theorem. In theoretical computer science , this is an important underlying principle connecting the adjacent areas of lambda calculus and type theory . It is often stated in the form proofs are programs . An alternate formulation is propositions as types . Secondly, and more formally, it specifies a formal isomorphism between two mathematical domains, that of

2. Curry-Howard-Lambek Correspondence - HaskellWiki The CurryHoward-Lambek correspondance is a three way isomorphism between types (in programming languages), propositions (in logic) and objects of a http://www.haskell.org/haskellwiki/Curry-Howard-Lambek_correspondence

Haskell Wiki community Recent changes Random page ... Special pages Not logged in Log in Help Edit this page Discuss this page ... Related changes Curry-Howard-Lambek correspondence Categories Theoretical foundations Haskell theoretical foundations General Mathematics Category theory Research Curry/Howard/Lambek Lambda calculus Alpha conversion Beta reduction Eta conversion ... Lambda abstraction Other Recursion Combinatory logic Chaitin's construction Turing machine ... Relational algebra The Curry-Howard-Lambek correspondance is a three way isomorphism between types (in programming languages), propositions (in logic) and objects of a Cartesian closed category . Interestingly, the isomorphism maps programs (functions in Haskell) to (constructive) proofs in logic (and vice versa Contents Life, the Universe and Everything Inference Connectives Theorems for free! ... edit 1 Life, the Universe and Everything As is well established by now, theAnswer Integer theAnswer = The logical interpretation of the program is that the type Integer is inhabited (by the value ), so the existence of this program

3. The Curry-Howard Correspondence The CurryHoward correspondence. Haskell Curry (1900-1982). Started studying medicine at Harvard in 1916; enlisted in the war on 18 October 1918 http://utsl.gen.nz/talks/perl6.does-ML/slide4a.html

perl6.does(ML) How Type Theorists Saved the Perl 6 Project The Curry-Howard correspondence Started studying medicine at Harvard in 1916 enlisted in the war on 18 October 1918 inspired by a 1924 paper by M Schoenfinkel Ph.D in mathematics from Goettingen in 1930 wrote on Combinatory Logic from 1958-1980 taught at Harvard, Princeton, Pennsylvania State University, and the University of Amsterdam continued... Index

4. The Curry-Howard Correspondence In Set Theory The CurryHoward correspondence between proofs and programs was originally discovered with the system of simple types, which uses the intuitionistic http://portal.acm.org/citation.cfm?id=788022.789004

5. Buy.com - Derivation And Computation: Taking The Curry-Howard Correspondence Ser Derivation and Computation Taking the CurryHoward correspondence Seriously Derivation Systems, Substitution Algorithms, Computation Mechanisms Harold http://www.buy.com/prod/derivation-and-computation-taking-the-curry-howard-corre

My Account Wishlist Help All Departments ... Warranties Books by Title by Author by ISBN by Publisher Buy.com Save $30 Instantly with the Buy.com Visa Card. Click here. Books Best-sellers New ... Rewards UpdateProductViewHistoryCookie('Derivation and Computation: Taking the Curry-Howard Correspondence Seriously: Derivation Systems, Substitution Algorithms, Computation Mechanisms','30776167'); Derivation and Computation: Taking the Curry-Howard Correspondence Seriously: Derivation Systems, Substitution Algorithms, Computation Mechanisms (Hardcover) Author: Harold Simmons Product Image Pricing Additional Info Price: Shipping: Total Price: Ships from and sold by What's this? In Stock: Usually ships in 1 to 2 business days. Format: Hardcover Format: Hardcover ISBN: Publish Date: Publisher: Cambridge University Press Dimensions (in Inches) 9.5H x 6.5L x 1.25T Buy.com Sku: More about this product Item#: View similar products Product Summary Reviews Introduction to simple type theory; 200 exercises with complete solutions. ISBN: Publisher: Cambridge University Press Write a Review Be the first user to review this item Back to top Every voice counts, so stand up and be heard! Your opinion is important to us. If you have spotted a typo, discovered an incorrect price, or encountered a technical issue on this page, we want to hear about it. Thanks again for your feedback, and happy shopping!

6. The Curry-Howard Correspondence In Haskell The CurryHoward correspondence is a mapping between logic and type systems. On the one hand you have logic systems with propositions and proofs. http://www.thenewsh.com/~newsham/formal/curryhoward/

The Curry-Howard Correspondence in Haskell Tim Newsham The Curry-Howard correspondence is a mapping between logic and type systems. On the one hand you have logic systems with propositions and proofs. On the other hand you have type systems with types and programs (or functions). As it turns out these two very different things have very similar rules. This article will explore the Curry-Howard correspondence by constructing a proof system using the Haskell type system (how appropriate since Haskell is named after Haskell Curry, the "Curry" in "Curry-Howard"). We'll set up the rules of logic using Haskell types and programs. Then we'll use these rules as an abstract interface to perform some logic profs. Propositions and proofs Propositions and proofs in logic systems correspond to types and programs (or functions) in programming languages. Each proposition will be represented by a type. Each proof will be represented with a program that has the matching type. The program need not do anything in particular. In fact, there may be many programs with the type we're after (just as there may be many proofs of a proposition). It doesn't matter. We just need to find a program with the given type. The existence of a program for the type will be a proof of the corresponding proposition! (Note: to be correct, the function must be total: it must terminate for all defined arguments. It's easy to cheat by using "undefined" in your proofs. In fact, this is a useful tool when debugging incomplete proofs). [

7. JSTOR Derivation And Computation. Taking The Curry-Howard Despite the subtitle of the book, it is not clear to me just how we have taken the Curry Howard correspondence seriously, and what it has gained us. http://links.jstor.org/sici?sici=1079-8986(200109)7:3<380:DACTTC>2.0.CO;2-A

8. LtU Classic Archives A gentle introduction to TLG, the CurryHoward correspondence, and cut-elimination. Barker Chris. A gentle introduction to Type Logical Grammar, http://lambda-the-ultimate.org/classic/message9080.html

Lambda the Ultimate A gentle introduction to TLG, the Curry-Howard correspondence, and cut-elimination started 10/11/2003; 2:58:16 AM - last post 10/16/2003; 5:44:29 PM Ehud Lamm - A gentle introduction to TLG, the Curry-Howard correspondence, and cut-elimination 10/11/2003; 2:58:16 AM (reads: 6300, responses: 6) A gentle introduction to TLG, the Curry-Howard correspondence, and cut-elimination Barker Chris. A gentle introduction to Type Logical Grammar, the Curry-Howard correspondence, and cut elimination This paper aims to give an introduction to Type Logical Grammar (TLG) for the general linguist who may not have a background in logic or proof theory. This paper will briefly describe the logical heritage of TLG, sketch a simple TLG analysis, convey the spirit of the Curry-Howard result, discuss Gentzen’s famous cut-elimination result, and motivate multimodal extensions of Lambek’s logic. A short introduction to some of the same topics discussed in Girard's book plus an introduction to Type Logical Grammar for those who are interested in linguistics. Posted to theory by Ehud Lamm on 10/11/03; 2:59:14 AM

9. Review Harold Simmons, Derivation And Computation. Taking The Taking the CurryHoward correspondence Seriously. Full-text Access via JSTOR (no additional login). Go to this article in JSTOR. Links and Identifiers http://projecteuclid.org/handle/euclid.bsl/1182353805

Log in RSS Title Author(s) Abstract Subject Keyword All Fields FullText more options Home Browse Search ... next Review: Harold Simmons, Derivation and Computation. Taking the Curry-Howard Correspondence Seriously Norman Danner Source: Bull. Symbolic Logic Volume 7, Number 3 (2001), 380-383. Reviewed Items: Harold Simmons, Derivation and Computation. Taking the Curry-Howard Correspondence Seriously. Full-text: Remote access If you are a member of the ASL, log in to Euclid for access. Full-text is available via JSTOR, for JSTOR subscribers. Go to this article in JSTOR. Links and Identifiers Permanent link to this document: http://projecteuclid.org/euclid.bsl/1182353805 JSTOR: links.jstor.org back to Table of Contents previous next Bulletin of Symbolic Logic Current Issue All Issues Search this Journal Editorial Board ... Log in RSS Cornell University Library

10. Re: [Haskell-cafe] Tutorial: Curry-Howard Correspondence A tutorial on the CurryHoward correspondence in Haskell http//www.thenewsh.com/%7Enewsham/formal/curryhoward/ Feedback appreciated. http://www.mail-archive.com/haskell-cafe@haskell.org/msg31496.html

haskell-cafe Thread Date Re: [Haskell-cafe] Tutorial: Curry-Howard Correspondence Dan Weston Wed, 17 Oct 2007 15:24:59 -0700 Also, I was wondering if the constructor and/or function arguments should be marked strict. Otherwise, types can be inhabited by defined arguments. Since Prop is not strict in its argument, we could have the (false) theorem That is a great tutorial. Thanks! But in the last two sentences of the introduction you say: even though (fix id) is well-typed and id is certainly not undefined (though fix id is). Tim Newsham wrote: A tutorial on the Curry-Howard Correspondence in Haskell: http://www.thenewsh.com/%7Enewsham/formal/curryhoward/ Feedback appreciated. Tim Newsham http://www.thenewsh.com/~newsham/ http://www.haskell.org/mailman/listinfo/haskell-cafe http://www.haskell.org/mailman/listinfo/haskell-cafe [Haskell-cafe] Tutorial: Curry-Howard Correspondence Tim Newsham Re: [Haskell-cafe] Tutorial: Curry-Howard Correspondence Andrea Rossato Re: [Haskell-cafe] Tutorial: Curry-Howard Correspondence Yitzchak Gale Re: [Haskell-cafe] Tutorial: Curry-Howard Correspondence Krzysztof Koà ›ciuszkiewicz Re: [Haskell-cafe] Tutorial: Curry-Howard Correspondence Tim Newsham Re: [Haskell-cafe] Tutorial: Curry-Howard Correspondence Vitaliy Akimov Re: [Haskell-cafe] Tutorial: Curry-Howard Correspondence Tim Newsham Re: [Haskell-cafe] Tutorial: Curry-Howard Correspondence Lennart Augustsson Re: [Haskell-cafe] Tutorial: Curry-Howard Correspondence Dan Weston Re: [Haskell-cafe] Tutorial: Curry-Howard Correspondence

11. Powell's Books - Cambridge Tracts In Theoretical Computer Science #51: Derivatio Cambridge Tracts in Theoretical Computer Science 51 Derivation and Computation Taking the CurryHoward correspondence Seriously. by Harold Simmons http://www.powells.com/biblio?isbn=9780521771733

12. Lectures On The Curry-Howard Isomorphism, 149 - Elsevier The CurryHoward isomorphism states an amazing correspondence between systems of formal logic as encountered in proof theory and computational calculi as http://www.elsevier.com/wps/product/cws_home/706927

Home Site map Elsevier websites Alerts ... Lectures on the Curry-Howard Isomorphism, 149 Book information Product description Audience Author information and services Ordering information Bibliographic and ordering information Conditions of sale Book-related information Submit your book proposal Other books in same subject area About Elsevier Select your view LECTURES ON THE CURRY-HOWARD ISOMORPHISM, 149 To order this title, and for more information, click here By , M.Sc, Ph.D, University of Copenhagen, Denmark Pawel Urzyczyn , prof. dr hab., Warsaw University, Poland Included in series Studies in Logic and the Foundations of Mathematics, 149 Description Key features - The Curry-Howard Isomorphism treated as common theme - Reader-friendly introduction to two complementary subjects: Lambda-calculus and constructive logics - Thorough study of the connection between calculi and logics - Elaborate study of classical logics and control operators - Account of dialogue games for classical and intuitionistic logic - Theoretical foundations of computer-assisted reasoning Audience Graduate students, lecturers and researchers in logic and theoretical computer science. Also for graduate students, lecturers and researchers in philosophy and mathematics.

13. Re: [Haskell-cafe] Tutorial: Curry-Howard Correspondence the actual statement of the CurryHoward correspondence, it s a. correspondence between intuitionistic propositional logic and the simply http://www.opensubscriber.com/message/haskell-cafe@haskell.org/7826449.html

haskell-cafe@haskell.org search all groups... Home Join Log In Watch this thread FAQ h haskell-cafe@haskell.org Re: [Haskell-cafe] Tutorial: Curry-Howard Correspondence by Derek Elkins Reply to author Reply to group On Wed, 2007-10-17 at 15:06 -0700, Dan Weston wrote: Yes it does. Yes it does. Terms in Haskell prove the propositions that the types of Haskell correspond to. *The logic that Haskell's type systems corresponds to is inconsistent.* This is what you are missing. Haskell's type systems does not correspond to intuitionistic propositional logic. Indeed, in the actual statement of the Curry-Howard correspondence, it's a correspondence between intuitionistic propositional logic and the simply typed lambda calculus which Haskell quite certainly is not. As is well known, it (CH) can be generalized beyond that, but generally you need a strongly normalizing language (or at least prove strong normalization for your particular term and note normalization means -normal form- not weak head normal form) to actually use the "programs" as proofs. Haskell-Cafe mailing list Haskell-Cafe@hask...

14. Advogato: Blog For Chalst Formulaeas-types correspondence;; Curry-Howard correspondence;; Curry-Howard isomorphism;. with the latter only under sufferance; also note that the phrase http://www.advogato.org/person/chalst/diary.html?start=132

15. Programs From Proofs In Haskell Programs from Proofs via the CurryHoward correspondence This time I want to use it to explore the Curry-Howard correspondence, which is the idea that http://www.polyomino.f2s.com/david/haskell/programsfromproofs.html

Haskell for Maths www.polyomino.f2s.com Home Code Articles Haskell ... Books Programs from Proofs via the Curry-Howard Correspondence Last time we wrote a theorem prover for intuitionistic propositional logic. This time I want to use it to explore the Curry-Howard correspondence, which is the idea that propositions in logic are like types in functional programming. The basic correspondence goes like this: Proposition Type Implication a->b Function a->b Conjunction Product type (a,b) Disjunction Sum type Either a b (If this seems strange at first, think about it this way: The product type (a,b) is an a and a b. The sum type Either a b is an a or a b. The function type a->b means that if you give me an a, then I can give you back a b, so an a implies a b.) So far so good. But the Curry-Howard correspondence goes further. First of all, it says that if there is a Haskell function having a particular (polymorphic) type, then the corresponding proposition is provable in intuitionistic logic. For example: (In Hugs and GHCi, :t tells you the type of an expression. We find that the type of "fst" - when translated into a proposition using the Curry-Howard correspondence - is provable in intuitionistic logic.) A function of a given type is called an inhabitant of that type, and a

16. Computing Reviews, The Leading Online Review Service For Computing Literature. Another advanced theoretical underpinning of the book is the CurryHoward isomorphism or correspondence, in which ordinary intuitionistic logic corresponds http://reviews.biz/review/review_review.cfm?review_id=134678

17. Hindley. Basic Simple Type Theory. Using the CurryHoward correspondence, this is seen to be related to Gentzen s We can show a Curry-Howard correspondence between TA and intuitionist http://mathgate.info/cebrown/notes/hindley97.php

TPS A higher-order theorem proving system The Omega Group This page was created and is maintained by Chad E Brown J. Roger Hindley, Basic Simple Type Theory. Cambridge University Press, 1997. Chapter 1: The type-free lambda calculus. Chapter 2: Assigning types to terms. Chapter 3: The principal-type algorithm. Chapter 4: Type assignment with equality. ... Chapter 9: Technical details. Introduction: This book studies the system TA (for "Type Assignment") which is lambda calculus (with variables but no constants) and types built from type variables and arrows. The main results discussed are the principal-type algorithm, the converse principal-type algorithm, and the inhabitant-counting algorithm. Chapter 1: The type-free lambda calculus. Lambda terms are built from term-variables by application and lambda abstraction. For each lambda term we have notions of length, subterms, occurrences, components, body, scope, covering abstractors (of a subterm [those abstractors which dominate the subterm]), free and bound non-binding variable-occurrences. We also have substitution, alpha-conversion, bound-variable clashes, and closed terms = combinators. The common combinators (including Curry's fixed point combinator Y) are given. Beta-contraction (one step of a beta-reduction), beta-reduction and beta-conversion are defined. The

18. Carl: Curry-Howard Isomorphism CurryHoward Isomorphism. Presented by Carl Eastlund Matthias note the correspondence between introduction and elimination rules. http://www.ccs.neu.edu/home/matthias/369-s04/Transcripts/curry-howard.html

Curry-Howard Isomorphism Presented by Carl Eastlund Transcribed by Sam Tobin-H. Curry-Feys 58 Uses combinators instead of explicit lambda terms Combinators Application Modus Ponens Matthias: What's the correspondence here? Dave: propositions and types Matthias: these are the basic axioms of logic Howard 69, published 80 Implication logic lambda-calc x A x A M B M N A B Propositions Types Proofs Terms Matthias: Types are propositions about programs Strongly normalizing x A M B N A B reduces to M B N A x A B Cut elimination is equivalent to beta reduction Why must our language be strongly normalizing?

19. CSL/KGC'03 - Alexandre Miquel: A Strongly Normalising Curry-Howard Correspondenc Alexandre Miquel A Strongly Normalising CurryHoward correspondence for IZF Set This method relies on the introduction of a Curry-style type theory http://www.logic.at/csl03/giveabs.php?102

20. CiteULike: Extended Curry-Howard Correspondence For A Basic Constructive Modal L Extended CurryHoward correspondence for a Basic Constructive Modal Logic title = {Extended Curry-Howard correspondence for a Basic Constructive Modal http://www.citeulike.org/user/vcvpaiva/article/401369

Register Log in FAQ CiteULike News Discussion Journals Browse current issues Groups Search groups Profile Library Watchlist ... Import Extended Curry-Howard Correspondence for a Basic Constructive Modal Logic Authors Bellin G de Paiva V Ritter E Online Article CiteSeer (at Penn State): View article online CiteSeer (at MIT): View article online CiteSeer (at Zurich): View article online CiteSeer (at Singapore): View article online Note: You or your institution must have access rights to this article. CiteULike will not help you view an online article which you aren't authorized to view. Copy-and-Pasteable Citation Citation format: Plain APA Chicago Elsevier Harvard MLA Nature Oxford Science Turabian Vancouver vcvpaiva's tags for this article categorical logic modal Other users who have posted this article kozima Everyone's tags for this article categorical logic modal modal-logic Abstract BibTeX Note: You may cite this page as: http://www.citeulike.org/user/vcvpaiva/article/401369 EndNote BibTeX vcvpaiva's tags All tags in vcvpaiva's library Filter: algebraic cat categorical combination ... sequent-calculus CiteULike organises scholarly (or academic) papers or literature and provides bibliographic (which means it makes bibliographies) for universities and higher education establishments. It helps undergraduates and postgraduates. People studying for PhDs or in postdoctoral (postdoc) positions. The service is similar in scope to EndNote or RefWorks or any other reference manager like BibTeX, but it is a social bookmarking service for scientists and humanities researchers.

21. The Curry-Howard Correspondence In Haskell - SWiK Recent Edits for Userjerryk; Recent Edits for del.icio.us bookmarks; Recent Edits for The CurryHoward correspondence in Haskell. created on 17 Oct 2007, http://swik.net/User:jerryk/del.icio.us bookmarks/The Curry-Howard Correspondenc

SWiK login / register changes) Return to del.icio.us bookmarks The Curry-Howard Correspondence in Haskell Your tags: or Cancel Tags Applied to this Entry 1 person has tagged this page: haskell logic user:jerryk type-systems ... Recent Edits for The Curry-Howard Correspondence in Haskell created on 17 Oct 2007, by Syndication, About SWiK Random Project Recent Edits All original text is available as Creative Commons Attribution-ShareAlike Privacy Terms Credits Your SWiK user name A new account Username: Password: Remember me on this computer Take credit for any changes I made as an anonymous user (or Cancel Username: Email: Optional Password: Verify: Remember me on this computer Take credit for any edits made as an anonymous user (or Cancel

22. Programming: The Curry-Howard Correspondence In Haskell The CurryHoward correspondence in Haskell (thenewsh.com). 34 points posted 15 days ago by nglynn5 comments. infocommentsrelateddetails http://programming.reddit.com/info/5ynu7/comments/c02a69z

register submit help blog ... stats search remember me recover password login sort by hot new top old other communities reddit.com science politics business ... The Curry-Howard Correspondence in Haskell (thenewsh.com) 32 points posted 2 months ago by nglynn 8 comments info comments related details you are viewing a single comment's thread jump to the above comments sciolizer (1 child) [+] sciolizer 2 points 2 months ago Thanks! That's exactly what I'm looking for! permalink parent feedback bookmarklets ... User Agreement please log in or register in to vote for the links you like or dislike. this will affect their ranking and help customize reddit for you. create a new account all it takes is a username and password username: email: (optional) password: verify password: setMessage($('captcha'), 'type the letters from the image above'); remember me User Agreement create account is it really that easy? only one way to find out... login already have an account and just want to login? username: password: remember me login forgot your password? close this window

23. Curry–Howard Correspondence The CurryHoward correspondence is the correspondence between the structure of proofs in logic, and the structure of computer programs. http://www.pkturner.org/programming/Curry-Howard.html

24. Derivation And Computation : Taking The Curry-Howard Correspondence Seriously Is Derivation and Computation Taking the CurryHoward correspondence Seriously only $160.39, get the Derivation and Computation Taking the Curry-Howard http://www.bestprices.com/cgi-bin/vlink/0521771730?id=nsession

25. British Library Direct: Order Details A Strongly Normalising CurryHoward correspondence for IZF Set Theory. Author. Miquel, A. Journal title. LECTURE NOTES IN COMPUTER SCIENCE http://direct.bl.uk/research/33/1A/RN137124049.html

This is an article from British Library Direct, a new service that allows you to search across 20,000 journals for free and order full text using your credit card. Buy this article Search British Library Direct Return to Search Engine Article details Article title A Strongly Normalising Curry-Howard Correspondence for IZF Set Theory Author Miquel, A. Journal title LECTURE NOTES IN COMPUTER SCIENCE Bibliographic details 2003, ISSU 2803, pages 441-454 Publisher Springer-Verlag; 1999 Country of publication Germany ISBN ISSN Language English Pricing To buy the full text of this article you pay: service charge Abstract: By using this site you agree to our Terms and Conditions Privacy policy We welcome your comments

26. Books - Lectures On The Curry-howard Isomorphism - 9780444520777 Synopsis The CurryHoward isomorphism states an amazing correspondence between systems of formal logic as encountered in proof theory and computational http://www.pricegrabber.com/search_getprod.php/isbn=9780444520777

Go back to home page Login Register Your Lists ... Holiday Guide SHOP FOR IN All Products Appliances Auto Parts Books Cameras Clothing Computers Electronics Furniture Indoor Living Magazines Movies Music Musical Instruments Office Outdoor Living Software Sporting Goods Toys Video Games SEARCH Sell Yours Save Product to Your List(s) (Javascript required) Set Price Alert Lectures on the Curry-howard Isomorphism (English) (ISBN: 9780444520777) Price range: from 8 Sellers Publisher: Elsevier Science Ltd Format: Hardcover MSRP: $ 121.00 Synopsis: The Curry-Howard isomorphism states an amazing correspondence between systems of formal logic as encountered in proof theory and computational calculi as found in type theory. For instance, minimal propositional logic corresponds to simply typed lambda-calculus, first-order logic correspon... Read More User Reviews Not Rated Write a Review Compare Prices Book Details New (1 Seller for $107.98) View All Conditions Enter Zip Code* Seller Price (USD) Tax* Shipping* BottomLinePrice* Availability Seller Rating Merchant Info No Tax Free In Stock 2323 Reviews Merchant Info 10% off Free In Stock Fewer than 10 reviews Amazon.com

27. DIKU Graduate/Ph.D. Course: The Curry-Howard Isomorphism The CurryHoward isomorphism states an amazing correspondence between systems of formal logic as encountered in proof theory and computational...... http://www.diku.dk/topps/activities/type-theory/index.html

Graduate/Ph.D. course: The Curry-Howard isomorphism (Spring 1998) Course description Title The Curry-Howard isomorphism Teachers Morten Heine S¸rensen (MHS) (Department of Computer Science, University of Copenhagen) Pawel Urzyczyn (PU) (University of Warsaw) Coordinator: Morten Heine S¸rensen Institution University of Copenhagen Department of Computer Science (DIKU) Universitetsparken 1 2100 Copenhagen East Denmark Tlf: +45-35 32 14 00 Fax: +45-35 32 14 01 Email: inform@diku.dk Time and place: Friday 9-12 in N034. During each of these periods there will be a 1-hour exercise/discussion session followed by a 2-hour lecture. Limitation: Maximum 20 participants. Credits 4 oral points (corresponding to 33% of full-time study at DIKU averaged over one semester). Examination form Weekly home exercises. Each home exercise will be graded with a score between and 100 percent. At the end of the course, an average of 50 percent is required. A number of written projects will be offered during and after the course. Exercises due 13/2: 1.66, 1.67, 1.68, 1.69, 1.70, 1.71, 1.76, 1.78, 1.82, 1.84.

28. Search Result 4, EE Alexandre Miquel A Strongly Normalising CurryHoward correspondence for IZF Set Theory. CSL 2003 441-454 DBLPconf/csl/Miquel03 http://www.informatik.uni-trier.de/ley/dbbin/dblpquery.cgi?query=Search&return=1

29. Fall 99, CSE 520: Lectures There is an interesting correspondence between the symply typed lambda calculus and the intuitionistic propositional logic, known as CurryHoward http://www.lix.polytechnique.fr/~catuscia/teaching/cg520/99Fall/lecture_notes/L1

Fall 99, CSE 520: Lectures 11 and 12 The Curry-Howard isomorphism There is an interesting correspondence between the symply typed lambda calculus and the intuitionistic propositional logic, known as Curry-Howard isomorphism. This correspondence has the following three levels: Types correspond to formulas A term M of type T correspond to a proof of the formula T (M is a representation, or encoding, of the proof) Beta-reduction corresponds to proof normalization (i.e. elimination of redundancy from a proof) Types as formulas The correspondence comes from interpreting the type variables as propositional letters, and the arrow -> as implication. Thus A -> B, for instance, corresponds to "A implies B". Program as proofs The fact that, for a given type T, there exists a lambda term (program) M with type T, corresponds to the fact that T as a formula is intuitionistically valid. Furthermore, M can be seen as a representation of the proof of T. Let us first observe that there is a correspondence one-to-one between the proofs in the type system of the simply typed lambda calculus and the lambda terms (modulo alpha-renaming). In fact, given a term M with type T, the proof of M:T is isomorphic to the parse tree of M. This is because each rule of the type system corresponds uniquely to a production in the grammar generating the lambda terms. We can therefore see a typeable lambda term as the encoding of the corresponding proof of typeability. The correspondence with intuitionistic validity comes from the observation that the rules of the type system, when we consider only the type part, are exactly the rules of the (implicational fragment of) intuitionistic logic. Namely, the following rules, where G represents a set of formulas:

30. Subject Guide To Television And Motion Picture Industry Materials In Manuscript Curry wrote western and mystery stories. His correspondence with publishers and and a screen treatment, “The Republic Of Irving,” by Howard Fast. http://libweb.uoregon.edu/speccoll/guides/tv.html

Look for books, magazines, videos, music, and more. Search for: Keyword Title Author Subject Call Number Entire Collection Audio Recordings UO Theses OIMB Portland Arch. Lib Summit WorldCat Advanced Search Options Home Find Resources Research Assistance Library Services About the Libraries Ask a Librarian My Account Hours Contact Us ... About Us Services Using the Collections Curriculum Support Collections Manuscripts Oregon Collection Rare Books Photograph Collections ... Exhibits Online Related Resources Electronic Records Program UO Digital Collections Northwest Digital Archives Oregon Newspapers Subject guide to television and motion picture industry materials in Special Collections Return to Guides list These collections may contain scripts for television series, ideas for series, and notes about series. This list only gives the name of the television shows found in each collection; it does not specify which are scripts, ideas, etc., and it does not give the titles of the episodes. For more complete information, see the individual inventories for each collection. Adams, Frank Ramsay

31. 15-312 Recitation 6 Curry-Howard 2002-10-02 Joshua Dunfield 15312 Recitation 6 Curry-Howard 2002-10-02 Joshua Dunfield (joshuad@cs) B. So in fact there is a second correspondence, between proofs and programs. http://www.cs.cmu.edu/~fp/courses/02-312/recitations/2002-10-02.txt

Type Proof term Program Provability

32. David Hare Papers, Original Folder List II Portable Theatre Group 32 4 ENGLAND S IRELAND receipts, correspondence, press release, scene breakdown, costume chart, actor Tim Curry s resume and http://www.hrc.utexas.edu/research/fa/hare.folder2.html

David Hare Papers Folder ListOriginal Acquisition (Continued) Series II. Collaborations, 1971-87, nd Box Folder Description Series III. Directing Activities, ca. 1969-86, nd Box Folder Description Series IV. Theatre Group Activities, 1965, 1971-88, nd Box Folder Description Series V. Career and Personal, 1968-92, nd Box Folder Description Series VI. Works by Others, 1993, nd Box Folder Description 36 4 Brenton, Howard. SKIN FLICKERScreenplay, mimeograph typescript, bound, nd 5-6 Evans, Colin Haydn. CASTLE OF THE STARPlayscript, photocopy of typescript with holograph revisions, nd. With letter from Andy of Young Indy Series II Ltd., nd 7 Rose-Price, Tim. THE SERPENT'S KISSScreenplay, printout typescript, 1993. With letter from Price to Hare, 24 March 1993 8 Shawn, Wallace. THE FEVERPerformance piece, photocopy typescript, bound, nd. With letter from Shawn to Hare, nd David Hare Papers Finding Aid Title Page Biographical Sketch Scope and ... Correspondents (Last modified: 30 October 1996) Reference queries to: reference@hrc.utexas.edu

33. Words And Other Things: Making It Explicit: Logical Expressivism As far as I can tell, getting a curryhoward correspondence for classical logic requires getting around to thinking about how to state the correspondence http://indexical.blogspot.com/2007/09/making-it-explicit-logical-expressivism.ht

skip to main skip to sidebar Words and Other Things Trying to generate more light than heat since 2006 Friday, September 14, 2007 Making It Explicit: logical expressivism There is nothing in Ch. 2, where logical expressivism is introduced, about quantifiers. At this point in the book, nothing has been said about objects, so I'm not sure what the quantifiers express since it is likely to be tied in with theoretical claims about objects. Modal operators aren't addressed in MIE, although they are tackled in the Locke Lectures. I don't remember that terribly well, although I think for the most part Brandom sticks to alethic modalities in S4 and S5. I could be wrong on this. I am almost positive he doesn't get to non-normal modal operators (to use Restall's terminology) such as the Kleene star. I currently have no idea what the Kleene star would express. I'm similarly unsure about intensional connectives as in relevant logic's fusion. It might be an interpretation similar to Restall's of application of data in the form of propositions to other data, although this is really speculative. There might be something in this. Something that I'm a little more immediately curious about is the status of translations of formulas. There are certain systems of logic that can be translated into others, e.g. S4 into intuitionistic logic. The conditional in S4 is classical, but the translation (in Goedel's translation at least) of the intuitionistic A->B looks like [](A'->B') where A' and B' are the translations of A and B. The classical conditional then will express a weaker acceptance of an inference but it will be modified in some way by the necessity operator in front. If the view of logic is right, one would expect the translation to preserve what is expressed in some form. I will have to track down the relevant part of the Locke Lectures in order to further test this idea.

34. Light Leaks - Something Nice About Ccg By the CurryHoward correspondence, each derivation corresponds to a term in a proof calculus, which is a certain sort of lambda calculus (bi-linear lambda http://simon.some-antics.com/lightleaks/?p=138

35. Ernest Hemingway Incoming Correspondence: H (#104) - John F. Kennedy Presidentia Incoming correspondence H arranged alphabetically by the name of the person writing Harris, W. Curry TLS 16 Feb 1953, Key West, 1 p. opened Sep 1998 http://www.jfklibrary.org/Historical Resources/Archives/Archives and Manuscripts

var isEditMode = "y"; Home Historical Resources Archives Hemingway, Ernest Search the archives, the web site, or other NARA resources Audiovisual Oral History Project Summaries Ernest Hemingway Incoming Correspondence: H (#104) A B C D ... G ] [H] [ Hemingway I J K ... Hynes, George Platt Hager, Ruth  (Kansas City Star colleague) ALS 8 Sept 1918, Kansas City, 8pp., w/envelope Hale, Juddy (Kansas City Star) TLS 21 Sept [1918, Kansas City] 5pp., w/newspaper clipping and envelope Hale, W. B. (reader) TLS 15 Oct 1936, Montevideo 1p. Hale, William Harlan See Horizon Hall, Brian See Gordon Harbord Hall, Ernest (EH's grandfather)  ANS Grandfather undated, 1p. Hall, Leicester C. (Grace's brother, Ernest's uncle) Cable 19 July [1918], to Grace Hall Hemingway, 1p. Hall, Mattis and Al

36. LILLY CORRESPONDENCE The Lilly correspondence, 19191954, consist of the correspondence of Josiah Barton Currie SEE ALSO Indiana Historical Society, Mrs. Anne C. Curry, http://www.indiana.edu/~liblilly/lilly/mss/html/lilly.html

Lilly Library Manuscript Collections Lilly Library Home Manuscript Collections Ask a Question LILLY CORRESPONDENCE The Lilly Correspondence, 1919-1954, consist of the correspondence of Josiah Kirby Lilly, 1893-1966, corporation executive of the Lilly Pharmaceutical Company of Indianapolis, Indiana, with bookdealers and individuals concerning the purchase of books and manuscripts for his library which reveal a concentration of interest in Edgar Allan Poe and James Whitcomb Riley, concerning the construction and equipment of Eaglecrest Library at his home, and his membership in the Grolier Club. Collection size: 6000 items (est.) For more information about this collection and any related materials contact the Public Services Department, Lilly Library, Indiana University, Bloomington, IN 47405. Call(812) 855-2452 or send an email using our Ask a Question form.

37. Http//hdl.loc.gov/loc.mss/eadmss.ms001001 William Dudley Foulke A The bulk of the collection consists of Foulke s correspondence reflecting his literary Herbert, 18741964correspondence Howard, O. O. (Oliver Otis), http://lcweb2.loc.gov/master/mss/eadxmlmss/2001/ms001001.xml

http://hdl.loc.gov/loc.mss/eadmss.ms001001 William Dudley Foulke A Register of His Papers in the Library of Congress Prepared by Wilhelmena B. Curry and Paul G. Sifton Revised by Connie L. Cartledge Manuscript Division, Library of Congress Washington, D.C. Contact information: http://lcweb.loc.gov/rr/mss/address.html Finding aid encoded by Library of Congress Manuscript Division, Finding aid written in English. converted from EAD 1.0 to EAD 2002 Collection Summary Papers of William Dudley Foulke ca. 1470-1952 (bulk 1868-1935) Foulke, William Dudley, 1848-1935 2,500 items 12 containers plus 1 oversize 5.2 linear feet Collection material in English Manuscript Division, Library of Congress Washington, D.C. Lawyer, public official, and author from Indiana. Correspondence, diaries, journals, copybook, speeches, writings, notes, legal papers, clippings, printed material, and other papers, including a late fifteenth century fragment of the Tristram Saga obtained by Arthur Middleton Reeves on a trip to Iceland. The bulk of the collection consists of Foulke's correspondence reflecting his literary career and public service, including letters from Theodore Roosevelt discussing civil service reform, the Progressive movement, Woodrow Wilson, the World Court (Permanent Court of International Justice), and pacifism. Selected Search Terms The following terms have been used to index the description of this collection in the Library's online catalog. They are grouped by name of person or organization, by subject or location, and by occupation and listed alphabetically therein.

38. Bibliography Of Hugo Herbelin We interpret Gentzen s sequent calculus as a lambdacalculus, hence providing a Curry-Howard correspondence for sequent calculus. http://yquem.inria.fr/~herbelin/publis/index-eng.html

Research articles "An approach to call-by-name delimited continuations" ACM for your personal use - not for redistribution) errata bibtex entry Abstract: It has been shown by Saurin that de Groote's variant of Parigot's lambda-mu-calculus is strictly more expressive in the untyped case than Parigot's original calculus. We show that this additional expressivity exactly corresponds to adding delimited control so that de Groote's calculus can be seen as the exact call-by-name counterpart of Danvy and Filinski's shift-reset calculus. This "duality" is expressed in the lambda-mu-tp-hat-calculus which is lambda-mu-calculus equipped with a single dynamically-bound continuation variable denoting a resettable toplevel. An equational correspondence having already been proved in A type-theoretic foundation of delimited continuations for call-by-value lambda-mu-tp-hat and Danvy and Filinski's calculus, we simply show here the equivalence between call-by-name lambda-mu-tp-hat and de Groote's calculus. We continue with a comparative study of the operational semantics, continuation-passing-style semantics, and simple typing of both call-by-name and call-by-value versions. Finally, we show the existence of two other canonical calculus of delimited continuations. The first one morally forms an equational correspondance with Sabry's shift/lazy-reset calculus while the second one is a "lazy" version of de Groote's calculus. "Control Reduction Theories: the Benefit of Structural Substitution",

39. Using Physician Correspondence And Postcard Reminders To Promote Mammography Use Using physician correspondence and postcard reminders to promote mammography use. S H Taplin, C Anderman, L Grothaus, S Curry, and D Montano http://www.pubmedcentral.nih.gov/articlerender.fcgi?artid=1614799

40. Recent Papers - Atsushi Ohori The Logical Abstract Machine a CurryHoward isomorphism for machine code . Proc. This logical correspondence enables us to present and analyze various http://www.pllab.riec.tohoku.ac.jp/~ohori/research/recent.html

Ohori's home page Recent papers of Atsushi Ohori See also a list of papers with pointers to dvi files Yutaka Matsuno and Atsushi Ohori. A Type System Equivalent to Static Single Assignment. to appear in ACM PPDP'06, 2006. (pdf file) Huu-Duc Nguyen and Atsushi Ohori. Compiling ML Polymorphism with Explicit Layout Bitmap to appear in ACM PPDP'06, 2006. (pdf file) Atsushi Ohori A Proof Theory for Machin Code ( To appear in ACM TOPLAS. A preliminary summary of some of the results were presented at the Fuji International Symposium on Functional and Logic Programming, 1999, as an invited paper entitled: ``The Logical Abstract Machine: A Curry-Howard Isomorphism for Machine Code,'' Springer LNCS 1722, pages 300318.) (pdf file) (revised Oct, 2005.) Tomoyuki Higuchi, Atsushi Ohori A Static Type System for JVM Access Control ( ACM Trans. Program. Lang. Syst. 29(1): (2007) A preliminary summary of this paper appeared in Proceedings of ACM International Conference on Functional Programming, pages 227237, Uppsala, Sweden, 2003.) (pdf file) This paper presents a static type system for the Java Virtual Machine (JVM) code that enforces an access control mechanism similar to that found in, for example, a Java implementation. In addition to verifying type consistency of a given JVM code, the type system statically verifies whether the code accesses only those resources that are granted by the prescribed access policy. The type system is proved to be sound with respect to an operational semantics that enforces access control dynamically, similar to Java stack inspection. This result ensures that ``well typed code cannot violate access policy.'' The authors then develop a type inference algorithm and show that it is sound with respect to the type system and that it always infers a minimal set of access privileges. These results allows us to develop a static system for JVM access control without resorting to costly runtime stack inspection.

41. Closed Categories « The Unapologetic Mathematician This is (one way of viewing) the CurryHoward correspondence (and why it’s sometimes referred to as the Curry-Howard-Lawvere or Curry-Howard-Lambek http://unapologetic.wordpress.com/2007/08/01/closed-categories/

The Unapologetic Mathematician Mathematics for the interested outsider Home About this weblog Closed Categories A closed category is a symmetric monoidal category where each functor . By what we said yesterday , this means that there is a unique way to sew all these adjoints parametrized by together into a functor. The canonical example of such a category is the category of sets with the cartesian product as its monoidal structure. For each set we need an adjunction and one from should be in bijection with functions from to . And indeed we have such an adjunction: is the set of all functions from to we have the function , which takes two numbers and gives back a third: if we stick in and we get back . But what if we just stick in the first number of the pair? Then what we get back is a function that will take the second number and give us the sum: if we just feed in we get back the function . That is, we can see addition either as a function taking a pair of numbers to a number, or we can see it as a function , taking a number to a function from numbers to numbers.

42. No Title Use of CurryHoward correspondance to prove the correctness of imperative an extension of Curry-Howard correspondence in a real mathematical theory, http://www.cs.chalmers.se/Cs/Research/Logic/TypesWG/report99.web/paris7/paris7.h

Next: Queen Mary and Westfield College, University of London Up: Progress Report Previous: University of Padova Paris 7 site: scientific report Paris 7 team studies most of the aspects of the correspondance between proofs and programs. This work can be classified along the following lines: - Computational interpretations of classical logic - Computational content of true mathematical theorems - Use of Curry-Howard correspondance to prove the correctness of imperative programs. - Game semantics for classical linear logic - Type systems for computer languages - Development of the AF2 proof assistant Computational interpretations of classical logic. M. Parigot introduces in [ ] a computional interpretation of classical logic, called -calculus which has been widely studied. In [ ], he gives two proofs of strong normalisation for second order typed -calculus. The first one is an adaptation of the method of reducibility candidates introduced by J.Y. Girard for second order typed -calculus; the extension to the classical case requires in particular a simplification of the notion of reducibility candidate. The second one is a reduction to the intuitionistic case, using a kind of cps translation. In [ ], V. Danos, J.B. Joinet and H.D Schellinx, packed a comprehensive study of sequent calculi for classical logic, most notably LKT, LKQ and LKTQ, that one could embed in linear logic. In [

43. Workshop On Implicit Computational Complexity Using the CurryHoward correspondence, we focus on the use of ELL as type system for lambda calculus, and more precisely, on type inference. http://www-lipn.univ-paris13.fr/~baillot/GEOCAL06/ICCworkshop.html

Workshop on Implicit Computational Complexity as part of GEOCAL'06 Marseille - Luminy February 13 - 17, 2006 NEW: CFP, Special Issue of ACM ToCL on Implicit Computational Complexity Context : This workshop is part of Geometry of Computation 2006 ( a special series of events in theoretical computer science organized by the GEOCAL group and taking place at the CIRM from January 30 to March 3. Geocal06 is supported by the following institutions: CIRM CNRS Luminy ParisNord ... Programme (with Slides of the talks) and Abstracts Invited speakers Martin Hofmann , LMU, Munich (Germany). James Royer , Syracuse University (USA). Kazushige Terui , NII, Tokyo (Japan). Timetable of the week (3 workshops) Presentation : Implicit Computational Complexity (ICC) has emerged from various propositions to use logic and formal methods like types, rewriting systems... to provide languages for complexity-bounded computation, in particular for polynomial time computing. It aims at studying the computational complexity of programs without refering to a particular machine model and explicit bounds on time or memory, but instead by relying on logical or computational principles that entail complexity properties. Several approaches have been explored for that purpose, like linear logic, restrictions on primitive recursion, rewriting systems, types and lambda-calculus... They often rely on the functional programming paradigm. Two objectives of ICC are: - on the one hand to find natural implicit logical characterizations of functions of various complexity classes

44. Woodruff Library Resources Also, extensive correspondence between Susie Bailey and her daughter Sue Bailey Thurman. Collection includes many photographs of Howard and Sue Bailey http://northstar.vassar.edu/volume5/woodruff.html

African-American Collections Related to Religious History in the Special Collections Department, Robert W. Woodruff Library, Emory University, Atlanta, Georgia Compiled by: Randall K. Burkett Curator of African-American Collections Special Collections Department Robert W. Woodruff Library Emory University Atlanta, GA 30322-2870 Email: rburket@emory.edu Black Print Culture Bailey-Thurman Papers . Papers of Isaac and Susie Bailey, Baptist religious leaders in Arkansas, colporteurs for the American Baptists, with print ephemera from Arkansas, books from their lending library, and the printed constitution of a late-19th century literary society they organized. Also, extensive correspondence between Susie Bailey and her daughter Sue Bailey Thurman. Collection includes many photographs of Howard and Sue Bailey Thurman. Finding aid available. Alexander Crummell Pamphlet Collection . (Founder, American Negro Academy, Episcopal priest d. 1895.) Approximately 20 black-published items from his personal library. Bibliographic records are available on EUCLID (Emory on-line catalog). Papers of the Civil Rights and Post-Civil Rights Movements Joan C. Browning Papers

45. Record Unit 7103 - Herbert Spencer Barber Papers, 1903-1950 Administration is the primary topic in folders of Leland Ossian Howard, Harold Morrison, and Sievert Allen Rohwer. correspondence exists with many http://siarchives.si.edu/findingaids/FARU7103.htm

Finding Aids to Personal Papers and Special Collections in the Smithsonian Institution Archives Record Unit 7103 Herbert Spencer Barber Papers, By Richard H. Lytle and Leslie E. Sagle Introduction Historical Note Descriptive Entry Series Descriptions ... Series 1. NOTEBOOKS, 1903-1918, 12 VOLUMES. Series 2. OUTGOING CORRESPONDENCE, 1904-1909, 1 BOUND VOLUME WITH PARTIAL INDEX. Series 3. CORRESPONDENCE, 1906-CIRCA 1939. Series 4. CORRESPONDENCE, CIRCA 1938-1950. Series 5. NOTES AND PAPERS. Series 6. ADD ACQUISITION, ACCESSION 89-014. INTRODUCTION This finding aid was digitized with funds generously provided by the Smithsonian Institution Women's Committee. HISTORICAL NOTE DESCRIPTIVE ENTRY Prominent correspondents are listed in the description of each series, followed by folder lists. Some Barber material remains in the Department of Entomology, notably random nomenclature and taxonomic notes on various genera of Chrysomelidae (.75 cubic foot) and card files of collecting and research work at Plummer's Island. SERIES DESCRIPTIONS SERIES 1.

46. The Burton Howard And Angelina Carhart Tallmon Jones Papers folder 17 Curry (?) Boyardis (?) (1832). folder 18 L. Monroe Bricker (1955) . folder 14 Howard Caswell Jones, correspondence (19161989) http://db3-sql.staff.library.utah.edu/lucene/Manuscripts/null/Accn2132.xml/compl

The Burton Howard and Angelina Carhart Tallmon Jones Papers Summary Complete Guide Bio/Hist Info Index Terms ... Back to Search The Manuscripts Librarian is Dr. Stan Larson. For further information, email: stan.larson@library.utah.edu or call (801) 585-3076. Summary Description Abstract: Biography Scope and Content Administrative Information Restrictions : Materials must be used on-site; advance notice suggested. Access to parts of this collection may be restricted under provisions of state or federal law. Related Material : Photographs were transferred to the Multimedia Division of Special Collections (P1155). Donor Information : Acq Method: donated by Acq Name: Charles H. Walker Acq Date: October 2004 and January 2005 Processing Information : This collection was processed by Sabrina Baksh-Riches and Lisa DeMille on 2005. Index Terms These records are indexed under the following headings in the catalog of the J.Willard Marriott Library, University of Utah. Researchers wishing to find related materials should search the catalog under these index terms.

47. Work Projects Administration Collection, 1909-1971 (bulk 1930-1946) 12, The American Guide Manual Manuscript and correspondence re . 192, Curry County - Pioneers. 1937. Example The Japanese Colony View all pages http://elibrary.unm.edu/oanm/NmAr/nmar#1959-232/nmar#1959-232_m8.html

48. ICU.SPCL.ZABEL Guide To The Morton Dauwen Zabel Papers 1901-1964 Series I correspondence and Items from Poetry A Magazine of Verse, . Richard PP 19311937 1 9 Blake, Howard 1934-1937 1 10 Bogan, Louise 192? http://ead.lib.uchicago.edu/view.xqy?id=ICU.SPCL.ZABEL&view=xml

49. Poynter Online - Romenesko Couric had her colonoscopy; now Curry has her bungee jump If Today show viewers respond to Ann Curry s jump the way they did to Katie Couric s http://www.poynter.org/column.asp?id=45&aid=134039

50. Thomas Hawtin's Weblog Also it is normal to write a curry function as part of a functional library, e.g. C++ STL and JGA both call this function bind. Posted by Howard Lovatt on http://www.jroller.com/tackline/entry/feeping_creaturism_new_fangled_closures

December 2007 Mon Tue Wed Thu Fri Sat Sun Today Tom Hawtin All Java Fluff Security Looking for a homeless Java programmer in southern England Scotland Dublin 1, Dublin tackline@tackline.plus.com The Closure proposal Main Using Applets in... Sunday August 27, 2006 Feeping Creaturism: New Fangled Closures vs Updated Local Classes Neal Gafter has weblogged more about the closure proposal ( Use cases for closures and Tennent's Correspondence Principle and Returning From a Closure Function types Function types are an extreme extension to the Java type system. Client code isn't going to use them. Pointless. BTW: To be clear, I'm not suggesting using the most general of interfaces. I don't want to see types of the form . I suggest interfaces allied to how the method will be used. The type documentation should be sufficiently concrete that the referring algorithm method @param should more or less specify just that it uses a particular type. Tennent's Correspondence Principle There are a couple of cases in which achieving Tennent's Correspondence with the closure proposal is not going to happen. Definite assignment goes out of the window. The exception simulating break, continue and return can be caught, or discarded by finally. A finally in an algorithm method wont be obvious to the application programmer. What is one to do? Discard exceptions caused by closing resources? Call std::abort Should there not be a correspondence between closures and local classes? That's got to be confusing - having two mechanisms that the compiler treats differently when asked to make up your mind. Code that could equally appear in outer methods, closures and inner classes should always have the same interpretation. I'm sure some syntax for qualifying the nested instance or outer method is more than doable. Old ambiguous code can throw up warnings.