August 2012 - Haskell

ANNOUNCE: tardis
by Dan Burton 07 Aug '12

07 Aug '12

I'm pleased to announce that I've uploaded the *tardis* package to hackage. http://hackage.haskell.org/package/tardis-0.2.0.0 *TardisT* is a monad transformer that combines the (regular, "forwards") State monad with the "backwards State monad", allowing you to communicate on two channels of state: one is "backwards travelling" state, while the other is "forwards travelling" state. Its primitives are comparable to the State monad's "get" and "put", but the names disambiguate which channel they operate on: getPast :: Monad m => TardisT bw fw m fw getFuture :: Monad m => TardisT bw fw m bw sendPast :: Monad m => bw -> TardisT bw fw m () sendFuture :: Monad m => fw -> TardisT bw fw m () These primitives allow you to write some very amusing timey-wimey code, but it only works in the presence of sufficient laziness. If you run into an infinite loop, try adding laziness annotations everywhere, and make sure that what you are trying to do is not a time paradox. I've provided both *transformers* and *mtl* style modules: Control.Monad.Trans.Tardis contains the transformer, while Control.Monad.Tardis.Class contains the MonadTardis class, and Control.Monad.Tardis re-exports both as well as the TardisT instance for MonadTardis. See the readme on github for more details: https://github.com/DanBurton/tardis#readme As a side note, since the code base is relatively small, it can also serve as a simple demonstration of how to use a cabal flag in conjunction with CPP to selectively include swaths of code (see Control/Monad/Tardis.hs and tardis.cabal). I'm not entirely sold on the naming conventions for the package (including the package name), and am open to suggestions. -- Dan Burton

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Call for Participation: HOPE 2012
by Amal Ahmed 06 Aug '12

06 Aug '12

********************************************************************* CALL FOR PARTICIPATION HOPE 2012 The 1st ACM SIGPLAN Workshop on Higher-Order Programming with Effects Sunday, September 9, 2012 Copenhagen, Denmark To be held in conjunction with ICFP 2012 http://hope2012.mpi-sws.org ********************************************************************* IMPORTANT DATES Early registration deadline: August 9, 2012 *** only days away! *** Hotel reservation deadline: August 9, 2012 (for most hotels) VENUE HOPE 2012 and all ICFP'12 affiliated events will take place at DGI-byen's conference center - CPH Conference, Tietgensgade 65, DK 1704 Copenhagen V. More information at: http://icfpconference.org/icfp2012/local.html HOPE 2012 HOPE is a *new workshop* that is intended to bring together researchers interested in the design, semantics, implementation, and verification of higher-order effectful programs. This 1st edition of HOPE is dedicated to John Reynolds, whose work is an inspiration to us all. There were 21 talk submissions, of extraordinarily high quality. As the workshop is only one day long, we were only able to accept 13 of them for presentation at the workshop. So there will be 13 contributed talks, but no invited talks or other sessions. We expect this to be a very high-octane workshop! PROGRAM The program is included at the end of this email; it can also be found here: http://hope2012.mpi-sws.org/ PROGRAM CHAIRS Amal Ahmed (Northeastern University) Derek Dreyer (MPI-SWS, Germany) PROGRAM COMMITTEE Jim Laird (University of Bath) Rasmus Møgelberg (IT University of Copenhagen) Greg Morrisett (Harvard University) Aleks Nanevski (IMDEA Software Institute) David Naumann (Stevens Institute of Technology) Matthew Parkinson (Microsoft Research Cambridge) François Pottier (INRIA Rocquencourt) Amr Sabry (Indiana University) Eijiro Sumii (Tohoku University) Nikhil Swamy (Microsoft Research Redmond) Nobuko Yoshida (Imperial College London) PRELIMINARY PROGRAM SUNDAY, September 9, 2012 Session 1: Verification 9:00 Modular Specification and Verification of Delegation with SMT Solvers Ioannis Kassios, Peter Müller 9:30 On Higher-Order Separation Logic for Higher-Order Concurrent Imperative Programs Kasper Svendsen, Lars Birkedal, Matthew Parkinson 10:00 Verifying an Open Compiler from ML to Assembly James T. Perconti, Amal Ahmed 10:30 BREAK Session 2: Monads and More 11:00 Handlers in Action Ohad Kammar, Sam Lindley, Nicolas Oury 11:30 Contract Monitoring as an Effect Zachary Owens 12:00 HOPE for a Type-Theoretic Understanding of Zero-Knowledge Noam Zeilberger 12:30 LUNCH Session 3: Types and Effects 2:00 Koka: A Language with Row-Polymorphic Effect Inference Daan Leijen 2:30 Effects for Funargs Jeremy Siek, Michael Vitousek, Jonathan Turner 3:00 Generative Names and Dependent Types Andrew Pitts 3:30 BREAK Session 4: Logical Relations and Parametricity 4:00 Logical Relations for Fine-Grained Concurrency Aaron Turon, Jacob Thamsborg, Amal Ahmed, Lars Birkedal, Derek Dreyer 4:30 Logical Relations for a Manifest Calculus, Fixed Taro Sekiyama, Atsushi Igarashi 5:00 Proof-Relevant Logical Relations Nick Benton, Martin Hofmann, Andrew Kennedy, Vivek Nigam 5:30 Two Theories of Information Hiding Uday Reddy

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Call for Participation: XLDI 2012 (@ ICFP 2012)
by Torsten Grust 03 Aug '12

03 Aug '12

CALL FOR PARTICIPATION XLDI 2012 First International Workshop on Cross-Model Language Design and Implementation http://workshops.inf.ed.ac.uk/xldi2012/ Affiliated with ICFP 2012, Copenhagen, Denmark Sponsored by ACM SIGPLAN September 9, 2012 (Sunday before ICFP) You need an ICFP Sunday pass to participate in XLDI 2012. For details on ICFP registration please see http://icfpconference.org/icfp2012/registration.html XLDI 2012 focuses on the foundations, design, implementation, and applications of languages that smoothly integrate different execution or data models. We have assembled an interesting program of 7 presentations, covering software-defined networks, Haskell DSLs for interactive web services, typing of massive JSON datasets, rewrite optimization of dataflow programs, and languages designed to build domain-specific runtimes. INVITED SPEAKERS: - Fritz Henglein (DIKU, University of Copenhagen) - Christopher Re (University of Wisconsin) SCIENTIFIC PROGRAMME: - Naga Praveen Katta, Jennifer Rexford, David Walker: Logic Programming for Software Defined Networks - Andrew Farmer, Andy Gill: Haskell DSLs for Interactive Web Services - Dario Colazzo, Giorgio Ghelli, Carlo Sartiani: Typing Massive JSON Datasets - Fabian Hueske, Aljoscha Krettek, Kostas Tzoumas: Enabling Rewrite Optimizations of Data Flow Programs Through Static Code Analysis - Panchapakesan Shyamshankar, Zachary Palmer, Yanif Ahmad: K3: Language Design for Building Multi-Platform, Domain-Specific Runtimes SPONSORS: XLDI 2012 is sponsored by LogicBlox and Oracle Labs. We are looking forward to see you in Copenhagen, --James Cheney, Torsten Grust (XLDI co-chairs)

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ANNOUNCE: time-recurrence-0.9.0
by Chris Heller 03 Aug '12

03 Aug '12

I am happy to announce a new version of time-recurrence, a library of functions for generating recurring sequences of dates: http://hackage.haskell.org/package/time-recurrence New in version 0.9.0 is a redesigned top layer API. Previously recurrences were described by combining generating functions to get the desired effect. This was quite functional but had the drawback that a recurrence was difficult to persist outside of the Haskell run-time. As of version 0.9.0 this limitation is no more. Now the actual recurrence rule is defined by combining types into a data structure which can either be persisted (and later read back) or evaluated into a function to generate dates. This also means that the type system now enforces correct rule creation! Additionally some convenience functions are available to construct the recurrence rule in a format familiar to previous users of this library. Here is a familiar example: Generate the 15th and 30th of the month, but only during the work week: > jan2011 = ptime "Sat, 01 Jan 2012 00:00:00 -0400" > jan2012 = ptime "Sun, 01 Jan 2013 00:00:00 -0400" > takeWhile (<= jan2013) $ starting jan2012 $ > recur monthly > >==> enum (Days [15,30]) > >==> filter (WeekDays [Monday .. Friday]) [2011-02-15 04:00:00 UTC ,2011-03-15 04:00:00 UTC, 2011-03-30 04:00:00 UTC ,2011-04-15 04:00:00 UTC ,2011-05-30 04:00:00 UTC ,2011-06-15 04:00:00 UTC, 2011-06-30 04:00:00 UTC ,2011-07-15 04:00:00 UTC ,2011-08-15 04:00:00 UTC, 2011-08-30 04:00:00 UTC ,2011-09-15 04:00:00 UTC, 2011-09-30 04:00:00 UTC ,2011-11-15 04:00:00 UTC, 2011-11-30 04:00:00 UTC ,2011-12-15 04:00:00 UTC, 2011-12-30 04:00:00 UTC ] On the road to version 1.0, I plan to add another type layer which strictly enforces RFC 5545 section 3.3.10. As always I encourage feedback, criticism, suggestions and pull requests. I would especially welcome any type system experts feedback: quite a few GHC extensions needed to be turned on to get this to work. -Chris

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ALife category
by Amy de Buitléir 02 Aug '12

02 Aug '12

I'm developing a framework for artificial life experiments that I would like to make available on Hackage eventually. I've read all the guidance and proposals I could find for where to place packages in the hierarchy: http://www.haskell.org/haskellwiki/Hierarchical_module_names http://www.cs.york.ac.uk/fp/libraries/layout.html http://www.cs.york.ac.uk/fp/libraries/layoutSM.html I've also examined the current hierarchy of modules: http://hackage.haskell.org/packages/archive/pkg-list.html The current hierarchy has a top-level AI category, so it would seem logical to me to add a top-level ALife category and put my package under that. But perhaps it would be best not to start a new top-level category? I could put my package under AI, because my framework does support the use of AI, and wouldn't look too out of place with the other packages there. Thoughts?

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[ANNOUNCE] dynamic-linker-template: automatically derive dynamic linking methods from a data type.
by Sylvain HENRY 02 Aug '12

02 Aug '12

Hi, A few days ago I uploaded on Hackage the first release of dynamic-linker-template package (System.Posix.DynamicLinker.Template). Basically, it uses Template Haskell to generate boilerplate code to dynamically load symbols of a shared library into a data defined using "record" syntax. Simple example: ---------------------- {-# LANGUAGE TemplateHaskell, ForeignFunctionInterface #-} import System.Posix.DynamicLinker.Template data MyLib = MyLib { -- Mandatory field (name and type) libHandle :: DL, -- Mandatory symbol. Will throw an exception if not available myFunction1 :: Int -> Float, -- Optional symbol myFunction2 :: Maybe (Int -> Int) } $(makeDynamicLinker ''MyLib CCall 'id) -- Use any String->String function instead of "id" to transform field names into symbol names -- The following function will be generated: -- loadMyLib :: FilePath -> [RTLDFlags] -> IO MyLib main = do lib <- loadMyLib "mylib.so" [RTLD_NOW,RTLD_LOCAL] putStrLn $ show (myFunction1 lib 10) ---------------------- For a real world example (with the OpenCL library), see [1]. I don't use optional symbols yet but I will as I need to support different OpenCL versions that expose different symbols (some become deprecated and new releases add new ones). I use a custom function to transform field names into symbol names (to strip prefix). This functionality will also be useful with CUDA library which appends "_v2" to every symbol in recent releases... Do not hesitate to report any bug or suggestion. Cheers Sylvain [1] http://github.com/hsyl20/HViperVM/commit/26d512e924f7097e536351c412ea5986d3… -- Sylvain Henry CS PhD Student at INRIA/LaBRI University of Bordeaux (France) sylvain.henry(a)inria.fr

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Haskell Implementors' Workshop 2012: Call for Participation
by Johan Tibell 02 Aug '12

02 Aug '12

===================================================================== Call for Participation ACM SIGPLAN Haskell Implementors' Workshop http://haskell.org/haskellwiki/HaskellImplementorsWorkshop/2012 Copenhagen, Denmark, September 14th, 2012 The workshop will be held in conjunction with ICFP 2012 http://www.icfpconference.org/icfp2012/ ===================================================================== There are less than nine days left until the early registration expires! The Haskell Implementors' Workshop is to be held alongside ICFP 2012 this year in Copenhagen, Denmark. There will be no proceedings; it is an informal gathering of people involved in the design and development of Haskell implementations, tools, libraries, and supporting infrastructure. This relatively new workshop reflects the growth of the user community: there is a clear need for a well-supported tool chain for the development, distribution, deployment, and configuration of Haskell software. The aim is for this workshop to give the people involved with building the infrastructure behind this ecosystem an opportunity to bat around ideas, share experiences, and ask for feedback from fellow experts. We intend the workshop to have an informal and interactive feel, with a flexible timetable and plenty of room for ad-hoc discussion, demos, and impromptu short talks. * Program: http://www.haskell.org/haskellwiki/HaskellImplementorsWorkshop/2012 * Local arrangements (including travel and accommodation): http://icfpconference.org/icfp2012/local.html * Registration is available via (workshop abbreviation: HIM): http://icfpconference.org/icfp2012/registration.html Workshop organizers: * Workshop Co-Chairs: Gregory Collins, Google Johan Tibell, Google * Program Committee: Lennart Augustsson, Standard Chartered Bank Manuel M T Chakravarty, University of New South Wales Simon Marlow, Microsoft Research David Terei, Stanford University =====================================================================

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Haskell Weekly News: Issue 238
by Daniel Santa Cruz 02 Aug '12

02 Aug '12

Welcome to issue 238 of the HWN, an issue covering crowd-sourced bits of information about Haskell from around the web. This issue covers the week of July 22 to 28, 2012. Quotes of the Week * clsmith: i find programming in haskell is mostly about reinventing things and then discovering them in Prelude * EvanR: ruby, cobol of the 2000s * monochrom: "customers who used == also liked: foldr, map, Ord, continuation passing style" * jmcarthur: we calmly talk trolls to death Top Reddit Stories * Haskell logo QR code Domain: self.haskell, Score: 44, Comments: 5 On Reddit: [1] http://goo.gl/DuSSU Original: [2] http://goo.gl/DuSSU * In Praise of EitherT Domain: ocharles.org.uk, Score: 43, Comments: 9 On Reddit: [3] http://goo.gl/V2R9B Original: [4] http://goo.gl/M7rTb * The must-know list of packages on hackage? Domain: self.haskell, Score: 39, Comments: 29 On Reddit: [5] http://goo.gl/N7i6J Original: [6] http://goo.gl/N7i6J * SmartCheck: a better QuickCheck for testing algebraic data and generalizing counterexamples found Domain: leepike.wordpress.com, Score: 39, Comments: 6 On Reddit: [7] http://goo.gl/ENFxH Original: [8] http://goo.gl/SZMCG * Compile Haskell (Fay) to Javascript using Javascript compiled with GHCJS Domain: ghcjs.github.com, Score: 36, Comments: 8 On Reddit: [9] http://goo.gl/YOSuG Original: [10] http://goo.gl/d7Af4 * Programming in Fay - Simple example Domain: youtube.com, Score: 30, Comments: 17 On Reddit: [11] http://goo.gl/Ieswf Original: [12] http://goo.gl/4DcLd * Flexibly-Phased Constraints in Haskell Domain: jonmsterling.com, Score: 28, Comments: 19 On Reddit: [13] http://goo.gl/uvYY4 Original: [14] http://goo.gl/3cRD4 * Do you use Haskell in business? What do you use it for? Domain: self.haskell, Score: 24, Comments: 57 On Reddit: [15] http://goo.gl/AcGlL Original: [16] http://goo.gl/AcGlL * ANN: CmdTheLine 0.2 released -- with new tutorial. Domain: elifrey.com, Score: 23, Comments: 11 On Reddit: [17] http://goo.gl/yezpc Original: [18] http://goo.gl/cM9kZ * State of the Shelly (Haskell scripting lib) Domain: yesodweb.com, Score: 23, Comments: 1 On Reddit: [19] http://goo.gl/siupj Original: [20] http://goo.gl/FyrDC * Hackage b0rked for cabal 0.10.2 Domain: self.haskell, Score: 22, Comments: 4 On Reddit: [21] http://goo.gl/HzgX8 Original: [22] http://goo.gl/HzgX8 * Pipes to Conduits part 0: Combining Functors Domain: unknownparallel.wordpress.com, Score: 22, Comments: 18 On Reddit: [23] http://goo.gl/sF95u Original: [24] http://goo.gl/Jepr5 * Deconstraining DSLs [PDF] Domain: doc.ic.ac.uk, Score: 19, Comments: 2 On Reddit: [25] http://goo.gl/Ur7Lz Original: [26] http://goo.gl/E2DhL * What is the reason for Haskell's cabal package problems? Domain: self.haskell, Score: 17, Comments: 41 On Reddit: [27] http://goo.gl/O0x9z Original: [28] http://goo.gl/O0x9z * Pipes to Conduits part 4: Recovering from Abort Domain: unknownparallel.wordpress.com, Score: 16, Comments: On Reddit: [29] http://goo.gl/tr9Jy Original: [30] http://goo.gl/XbAUR * Pipes to Conduits part 1: Yield and Await Domain: unknownparallel.wordpress.com, Score: 15, Comments: 5 On Reddit: [31] http://goo.gl/KV0io Original: [32] http://goo.gl/GuFqX * Pipes to Conduits part 2: Upstream Results Domain: unknownparallel.wordpress.com, Score: 15, Comments: 9 On Reddit: [33] http://goo.gl/ONYzN Original: [34] http://goo.gl/Tf3Si * Instance Templates: a proposed feature to change type class hierarchies without breaking compatibility Domain: github.com, Score: 15, Comments: 6 On Reddit: [35] http://goo.gl/7Jx8c Original: [36] http://goo.gl/LG1YK * Categories over pairs of types Domain: twanvl.nl, Score: 15, Comments: 1 On Reddit: [37] http://goo.gl/8ee77 Original: [38] http://goo.gl/jxLPR * Pipes to Conduits part 3: Abort Domain: unknownparallel.wordpress.com, Score: 14, Comments: 12 On Reddit: [39] http://goo.gl/IZbij Original: [40] http://goo.gl/2kgLg Top StackOverflow Questions * What does “Pure” mean, in the context of programming languages and paradigms? votes: 21, answers: 2 Read on SO: [41] http://goo.gl/a0IUe * Can a thunk be duplicated to improve memory performance? votes: 17, answers: 3 Read on SO: [42] http://goo.gl/rznKJ * What's the current status of restricted monads? votes: 14, answers: 1 Read on SO: [43] http://goo.gl/UnMbE * Is it good style to use a case expression on an Unit value just to use guards? votes: 13, answers: 3 Read on SO: [44] http://goo.gl/E8xn3 * Temporary namespace/context in Haskell votes: 12, answers: 3 Read on SO: [45] http://goo.gl/AWg4O * Using the LogicT Monad Transformer in Haskell votes: 12, answers: 1 Read on SO: [46] http://goo.gl/DOw0H * Irrefutable pattern does not leak memory in recursion, but why? votes: 11, answers: 1 Read on SO: [47] http://goo.gl/qK7rx * How to determine type of Haskell functions? votes: 11, answers: 3 Read on SO: [48] http://goo.gl/Rn5F7 * Haskell: map runST votes: 9, answers: 3 Read on SO: [49] http://goo.gl/mWnvL * How to play with Control.Monad.Writer in haskell? votes: 9, answers: 1 Read on SO: [50] http://goo.gl/GLTJc Until next time, Daniel Santa Cruz References 1. http://www.reddit.com/r/haskell/comments/xb3ig/haskell_logo_qr_code/ 2. http://www.reddit.com/r/haskell/comments/xb3ig/haskell_logo_qr_code/ 3. http://ocharles.org.uk/blog/posts/2012-07-24-in-praise-of-EitherT.html 4. http://www.reddit.com/r/haskell/comments/x3ikr/in_praise_of_eithert/ 5. http://www.reddit.com/r/haskell/comments/x4g18/the_mustknow_list_of_package… 6. http://www.reddit.com/r/haskell/comments/x4g18/the_mustknow_list_of_package… 7. http://leepike.wordpress.com/2012/07/26/smartcheck/ 8. http://www.reddit.com/r/haskell/comments/x7fyt/smartcheck_a_better_quickche… 9. http://ghcjs.github.com/fay-hello-js.jsexe/ 10. http://www.reddit.com/r/haskell/comments/x43nd/compile_haskell_fay_to_javas… 11. https://www.youtube.com/watch?v=dhFZ8vx9byc 12. http://www.reddit.com/r/haskell/comments/xbihk/programming_in_fay_simple_ex… 13. http://www.jonmsterling.com/posts/2012-07-22-flexibly-phased-constraints-in… 14. http://www.reddit.com/r/haskell/comments/wzwda/flexiblyphased_constraints_i… 15. http://www.reddit.com/r/haskell/comments/x8qnh/do_you_use_haskell_in_busine… 16. http://www.reddit.com/r/haskell/comments/x8qnh/do_you_use_haskell_in_busine… 17. http://elifrey.com/2012/07/23/CmdTheLine-Tutorial/ 18. http://www.reddit.com/r/haskell/comments/x0xda/ann_cmdtheline_02_released_w… 19. http://www.yesodweb.com/blog/2012/07/shelly-update 20. http://www.reddit.com/r/haskell/comments/x9etz/state_of_the_shelly_haskell_… 21. http://www.reddit.com/r/haskell/comments/x16h7/hackage_b0rked_for_cabal_010… 22. http://www.reddit.com/r/haskell/comments/x16h7/hackage_b0rked_for_cabal_010… 23. http://unknownparallel.wordpress.com/2012/07/24/pipes-to-conduits-part-0-co… 24. http://www.reddit.com/r/haskell/comments/x2lao/pipes_to_conduits_part_0_com… 25. http://www.doc.ic.ac.uk/~wlj05/files/Deconstraining.pdf 26. http://www.reddit.com/r/haskell/comments/x3bta/deconstraining_dsls_pdf/ 27. http://www.reddit.com/r/haskell/comments/x4knd/what_is_the_reason_for_haske… 28. http://www.reddit.com/r/haskell/comments/x4knd/what_is_the_reason_for_haske… 29. http://unknownparallel.wordpress.com/2012/07/28/pipes-to-conduits-part-4-re… 30. http://www.reddit.com/r/haskell/comments/xar9r/pipes_to_conduits_part_4_rec… 31. http://unknownparallel.wordpress.com/2012/07/25/pipes-to-conduits-part-1-yi… 32. http://www.reddit.com/r/haskell/comments/x4si1/pipes_to_conduits_part_1_yie… 33. http://unknownparallel.wordpress.com/2012/07/26/pipes-and-conduits-part-2-u… 34. http://www.reddit.com/r/haskell/comments/x6w9k/pipes_to_conduits_part_2_ups… 35. https://github.com/mgsloan/instance-templates 36. http://www.reddit.com/r/haskell/comments/x71ll/instance_templates_a_propose… 37. http://twanvl.nl/blog/haskell/categories-over-pairs-of-types 38. http://www.reddit.com/r/haskell/comments/xab88/categories_over_pairs_of_typ… 39. http://unknownparallel.wordpress.com/2012/07/27/pipes-to-conduits-part-3-ab… 40. http://www.reddit.com/r/haskell/comments/x8yx2/pipes_to_conduits_part_3_abo… 41. http://stackoverflow.com/questions/11607927/what-does-pure-mean-in-the-cont… 42. http://stackoverflow.com/questions/11675807/can-a-thunk-be-duplicated-to-im… 43. http://stackoverflow.com/questions/11599685/whats-the-current-status-of-res… 44. http://stackoverflow.com/questions/11620649/is-it-good-style-to-use-a-case-… 45. http://stackoverflow.com/questions/11661963/temporary-namespace-context-in-… 46. http://stackoverflow.com/questions/11695961/using-the-logict-monad-transfor… 47. http://stackoverflow.com/questions/11625840/irrefutable-pattern-does-not-le… 48. http://stackoverflow.com/questions/11638232/how-to-determine-type-of-haskel… 49. http://stackoverflow.com/questions/11662696/haskell-map-runst 50. http://stackoverflow.com/questions/11684321/how-to-play-with-control-monad-…

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ANNOUNCE: cyclotomic 0.3.1: exact calculations with a subfield of the complex numbers
by Scott N. Walck 01 Aug '12

01 Aug '12

cyclotomic is a library that allows exact calculations with a subfield of the complex numbers. The cyclotomic numbers are a subset of the complex numbers with the following properties: * The cyclotomic numbers are represented exactly, enabling exact computations and equality comparisons. * The cyclotomic numbers contain the Gaussian rationals (complex numbers of the form p + q i with p and q rational). As a consequence, the cyclotomic numbers are a dense subset of the complex numbers. * The cyclotomic numbers contain the square roots of all rational numbers. * The cyclotomic numbers form a field: they are closed under addition, subtraction, multiplication, and division. * The cyclotomic numbers contain the sine and cosine of all rational multiples of pi. * The cyclotomic numbers can be thought of as the rational field extended with nth roots of unity for arbitrarily large integers n. To install, just cabal install cyclotomic To use, import Data.Complex.Cyclotomic I'm happy to hear about bugs or feature requests. Scott -- Scott N. Walck Chair, Department of Physics Professor of Physics Lebanon Valley College Annville, PA 17003 phone: 717-867-6153 fax: 717-867-6075 email: walck(a)lvc.edu

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