- Haskell-Cafe - Haskell.org

Injective type families for GHC - syntax proposals
by Jan Stolarek 19 Sep '14

19 Sep '14

Haskellers, there is some discussion going on at the moment about implementing injective type families in GHC [1]. I'd like to hear your opinions on proposed syntax for this new feature. == Problem == Currently GHC assumes that type families are not injective. This is of course conservative and the idea behind implementing injective type families is to allow the programmer to explicitly declare that a type family has the injectivity property (which GHC will of course verify). == Forms of injectivity == Injectivity can take forms more complicated than just determining the LHS from RHS: A. RHS determines all arguments on the LHS. Example: type family Id a where Id a = a Here the RHS uniquely determines LHS. B. RHS determines some but not all arguments on the LHS. Example (contrieved): type family G a b c where G Int Char Bool = Bool G Int Char Int = Bool G Bool Int Int = Int Here RHS uniquely determines `a` and `b` but not `c`. C. RHS and some LHS arguments uniquely determine some LHS arguments. Example: type family Plus a b where Plus Z m = m Plus (S n) m = S (Plus n m) Here knowing the RHS and one of LHS arguments uniqely determines the other LHS argument. At the moment we've only seen use cases for A, which means that we will most likely only implement A. If someone comes up with compelling examples of either B or C we will revise and consider implementing these more involved forms of injectivity. == Syntax == So the most important decission to make is what syntax do we want for this new feature :-) One of the features we would like is extensibility, ie. if we only implement injectivity of type A we still want to be able to add injectivities B and C sometime in the future without breaking A. When thinking about syntax an important (and open) question is whether injectivity becomes part of TypeFamilies language extension or do we add a new InjectiveTypeFamilies extension for this feature. The problem with incorporating injectivity into existing TypeFamilies is that we would have to come up with syntax that is fully backwards compatible with what we have now. Below is a list of proposals that have come up until now in the discussion between developers. Note that all proposals are given for closed type families. For open type families things would be identical except that the `where` keyword would be skipped. === Proposal 1 === Use syntax similar to functional dependencies. The injectivity declaration begins with `|` following type family declaration head. `|` is followed by a list of comma-separated injectivity conditions. Each injectivity condition has the form: {{{ result A -> B }}} where `A` is a possibly-empty list of type variables declared in type family head and `B` is non-empty list of said type variables. Things on the left and right of `->` are called LHS and RHS of an injectivity condition, respectively. `result` becomes a restricted word that cannot be used as a type variable's identifier in a type family head. Examples: type family Id a | result -> a where type family G a b c | result -> a b where type family Plus a b | result a -> b, result b -> a where Pros: * has natural reading: `result a -> b` reads as "knowing the result and the type variable a determines b". * extensible for the future Cons: * steals `result` identifier in the type family head. This means it would be illegal to have a type variable named `result` in a type family. * the above also makes this proposal backwards incompatible with TypeFamilies extension. Further proposals are based on this one in an attempt to solve the problem of stealing syntax and backwards incompatibility. === Proposal 2 === Use `Result` instead of `result`: type family Id a | Result -> a where type family G a b c | Result -> a b where type family Plus a b | Result a -> b, Result b -> a where Pros: * has natural reading * extensible for the future * allows to have type variables named `result` (does not steal syntax) Cons: * all other keywords in Haskell are lowercase. This would be the first one that is capitalized. * confusion could arise if we have a type `Result` and use it in the type family head. Unknowns (for me): * not sure if it would be possible to avoid name clash between `Result` and type of the same name. If not then this proposal would also be backwards incompatible with TypeFamilies. === Proposal 3 === Use `type` instead of `result`: type family Id a | type -> a where type family G a b c | type -> a b where type family Plus a b | type a -> b, type b -> a where Pros: * extensible for the future * no syntax stealing Cons: * no natural reading * usage of `type` here might seem unintuitive === Proposal 4 === Use name of the type family instead of `result`: type family Id a | Id -> a where type family G a b c | G -> a b where type family Plus a b | Plus a -> b, Plus b -> a where Pros: * extensible for the future * no syntax stealing Cons: * writing something like `Plus a` might be confusing. It looks as if Plus could be partially applied. == Further discussion == I'd like to hear what you think about these proposals. Neither of them is perfect so perhaps someone can come with something better. You can also check out the GHC Trac ticket [1] and the GHC Wiki page [2] (which repeats most of this but has some more details as well). [1] https://ghc.haskell.org/trac/ghc/ticket/6018 [2] https://ghc.haskell.org/trac/ghc/wiki/InjectiveTypeFamilies Janek

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optional ghc-options based on GHC version?
by Mateusz Kowalczyk 19 Sep '14

19 Sep '14

Hi, I have a project here where GHC's option -flate-dmd-anal gets out some extra speed but the flag is not available on 7.6.3. How can I specify in the cabal file that I only want to pass this through when building with 7.8.3 or newer? It'd be a shame to not take advantage of the extra speed on 7.8.3 just because we want to support 7.6.3 too for a bit longer. I was unable to find the info online. Thanks. -- Mateusz K.

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Re: [Haskell-cafe] Hello and type-level SKI
by oleg＠okmij.org 18 Sep '14

18 Sep '14

Yet another demonstration of Turing completeness of the type checker (given the unrestricted context reduction stack) was lambda-calculator in types, posted back in 2006. http://okmij.org/ftp/Computation/lambda-calc.html#haskell-type-level The examples included the Fibonacci function (encoded using the fix-point combinator) and the SKI calculator (expressing combinators as lambda-terms).

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Improving ghc error messages
by Toby Goodwin 18 Sep '14

18 Sep '14

Interesting article: https://izbicki.me/blog/error-messages-in-ghc-vs-g++.html I do hope some of these changes make it into a future ghc. I'd particularly like to highlight this one: No instance for (Show ([a0] -> Int)) arising from a use of `show' Possible fix: add an instance declaration for (Show ([a0] -> Int)) The second line looks like it was added by someone who'd read an article about making error messages helpful: "suggest a possible way to fix the error". Like creating a Show instance for a function type!?! I must have seen that "possible fix" 1000 times, and 999 of them it was nothing like the right fix. Now I know just to ignore it. Simply removing the second line would be an improvement: it doesn't add anything to the first line. Toby.

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cryptography and homomorphic library support?
by Vasili I. Galchin 18 Sep '14

18 Sep '14

Hi, I just perused the crypto section of Hackage and I didn't see any support for homomorphc functions. I didn't see anything .. maybe I missed. If no support, I wouldn't mind giving a shot at working on this as long as no one has already implemented. If someone is working on this, please inform me of contact info so perhaps I can join the team. Kind regards, Vasya

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Haskell Weekly News: Issue 306
by Daniel Santa Cruz 18 Sep '14

18 Sep '14

Welcome to issue 306 of the HWN, an issue covering crowd-sourced bits of information about Haskell from around the web. This issue covers from September 07 to 13, 2014 Quotes of the Week * prophile: at this point ekmett is more part of the language than a practitioner of it * Qfwfq: Simon is a title, not a forename. Top Reddit Stories * Haskell for all: Morte: an intermediate language for super-optimizing functional programs Domain: haskellforall.com, Score: 110, Comments: 83 Original: [1] http://goo.gl/MjPyyr On Reddit: [2] http://goo.gl/v2btl4 * AMP has landed in GHC Main! Domain: haskell.org, Score: 88, Comments: 71 Original: [3] http://goo.gl/giu1Xh On Reddit: [4] http://goo.gl/ZGJ76S * [Meta] What's with all these downvotes on beginner questions? Domain: self.haskell, Score: 69, Comments: 67 Original: [5] http://goo.gl/ik2uu2 On Reddit: [6] http://goo.gl/ik2uu2 * Haskell Implementors Workshop 2014 videos [youtube] Domain: youtube.com, Score: 59, Comments: 11 Original: [7] http://goo.gl/ijM6hs On Reddit: [8] http://goo.gl/48GOSr * FP Complete is hiring: Haskell web UI developer Domain: fpcomplete.com, Score: 59, Comments: 14 Original: [9] http://goo.gl/0kPlFl On Reddit: [10] http://goo.gl/WtivSo * How to get (approx) stack traces with profiled builds Domain: self.haskell, Score: 46, Comments: 15 Original: [11] http://goo.gl/ZAurK6 On Reddit: [12] http://goo.gl/ZAurK6 * Hakaru: An embedded probabilistic programming language Domain: indiana.edu, Score: 40, Comments: 10 Original: [13] http://goo.gl/PLcCGW On Reddit: [14] http://goo.gl/aP7giY * Why does David Turner say type classes were a bad idea? Domain: self.haskell, Score: 37, Comments: 96 Original: [15] http://goo.gl/WqRLZQ On Reddit: [16] http://goo.gl/WqRLZQ * Let's Build a Browser Engine in Haskell: Part 2 Domain: hrothen.github.io, Score: 33, Comments: 14 Original: [17] http://goo.gl/PyxMOy On Reddit: [18] http://goo.gl/45L7hs * Proposal for copatterns in Idris Domain: github.com, Score: 30, Comments: 38 Original: [19] http://goo.gl/7Zv7U1 On Reddit: [20] http://goo.gl/pPIq8p * GHC Blog: Static pointers and serialisation (by SPJ) Domain: ghc.haskell.org, Score: 28, Comments: 2 Original: [21] http://goo.gl/HJrm4t On Reddit: [22] http://goo.gl/kPxJj5 * introduction to the basic lens operators Domain: intolerable.me, Score: 26, Comments: 12 Original: [23] http://goo.gl/VXlKnm On Reddit: [24] http://goo.gl/b0bLfE * Prisms lead to typeclasses for subtractive types Domain: gelisam.blogspot.ca, Score: 22, Comments: 6 Original: [25] http://goo.gl/l9QIIm On Reddit: [26] http://goo.gl/GMD5Cj * Preventing memoization in (AI) search problems Domain: okmij.org, Score: 22, Comments: 16 Original: [27] http://goo.gl/oEb6WD On Reddit: [28] http://goo.gl/jqVKPS * A shallow survey of formal methods for C code Domain: imperialviolet.org, Score: 21, Comments: 7 Original: [29] http://goo.gl/rJgycy On Reddit: [30] http://goo.gl/RrXwns * Haskell Lectures Domain: shuklan.com, Score: 21, Comments: 1 Original: [31] http://goo.gl/Ef0E4 On Reddit: [32] http://goo.gl/VASdCX * A Netwire 5 Tutorial Domain: self.haskell, Score: 20, Comments: 5 Original: [33] http://goo.gl/BmcKWr On Reddit: [34] http://goo.gl/BmcKWr * Haskell Symposium talk on inline Objective-C in Haskell Domain: speakerdeck.com, Score: 20, Comments: 0 Original: [35] http://goo.gl/VDHOiP On Reddit: [36] http://goo.gl/TyL90G * HaLVM / Unikernel talk at the Xen User Summit on Monday, September 15th Domain: sched.co, Score: 19, Comments: 8 Original: [37] http://goo.gl/HoVwWT On Reddit: [38] http://goo.gl/9lqCE0 * Fun with (Extended Kalman) Filters Domain: idontgetoutmuch.wordpress.com, Score: 18, Comments: 2 Original: [39] http://goo.gl/8EGSQR On Reddit: [40] http://goo.gl/aTASRU Top StackOverflow Questions * Why does OCaml sometimes require eta expansion? votes: 12, answers: 1 Read on SO: [41] http://goo.gl/TsBuz5 * Can Haskell evaluate and not garbage collect random indexes in a list? votes: 11, answers: 2 Read on SO: [42] http://goo.gl/zXsBT1 * How do I install dependencies when cross compiling haskell code? votes: 10, answers: 1 Read on SO: [43] http://goo.gl/3qH6zK * Haskell lenses: how to make view play nicely with traverse? votes: 10, answers: 3 Read on SO: [44] http://goo.gl/EWrR5j * Is there an instance of Monad but not of MonadFix? votes: 10, answers: 2 Read on SO: [45] http://goo.gl/EAh0qc * How can the continuation monad be expressed using the free monad? votes: 10, answers: 3 Read on SO: [46] http://goo.gl/ymMoFw Until next time, [47]+Daniel Santa Cruz References 1. http://www.haskellforall.com/2014/09/morte-intermediate-language-for-super.… 2. http://www.reddit.com/r/haskell/comments/2g6wsx/haskell_for_all_morte_an_in… 3. http://www.haskell.org/pipermail/ghc-devs/2014-September/006265.html 4. http://www.reddit.com/r/haskell/comments/2fxqts/amp_has_landed_in_ghc_main/ 5. http://www.reddit.com/r/haskell/comments/2g3em9/meta_whats_with_all_these_d… 6. http://www.reddit.com/r/haskell/comments/2g3em9/meta_whats_with_all_these_d… 7. https://www.youtube.com/playlist?list=PL4UWOFngo5DW6nKDjK0UB5Oy9zmdWdo7K 8. http://www.reddit.com/r/haskell/comments/2frhfn/haskell_implementors_worksh… 9. https://www.fpcomplete.com/blog/2014/09/hiring-haskell-web-ui-dev 10. http://www.reddit.com/r/haskell/comments/2g4mdu/fp_complete_is_hiring_haske… 11. http://www.reddit.com/r/haskell/comments/2fwwx3/how_to_get_approx_stack_tra… 12. http://www.reddit.com/r/haskell/comments/2fwwx3/how_to_get_approx_stack_tra… 13. http://indiana.edu/~ppaml/ 14. http://www.reddit.com/r/haskell/comments/2g4q81/hakaru_an_embedded_probabil… 15. http://www.reddit.com/r/haskell/comments/2foggq/why_does_david_turner_say_t… 16. http://www.reddit.com/r/haskell/comments/2foggq/why_does_david_turner_say_t… 17. http://hrothen.github.io/2014/09/08/lets-build-a-browser-engine-in-haskell-… 18. http://www.reddit.com/r/haskell/comments/2fu2l5/lets_build_a_browser_engine… 19. https://github.com/idris-lang/Idris-dev/wiki/Copatterns 20. http://www.reddit.com/r/haskell/comments/2fy1hj/proposal_for_copatterns_in_… 21. https://ghc.haskell.org/trac/ghc/blog/simonpj/StaticPointers 22. http://www.reddit.com/r/haskell/comments/2g4vvf/ghc_blog_static_pointers_an… 23. http://intolerable.me/lens-operators-intro/ 24. http://www.reddit.com/r/haskell/comments/2fud8k/introduction_to_the_basic_l… 25. http://gelisam.blogspot.ca/2014/09/prisms-lead-to-typeclasses-for.html 26. http://www.reddit.com/r/haskell/comments/2foz4a/prisms_lead_to_typeclasses_… 27. http://okmij.org/ftp/Haskell/#memo-off 28. http://www.reddit.com/r/haskell/comments/2g9akh/preventing_memoization_in_a… 29. https://www.imperialviolet.org/2014/09/07/provers.html 30. http://www.reddit.com/r/haskell/comments/2fsvns/a_shallow_survey_of_formal_… 31. http://shuklan.com/haskell/ 32. http://www.reddit.com/r/haskell/comments/2g672e/haskell_lectures/ 33. http://www.reddit.com/r/haskell/comments/2fs4mv/a_netwire_5_tutorial/ 34. http://www.reddit.com/r/haskell/comments/2fs4mv/a_netwire_5_tutorial/ 35. https://speakerdeck.com/mchakravarty/foreign-inline-code-in-haskell-haskell… 36. http://www.reddit.com/r/haskell/comments/2fve6k/haskell_symposium_talk_on_i… 37. http://sched.co/1rFBMed 38. http://www.reddit.com/r/haskell/comments/2g2sa0/halvm_unikernel_talk_at_the… 39. http://idontgetoutmuch.wordpress.com/2014/09/09/fun-with-extended-kalman-fi… 40. http://www.reddit.com/r/haskell/comments/2fwbhd/fun_with_extended_kalman_fi… 41. http://stackoverflow.com/questions/25763412/why-does-ocaml-sometimes-requir… 42. http://stackoverflow.com/questions/25751194/can-haskell-evaluate-and-not-ga… 43. http://stackoverflow.com/questions/25765893/how-do-i-install-dependencies-w… 44. http://stackoverflow.com/questions/25773444/haskell-lenses-how-to-make-view… 45. http://stackoverflow.com/questions/25814489/is-there-an-instance-of-monad-b… 46. http://stackoverflow.com/questions/25827271/how-can-the-continuation-monad-… 47. https://plus.google.com/105107667630152149014/about

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Boolean formula: part2
by Dmitry Bogatov 17 Sep '14

17 Sep '14

Hello! I have following code: buildFormulas :: [Variable] -> Int -> [Formula] buildFormulas vars 0 = map Var vars buildFormulas vars n = join $ forM [0 .. n - 1 ] $ \i -> do x <- buildFormulas vars i y <- buildFormulas vars (n - i - 1) z <- buildFormulas vars (n - 1) let t1 = case z of (Negation _) -> [] _ -> [Negation z] t1 ++ [conj x y, impl x y, disj x y] It is correct, typechecks, but it is insanely slow (calculating take 35 (buildFormulas [P, Q, R] 5) hangs my computer). My guess is that it builds too much before returning first results. Can you suggest more efficent way enumerate formulas of set of variables? -- Best regards, Dmitry Bogatov <KAction(a)gnu.org>, Free Software supporter, esperantisto and netiquette guardian. GPG: 54B7F00D

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Re: [Haskell-cafe] Hackage package "synopsis" sections
by Mike Izbicki 17 Sep '14

17 Sep '14

One problem with using the README file as the synopsis is that a lot of the standard information in a README file would be out of place when displayed on hackage. For example, many READMEs have: * installation instructions * a list of contributors * a list of known bugs * how to contribute bug reports * licensing information Some of this information is very out of place on hackage, some of it is duplication of the standard fields in the cabal file, and some of it is just not things that a new user needs to see on their first visit to the package documentation. Maybe this could be solved by having the name of the synopsis file as a variable the author can specify. It can default to README(.md) but can be overridden to something else for authors who choose to do so. On Tue, Sep 16, 2014 at 11:20 PM, Mike Izbicki <mike.izbicki(a)gmail.com> wrote: > One problem with using the README file as the synopsis is that a lot > of the standard information in a README file would be out of place > when displayed on hackage. For example, many READMEs have: > > * installation instructions > * a list of contributors > * a list of known bugs > * how to contribute bug reports > * licensing information > > Some of this information is very out of place on hackage, some of it > is duplication of the standard fields in the cabal file, and some of > it is just not things that a new user needs to see on their first > visit to the package documentation. > > Maybe this could be solved by having the name of the synopsis file as > a variable the author can specify. It can default to README(.md) but > can be overridden to something else for authors who choose to do so. > > On Tue, Sep 16, 2014 at 8:58 PM, Michael Snoyman <michael(a)snoyman.com> wrote: >> >> >> On Wed, Sep 17, 2014 at 12:10 AM, Richard Lewis <richard(a)rjlewis.me.uk> >> wrote: >>> >>> So there's clearly an important technical hurdle to be overcome for >>> this: what markup language is to be used?; and where should the >>> synposis be stored? >>> >>> But I can't help thinking that the real work is in getting the >>> synopses written. Encouraging package authors/maintainers to add them >>> to their own packages is one possible way forward. >>> >> >> Actually, if we get the README support in place, I think it should be much >> easier to get package authors to write synopses. Most projects have a README >> file already, and getting it included in Hackage would now be a one-line >> pull request (adding `extra-source-files: README.extension`). It will >> hopefully be easier to get authors to elaborate on their READMEs then >> because: >> >> 1. They're serving double duty, both in the project repository and on >> Hackage. >> 2. It's trivial for outside developers to send pull requests against a >> simple text file. I've received quite a few such contributions on projects I >> maintain, even from people not ready to work on the code itself. >> >>> >>> At Mon, 15 Sep 2014 11:28:38 -0700, >>> Tikhon Jelvis wrote: >>> >>> > Maybe we could have a guerrilla campaign of pull requests adding >>> > examples and a bit of explanation to every package you like that >>> > doesn't have them... That could also be a good way for beginners who >>> > want to contribute to start. >>> >>> Another, as Tikhon suggests, would be for others to write them and >>> send pull requests (or whatever) to the maintainers. >>> >>> At Mon, 15 Sep 2014 20:10:18 -0400, >>> Dominick Samperi wrote: >>> >>> > I think this is a great idea, but it probably needs a complementary >>> > "nudge" if it is going to have a significant impact. This could be >>> > incorporated into the package submission process where the submitter >>> > runs a final check and is warned when examples are not provided for >>> > exported functions (unless an "opt out" flag is turned on for >>> > functions that have "obvious" semantics). >>> >>> And yet another, as Dominick suggests, is effectively to require a >>> synposis when a package is submitted. In CPAN, it's just become part >>> of the culture, but it's also not required and you do find packages >>> without a synposis. >>> >>> If there's interest, I'd like to solicit some discussion on this part >>> of the proposal on this thread... >>> >>> There may also be a potentially significant difference between >>> Hackage/Haskell and CPAN/Perl: most CPAN packages tend to be quite >>> small and specific in their purpose and consequently have just a few, >>> simple common use cases which suit a synposis very well. Hackage >>> packages, on the other hand, are quite often more broad in their >>> scope, often comprising many modules. Also, Perl has only one >>> semantics for organising code at the finest level: sequential, >>> imperative statements. In Haskell, some packages actually define whole >>> coding styles. As a result, it's always pretty obvious how to write a >>> few isolated lines of Perl code, but not necessarily so with Haskell >>> code. Anyway, I'm sure all this can be overcome, and/or argued >>> against. >>> >>> Richard >>> -- >>> -=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=- >>> Richard Lewis >>> j: ironchicken(a)jabber.earth.li >>> @: lewisrichard >>> http://www.richardlewis.me.uk/ >>> -=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=- >>> _______________________________________________ >>> Haskell-Cafe mailing list >>> Haskell-Cafe(a)haskell.org >>> http://www.haskell.org/mailman/listinfo/haskell-cafe >> >> >> >> _______________________________________________ >> Haskell-Cafe mailing list >> Haskell-Cafe(a)haskell.org >> http://www.haskell.org/mailman/listinfo/haskell-cafe >>

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Mapping over Type Level Literals
by Dominic Steinitz 17 Sep '14

17 Sep '14

I was playing around with Haar functions and realised I could encode the constraints in the types > > {-# LANGUAGE DataKinds #-} > > {-# LANGUAGE TypeOperators #-} > > {-# LANGUAGE KindSignatures #-} > > {-# LANGUAGE TypeFamilies #-} > > {-# LANGUAGE TypeOperators #-} > > {-# LANGUAGE Rank2Types #-} > > {-# LANGUAGE ScopedTypeVariables #-} > > > import GHC.TypeLits > > import Data.Proxy > > > data Haar (a :: Nat) (b :: Nat) = Haar { unHaar :: Double -> Double } > > > haar :: forall n k . > > (KnownNat n, KnownNat k, (2 * k - 1 <=? 2^n - 1) ~ 'True) => > > Haar n (2 * k - 1) > > haar = Haar g where > > g t | (k' - 1) * 2 ** (-n') < t && t <= k' * 2 ** (-n') = 2 ** ((n' - 1) / 2) > > | k' * 2 ** (-n') < t && t <= (k' + 1) * 2 ** (-n') = -2 ** ((n' - 1) / 2) > > | otherwise = 0 > > where > > n' = fromIntegral (natVal (Proxy :: Proxy n)) > > k' = 2 * (fromIntegral (natVal (Proxy :: Proxy k))) - 1 So now I can do e.g. > *Main> unHaar (haar :: Haar 3 7) 0.05 > 0.0 > *Main> unHaar (haar :: Haar 3 6) 0.05 > > <interactive>:359:9: > Couldn't match type ‘2 * k0’ with ‘7’ > The type variable ‘k0’ is ambiguous > Expected type: 'True > Actual type: ((2 * k0) - 1) <=? ((2 ^ 3) - 1) > In the first argument of ‘unHaar’, namely ‘(haar :: Haar 3 6)’ > In the expression: unHaar (haar :: Haar 3 6) 0.05 > In an equation for ‘it’: it = unHaar (haar :: Haar 3 6) 0.05 > *Main> unHaar (haar :: Haar 3 9) 0.05 > > <interactive>:360:9: > Couldn't match type ‘'False’ with ‘'True’ > Expected type: 'True > Actual type: ((2 * 5) - 1) <=? ((2 ^ 3) - 1) > In the first argument of ‘unHaar’, namely ‘(haar :: Haar 3 9)’ > In the expression: unHaar (haar :: Haar 3 9) 0.05 > In an equation for ‘it’: it = unHaar (haar :: Haar 3 9) 0.05 > *Main> So errors get rejected at compilation time as one would like and with moderately informative error messages. But now of course I would like to map over n and k but these are at the type level. Can this be done? I imagine unsafeCoerce would have to come into it somewhere. Dominic Steinitz dominic(a)steinitz.org http://idontgetoutmuch.wordpress.com

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Re: [Haskell-cafe] Type union
by oleg＠okmij.org 17 Sep '14

17 Sep '14

Type unions are also necessary for extensible effects. In fact, they are the foundation of extensible effects. One implementation http://okmij.org/ftp/Haskell/extensible/TList.hs uses only common and uncontroversial extensions (No Typeable). It could be converted to closed type families. The other, more optimal implementation, relies on Typeable, so that injection and projection become constant time, regardless of the size of the union. The Typeable constraint can be dispensed with; see the HList implementation of type-indexed coproducts (TIC), which are essentially open unions.

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