[Haskell-cafe] Fun with type functions
Friends Ken, Oleg, and I have finished Version 2 of our paper Fun with Type Functions, which gives a programmer's tour of what type functions are and how they are useful. http://haskell.org/haskellwiki/Simonpj/Talk:FunWithTypeFuns If you have a moment to look at, and wanted to help us improve it, the above link goes to a wiki page where you can comment on the paper or discuss it. We still have time to improve it. Thanks Simon ___ Haskell-Cafe mailing list Haskell-Cafe@haskell.org http://www.haskell.org/mailman/listinfo/haskell-cafe
[Haskell-cafe] Fun with type functions
Friends Ken, Oleg, and I have been working on a tutorial paper about type families (aka associated data types, or type functions). It's in draft at the moment, and we'd really appreciate feedback that would help us improve it. Here it is: http://haskell.org/haskellwiki/Simonpj/Talk:FunWithTypeFuns Thank you! Simon ___ Haskell-Cafe mailing list Haskell-Cafe@haskell.org http://www.haskell.org/mailman/listinfo/haskell-cafe
Re: [Haskell-cafe] Fun with type functions
Pointless Haskell a library for point-free programming with recursion patterns that uses type synonym families to provide a view of data types as the fixed points of functors. It defines two type functions type family PF a :: * - * -- returns the pattern functor for a data type type family Rep (f :: * - *) x :: * -- returns the result type of applying a functor to a type argument that can be combined to derive the structurally equivalent sum of products for some type: type F a x = Rep (PF a) x class Mu a where inn :: F a a - a out :: a - F a a For Haskell polymorphic lists, we need to define: type instance PF [a] = Const One :+: Const a :*: Id instance Mu [a] where inn (Left _) = [] inn (Right (x,xs)) = x:xs out [] = Left _L out (x:xs) = Right (x,xs) Some of the typical recursion patterns are: hylo :: Functor (PF b) = b - (F b c - c) - (a - F b a) - a - c cata :: (Mu a,Functor (PF a)) = a - (F a b - b) - a - b ana :: (Mu b,Functor (PF b)) = b - (a - F b a) - a - b One simple example is the foldr (catamorphism) for calculating the lenght of a list: length :: [a] - Int length = cata (_L::[a]) f where f = zero \/ succ . snd length [1,2,3,4] 4 I have promoted the library into a cabal package (pointless-haskell) today and am creating an homepage ( http://haskell.di.uminho.pt/wiki/Pointless+Haskell) with examples. cheers, hugo On Thu, Nov 27, 2008 at 9:29 AM, Simon Peyton-Jones [EMAIL PROTECTED]wrote: Friends GHC has embodied data type families since 6.8, and now type synonym families (aka type functions) in 6.10. However, apart from our initial papers there isn't much published material about how to *use* type families. But that hasn't stopped you: quite a few people are using them already, and of course there is a rich seam of work on using functional dependencies to express type-level computation. Ken Shan and Oleg Kiselyov and I are collaborating to write a paper for an upcoming workshop, under the general rubric of Fun with type functions (in homage to Thomas Hallgren's paper Fun with functional dependencies and Ralf Hinze's paper Fun with phantom types). So this message is to ask you: can you tell us about the most persuasive, fun application you've encountered, for type families or functional dependencies? Simple is good. It doesn't have to be elaborate: just something that does something useful you could not have done otherwise. Pointers to email threads are fine. Don't assume we already know about them (even if we participated in the thread :-) Part of what we're interested in is that *you* found the example compelling. Many thanks Simon, Ken, Oleg PS: I'm broadcasting this message to GHC-users and Haskell-cafe, but to avoid deluging ghc-users, please reply just to us and Haskell cafe. (Interested ghc-users can follow the threads there from the archives if they want.) ___ Haskell-Cafe mailing list Haskell-Cafe@haskell.org http://www.haskell.org/mailman/listinfo/haskell-cafe -- www.di.uminho.pt/~hpacheco ___ Haskell-Cafe mailing list Haskell-Cafe@haskell.org http://www.haskell.org/mailman/listinfo/haskell-cafe
Re: [Haskell-cafe] Fun with type functions
2008/11/27 Simon Peyton-Jones [EMAIL PROTECTED]: can you tell us about the most persuasive, fun application you've encountered, for type families or functional dependencies? Hi, I certainly had fun with the Instant Insanity puzzle, in Monad.Reader issue 8: http://www.haskell.org/haskellwiki/User:ConradParker/InstantInsanity That was using functional dependencies. Then Pepe Iborra pasted a version of Instant Insanity with type families: http://hpaste.org/2689 Looking back at this, Manuel left the following comment: -- There is unfortunately, no simple way to print the normalised type. -- In fact, GHC goes to great length to show types with as little -- normalisation as possible to users. (Especially for error messages, -- that usually makes them much easier to understand.) However, with -- type families, I think we really ought to have a ghci command to -- specifically request a normalised type. I'll put that on my -- TODO list! -- For the moment, you can of course try forcing normalisation by -- triggering type errors; eg -- :t solution :: Int (Does ghci now have a command for printing normalised types?) There are also links to haskell-cafe discussion and some other implementations (in C++ templates and D) to, um, compare: http://www.haskell.org/haskellwiki/User_talk:ConradParker/InstantInsanity cheers, Conrad. ___ Haskell-Cafe mailing list Haskell-Cafe@haskell.org http://www.haskell.org/mailman/listinfo/haskell-cafe
Re: [Haskell-cafe] Fun with type functions
On Thu, Nov 27, 2008 at 9:29 AM, Simon Peyton-Jones [EMAIL PROTECTED] wrote: Friends GHC has embodied data type families since 6.8, and now type synonym families (aka type functions) in 6.10. However, apart from our initial papers there isn't much published material about how to *use* type families. But that hasn't stopped you: quite a few people are using them already, and of course there is a rich seam of work on using functional dependencies to express type-level computation. Ken Shan and Oleg Kiselyov and I are collaborating to write a paper for an upcoming workshop, under the general rubric of Fun with type functions (in homage to Thomas Hallgren's paper Fun with functional dependencies and Ralf Hinze's paper Fun with phantom types). So this message is to ask you: can you tell us about the most persuasive, fun application you've encountered, for type families or functional dependencies? Simple is good. It doesn't have to be elaborate: just something that does something useful you could not have done otherwise. Pointers to email threads are fine. Don't assume we already know about them (even if we participated in the thread :-) Part of what we're interested in is that *you* found the example compelling. Many thanks I documented, [1] and [2], my first encounter with functional dependencies. Maybe not a persuasive example, but I felt it was a fairly good introduction to them. /M [1]: http://therning.org/magnus/archives/354 [2]: http://therning.org/magnus/archives/355 -- Magnus Therning(OpenPGP: 0xAB4DFBA4) magnus＠therning．org Jabber: magnus＠therning．org http://therning.org/magnus identi.ca|twitter: magthe ___ Haskell-Cafe mailing list Haskell-Cafe@haskell.org http://www.haskell.org/mailman/listinfo/haskell-cafe
Re: [Haskell-cafe] Fun with type functions
My work on lightweight session types (modeled after this year's ICFP paper on the same subject) used type and data families extensively for an elegant way of connecting communicating coroutines: Empty types are used for sessions: data Eps -- empty session data a :?: s -- read an a followed by session s data a :!: s -- write an a followed by session s -- etc. These have kind *, which makes them easy to use in other type-level code; my first formulation had the session types as functors directly, but that led to needing kind signatures elsewhere and made working with these types much more difficult.. Type families are used to represent the dual of a session; that is, a session that reads an Int can connect with a session that writes an Int. type family Dual s type instance Dual Eps = Eps type instance Dual (a :?: s) = a :!: Dual s type instance Dual (a :!: s) = a :?: Dual s -- etc. Then data families give structure to the session: data family Rep s a newtype instance Rep Eps a = Done a data instance Rep (x :!: s) a = Send x (Rep s a) newtype instance Rep (x :?: s) a = Receive (x - Rep s a) -- etc. Rep s converts a sessions (kind *) into a functor (kind * - *). It also allows easy experimentation with alternate formulations of the problem that potentially have different kinds. Finally, a typeclass allows interpretation of these types, connecting two sessions together to run as coroutines: class Coroutine s where connect :: (Dual s ~ c, Dual c ~ s) = Rep s a - Rep c b - (a,b) instance Coroutine Eps where connect (Done a) (Done b) = (a,b) instance Coroutine s = Coroutine (x :!: s) where connect (Send x s) (Receive k) = connect s (k x) instance Coroutine s = Coroutine (x :?: s) where connect (Receive k) (Send x c) = connect (k x) c The proof that two routines can safely connect is done entirely at compile time; the connection routine just takes care of routing data between the two processes. -- ryan On Thu, Nov 27, 2008 at 1:29 AM, Simon Peyton-Jones [EMAIL PROTECTED] wrote: Friends GHC has embodied data type families since 6.8, and now type synonym families (aka type functions) in 6.10. However, apart from our initial papers there isn't much published material about how to *use* type families. But that hasn't stopped you: quite a few people are using them already, and of course there is a rich seam of work on using functional dependencies to express type-level computation. Ken Shan and Oleg Kiselyov and I are collaborating to write a paper for an upcoming workshop, under the general rubric of Fun with type functions (in homage to Thomas Hallgren's paper Fun with functional dependencies and Ralf Hinze's paper Fun with phantom types). So this message is to ask you: can you tell us about the most persuasive, fun application you've encountered, for type families or functional dependencies? Simple is good. It doesn't have to be elaborate: just something that does something useful you could not have done otherwise. Pointers to email threads are fine. Don't assume we already know about them (even if we participated in the thread :-) Part of what we're interested in is that *you* found the example compelling. Many thanks Simon, Ken, Oleg PS: I'm broadcasting this message to GHC-users and Haskell-cafe, but to avoid deluging ghc-users, please reply just to us and Haskell cafe. (Interested ghc-users can follow the threads there from the archives if they want.) ___ Haskell-Cafe mailing list Haskell-Cafe@haskell.org http://www.haskell.org/mailman/listinfo/haskell-cafe ___ Haskell-Cafe mailing list Haskell-Cafe@haskell.org http://www.haskell.org/mailman/listinfo/haskell-cafe
