[Haskell-cafe] Rank N Kinds
It was discussed a bit here: http://ghc.haskell.org/trac/ghc/ticket/8090 Rank N Kinds: Main Idea is: If we assume an infinite hierarchy of classifications, we have True :: Bool :: * :: ** :: *** :: :: ... Bool = False, True, ... * = Bool, Sting, Maybe Int, ... **= *, *->Bool, *->(*->*), ... *** = **, **->*, (**->**)->*, ... ... RankNKinds is also a part of lambda-cube. PlyKinds is just type of ** (Rank2Kinds) class Foo (a :: k) where <<==>> class Foo (a :: **) where *** is significant to work with ** data and classes; more general: Rank(N)Kinds is significant to work with Rank(N-1)Kinds First useful use is in Typeable. In GHC 7.8 class Typeable (a::k) where ... <<==>> class Typeable (a ::**) where ... But we can't write data Foo (a::k)->(a::k)->* ... deriving Typeable If we redeclare class Typeable (a ::***) where ... or even class Typeable (a ::**) where ... it becomes far enough for many years I'm asking to find other useful examples -- View this message in context: http://haskell.1045720.n5.nabble.com/Rank-N-Kinds-tp5733482.html Sent from the Haskell - Haskell-Cafe mailing list archive at Nabble.com. ___ Haskell-Cafe mailing list Haskell-Cafe@haskell.org http://www.haskell.org/mailman/listinfo/haskell-cafe
Re: [Haskell-cafe] Rank N Kinds
Yes, True :: Bool :: * :: ** :: *** :: :: ... in Haskell is the same as True :: Bool :: Set0 :: Set1 :: Set2 :: Set3 :: ... in Agda And I'm asking for useful examples for *** (Set2 in Agda) and higher cheers Wvv 28 Jul 2013 at 8:44:08, Schonwald [via Haskell] (ml-node+s1045720n5733510...@n5.nabble.com) wrote: hello Wvv, a lot of these ideas have been explored before in related (albeit "simpler") languages to haskell, are you familiar with idris, coq, or agda? cheers-Carter On Fri, Jul 26, 2013 at 4:42 PM, Wvv <[hidden email]> wrote: It was discussed a bit here: http://ghc.haskell.org/trac/ghc/ticket/8090 Rank N Kinds: Main Idea is: If we assume an infinite hierarchy of classifications, we have True :: Bool :: * :: ** :: *** :: :: ... Bool = False, True, ... * = Bool, Sting, Maybe Int, ... ** = *, *->Bool, *->(*->*), ... *** = **, **->*, (**->**)->*, ... ... RankNKinds is also a part of lambda-cube. PlyKinds is just type of ** (Rank2Kinds) class Foo (a :: k) where <<==>> class Foo (a :: **) where *** is significant to work with ** data and classes; more general: Rank(N)Kinds is significant to work with Rank(N-1)Kinds First useful use is in Typeable. In GHC 7.8 class Typeable (a::k) where ... <<==>> class Typeable (a ::**) where ... But we can't write data Foo (a::k)->(a::k)->* ... deriving Typeable If we redeclare class Typeable (a ::***) where ... or even class Typeable (a ::**) where ... it becomes far enough for many years I'm asking to find other useful examples -- View this message in context: http://haskell.1045720.n5.nabble.com/Rank-N-Kinds-tp5733482.html Sent from the Haskell - Haskell-Cafe mailing list archive at Nabble.com. ___ Haskell-Cafe mailing list [hidden email] http://www.haskell.org/mailman/listinfo/haskell-cafe ___ Haskell-Cafe mailing list [hidden email] http://www.haskell.org/mailman/listinfo/haskell-cafe If you reply to this email, your message will be added to the discussion below:http://haskell.1045720.n5.nabble.com/Rank-N-Kinds-tp5733482p5733510.html To unsubscribe from Rank N Kinds, click here. NAML -- View this message in context: http://haskell.1045720.n5.nabble.com/Rank-N-Kinds-tp5733482p5733545.html Sent from the Haskell - Haskell-Cafe mailing list archive at Nabble.com.___ Haskell-Cafe mailing list Haskell-Cafe@haskell.org http://www.haskell.org/mailman/listinfo/haskell-cafe
Re: [Haskell-cafe] Rank N Kinds
OMG! I still have 7.6.3. It has old Typeable. I misunderstood PolyKinds a bit. It looks like k /= **, k ~ ***... But we cannot use "CloseKinds" like data Foo (a::k) = Foo a -- catch an error "Expected kind `OpenKind', but `a' has kind `k'" with RankNKinds we could write: data Foo (a::**) = Foo a data Bar (a::***) = Bar a So, now the task is more easy: I'm asking for useful examples with "CloseKinds" with ** and higher, and any useful examples for *** and higher cheers, Wvv 29 Jul 2013 at 14:44:50, José Pedro Magalhães [via Haskell] (ml-node+s1045720n5733561...@n5.nabble.com) wrote: Hi, On Fri, Jul 26, 2013 at 10:42 PM, Wvv <[hidden email]> wrote: First useful use is in Typeable. In GHC 7.8 class Typeable (a::k) where ... <<==>> class Typeable (a ::**) where ... But we can't write data Foo (a::k)->(a::k)->* ... deriving Typeable Why not? This works fine in 7.7, as far as I know. Cheers, Pedro -- View this message in context: http://haskell.1045720.n5.nabble.com/Rank-N-Kinds-tp5733482p5733667.html Sent from the Haskell - Haskell-Cafe mailing list archive at Nabble.com.___ Haskell-Cafe mailing list Haskell-Cafe@haskell.org http://www.haskell.org/mailman/listinfo/haskell-cafe
Re: [Haskell-cafe] Rank N Kinds
How about this, I found it bt myself: data TupleList (t :: **) = TupleNil | TupleUnit t (TupleList t) fstL :: TupleList (a -> **) -> a fstL TupleNil = error "TupleList2 is TupleNil" fstL (TupleUnit a _ ) = a sndL :: TupleList (* -> a -> **) -> a sndL TupleNil = error "TupleList2 is TupleNil" sndL (TupleUnit a TupleNil ) = error "TupleList2 is TupleUnit a TupleNil" sndL (TupleUnit _ (TupleUnit a _ ) ) = a headL :: TupleList (a -> **) -> a headL TupleNil = error "TupleList2 is TupleNil" headL (TupleUnit a _ ) = a tailL :: TupleList (* -> a) -> a tailL TupleNil = error "TupleList2 is TupleNil" tailL (TupleUnit _ a ) = a instance Functor (TupleList (a :: **)) where fmap _ TupleNil = TupleNil fmap f (TupleUnit x xs) = TupleUnit (f x) (fmap xs) tupleL :: TupleList ( (Int :: *) -> (String :: *) -> (Bool :: *) ) tupleL = TupleUnit 5 (TupleUnit "inside tuple" (TupleUnit True TupleNil))) fstTuppleL :: Int fstTuppleL = fstL tupleL -- = 2 sndTuppleL :: String sndTuppleL = sndL tupleL -- = "inside tuple" tlTuppleL :: TupleList ( (String :: *) -> (Bool :: *) ) tlTuppleL = tailL tupleL -- = TupleUnit "inside tuple" (TupleUnit True TupleNil)) cheers, Wvv 31 Jul 2013 at 22:48:19, Roman Cheplyaka-2 [via Haskell] (ml-node+s1045720n5733671...@n5.nabble.com) wrote: That's because types that belong to most non-star kinds cannot have values. data Foo (a :: k) = Foo is okay, data Foo (a :: k) = Foo a is bad because there cannot be a field of type a :: k. So no, no useful examples exist, because you wouldn't be able to use such a data constructor even if you could declare it. Roman * Wvv <[hidden email]> [2013-07-31 11:40:17-0700] > OMG! > I still have 7.6.3. It has old Typeable. > > I misunderstood PolyKinds a bit. It looks like k /= **, k ~ ***... > > But we cannot use "CloseKinds" like > > data Foo (a::k) = Foo a -- catch an error "Expected kind `OpenKind', but `a' has > kind `k'" > > > with RankNKinds we could write: > data Foo (a::**) = Foo a > data Bar (a::***) = Bar a > > So, now the task is more easy: > I'm asking for useful examples with "CloseKinds" with ** and higher, and any > useful examples for *** and higher > > cheers, Wvv > > 29 Jul 2013 at 14:44:50, José Pedro Magalhães [via Haskell] > ([hidden email]) wrote: > > Hi, > > On Fri, Jul 26, 2013 at 10:42 PM, Wvv <[hidden email]> wrote: > > First useful use is in Typeable. > In GHC 7.8 > class Typeable (a::k) where ... <<==>> class Typeable (a ::**) where ... > > But we can't write > data Foo (a::k)->(a::k)->* ... deriving Typeable > > > Why not? This works fine in 7.7, as far as I know. > > > Cheers, > Pedro > > > > > -- > View this message in context: http://haskell.1045720.n5.nabble.com/Rank-N-Kinds-tp5733482p5733667.html > Sent from the Haskell - Haskell-Cafe mailing list archive at Nabble.com. > ___ > Haskell-Cafe mailing list > [hidden email] > http://www.haskell.org/mailman/listinfo/haskell-cafe ___ Haskell-Cafe mailing list [hidden email] http://www.haskell.org/mailman/listinfo/haskell-cafe -- View this message in context: http://haskell.1045720.n5.nabble.com/Rank-N-Kinds-tp5733482p5733672.html Sent from the Haskell - Haskell-Cafe mailing list archive at Nabble.com.___ Haskell-Cafe mailing list Haskell-Cafe@haskell.org http://www.haskell.org/mailman/listinfo/haskell-cafe
Re: [Haskell-cafe] Rank N Kinds
I still asking for good examples of ranNkinds data (and classes) But now let's look at my example, TupleList data TupleList (t :: **) = TupleNil | TupleUnit t (TupleList t) we can easily define tupleList tupleL :: TupleList ( (Int :: **) -> (String :: **) -> (Bool :: **) ) tupleL = TupleUnit 5 (TupleUnit "inside tuple" (TupleUnit True TupleNil))) And we can easily define rankNkinds functions, which can only work with rankNkinds data, like fstL, sndL, headL, tailL (see my previous letter) But Haskell is weak to work with truly rankNkinds functions. Let's look at Functor instance Functor (TupleList (a :: **)) where fmap :: ? fmap = tmap What's the signature of fmap? Even with rankNkinds we can't define a signature. Without new extensions. Let's look at tmap ~ map for list. It's bit simplier for us tmap :: tmap _ TupleNil = TupleNil tmap f (TupleUnit x xs) = TupleUnit (f x) (tmap f xs) If we wish to work with `f` like in this example, we must use `rankNkindsFunctions` extension. It's very hard to implement this extension into Haskell (imho) Let's think we've already had this extension and we have a `tmap` Let's try to write rankNkinds functions for next tupleLists: tupleL :: TupleList ( (Int :: **) -> (String :: **) -> (Bool :: **) ) tupleL = TupleUnit 5 (TupleUnit "inside tuple" (TupleUnit True TupleNil))) tupleL' :: TupleList ( (Int :: **) -> (Int :: **) -> (Bool :: **) ) tupleL' = TupleUnit 5 (TupleUnit 42 (TupleUnit True TupleNil))) tupleL'' :: TupleList ( (Int :: **) -> (Int :: **) -> (Int :: **) ) tupleL'' = TupleUnit 5 (TupleUnit 42 (TupleUnit 777 TupleNil))) here they are: f :: ((Int -> Int) :: **) -> ((String -> String) :: **) -> ((Bool -> Bool) :: **) f :: Int -> Int f = (+ 2) f :: String -> String f = ("Hello " ++) f :: Bool -> Bool f = (True &&) 2nd: f' :: c@((Int -> Int) :: **) -> c'@((Int -> Int) :: **) -> ((Bool -> Bool) :: **) f' :: c@(Int -> Int) f' = (+ 2) f' :: c'@(Int -> Int) f' = (* 5) f' :: Bool -> Bool f' = (True &&) 3rd: f'' :: c@((Int -> Int) :: **) -> c@((Int -> Int) :: **) -> c@((Int -> Int) :: **) f'' :: c@(Int -> Int) f'' = (+ 2) These functions not only look weird, they look like overloading, but they are not. But truly, they are really weird. Le's look deeply at line `tmap f (TupleUnit x xs) = TupleUnit (f x) (tmap f xs)` Truly rankNkinds functions works like ST Monad and partly applied function together! This is awesome! ((Int -> Int) :: **) -> ((String -> String) :: **) -> ((Bool -> Bool) :: **) `op` (Int ::*) = (Int :: **) -> ((String -> String) :: **) -> ((Bool -> Bool) :: **) >>> (Int :: **) -> ((String -> String) :: **) -> ((Bool -> Bool) :: **) >>> `op` (String ::*) = (Int :: **) -> (String :: **) -> ((Bool -> Bool) :: **) >>> (Int :: **) -> (String :: **) -> ((Bool -> Bool) :: **) `op` (Bool ::*) >>> = (Int :: **) -> (String :: **) -> (Bool :: **) <<==>> TupleUnit (f x) (TupleUnit (f x') (TupleUnit (f x'') TupleNil)) Ok. Now we are ready to redefine f'' in a general way. We need to have one extra extension: RecursiveSignatures. We add 2 quantifications: 'forany' and 'forrec' (it's just my suggestion, may be is too complicated and exists easier way to do this): f''' :: forany i. forrec{i} c. c@((Int -> Int) :: **) -> { -> c } f''' :: forrec{i=0..3} c. c@(Int -> Int) f''' = (+ 2) Let's write `f` function using these quantifications: g :: forany i. forrec{i} a c. c@(a -> a :: **) { -> c } g :: forrec c{0}. Int -> Int <<==>> g :: forrec c{0} (a{0} ~ Int). a -> a g = (+ 2) g :: forrec c{1}. String -> String g = ("Hello " ++) g :: forrec c{2}. Bool -> Bool g = (True &&) And now it is possible to write signatures to `tmap` and `fmap` tmap :: forany i. forrec{i} a b c c' c''. c@( (a -> b) :: **) { -> c } -> c'@(a :: * :: **) { -> c' } -> c''@(b :: * :: **) { -> c'' } fmap :: forany i. forrec{i} a b c c' c''. c@( (a -> b) :: **) { -> c } -> f (c'@(a :: **) { -> c' }) -> f (c''@(b :: **) { -> c'' }) P.S. We could write foldr function for our tupleLists as: folded :: Bool folded = foldr h True tupleL h :: forany i. forrec{i} a c. c@( a -> b -> b :: **) { -> c } h :: forrec c{0}. Int-> Bool -> Bool h :: forrec c{1}. String -> Bool -> Bool h :: forrec c{2}. Bool -> Bool -> Bool P.S.S. All this staff is open for discussion )) cheers, Wvv -- View this message in context: http://haskell.1045720.n5.nabble.com/Rank-N-Kinds-tp5733482p5733699.html Sent from the Haskell - Haskell-Cafe mailing list archive at Nabble.com. ___ Haskell-Cafe mailing list Haskell-Cafe@haskell.org http://www.haskell.org/mailman/listinfo/haskell-cafe
Re: [Haskell-cafe] Rank N Kinds
I'm sorry, `instance Functor (TupleList (a :: **)) where ...` isn't right, sure. The right one is `instance Functor TupleList where ...` -- View this message in context: http://haskell.1045720.n5.nabble.com/Rank-N-Kinds-tp5733482p5733700.html Sent from the Haskell - Haskell-Cafe mailing list archive at Nabble.com. ___ Haskell-Cafe mailing list Haskell-Cafe@haskell.org http://www.haskell.org/mailman/listinfo/haskell-cafe
Re: [Haskell-cafe] Rank N Kinds
Paradoxes there are at logic and math. At programing languages we have bugs or features :)) Higher universe levels are needed first of all for more abstract programming. P.S. By the way, we don't need have extra TupleList, we have already list! t3 :: [ (Int :: **) -> (Bool -> Bool -> Bool :: **) -> (String :: **) ] t3 = [42 :: Int, (&&), "This is true *** type" ] > :k t3 * > head t3 42 :: Int > (head $ tail t3) True True True :: Bool Wvv 2 Aug 2013 at 5:34:26, Daniel Peebles [via Haskell] (ml-node+s1045720n5733708...@n5.nabble.com) wrote: The higher universe levels are mostly "used" to stave off logical paradoxes in languages where you care about that kind of stuff. In a fundamentally impredicative language like Haskell I don't see much point, but I'd be happy to find there is one :) On Thu, Aug 1, 2013 at 4:55 PM, Wvv <[hidden email]> wrote: The right one is `instance Functor TupleList where ...` -- View this message in context: http://haskell.1045720.n5.nabble.com/Rank-N-Kinds-tp5733482p5734055.html Sent from the Haskell - Haskell-Cafe mailing list archive at Nabble.com.___ Haskell-Cafe mailing list Haskell-Cafe@haskell.org http://www.haskell.org/mailman/listinfo/haskell-cafe
[Haskell-cafe] Proposal: Polymorphic typeclass and Records
Let we have data in one module as this: data Person = Person { personId :: Int, name :: String } data Address a = Address { personId :: Int, address :: String , way :: a} It was discussed a lot in topics "OverloadedRecordFields" This is an alternative: Let we have polymorphic typeclass: class Record{f} a b | a -> b where f :: a -> b so, compiler could create instances for our data as: instance Record{personId} Person Int where personId (Person x _) = x instance Record{personId} (Address a) Int where personId (Address x _ _) = x instance Record{way} (Address Int) Int where way (Address _ _ x) = x and we could use this: p:: Record {personId} r Int => r -> Int p = personId What do you think about this? -- View this message in context: http://haskell.1045720.n5.nabble.com/Proposal-Polymorphic-typeclass-and-Records-tp5735096.html Sent from the Haskell - Haskell-Cafe mailing list archive at Nabble.com. ___ Haskell-Cafe mailing list Haskell-Cafe@haskell.org http://www.haskell.org/mailman/listinfo/haskell-cafe
Re: [Haskell-cafe] Proposal: Polymorphic typeclass and Records
Thanks! You do a great job! Adam Gundry wrote >> Haskell doesn't allow classes to be polymorphic in the names of their >> methods Yes, still not (( -- View this message in context: http://haskell.1045720.n5.nabble.com/Proposal-Polymorphic-typeclass-and-Records-tp5735096p5735365.html Sent from the Haskell - Haskell-Cafe mailing list archive at Nabble.com. ___ Haskell-Cafe mailing list Haskell-Cafe@haskell.org http://www.haskell.org/mailman/listinfo/haskell-cafe
[Haskell-cafe] Proposal: Generic conditions for 'if' and 'case'
I think it is an old idea, but nevertheless. Now we have next functions: if (a :: Bool) then x else y case b of a1 :: Bool -> x1 a2 :: Bool -> x2 ... Let we have generic conditions for 'if' and 'case': class Boolean a where toBool :: a -> Bool instance Boolean Bool where toBool = id instance Boolean [a] where toBool [] = False toBool _ = True instance Boolean (Maybe a) where toBool Nothing = False toBool _ = True instance Boolean Int where toBool 0 = False toBool _ = True if' (a :: Boolean b) then x else y case' d of a1 :: Boolean b1 -> x1 a2 :: Boolean b2 -> x2 ... It is very easy to implement to desugar: if' a then ... == if toBool ( a ) then ... -- View this message in context: http://haskell.1045720.n5.nabble.com/Proposal-Generic-conditions-for-if-and-case-tp5735366.html Sent from the Haskell - Haskell-Cafe mailing list archive at Nabble.com. ___ Haskell-Cafe mailing list Haskell-Cafe@haskell.org http://www.haskell.org/mailman/listinfo/haskell-cafe
Re: [Haskell-cafe] Proposal: Generic conditions for 'if' and 'case'
Thanks! It is a good toy for testing! Nicolas Trangez wrote > Here's an example implementing your proposal: > > {-# LANGUAGE RebindableSyntax #-} > > import Prelude > > class Boolean a where > toBool :: a -> Bool > > instance Boolean Bool where > toBool = id > > instance Boolean [a] where > toBool = not . null > > instance Boolean (Maybe a) where > toBool = maybe False (const True) > > instance Boolean Int where > toBool = (/= 0) > > ifThenElse :: Boolean a => a -> b -> b -> b > ifThenElse i t e = case toBool i of > True -> t > False -> e > > main :: IO () > main = do > test False > test ([] :: [Int]) > test [1] > test (Nothing :: Maybe Int) > test (Just 1 :: Maybe Int) > test (0 :: Int) > test (1 :: Int) > {- test 'c' fails to type-check: no instance Boolean Char defined! > -} > where > test v = putStrLn $ show v ++ " is " ++ (if v then "true" else > "false") > > which outputs > > False is false > [] is false > [1] is true > Nothing is false > Just 1 is true > 0 is false > 1 is true > > Using RebindableSyntax, 'if I then T else E' is rewritten into > 'ifThenElse I T E' by the compiler, for whatever 'ifThenElse' is in > scope. > > Nicolas > > > ___ > Haskell-Cafe mailing list > Haskell-Cafe@ > http://www.haskell.org/mailman/listinfo/haskell-cafe -- View this message in context: http://haskell.1045720.n5.nabble.com/Proposal-Generic-conditions-for-if-and-case-tp5735366p5735424.html Sent from the Haskell - Haskell-Cafe mailing list archive at Nabble.com. ___ Haskell-Cafe mailing list Haskell-Cafe@haskell.org http://www.haskell.org/mailman/listinfo/haskell-cafe
Re: [Haskell-cafe] Unary functions and infix notation
But we can do next: Prelude> :set XPostfixOperators Prelude> let z = (\y -> True) :: a -> Bool Prelude> :t (True `z`) But still `z` True ~\a -> a `z` True~ \a -> z a True and `z` must be a function with minimum 2 arguments -- View this message in context: http://haskell.1045720.n5.nabble.com/Unary-functions-and-infix-notation-tp5735766p5735807.html Sent from the Haskell - Haskell-Cafe mailing list archive at Nabble.com. ___ Haskell-Cafe mailing list Haskell-Cafe@haskell.org http://www.haskell.org/mailman/listinfo/haskell-cafe
[Haskell-cafe] Proposal: Pragma EXPORT
I suggest to add instead of (or with) export section Pragma EXPORT: We have 3 values: public, abstract and private. Data(with newtypes and types,..) could be public, like `Data(...)` or abstract `Data`. Other cases abstract = public. {-# EXPORT #-} pragma is valid till next {-# EXPORT #-}. We also can add local pragma: {-# EXPORT from #-} ... {-# EXPORT untill #-} Outside of block is rule of previous {-# EXPORT #-}. Finally we also have rule for 1: {-# EXPORT one #-} Example module C where {-# EXPORT public #-} data A1... data A2... {-# EXPORT abstract from #-} newtype A3... data A4... {-# EXPORT abstract until #-} type A5... {-# EXPORT private one #-} data A6... foo = ... {-# EXPORT private one #-} bar = ... baz = ... lorem = ... {-# EXPORT private #-} insput ... dolor = .. sit = ... {-# EXPORT public one #-} amen = ... consectetur = ... adipisicing = ... elit = ... sed = ... eiusmod = ... tempor = ... incididunt = ... {-# EXPORT public from #-} ut = ... labore = ... et = ... {-# EXPORT public until #-} dolore = ... magna = ... aliqua = ... is the same as module C ( A1(..) , A2(..) , A3 , A4 , A5(..) , foo , baz , lorem , amen , ut , labore , et ) where data A1... data A2... newtype A3... data A4... type A5... data A6... foo = ... bar = ... baz = ... lorem = ... insput ... dolor = .. sit = ... amen = ... consectetur = ... adipisicing = ... elit = ... sed = ... eiusmod = ... tempor = ... incididunt = ... ut = ... labore = ... et = ... dolore = ... magna = ... aliqua = ... We also could have complex pragma, like {-# EXPORT inherit one foo #-} bar=... Backward compatibility: module A where ... ~ module A where {-# EXPORT public #-} ... module B ( ) where ... ~ module B ( ) where {-# EXPORT private #-} ... -- View this message in context: http://haskell.1045720.n5.nabble.com/Proposal-Pragma-EXPORT-tp5736547.html Sent from the Haskell - Haskell-Cafe mailing list archive at Nabble.com. ___ Haskell-Cafe mailing list Haskell-Cafe@haskell.org http://www.haskell.org/mailman/listinfo/haskell-cafe
[Haskell-cafe] Why superclass' instances are bad idea?
I suggest to add superclass' instances into libraries. http://ghc.haskell.org/trac/ghc/ticket/8348 In brief, we could write next: >{-# LANGUAGE FlexibleInstances #-} >{-# LANGUAGE UndecidableInstances #-} > >instance Monad m => Applicative m where >pure = return >(<*>) = ap > >instance Monad m => Functor m where >fmap = liftM > >instance Monad m => Bind m where >(>>-) = flip (>>=) >B.join = M.join this code is valid! I've already defined 3 "superclassses" for Monad: Functor, Applicative and Bind! Similar idea said Edward Kmett in 2010 (founded by monoidal) ( http://stackoverflow.com/questions/3213490/how-do-i-write-if-typeclass-a-then-a-is-also-an-instance-of-b-by-this-definit/3216937#3216937 ) And he said "but effectively what this instance is saying is that every Applicative should be derived by first finding an instance for Monad, and then dispatching to it. So while it would have the intention of saying that every Monad is Applicative (by the way the implication-like => reads) what it actually says is that every Applicative is a Monad, because having an instance head 't' matches any type. In many ways, the syntax for 'instance' and 'class' definitions is backwards." Why? I don't understand. Not every Applicative is a Monad, but every Monad is Applicative -- View this message in context: http://haskell.1045720.n5.nabble.com/Why-superclass-instances-are-bad-idea-tp5737056.html Sent from the Haskell - Haskell-Cafe mailing list archive at Nabble.com. ___ Haskell-Cafe mailing list Haskell-Cafe@haskell.org http://www.haskell.org/mailman/listinfo/haskell-cafe
Re: [Haskell-cafe] Why superclass' instances are bad idea?
Thanks a lot! This makes clear. I haven't noticed before that OverlappingInstances don't look at constraint! John Lato-2 wrote > This line > > instance Monad m => Applicative m where > > tells the compiler "Every type (of the appropriate kind) is an instance of > Applicative. And it needs to have a Monad instance as well." > > That's what Edward means when he said that it means "every Applicative is > a > Monad". Theoretically the statement makes no sense, but that's what this > instance head means. Everything is Applicative, and it also needs a Monad > instance to use that Applicative. > > Consider what happens for something that isn't a Monad, e.g. ZipList. > Since it's not a Monad, it would need its own instance > > instance Applicative ZipList where > ... > > But now you'd need to enable OverlappingInstances, because ZipList matches > both this instance and the general one you've defined above (GHC doesn't > consider constraints when matching instance heads). OverlappingInstances > is much more problematic than the other extensions because it could (and > almost certainly would in this case) give rise to incoherence (see the > warning under > http://www.haskell.org/ghc/docs/latest/html/users_guide/type-class-extensions.html#instance-overlap > ). >> > > ___ > Haskell-Cafe mailing list > Haskell-Cafe@ > http://www.haskell.org/mailman/listinfo/haskell-cafe -- View this message in context: http://haskell.1045720.n5.nabble.com/Why-superclass-instances-are-bad-idea-tp5737056p5737139.html Sent from the Haskell - Haskell-Cafe mailing list archive at Nabble.com. ___ Haskell-Cafe mailing list Haskell-Cafe@haskell.org http://www.haskell.org/mailman/listinfo/haskell-cafe
[Haskell-cafe] Proposal: RankedInstances
The main power of Haskell is on instances. But Haskell instances system work fine with lower number of instances (rare instances). But we want hight density of instances! If we wish to have more selective instances we use `OverlappingInstances` (which are desined in a poor way) and if we still have too many instances we use `IncoherentInstances`. ~~`RankedInstances` extension ~~ I suggest simple `RankedInstances` extension. We use it (!)before OverlappingInstances (it must include `RankedInstances`), and in many cases instead of. This extension is easy to implement and it give us a lot of new possibilities and instruments. Now the system of instances is flat, and compiler takes all of them and check if only 1 match. If it is not(less or more than) - compiler trow an error. I suggest to add rankings, so compiler * compiler set N=0 * took all N-ranked instances and ** try to find only one match instance. *** If it found 1 - this is RESULT: needed instance, *** If it found many instances - still throw an error *** (then we use `OverlappingInstances` to resolve this) *** If compiler found NO instances, compiler set N=N+1 and repeat * If N=MaxRank and still no matches compiler throw an error ~~How to add a rank~~ I suggest next grammar: {-# LANGUAGE RankedInstances #-} instance rank 1. C a => D a where ... instance C2 a => E a where ... <<==>> instance rank 0. C2 a => E a where ... So, all written instances(without ranking) are 0-ranked instances. Backward compatibility => without -XRankedInstances all instances with rank n, where n >0 - are not exported ~Example~ 1) instance rank 1. C Int a where ... -- (A) instance C a Bool where ... -- (B) rank 0 1+) instance rank 1. C Int a where ... -- (A) instance rank 1. C a Bool where ... -- (B) instance C Int Bool where ... -- (C) rank 0 2) instance rank 1. C Int [a] where ... -- (C) instance C Int [Int] where ... -- (D) As we see, all instances are unambiguous! ~~ Rank Scale~~ It is for discussion, I see this like: 0 - default 1 ..9 - user free (without fear to overlap with devs instances) 10 .. 14 - Generic 15 .. - superclass' instances ~~ Higher Rank instances~~ We don't need to use `default` inside of class: instance rank 10. (Generic a, GToJSON (Rep a)) => ToJSON a where toJSON = genericToJSON defaultOptions We could add superclass' instances now, something like these: instance rank 15. Monad m => Applicative m where pure = return (<*>) = ap instance rank 16. Monad m => Functor m where fmap = liftM instance rank 17. Applicative m => Functor m where fmap f x = pure f <*> x ~~Inherit mechanism~~ What do if we want to use any proposed instance, not in the rank order ? For example we have data, which is Monad and Applicative, but not a Functor. We'll use automatically "instance rank 16. Monad m => Functor m", but not "instance rank 17. Applicative m => Functor m" . But we wish to use the last one. We need to create a new instance and inherit the behavior of needed instance data D a instance Monad D where ... instance Applicative D where ... instance rank 1. Functor D inherit (D ~ m) instance Applicative m => Functor m foo = ... fmap So, in this case we'll use `fmap` as Applicative Functor. Inherit mechanism defaulting : instance C a => D a where ... <<==>> instance C a => D a inherit (a ~ b) class D b where ~~ "As" pattern in RankedInstances~~ Now we add "as" pattern and rewrite both of our instances: instance rank 17. Applicative m => ApFunctor@Functor m where fmap f x = pure f <*> x instance ApFunctor D --by the way 0-ranked Wow!!! It is simple, safe and looks nicer! ~~Partly Applied Instances~~ We describe a situation when we write a child class and want automatically get access to parent's classes. But sometimes we need to use already defined parent classes to describe children classes We CANNOT do next: instance rank 20. (Functor m, Applicative m) => Monad m where ma >> mb = (fmap (const id) ma) `apply` mb instance rank 21. Applicative m => Monad m where ma >> mb = (pure (const id) <*> ma) `apply` mb Because if we define data D a ... instance Functor D ... instance Applicative D ... D a >>= D b -- this will compiler, but we have no full applied MonadInstance How to resolve this? I suggest to add one reserved world "newclass" (as an analog of newtype) --instance (Functor m, Applicative m) => FAMonad@Monad m where newclass (Functor m, Applicative m) => FAMonad@Monad m where ma >> mb = (fmap (const id) ma) `apply` mb --instance Applicative m => AMonad@Monad m where newclass (Applicative m) => AMonad@Monad m where ma >> mb = (pure (const id) <*> ma) `apply` mb The "newclass" is just an instance, but guarded - compiler did count it when it try
Re: [Haskell-cafe] Proposal: new function for lifting
Which "lift"? This one? class MonadTrans t where lift :: Monad m => m a -> t m a -- View this message in context: http://haskell.1045720.n5.nabble.com/Proposal-new-function-for-lifting-tp5737189p5737196.html Sent from the Haskell - Haskell-Cafe mailing list archive at Nabble.com. ___ Haskell-Cafe mailing list Haskell-Cafe@haskell.org http://www.haskell.org/mailman/listinfo/haskell-cafe
[Haskell-cafe] Newclasses
"Newclasses" are not a new vision of classes! Not at all! Newclasses could elegant solve several instance problems! 1) we want to have "partly applied instances", like Parent2Child: Parent a => Child a like instance Applicative m => Monad m where return = pure -- we won't define here (>>=) 2) we want to have superclass' instances, like Child2Parent: Child a => Parent a like instance Monad m => Applicative m where pure = return (<*>) = ap 3) we want to have default instances outside of class and as many as possible, not the only one. like class Foo a where foo :: ... default foo :: ... foo = ... 4) we want to have multi-class instances to separate (or unite) classes like type Stringy a = (Show a, Read a) instance Stringy SomeData where read = ... show = ... (4)th problem we could solve separately, but maybe it isn't easy enough to do such de-sugaring, and it could much easier to add them in newclasses. (3)rd problem is solved partly, but not in universal way, non-flexible and a bit ugly. (2)nd problem is solved, but it is mostly impossible to use them and it is not recommend to use it for overlapping and incoherent issues. (1)st problem is unsolved at all (partly, it is possible to make depended classes, but checker don't check if we implement parent classes). This is a compose proposal. Newclasses solve these problems at once! As newtype is a data looking like a type, same newclass is looking like a class, but is mostly an instance! Mostly, but not full. To best understanding what "newclasses" is, let's look at (1)st problem: -- we wish to write -- instance Applicative m => Monad m where -- return = pure -- we write "newclass" instead of "instance" -- add "=>" and giving a name to newclass like a class -- this is not instance, so newclass can't overlap with any instance newclass (Applicative m) => Monad m => ApMonad m where return = pure data D a instance Applicative D where pure = ... (<*>) = ... -- creating instances from newclass is intuitive -- we implement here Monad class, not "ApMonad"; ApMonad is a just newclass instance ApMonad D where -- we already have 'return = pure', so we define only (>>=) (>>=) = ... What do we see here? Newclass looks like class, but it's mostly an instance! Newclass: Grammar: newclass constraint => Parent a => NewClassName a where ... As class, newclass has a name, which is unique and can't conflict with any other newclass or class names. As class, methods of newclass could be empty or implemented. As class, methods of newclass are not use in function inference. As class we can make an instance of newclasses and overwrite any of his functions! But, instance of newclass IS an instance of the parent (!)class! So, newclasses is like a de-sugaring. As instance, newclass contains only parents methods! On contrary to instancess, we don't use newclasse directly, it only help us to create instances. If we allow for newclass to be as Parent not only classes, but newclasses, then newclass can't be recursive: neither of his (Grand)Parent could be he by himself. If we allow for newclass muliple Parents, we solve (4)th problem too. Examples: We have: class Functor f where fmap :: (a -> b) -> f a -> f b class Applicative f where -- without "Functor f =>", this is a misfeature pure :: a -> f a (<*>) :: f (a -> b) -> f a -> f b class Monad m where return :: a -> m a (>>=) :: m a -> (a -> m b) -> m b class Ord' a where -- without "Eq a =>", this is a misfeature ... compare a b-- not as in Prelude | a < b = LT | a > b = GT | otherwise = EQ (1)st, Parent2Child: Common pattern to write newclass like: newclass Parent a => Child a => ParChild a where ... Examples: newclass (Applicative m) => Monad m => ApMonad m where return = pure data C1 a ... instance Applicative C1 where pure = ... (<*>) = ... instance ApMonad C1 where -- return is already defined (>>=) = ... -- newclass (Ord' a) => Eq a => OEq a where a == b = case compare a b of EQ -> True _ -> False data C2
Re: [Haskell-cafe] Newclasses
> Your first two cases will be fixed in 7.10, as Applicative finally becomes a superclass of Monad. Sure, newclassses not about Applicative and Monads only. This question is more wider. Must Apply be a superclass of Bind? Must Bind be a superclass of Monad? So, must Monad has 2 superclasses at once: Bind and Applicative? Must Semigroupoids be a superclass of Category? Must Category be a superclass of Arrow? With newclasses we could write empty instances to provide correct functional dependencies: instance ArrCategory MyArrow instance CatSemigroupoids MyCategory instance MBind MyMonad instance MApply MyMonad instance MApplicative MyMonad instance MFunctor MyMonad > Also, I don't see why it would be a misfeature to have Eq as a superclass > of Ord, or Functor as a superclass of Applicative. I see 2 reasons: 1) class functions in reality don't depend of superclass functions 2) Haskell can't check if superclass instance is correspond with class laws -- View this message in context: http://haskell.1045720.n5.nabble.com/Newclasses-tp5737596p5737625.html Sent from the Haskell - Haskell-Cafe mailing list archive at Nabble.com. ___ Haskell-Cafe mailing list Haskell-Cafe@haskell.org http://www.haskell.org/mailman/listinfo/haskell-cafe
Re: [Haskell-cafe] Newclasses
Yes, multi-class instances allow us write type Monad a = (Applicative a, Bind a) But at least 1 issue remains: Applicative : pure; Monad: return Bind : (>-); Monad: (>>=) With MultiClassInstances we could write only instance Monad MyMonad where { pure= ...; (>-)= ...} But we don't want to break the existent code. Fortunately, an easy extension FunctionSynonyms could help us: type return = pure-- this allow us to use 'return' instead of 'pure' in instances type (>>=) = (>-)-- this allow us to use '(>>=)' instead of '(>-)' in instances 2) Still remains issue with several default instances, like 'Generic a => ToJSON a' and 'Data a => ToJSON a', which we can't unite to 1 instance 3) If devs of library don't want to change the behavior, (for example divide Monad to Applicative and Bind), but we still want easy connection to that class, newclasses is our choice! Yes, this solution is good! Very nice! I like it! I should name it solution from derivatives. From bottom to top. We have only independent classes and unite them with "types". Newclasses solve same problem in integral way. From top to bottom. Instead of having independent little classes, it allow to have big classes with dependences, which are written in newclasses, and they allow to connect easy to any dependent class. newclass Bind a => Monad a => BMonad a where { (>>=) = (>>-) } newclass Applicative a => Monad a => ApMonad a where { return = pure } newclass (BMonad a, ApMonad a) => BApMonad a --empty type ApBMonad = BApMonad --then connect these classes: instance Bind MyDataAB where { (>-) = ...} instance Applicative MyDataAB where { pure = ... ; (<*>) = ...} instance ApBMonad MyDataAB --empty --or these instance Monad MyDataM where {return= ... ; (>>=) = ...} instance MBind MyDataM --empty instance MApply MyDataM --empty instance MApplicative MyDataM--empty instance MFunctor MyDataM--empty If Haskell add MultiClassInstances + FunctionSynonyms, or Newclasses, or both of them, Haskell would be the best language in nearest future!!! About the "misfeature". If class is independent of superclass functions and can't check dependence's laws, why does it order to have instances of unnecessary class? Stijn van Drongelen wrote > On Thu, Oct 3, 2013 at 8:16 AM, Wvv < > vitea3v@ > > wrote: > >> > Your first two cases will be fixed in 7.10, as Applicative finally >> becomes >> a superclass of Monad. >> >> Sure, newclassses not about Applicative and Monads only. >> This question is more wider. >> >> Must Apply be a superclass of Bind? >> Must Bind be a superclass of Monad? >> So, must Monad has 2 superclasses at once: Bind and Applicative? >> >> Must Semigroupoids be a superclass of Category? >> Must Category be a superclass of Arrow? > > > There is no theoretical problem here, just a practical one. It would be > resolved by solving your 4th problem, for which you don't need newclasses. > Consider: > > {-# LANGUAGE ConstraintKinds #-} > class Functor f where { fmap :: (a -> b) -> f a -> f b } > class Functor f => Apply f where { (<*>) :: f (a -> b) -> f a -> f b } > class Apply f => Applicative f where { pure :: a -> f a } > class Apply f => Bind f where { (=<<) :: (a -> f b) -> f a -> f b } > > type Monad f = (Applicative f, Bind f) > return :: Monad f => a -> f a > return = pure > > I might have made some mistakes in the exact hierarchy, but something like > this should work. There are no problems with having hierarchies like this, > as far as I'm aware. > > The current problem is that nobody wants to use this hierarchy: to get a > Monad instance, you have to write four separate instances for your type. > What would be nicer is a feature (ConstraintSynonymInstances?) where > something like this can be written: > > instance (Functor Maybe, Apply Maybe, Monad Maybe) where > fmap _ Nothing = Nothing > fmap f (Just x) = Just (f x) > > Just f <*> Just x = Just (f x) > _ <*> _ = Nothing > > pure = Just > > f =<< Just x = f x > _ =<< Nothing = Nothing > > This would be sugar for > > instance Functor Maybe where { fmap = ... } > instance Apply Maybe where { (<*>) = ... } > instance Monad Maybe where { pure = ... ; (=<<) = ... } > > and the last would be sugar for > > instan
Re: [Haskell-cafe] Newclasses
Newclasses are something like instances, but out of scope. In a baggage. We don't use them for interfere their functions. This why newclasses never overlap each other and between them and any instances. We use newclasses to plug-in/connect to any related class or combine data Replying to you question, yes, instance of newclass desugar to instance of class: instance BMonad MyBind where {return= ...} desugar into instance Monad MyBind where {return= ...; (>>=) = (>>-)} We already have too many classes: look at Edward Kmett http://hackage.haskell.org/package/semigroupoids 13 dependent classes (from Foldable to MonadPlus) http://hackage.haskell.org/package/category-extras 30-60 dependent class http://hackage.haskell.org/package/lens 11 dependent classes We can't divide all classes to atimic ones. I do not want to implement all depended class instances, even of atomic, if I want to work with hight class only. But I want easy connection with any related class! And newclasses solve this situation. Also in reality we have several realizations of same class/compose data and we want to mix them for better realizations. Newclasses allows switch them as engines! Easy. Main purpose of newclasses is to make instances as minimal as possible. In many cases empty. About newclass and compose data, we can do next: newclass Foo [a] => FooList a where {containerMainipulation=...} newclass Foo (Set a) => FooSet a where {containerMainipulation=...} newclass Foo (Sequence a) => FooSeq a where {containerMainipulation=...} so now I can switch any container of my data, changing only name of newclass: instance FooList MyData where {dataMainipulation=...} Or let I have an MyArrow data. And I need some semigroupoid manipulations. I just write instance ArrSemigroupoid MyArrow --empty that's all, I plug-in, let's just use semigroupoids functions! Or I have MyMonad and I want some Functor, so I just plug-in: instance MFunctor MyMonad --empty that's all. I also need some Applicative! Easy: instance MApplicative MyMonad --empty again done! About conflicts, I don't understand a bit. Which ones? We catch Overlapped instances or even Incoherent instances at once we add both newclass instances of the same class. John Lato-2 wrote > I meant to say, does it mean that by > writing a BMonad instance a Monad instance would be automatically > generated? If so, that seems like it would cause conflicts in many cases. > Regardless, I think "newclass" needs to be better specified if you want > other people to be able to support it. > > > On Thu, Oct 3, 2013 at 7:53 PM, John Lato < > jwlato@ > > wrote: > >> I don't really understand what a "newclass" is supposed to be. >> >> >> On Thu, Oct 3, 2013 at 2:15 PM, Wvv < > vitea3v@ > > wrote: >> >>> >>> newclass Bind a => Monad a => BMonad a where { (>>=) = (>>-) } >> >> >> I think this means that `BMonad` is supposed to be a new class that has >> both Bind and Monad in scope, the same as >> >> class (Bind a, Monad a) => BMonad a >> >> except that the Monad instance's (>>=) is replaced by (>>-). >> >> If that's what "newclass" means, it seems absolutely pointless. >> >> Does it instead mean that one could write >> >> instance Bind MyType where >> >> instance BMonad MyType >> > > ___ > Haskell-Cafe mailing list > Haskell-Cafe@ > http://www.haskell.org/mailman/listinfo/haskell-cafe -- View this message in context: http://haskell.1045720.n5.nabble.com/Newclasses-tp5737596p5737792.html Sent from the Haskell - Haskell-Cafe mailing list archive at Nabble.com. ___ Haskell-Cafe mailing list Haskell-Cafe@haskell.org http://www.haskell.org/mailman/listinfo/haskell-cafe
Re: [Haskell-cafe] Newclasses
Stijn van Drongelen wrote > On Fri, Oct 4, 2013 at 10:31 PM, Wvv < > vitea3v@ > > wrote: >> About newclass and compose data, we can do next: >> >>newclass Foo [a] => FooList a where {containerMainipulation=...} >> >>newclass Foo (Set a) => FooSet a where {containerMainipulation=...} >> >>newclass Foo (Sequence a) => FooSeq a where >> {containerMainipulation=...} >> >> so now I can switch any container of my data, changing only name of >> newclass: >> >> instance FooList MyData where {dataMainipulation=...} >> > > You can already solve that in Haskell 98: > > class Foo2 f where { containerManipulation = ... } > instance Foo2 [] where { ... } > instance Foo2 Set where { ... } > instance Foo2 Sequence where { ... } > > class (Foo2 f) => Foo1 f a where { dataManipulation = ... } > > Or even: > > class Foo' a where { dataManipulation' = ... } > dataManipulation = dataManipulation' yourDefaultContainerManipulation Yes, I agree, use newclasses for composite data is an additional, secondary feature. Haskell has huge infrastructure of data to use alternative ways instead using newclasses this way. Stijn van Drongelen wrote > On Fri, Oct 4, 2013 at 10:31 PM, Wvv < > vitea3v@ > > wrote: > > Let's see how many lines of code this costs in Haskell 98: > > instance Monad MyMonad where { ... } > instance Functor MyMonad where > fmap = liftM > instance Applicative MyMonad where > pure = return > (<*>) = ap > > Only three lines more, and they're readable. I see, we are looking to the same situation from different angles. I try to show you why I think my point of view is important. 2 situations: first is more practical, second is more philosophical. (1) we have several libraries with lenses and lens-looking like libraries. Why is the main popularity going to Kmett's library? My answer: easy connection: just add one line " makeLens MyRecord'' " and we already could use all their abilities. Why Kmett's library of JSON is so popular. Sure, it more quicker, but what is the main reason? My answer: easy connection. Why Pipes, Streams, Conduit, are not as super-popular as they could be? They have very powerful abilities. You need time not only for studying how this library works, but also how to switch your data to library functions. If you need to work with ... RMonad or MonadDatabase or something like this, do you always know how to switch your data on? (2) Let I have a lamp and I wish to switch it on. So, I say, I want to have a plug. But you argue: this isn't necessary: you take 3 wires, green one you contact here, blue one contact here, and finally, brown one contact there! Easy! Ok, now I wish to connect computer with iPhone. You say: take 12 wires , pins-scheme, But I want USB-30pin cable. Newclasses are those connectors-plugs and adapters. Deriving are those plugs. Generic instances and Data instances are those plugs. Newclasses are something like deriving, but much-much flexible and more universal (sure, we can't replace deriving with newclasses). If I have a Data which has an instance of Foo and I want to switch it to class Bar, and I have 2 newclasses: Foo2Tmp and Tmp2Bar, I do the next: instance Foo2Tmp MyData instance Tmp2Bar MyData done! or much simpler if I have Foo2Bar newclass: instance Foo2Bar MyData I do not care how easy or complex those instances I could write without newclasses. My aim is not to connect, but use abilities, which I take after connection. And newclass is amazing tool for easy connection between classes. -- View this message in context: http://haskell.1045720.n5.nabble.com/Newclasses-tp5737596p5737833.html Sent from the Haskell - Haskell-Cafe mailing list archive at Nabble.com. ___ Haskell-Cafe mailing list Haskell-Cafe@haskell.org http://www.haskell.org/mailman/listinfo/haskell-cafe