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PolyKind for Fixed and HasResolution from Data.Fixed

haskell-cafe - Sun, 03/06/2016 - 7:29pm
Hi all! If we define HasResolution and Fixed like that: class HasResolution (a :: k) where resolution :: p a -> Integer newtype Fixed (a :: k) = Fixed Integer We can do something like that: instance KnownNat a => HasResolution a where resolution = natVal 2.3 :: Fixed 1
Categories: Offsite Discussion

GADTs and Exponentiated Functors

haskell-cafe - Sun, 03/06/2016 - 2:11pm
Hi, I have been recently playing around with GADTs, using them to keep track of how many times a functor has been applied. This provides a solution to what seems to be a long standing problem, summarized here: https://byorgey.wordpress.com/2007/08/16/mapping-over-a-nested-functor/ If the nesting depth is part of the type, it is possible to apply fmap automatically as needed. This allows you to write fairly elegant expressions like: data Person = Person { name :: String, age :: Integer, gender :: String, status :: String } deriving Show let persons = fromList' [Person {name="Alice", age=20, gender="F", status="Good"}, Person {name="Bob", age=18, gender="M", status="Good"}, Person {name="Chuck", age=16, gender="M", status="Bad"}] :: NList N1 Person persons `select` age
Categories: Offsite Discussion

Philip Wadler: The Ask

Planet Haskell - Sun, 03/06/2016 - 9:40am
Scottish elections take place on 5 May 2016.

The Scottish Government have set a target of 10% of all trips by foot or bicycle, but less than 2% of the Scottish travel budget goes to 'active travel' (the buzzword for getting from one place to another minus a motor). We Walk, We Cycle, We Vote and Spokes suggest you ask your candidate to pledge the following:
To raise the share of the transport budget spent on walking and cycling to 10% over the course of the next parliament.See the pages linked above for more info, including hustings you can attend to put the question to your local candidates. A don't forget to Pedal on Parliament on 23 April 2016.


Categories: Offsite Blogs

Type-level list "elem" inference

haskell-cafe - Sat, 03/05/2016 - 9:34pm
So I've got some code that looks like: {-# LANGUAGE DataKinds, UndecidableInstances, TypeFamilies, KindSignatures, TypeOperators #-} import Data.Proxy import GHC.TypeLits type family IsSubset (as :: [Symbol]) (bs :: [Symbol]) where IsSubset as bs = IsSubsetPrime as bs bs type family IsSubsetPrime (as :: [Symbol]) bs bs' where IsSubsetPrime as '[] bs' = 'False IsSubsetPrime '[] bs bs' = 'True IsSubsetPrime (a ': as) (a ': bs) bs' = IsSubsetPrime as bs' bs' IsSubsetPrime (a ': as) (b ': bs) bs' = IsSubsetPrime (a ': as) bs bs' This lets me write functions like: foo :: (IsSubset '["foo", "bar"] args ~ 'True) => Proxy args -> Int foo args = undefined I've also got a type family: type family IsElem (a :: Symbol) (bs :: [Symbol]) where IsElem a (a ': bs) = 'True IsElem a (b ': bs) = IsElem a bs IsElem a '[] = 'False This lets me write functions like: bar :: (IsElem "foo" args ~ 'True) => Proxy args -> Int bar args = undefined The problem comes when I want to use "bar args"
Categories: Offsite Discussion

Gabriel Gonzalez: From mathematics to map-reduce

Planet Haskell - Sat, 03/05/2016 - 9:24pm

There's more mathematics to programming than meets the eye. This post will highlight one such connection that explains the link between map-reduce and category theory. I will then conclude with some wild speculation about what this might imply for future programming paradigms.

This post assumes that you already know Haskell and explains the mathematics behind the map-reduce using Haskell concepts and terminology. This means that this post will oversimplify some of the category theory concepts in order to embed them in Haskell, but the overall gist will still be correct.

Background (Isomorphism)

In Haskell, we like to say that two types, s and t, are "isomorphic" if and only if there are two functions, fw and bw, of types

fw :: s -> t
bw :: t -> s

... that are inverse of each other:

fw . bw = id
bw . fw = id

We will use the symbol ≅ to denote that two types are isomorphic. So, for example, we would summarize all of the above by just writing:

s ≅ t

The fully general definition of isomorphism from category theory is actually much broader than this, but this definition will do for now.

Background (Adjoint functors)

Given two functors, f and g, f is left-adjoint to g if and only if:

f a -> b ≅ a -> g b

In other words, for them to be adjoint there must be two functions, fw and bw of types:

fw :: (f a -> b) -> (a -> g b)
bw :: (a -> g b) -> (f a -> b)

... such that:

fw . bw = id
bw . fw = id

These "functors" are not necessarily the same as Haskell's Functor class. The category theory definition of "functor" is more general than Haskell's Functor class and we'll be taking advantage of that extra generality in the next section.

Free functors

Imagine a functor named g that acted more like a type-level function that transforms one type into another type. In this case, g will be a function that erases a constraint named C. For example:

-- `g` is a *type-level* function, and `t` is a *type*
g (C t => t) = t

In other words, g "forgets" the C constraint on type t. We call g a "forgetful functor".

If some other functor, f is left-adjoint to g then we say that f is the "free C" (where C is the constraint that g "forgets").

In other words, a "free C" is a functor that is left-adjoint to another functor that forgets the constraint C.

Free monoid

The list type constructor, [], is the "free Monoid"

The "free Monoid" is, by definition, a functor [] that is left-adjoint to some other functor g that deletes Monoid constraints.

When we say that g deletes Monoid constraints we mean that:

g (Monoid m => m) = m

... and when we say that [] is left-adjoint to g that means that:

[] a -> b ≅ a -> g b

... and the type [a] is syntactic sugar for [] a, so we can also write:

[a] -> b ≅ a -> g b

Now substitute b with some type with a Monoid constraint, like this one:

b = Monoid m => m

That gives us:

[a] -> (Monoid m => m) ≅ a -> g (Monoid m => m)

... and since g deletes Monoid constraints, that leaves us with:

[a] -> (Monoid m => m) ≅ a -> m

The above isomorphism in turn implies that there must be two functions, fw and bw, of types:

fw :: ([a] -> (Monoid m => m)) -> (a -> m)
bw :: (a -> m) -> ([a] -> (Monoid m => m))

... and these two functions must be inverses of each other:

fw . bw = id
bw . fw = id

We can pull out the Monoid constraints to the left to give us these more idiomatic types:

fw :: (Monoid m => [a] -> m)) -> (a -> m)
bw :: Monoid m => ( a -> m) -> ([a] -> m)

Both of these types have "obvious" implementations:

fw :: (Monoid m => [a] -> m)) -> (a -> m)
fw k x = k [x]

bw :: Monoid m => (a -> m) -> ([a] -> m)
bw k xs = mconcat (map k xs)

Now we need to prove that the fw and bw functions are inverse of each other. Here are the proofs:

-- Proof #1
fw . bw

-- eta-expand
= \k -> fw (bw k)

-- eta-expand
= \k x -> fw (bw k) x

-- Definition of `fw`
= \k x -> bw k [x]

-- Definition of `bw`
= \k x -> mconcat (map k [x])

-- Definition of `map`
= \k x -> mconcat [k x]

-- Definition of `mconcat`
= \k x -> k x

-- eta-reduce
= \k -> k

-- Definition of `id`
= id



-- Proof #2
bw . fw

-- eta-expand
= \k -> bw (fw k)

-- eta-expand
= \k xs -> bw (fw k) xs

-- Definition of `bw`
= \k xs -> mconcat (map (fw k) xs)

-- eta-expand
= \k xs -> mconcat (map (\x -> fw k x) xs)

-- Definition of `fw`
= \k xs -> mconcat (map (\x -> k [x]) xs)

-- map (f . g) = map f . map g
= \k xs -> mconcat (map k (map (\x -> [x]) xs))

-- ... and then a miracle occurs ...
--
-- In all seriousness this step uses a "free theorem" which says
-- that:
--
-- forall (k :: Monoid m => [a] -> m) . mconcat . map k = k . mconcat
--
-- We haven't covered free theorems, but you can read more about them
-- here: http://ttic.uchicago.edu/~dreyer/course/papers/wadler.pdf
= \k xs -> k (mconcat (map (\x -> [x]) xs)

-- This next step is a proof by induction, which I've omitted
= \k xs -> k xs

-- eta-reduce
= \k -> k

-- Definition of `id`
= idMap reduce

Let's revisit the type and implementation of our bw function:

bw :: Monoid m => (a -> m) -> ([a] -> m)
bw k xs = mconcat (map k xs)

That bw function is significant because it is a simplified form of map-reduce:

  • First you "map" a function named k over the list of xs
  • Then you "reduce" the list using mconcat

In other words, bw is a pure "map-reduce" function and actually already exists in Haskell's standard library as the foldMap function.

The theory of free objects predict that all other functions of interest over a free object (like the free Monoid) can be reduced to the above fundamental function. In other words, the theory indicates that we can implement all other functions over lists in terms of this very general map-reduce function. We could have predicted the importance of "map-reduce purely from the theory of "free Monoids"!

However, there are other free objects besides free Monoids. For example, there are "free Monads" and "free Categorys" and "free Applicatives" and each of them is equipped with a similarly fundamental function that we can use to express all other functions of interest. I believe that each one of these fundamental functions is a programming paradigm waiting to be discovered just like the map-reduce paradigm.

Categories: Offsite Blogs

Magnus Therning: From JSON to sum type

Planet Haskell - Sat, 03/05/2016 - 6:00pm

For a while I’ve been planning to take full ownership of the JSON serialisation and parsing in cblrepo. The recent inclusion of instances of ToJSON and FromJSON for Version pushed me to take the first step by writing my own instances for all external types.

When doing this I noticed that all examples in the aeson docs use a product

data Person = Person { name :: Text , age :: Int }

whereas I had to deal with quite a few sums, e.g. VersionRange. At first I struggled a little with how to write an instance of FromJSON. After quite a bit of thinking I came up with the following, which I think is fairly nice, but I’d really like to hear what others think about it. Maybe I’ve just missed a much simpler way of implementing parseJSON:

instance FromJSON V.VersionRange where parseJSON = withObject "VersionRange" go where go o = do lv <- (o .:? "LaterVersion") >>= return . fmap V.laterVersion tv <- (o .:? "ThisVersion") >>= return . fmap V.thisVersion ev <- (o .:? "EarlierVersion") >>= return . fmap V.earlierVersion av <- (o .:? "AnyVersion") >>= \ (_::Maybe [(Int,Int)]) -> return $ Just V.anyVersion wv <- (o .:? "WildcardVersion") >>= return . fmap V.WildcardVersion uvr <- (o .:? "UnionVersionRanges") >>= return . fmap toUvr ivr <- (o .:? "IntersectVersionRanges") >>= return . fmap toIvr vrp <- (o .:? "VersionRangeParens") >>= return . fmap V.VersionRangeParens maybe (typeMismatch "VersionRange" $ Object o) return (lv <|> tv <|> ev <|> uvr <|> ivr <|> wv <|> vrp <|> av) toUvr [v0, v1] = V.unionVersionRanges v0 v1 toIvr [v0, v1] = V.intersectVersionRanges v0 v1

Any and all comments and suggestions are more than welcome!

Categories: Offsite Blogs

Reducing boilerplate

haskell-cafe - Sat, 03/05/2016 - 3:56pm
Hi, To write FFI bindings, I use c-storable-deriving [1] to automatically derive CStorable instances for many data types (the only difference between Storable and CStorable is that CStorable provides default methods for types that have Generic instances): {-# LANGUAGE DeriveGeneric #-} {-# LANGUAGE DeriveAnyClass #-} ... data X = X { fieldStatus :: Vector 24 Word8 , fieldPadding :: Word8 } deriving (Generic, CStorable) However I also need a Storable instance, hence I have to write (the "c*" methods are provided by CStorable): instance Storable X where peek = cPeek poke = cPoke alignment = cAlignment sizeOf = cSizeOf Is there a way to automatically generate this instance for every data that has an instance of CStorable? Ideally, I would like to say once and for all: instance CStorable a => Storable a where peek = cPeek poke = cPoke alignment = cAlignment sizeOf = cSizeOf As I don't think it is currently possible, w
Categories: Offsite Discussion

Digraphs With Text: More flexible than graphs,eager to hear from you

haskell-cafe - Sat, 03/05/2016 - 10:06am
This is a demonstration of DWT, a data structure built from and more flexible than graphs. It is powered by the *wonderful* Functional Graph Library. We beseech your involvement! DWT is open-source and actively seeking co-developers. I would happily trade any and all the privilege of determining tasks, teaching haskell or math, learning anything, and receiving obligations. We surely have much knowledge to trade! Even just a "hey why don't you do [this]!" could be precious to me. This transcript makes tiny digressions about what monads make possible. graph). (0,"0: frog") that expression. None do, because none yet exist. Such contexts offer many possibilities for tracking where you are (the data) and how you got there (also kind of the data, and perhaps enabling a desirable kind of removal of self|redaction). (0,"0: frog") (0,"1: moist") (0,"2: springy") (0,"0: frog") (0,"1: moist") (0,"2: springy") (0,":3 _ #(is a quality of) _") a : to indicate that it is a template, as opposed to the string "_ is a qual
Categories: Offsite Discussion

Accuracy of Data.Number.Fixed

haskell-cafe - Sat, 03/05/2016 - 5:50am
This does not seem right to me: Prelude Data.Number.Fixed> read "4.00" :: Fixed (EpsDiv10 (EpsDiv10 Eps1)) 4.00 Prelude Data.Number.Fixed> read "4.01" :: Fixed (EpsDiv10 (EpsDiv10 Eps1)) 4.00 Prelude Data.Number.Fixed> read "4.02" :: Fixed (EpsDiv10 (EpsDiv10 Eps1)) 4.03 Prelude Data.Number.Fixed> read "4.03" :: Fixed (EpsDiv10 (EpsDiv10 Eps1)) 4.04 Prelude Data.Number.Fixed> read "4.04" :: Fixed (EpsDiv10 (EpsDiv10 Eps1)) 4.05 Maybe I am misunderstanding the purpose of this library. I guess that "two digits" of precision means that it is accurate within +/- 0.01? I think that this library is meant for doing arbitrary-precision transcendental operations. But it would not be good as a model for something like currency. It's using ratios as an internal representation, and I'm not sure what ratios it's choosing, but I think I'd choose, say, 401/100 for the "4.01" representation. I guess it's picking a slightly smaller factor than that. The non-reversibility of read/show is somewhat disconcerting. I think I
Categories: Offsite Discussion

Call for Participation: PLACES 2016

General haskell list - Fri, 03/04/2016 - 6:50pm
--------------------------------------------------------- Call for participation: 9th Workshop on Programming Language Approaches to Concurrency- and Communication-cEntric Software Friday 8th April 2016 Co-located with ETAPS 2016, Eindhoven, The Netherlands --------------------------------------------------------- For more information: http://places16.by.di.fc.ul.pt --------------------------------------------------------- Modern hardware platforms, from the very small to the very large, increasingly provide parallel computing resources for applications to maximise performance. Many applications therefore need to make effective use of tens, hundreds, and even thousands of compute nodes. Computation in such systems is thus inherently concurrent and communication centric. Effectively programming such applications is challenging; performance, correctness, and scalability are difficult to achieve. Various programming paradigms and methods have emerged to aid this task. The
Categories: Incoming News

HasCallStack - runtime costs?

haskell-cafe - Fri, 03/04/2016 - 4:53pm
Dear Cafe, the new (8.*) call stack feature https://downloads.haskell.org/~ghc/8.0.1-rc2/docs/html/users_guide/glasgow_exts.html#hascallstack is certainly nice for debugging during development. But how costly is it at runtime? I notice a 5 percent slowdown. That's not a problem if there's an easy way to switch this off for production (without changing the code). Related: how to make code that uses it, compile with older ghcs that don't have it. I made this hack: do not import GHC.Stack.Types, but instead {-# language CPP, MultiParamTypeClasses #-} #if (__GLASGOW_HASKELL__ < 710) {-# language NullaryTypeClasses #-} #endif module Stack ( HasCallStack ) where #if (__GLASGOW_HASKELL__ >= 800) import GHC.Stack.Types #else class HasCallStack instance HasCallStack #endif When I compile with 8.rc2, and change ">= 800" to ">= 900", I am getting the 5 percent speedup mentioned above. But does it really do what I hope it does (remove all runtime overhead that call stacks may have)? When I compile with 7.10.
Categories: Offsite Discussion

Month in Haskell Mode February 2016

haskell-cafe - Fri, 03/04/2016 - 4:49pm
Welcome Haskell Mode users, Haskell Mode progress report for February 2016. For previous issue see January 2015 <https://github.com/haskell/haskell-mode/wiki/Month-in-Haskell-Mode-January-2015> . Reddit discussion <https://www.reddit.com/r/haskell/comments/48wrru/month_in_haskell_mode_february_2016/> . <https://github.com/haskell/haskell-mode/wiki/Month-in-Haskell-Mode-February-2016#what-is-haskell-mode>What is Haskell Mode? Haskell Mode is an umbrella project for multiple Emacs tools for efficient Haskell development. Haskell Mode is an open source project developed by a group of volunteers constantly looking for contributions. For more information how to help see https://github.com/haskell/haskell-mode. <https://github.com/haskell/haskell-mode/wiki/Month-in-Haskell-Mode-February-2016#important-developments>Important developments Fontification received improvements so that it closer follows Haskell lexical rules. It was necessary to change to syntax-propertize-function available only starting with Emac
Categories: Offsite Discussion

Test email

libraries list - Thu, 03/03/2016 - 7:54pm
Please disregard -- sorry for the noise. Gershom
Categories: Offsite Discussion

New gtk2hs 0.12.4 release

gtk2hs - Wed, 11/21/2012 - 12:56pm

Thanks to John Lato and Duncan Coutts for the latest bugfix release! The latest packages should be buildable on GHC 7.6, and the cairo package should behave a bit nicer in ghci on Windows. Thanks to all!

~d

Categories: Incoming News