[Haskell] ANNOUNCE: set-monad

[Dan Burton]

Convenience aside, doesn't the functor instance conceptually violate some
sort of law?

fmap (const 1) someSet

The entire shape of the set changes.

fmap (g . h) = fmap g . fmap h

This law wouldn't hold given the following contrived ord instance

data Foo = Foo { a, b :: Int }
instance Ord Foo where
  compare = compare `on` a

Given functions

h foo = foo { a = 1 }
g foo = foo { a = b foo }

Does this library address this? If so, how? If not, then you'd best note it
in the docs.

On Jun 15, 2012 6:42 PM, "George Giorgidze" <giorgidze at gmail.com> wrote:

I would like to announce the first release of the set-monad library.

On Hackage: http://hackage.haskell.org/package/set-monad

The set-monad library exports the Set abstract data type and
set-manipulating functions. These functions behave exactly as their
namesakes from the Data.Set module of the containers library. In
addition, the set-monad library extends Data.Set by providing Functor,
Applicative, Alternative, Monad, and MonadPlus instances for sets.

In other words, you can use the set-monad library as a drop-in
replacement for the Data.Set module of the containers library and, in
addition, you will also get the aforementioned instances which are not
available in the containers package.

It is not possible to directly implement instances for the
aforementioned standard Haskell type classes for the Set data type
from the containers library. This is because the key operations map
and union, are constrained with Ord as follows.

map :: (Ord a, Ord b) => (a -> b) -> Set a -> Set b
union :: (Ord a) => Set a -> Set a -> Set a

The set-monad library provides the type class instances by wrapping
the constrained Set type into a data type that has unconstrained
constructors corresponding to monadic combinators. The data type
constructors that represent monadic combinators are evaluated with a
constrained run function. This elevates the need to use the
constraints in the instance definitions (this is what prevents a
direct definition). The wrapping and unwrapping happens internally in
the library and does not affect its interface.

For details, see the rather compact definitions of the run function
and type class instances. The left identity and associativity monad
laws play a crucial role in the definition of the run function. The
rest of the code should be self explanatory.

The technique is not new. This library was inspired by [1]. To my
knowledge, the original, systematic presentation of the idea to
represent monadic combinators as data is given in [2]. There is also a
Haskell library that provides a generic infrastructure for the
aforementioned wrapping and unwrapping [3].

The set-monad library is particularly useful for writing set-oriented
code using the do and/or monad comprehension notations. For example,
the following definitions now type check.

 s1 :: Set (Int,Int)
 s1 = do a <- fromList [1 .. 4]
        b <- fromList [1 .. 4]
        return (a,b)

 -- with -XMonadComprehensions
 s2 :: Set (Int,Int)
 s2 = [ (a,b) | (a,b) <- s1, even a, even b ]

 s3 :: Set Int
 s3 = fmap (+1) (fromList [1 .. 4])

As noted in [1], the implementation technique can be used for monadic
libraries and EDSLs with restricted types (compiled EDSLs often
restrict the types that they can handle). Haskell's standard monad
type class can be used for restricted monad instances. There is no
need to resort to GHC extensions that rebind the standard monadic
combinators with the library or EDSL specific ones.

[1] CSDL Blog: The home of applied functional programming at KU. Monad
Reification in Haskell and the Sunroof Javascript compiler.
http://www.ittc.ku.edu/csdlblog/?p=88

[2] Chuan-kai Lin. 2006. Programming monads operationally with Unimo.
In Proceedings of the eleventh ACM SIGPLAN International Conference on
Functional Programming (ICFP '06). ACM.

[3] Heinrich Apfelmus. The operational package.
http://hackage.haskell.org/package/operational

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