Free à la Carte

Free à la Carte

Free monads based on from intuitions from the Data types à la Carte paper. Combine functors and make embedded DSLs in Haskell.

See the original paper, by Wouter Swierstra: .

See the Haskell library I built around it: .

How do you use this ?

This section gives a brief demonstration of using free monads to model effects.

Four effectful functions are defined, categorized into two separate data types.

data Teletype a = GetChar (Char -> a) | PutChar Char a deriving (Functor) data FileSystem a = ReadFile FilePath (String -> a) | WriteFile FilePath String a deriving (Functor)

If you are into it, you can also write the Functor instances by hand, for your free monads, e.g.:

instance Functor Teletype where fmap :: (a -> b) -> Teletype a -> Teletype b fmap f = \case GetChar g -> GetChar (f . g) PutChar c g -> PutChar c (f g)

An exec function can execute values of these data types using the Free free monad. This uses intuitions of category theory to describe imperative sequence of computations as a fold over a functor. NOTE: the exec function is provided by this library and you don't need to implement it yourself.

exec :: Exec f => Free f a -> IO a exec = foldFree return execAlgebra

You should then write the Exec instances, in other words, the concrete implementations. NOTE: the typeclass Exec, and Exec (f :+: g) instance are also provided by this library, and you don't need to implement it yourself.

class Functor f => Exec f where execAlgebra :: f (IO a) -> IO a instance (Exec f, Exec g) => Exec (f :+: g) where execAlgebra = \case Left' e -> execAlgebra e Right' e -> execAlgebra e -- write your own implementations instance Exec Teletype where execAlgebra = \case GetChar f -> Prelude.getChar >>= f PutChar c io -> Prelude.putChar c >> io instance Exec FileSystem where execAlgebra (ReadFile path f) = Prelude.readFile path >>= f execAlgebra (WriteFile path s f) = Prelude.writeFile path s >> f

Then we can define some smart constructors to create our embedded DSL and save us some boilerplate, while adding syntactic sugar.

getChar :: (Teletype :<: f) => Free f Char getChar = injectFree (GetChar Pure) putChar :: (Teletype :<: f) => Char -> Free f () putChar c = injectFree (PutChar c (Pure ())) readFile :: (FileSystem :<: f) => FilePath -> Free f String readFile path = injectFree (ReadFile path Pure) writeFile :: (FileSystem :<: f) => FilePath -> String -> Free f () writeFile path s = injectFree (WriteFile path s (Pure ()))

The cat function serves as an example of composition. In the following, I use a more general type than that used in the paper. Here we use mapM_ instead of mapM to discard the resulting list of unit.

cat :: (FileSystem :<: f, Teletype :<: f) => FilePath -> Free f () cat path = mapM_ putChar =<< readFile path

The following example uses the cat function to print the content of the file in this directory.

main :: IO () main = exec @(FileSystem :+: Teletype) $ cat ""

More on the topic

I can only extremely recommend the following resources to gain more understanding about the ideas and intuitions behind this library, and behind Data types à la Carte.