CIS 552: Advanced Programmingundefined.
Eventually, the complete
version will be made available.
Exercise: General Monadic Functions
> module MonadExercise where> import Prelude hiding (mapM, foldM, sequence)
> import Test.HUnit
> import Test.QuickCheckGeneric Monad Operations
This problem asks you to recreate some of the operations in the Control.Monad library. You should not use any of the functions defined in that library to solve this problem. (These functions also appear in more general forms elsewhere, so other libraries that are off limits for this problem include Control.Applicative, Data.Traversable and Data.Foldable.)
Add tests for each of these functions with at least two test cases, one using the Maybe monad, and one using the List monad.
> -- (a) Define a monadic generalization of map> mapM :: Monad m => (a -> m b) -> [a] -> m [b]
> mapM = error "mapM: unimplemented"> testMapM :: Test
> testMapM = undefined> -- (b) Define a monadic generalization of foldl> foldM :: Monad m => (a -> b -> m a) -> a -> [b] -> m a
> foldM = error "foldM: unimplemented"> testFoldM :: Test
> testFoldM = undefined> -- (c) Define a generalization of monadic sequencing that evaluates
> -- each action in a list from left to right, collecting the results
> -- in a list.> sequence :: Monad m => [m a] -> m [a]
> sequence = error "sequence: unimplemented"> testSequence :: Test
> testSequence = undefined> -- (d) Define the Kleisli "fish operator", a variant of composition> (>=>) :: Monad m => (a -> m b) -> (b -> m c) -> a -> m c
> (>=>) = error ">=>: unimplemented"> testKleisli :: Test
> testKleisli = undefinedFor more information about this operator, see the explanation at the bottom of this page.
> -- (e) Define the 'join' operator, which removes one level of
> -- monadic structure.> join :: (Monad m) => m (m a) -> m a
> join = error "join: unimplemented"> testJoin :: Test
> testJoin = undefined> -- (f) Define the 'liftM' functionDefine liftM, which promotes functions a -> b to functions over actions in a monad m a -> m b.
> liftM :: (Monad m) => (a -> b) -> m a -> m b
> liftM = error "liftM: unimplemented"> testLiftM :: Test
> testLiftM = undefinedThought question: Is the type of liftM similar to that of another function we've discussed recently?
> -- (g) And its two-argument version ...Now define a variation of liftM, liftM2, that works for functions taking two arguments:
> liftM2 :: (Monad m) => (a -> b -> r) -> m a -> m b -> m r
> liftM2 = error "liftM2: unimplemented"> testLiftM2 :: Test
> testLiftM2 = undefined> -------------------------------------------------------------------------General Applicative Functions
Which of these functions above can you equivalently rewrite using Applicative? i.e. for which of the definitions below, can you replace undefined with a definition that only uses members of the Applicative type class. (Again, do not use functions from Control.Applicative, Data.Foldable or Data.Traversable in your solution.)
If you provide a definition, you should write test cases that demonstrate that it has the same behavior on List and Maybe as the monadic versions above.
> -- NOTE: you may not be able to define all of these, but be sure to test the
> -- ones that you do> mapA :: Applicative f => (a -> f b) -> [a] -> f [b]
> mapA f xs = undefined> foldA :: Applicative f => (a -> b -> f a) -> a -> [b] -> f a
> foldA = undefined> sequenceA :: Applicative f => [f a] -> f [a]
> sequenceA = undefined> kleisliA :: Applicative f => (a -> f b) -> (b -> f c) -> a -> f c
> kleisliA = undefined> joinA :: (Applicative f) => f (f a) -> f a
> joinA = undefined> liftA :: (Applicative f) => (a -> b) -> f a -> f b
> liftA f x = undefined> liftA2 :: (Applicative f) => (a -> b -> r) -> f a -> f b -> f r
> liftA2 f x y = undefined