Data.Equivalence.Monad

This is an alternative interface to the union-find implementation in ''Data.Equivalence.STT''. It is wrapped into the monad transformer EquivT.

Documentation

class (Monad m, Ord v) => MonadEquiv c v d m | m -> v, m -> c, m -> d where

This class specifies the interface for a monadic computation that maintains an equivalence relation.

Minimal complete definition

equivalent, classDesc, equateAll, removeClass, getClass, combineAll, (===), desc, remove

Methods

equivalent :: v -> v -> m Bool

This function decides whether the two given elements are equivalent in the current equivalence relation

classDesc :: v -> m d

This function obtains the descriptor of the given element's equivalence class.

equateAll :: [v] -> m ()

This function equates the element in the given list. That is, it unions the equivalence classes of the elements and combines their descriptor.

equate :: v -> v -> m ()

This function equates the given two elements. That is it unions the equivalence classes of the two elements.

removeClass :: v -> m Bool

This function removes the equivalence class of the given element. If there is no corresponding equivalence class, False is returned; otherwise True.

getClass :: v -> m c

This function provides the equivalence class the given element is contained in.

combineAll :: [c] -> m ()

This function combines all equivalence classes in the given list. Afterwards all elements in the argument list represent the same equivalence class!

combine :: c -> c -> m c

This function combines the two given equivalence classes. Afterwards both arguments represent the same equivalence class! One of it is returned in order to represent the new combined equivalence class.

(===) :: c -> c -> m Bool

This function decides whether the two given equivalence classes are the same.

desc :: c -> m d

This function returns the descriptor of the given equivalence class.

remove :: c -> m Bool

This function removes the given equivalence class. If the equivalence class does not exists anymore False is returned; otherwise True.

Instances

MonadEquiv c v d m => MonadEquiv c v d (ReaderT r m)

MonadEquiv c v d m => MonadEquiv c v d (StateT s m)

MonadEquiv c v d m => MonadEquiv c v d (ExceptT e m)

(MonadEquiv c v d m, Error e) => MonadEquiv c v d (ErrorT e m)

(MonadEquiv c v d m, Monoid w) => MonadEquiv c v d (WriterT w m)

(Monad m, Ord v) => MonadEquiv (Class s d v) v d (EquivT s d v m)

newtype EquivT s c v m a

This monad transformer encapsulates computations maintaining an equivalence relation. A monadic computation of type EquivT s c v m a maintains a state space indexed by type s, maintains an equivalence relation over elements of type v with equivalence class descriptors of type c and contains an internal monadic computation of type m a.

Constructors

EquivT

Fields

unEquivT :: ReaderT (Equiv s c v) (STT s m) a

Instances

MonadError e m => MonadError e (EquivT s c v m)

MonadReader r m => MonadReader r (EquivT s c v m)

MonadState st m => MonadState st (EquivT s c v m)

(Monoid w, MonadWriter w m) => MonadWriter w (EquivT s c v m)

MonadTrans (EquivT s c v)

(Monad m, Ord v) => MonadEquiv (Class s d v) v d (EquivT s d v m)

Monad m => Monad (EquivT s c v m)

Functor m => Functor (EquivT s c v m)

(Functor m, Monad m) => Applicative (EquivT s c v m)

type EquivT' s = EquivT s ()

This monad transformer is a special case of EquivT that only maintains trivial equivalence class descriptors of type ().

type EquivM s c v = EquivT s c v Identity

This monad encapsulates computations maintaining an equivalence relation. A monadic computation of type EquivM s c v a maintains a state space indexed by type s, maintains an equivalence relation over elements of type v with equivalence class descriptors of type c and returns a value of type a.

type EquivM' s v = EquivM s () v

This monad is a special case of EquivM that only maintains trivial equivalence class descriptors of type ().

runEquivT

Arguments

:: Monad m

=> (v -> c)

used to construct an equivalence class descriptor for a singleton class

-> (c -> c -> c)

used to combine the equivalence class descriptor of two classes which are meant to be combined.

-> (forall s. EquivT s c v m a)

-> m a

This function runs a monadic computation that maintains an equivalence relation. The first tow arguments specify how to construct an equivalence class descriptor for a singleton class and how to combine two equivalence class descriptors.

runEquivT' :: Monad m => (forall s. EquivT' s v m a) -> m a

This function is a special case of runEquivT that only maintains trivial equivalence class descriptors of type ().

runEquivM

Arguments

:: (v -> c)

used to construct an equivalence class descriptor for a singleton class

-> (c -> c -> c)

used to combine the equivalence class descriptor of two classes which are meant to be combined.

-> (forall s. EquivM s c v a)

-> a

This function runs a monadic computation that maintains an equivalence relation. The first tow arguments specify how to construct an equivalence class descriptor for a singleton class and how to combine two equivalence class descriptors.

runEquivM' :: (forall s. EquivM' s v a) -> a

This function is a special case of runEquivM that only maintains trivial equivalence class descriptors of type ().