Language.KURE.Translate

This module defines the main KURE types: Translate, Rewrite and Lens. Rewrite and Lens are just special cases of Translate, and so any function that operates on Translate is also applicable to Rewrite and Lens (although care should be taken in the Lens case).

This module also contains Translate instance declarations for the Monad and Arrow type-class families. Given these instances, many of the desirable combinators over Translate and Rewrite are special cases of existing monadic or arrow combinators. Language.KURE.Combinators provides some additional combinators that aren't in the standard libraries.

Translations

data Translate c m a b

Translate is a translation or strategy that translates from a value in a context to a monadic value.

Constructors

Translate

Fields

apply :: c -> a -> m b

Apply a Translate to a value and its context.

Instances

Monad m => Arrow (Translate c m)

The Kleisli Arrow induced by m, lifting through a Reader transformer, where c is the read-only environment.

MonadPlus m => ArrowZero (Translate c m)

The Kleisli Arrow induced by m, lifting through a Reader transformer, where c is the read-only environment.

MonadPlus m => ArrowPlus (Translate c m)

The Kleisli Arrow induced by m, lifting through a Reader transformer, where c is the read-only environment.

Monad m => ArrowApply (Translate c m)

The Kleisli Arrow induced by m, lifting through a Reader transformer, where c is the read-only environment.

Monad m => Category (Translate c m)

The Kleisli Category induced by m, lifting through a Reader transformer, where c is the read-only environment.

Monad m => Monad (Translate c m a)

Lifting through a Reader transformer, where (c,a) is the read-only environment.

Functor m => Functor (Translate c m a)

Lifting through a Reader transformer, where (c,a) is the read-only environment.

MonadPlus m => MonadPlus (Translate c m a)

Lifting through a Reader transformer, where (c,a) is the read-only environment.

Applicative m => Applicative (Translate c m a)

Lifting through a Reader transformer, where (c,a) is the read-only environment.

Alternative m => Alternative (Translate c m a)

Lifting through a Reader transformer, where (c,a) is the read-only environment.

(Monad m, Monoid b) => Monoid (Translate c m a b)

Lifting through the Monad and a Reader transformer, where (c,a) is the read-only environment.

type Rewrite c m a = Translate c m a a

A Rewrite is a Translate that shares the same source and target type.

translate :: (c -> a -> m b) -> Translate c m a b

The primitive way of building a Translate.

rewrite :: (c -> a -> m a) -> Rewrite c m a

The primitive way of building a Rewrite.

contextfreeT :: (a -> m b) -> Translate c m a b

Build a Translate that doesn't depend on the context.

constT :: m b -> Translate c m a b

Build a constant Translate from a monadic computation.

contextT :: Monad m => Translate c m a c

Extract the current context.

exposeT :: Monad m => Translate c m a (c, a)

Expose the current context and value.

mapT :: Monad m => Translate c m a b -> Translate c m [a] [b]

Map a Translate over a list.

Lenses

type Lens c m a b = Translate c m a ((c, b), b -> m a)

A Lens is a way to focus in on a particular point in a structure.

lens :: (c -> a -> m ((c, b), b -> m a)) -> Lens c m a b

lens is the primitive way of building a Lens.

idL :: Monad m => Lens c m a a

Identity Lens.

tryL :: MonadPlus m => Lens c m a a -> Lens c m a a

Catch a failing endoLens, making it into an identity.

composeL :: Monad m => Lens c m a b -> Lens c m b d -> Lens c m a d

Composition of Lenss.

sequenceL :: MonadPlus m => [Lens c m a a] -> Lens c m a a

Sequence a list of endoLenss.

pureL :: Monad m => (a -> b) -> (b -> a) -> Lens c m a b

Construct a Lens from two pure functions.

focusR :: Monad m => Lens c m a b -> Rewrite c m b -> Rewrite c m a

Apply a Rewrite at a point specified by a Lens.

focusT :: Monad m => Lens c m a b -> Translate c m b d -> Translate c m a d

Apply a Translate at a point specified by a Lens.