Safe Haskell	None
Language	GHC2021

Bowtie.Fix

Synopsis

newtype Fix (f :: Type -> Type) = Fix {
- unFix :: f (Fix f)
}
mkFix :: forall t (f :: Type -> Type). (Recursive t, Base t ~ f) => t -> Fix f
unMkFix :: forall t (f :: Type -> Type). (Corecursive t, Base t ~ f) => Fix f -> t
transFix :: Functor f => (forall x. f x -> g x) -> Fix f -> Fix g

Documentation

newtype Fix (f :: Type -> Type) Source #

A basic Functor fixpoint like you'd see anywhere.

Constructors

Fix
Fields unFix :: f (Fix f)

Instances

Instances details

IsString (f (Fix f)) => IsString (Fix f) Source #
Instance details Defined in Bowtie.Fix Methods fromString :: String -> Fix f #
Show (f (Fix f)) => Show (Fix f) Source #
Instance details Defined in Bowtie.Fix Methods showsPrec :: Int -> Fix f -> ShowS # show :: Fix f -> String # showList :: [Fix f] -> ShowS #
Eq (f (Fix f)) => Eq (Fix f) Source #
Instance details Defined in Bowtie.Fix Methods (==) :: Fix f -> Fix f -> Bool # (/=) :: Fix f -> Fix f -> Bool #
Ord (f (Fix f)) => Ord (Fix f) Source #
Instance details Defined in Bowtie.Fix Methods compare :: Fix f -> Fix f -> Ordering # (<) :: Fix f -> Fix f -> Bool # (<=) :: Fix f -> Fix f -> Bool # (>) :: Fix f -> Fix f -> Bool # (>=) :: Fix f -> Fix f -> Bool # max :: Fix f -> Fix f -> Fix f # min :: Fix f -> Fix f -> Fix f #
Pretty (f (Fix f)) => Pretty (Fix f) Source #
Instance details Defined in Bowtie.Fix Methods pretty :: Fix f -> Doc ann # prettyList :: [Fix f] -> Doc ann #
Functor f => Corecursive (Fix f) Source #
Instance details Defined in Bowtie.Fix Methods embed :: Base (Fix f) (Fix f) -> Fix f # ana :: (a -> Base (Fix f) a) -> a -> Fix f # apo :: (a -> Base (Fix f) (Either (Fix f) a)) -> a -> Fix f # postpro :: Recursive (Fix f) => (forall b. Base (Fix f) b -> Base (Fix f) b) -> (a -> Base (Fix f) a) -> a -> Fix f # gpostpro :: (Recursive (Fix f), Monad m) => (forall b. m (Base (Fix f) b) -> Base (Fix f) (m b)) -> (forall c. Base (Fix f) c -> Base (Fix f) c) -> (a -> Base (Fix f) (m a)) -> a -> Fix f #
Functor f => Recursive (Fix f) Source #
Instance details Defined in Bowtie.Fix Methods project :: Fix f -> Base (Fix f) (Fix f) # cata :: (Base (Fix f) a -> a) -> Fix f -> a # para :: (Base (Fix f) (Fix f, a) -> a) -> Fix f -> a # gpara :: (Corecursive (Fix f), Comonad w) => (forall b. Base (Fix f) (w b) -> w (Base (Fix f) b)) -> (Base (Fix f) (EnvT (Fix f) w a) -> a) -> Fix f -> a # prepro :: Corecursive (Fix f) => (forall b. Base (Fix f) b -> Base (Fix f) b) -> (Base (Fix f) a -> a) -> Fix f -> a # gprepro :: (Corecursive (Fix f), Comonad w) => (forall b. Base (Fix f) (w b) -> w (Base (Fix f) b)) -> (forall c. Base (Fix f) c -> Base (Fix f) c) -> (Base (Fix f) (w a) -> a) -> Fix f -> a #
type Base (Fix f) Source #
Instance details Defined in Bowtie.Fix type Base (Fix f) = f

mkFix :: forall t (f :: Type -> Type). (Recursive t, Base t ~ f) => t -> Fix f Source #

Pull a recursive structure apart and retie as a Fix.

unMkFix :: forall t (f :: Type -> Type). (Corecursive t, Base t ~ f) => Fix f -> t Source #

Go the other way.

transFix :: Functor f => (forall x. f x -> g x) -> Fix f -> Fix g Source #

Transform the base Functor.