Annotations.F.Fixpoints

Fixed points of functors

newtype Fix fT

Fixpoint of functors.

Constructors

In

Fields

out :: fT (Fix fT)

Instances

Eq (f (Fix f)) => Eq (Fix f)

Show (f (Fix f)) => Show (Fix f)

compos :: Functor f => (Fix f -> Fix f) -> Fix f -> Fix f

Apply a transformation to a tree's direct children.

type Algebra fT aT = fT aT -> aT

Algebras for catamorphisms.

cata :: Functor fT => Algebra fT aT -> Fix fT -> aT

Reduces a tree to a value according to the algebra.

type Coalgebra fT aT = aT -> fT aT

Coalgebras for anamorphisms.

ana :: Functor fT => Coalgebra fT aT -> aT -> Fix fT

Constructs a tree from a value according to the coalgebra.

type ErrorAlgebra fT eT aT = fT aT -> Either eT aT

Algebras for error catamorphisms.

cascade :: (Traversable fT, Monoid eT) => ErrorAlgebra fT eT aT -> Algebra fT (Except eT aT)

Reduces a tree to a value according to the algebra, propagating potential errors.