Safe Haskell	Safe
Language	Haskell2010

Data.Functor.Foldable.Monadic

Synopsis

cataM :: (Monad m, Traversable (Base t), Recursive t) => (Base t a -> m a) -> t -> m a
anaM :: (Monad m, Traversable (Base t), Corecursive t) => (a -> m (Base t a)) -> a -> m t
paraM :: (Monad m, Traversable (Base t), Recursive t) => (Base t (t, a) -> m a) -> t -> m a
apoM :: (Monad m, Traversable (Base t), Corecursive t) => (a -> m (Base t (Either t a))) -> a -> m t
histoM :: (Monad m, Traversable (Base t), Recursive t) => (Base t (Cofree (Base t) a) -> m a) -> t -> m a
futuM :: (Monad m, Traversable (Base t), Corecursive t) => (a -> m (Base t (Free (Base t) a))) -> a -> m t
histoM' :: (Monad m, Traversable (Base t), Recursive t) => (Base t (Cofree (Base t) a) -> m a) -> t -> m a
futuM' :: (Monad m, Traversable (Base t), Corecursive t) => (a -> m (Base t (Free (Base t) a))) -> a -> m t
zygoM :: (Monad m, Traversable (Base t), Recursive t) => (Base t a -> m a) -> (Base t (a, b) -> m b) -> t -> m b
cozygoM :: (Monad m, Traversable (Base t), Corecursive t) => (a -> m (Base t a)) -> (b -> m (Base t (Either a b))) -> b -> m t
hyloM :: (Monad m, Traversable t) => (t b -> m b) -> (a -> m (t a)) -> a -> m b
metaM :: (Monad m, Traversable (Base t), Recursive s, Corecursive t, Base s ~ Base t) => (Base t t -> m t) -> (s -> m (Base s s)) -> s -> m t
hyloM' :: forall m t a b. (Monad m, Traversable (Base t), Recursive t, Corecursive t) => (Base t b -> m b) -> (a -> m (Base t a)) -> a -> m b
metaM' :: (Monad m, Corecursive c, Traversable (Base c), Traversable (Base t), Recursive t) => (Base t a -> m a) -> (a -> m (Base c a)) -> t -> m c
chronoM :: forall m t a b. (Monad m, Traversable (Base t), Recursive t, Corecursive t) => (Base t (Cofree (Base t) b) -> m b) -> (a -> m (Base t (Free (Base t) a))) -> a -> m b
cochronoM :: (Monad m, Corecursive c, Traversable (Base c), Traversable (Base t), Recursive t) => (Base t (Cofree (Base t) a) -> m a) -> (a -> m (Base c (Free (Base c) a))) -> t -> m c
chronoM' :: (Monad m, Traversable t) => (t (Cofree t b) -> m b) -> (a -> m (t (Free t a))) -> a -> m b
dynaM :: (Monad m, Traversable (Base t), Recursive t, Corecursive t) => (Base t (Cofree (Base t) b) -> m b) -> (a -> m (Base t a)) -> a -> m b
codynaM :: (Monad m, Traversable t) => (t b -> m b) -> (a -> m (t (Free t a))) -> a -> m b
dynaM' :: forall m t a c. (Monad m, Traversable (Base t), Recursive t, Corecursive t) => (Base t (Cofree (Base t) c) -> m c) -> (a -> m (Base t a)) -> a -> m c
codynaM' :: (Monad m, Corecursive c, Traversable (Base c), Traversable (Base t), Recursive t) => (Base t (Cofree (Base t) a) -> m a) -> (a -> m (Base c a)) -> t -> m c
dynaM'' :: (Monad m, Traversable t) => (t (Cofree t c) -> m c) -> (a -> m (t a)) -> a -> m c
codynaM'' :: (Monad m, Traversable t) => (t b -> m b) -> (a -> m (t (Free t a))) -> a -> m b

Documentation

cataM Source #

Arguments

:: (Monad m, Traversable (Base t), Recursive t)
=> (Base t a -> m a)	algebra
-> t
-> m a

catamorphism

anaM Source #

Arguments

:: (Monad m, Traversable (Base t), Corecursive t)
=> (a -> m (Base t a))	coalgebra
-> a
-> m t

anamorphism

paraM Source #

Arguments

:: (Monad m, Traversable (Base t), Recursive t)
=> (Base t (t, a) -> m a)	algebra
-> t
-> m a

paramorphism

apoM Source #

Arguments

:: (Monad m, Traversable (Base t), Corecursive t)
=> (a -> m (Base t (Either t a)))	coalgebra
-> a
-> m t

apomorphism

histoM Source #

Arguments

:: (Monad m, Traversable (Base t), Recursive t)
=> (Base t (Cofree (Base t) a) -> m a)	algebra
-> t
-> m a

histomorphism on anamorphism variant

futuM Source #

Arguments

:: (Monad m, Traversable (Base t), Corecursive t)
=> (a -> m (Base t (Free (Base t) a)))	coalgebra
-> a
-> m t

futumorphism on catamorphism variant

histoM' Source #

Arguments

:: (Monad m, Traversable (Base t), Recursive t)
=> (Base t (Cofree (Base t) a) -> m a)	algebra
-> t
-> m a

histomorphism on catamorphism variant

futuM' Source #

Arguments

:: (Monad m, Traversable (Base t), Corecursive t)
=> (a -> m (Base t (Free (Base t) a)))	coalgebra
-> a
-> m t

futumorphism on anamorphism variant

zygoM Source #

Arguments

:: (Monad m, Traversable (Base t), Recursive t)
=> (Base t a -> m a)	algebra for fst
-> (Base t (a, b) -> m b)	algebra for snd from product
-> t
-> m b

zygomorphism

cozygoM Source #

Arguments

:: (Monad m, Traversable (Base t), Corecursive t)
=> (a -> m (Base t a))	coalgebra for fst
-> (b -> m (Base t (Either a b)))	coalgebra for snd to coproduct
-> b
-> m t

cozygomorphism

hyloM Source #

Arguments

:: (Monad m, Traversable t)
=> (t b -> m b)	algebra
-> (a -> m (t a))	coalgebra
-> a
-> m b

hylomorphism on recursive variant

metaM Source #

Arguments

:: (Monad m, Traversable (Base t), Recursive s, Corecursive t, Base s ~ Base t)
=> (Base t t -> m t)	algebra
-> (s -> m (Base s s))	coalgebra
-> s
-> m t

metamorphism on recursive variant

hyloM' Source #

Arguments

:: (Monad m, Traversable (Base t), Recursive t, Corecursive t)
=> (Base t b -> m b)	algebra
-> (a -> m (Base t a))	coalgebra
-> a
-> m b

hylomorphism on combination variant of ana to cata

metaM' Source #

Arguments

:: (Monad m, Corecursive c, Traversable (Base c), Traversable (Base t), Recursive t)
=> (Base t a -> m a)	algebra
-> (a -> m (Base c a))	coalgebra
-> t
-> m c

metamorphism on combination variant of cata to ana

chronoM Source #

Arguments

:: (Monad m, Traversable (Base t), Recursive t, Corecursive t)
=> (Base t (Cofree (Base t) b) -> m b)	algebra
-> (a -> m (Base t (Free (Base t) a)))	coalgebra
-> a
-> m b

chronomorphism on combination variant of futu to hist

cochronoM Source #

Arguments

:: (Monad m, Corecursive c, Traversable (Base c), Traversable (Base t), Recursive t)
=> (Base t (Cofree (Base t) a) -> m a)	algebra
-> (a -> m (Base c (Free (Base c) a)))	coalgebra
-> t
-> m c

cochronomorphism on combination variant of histo to futu

chronoM' Source #

Arguments

:: (Monad m, Traversable t)
=> (t (Cofree t b) -> m b)	algebra
-> (a -> m (t (Free t a)))	coalgebra
-> a
-> m b

chronomorphism on recursive variant over hylomorphism

dynaM Source #

Arguments

:: (Monad m, Traversable (Base t), Recursive t, Corecursive t)
=> (Base t (Cofree (Base t) b) -> m b)	algebra
-> (a -> m (Base t a))	coalgebra
-> a
-> m b

dynamorphism on recursive variant over chronomorphism

codynaM Source #

Arguments

:: (Monad m, Traversable t)
=> (t b -> m b)	algebra
-> (a -> m (t (Free t a)))	coalgebra
-> a
-> m b

dynaM' Source #

Arguments

:: (Monad m, Traversable (Base t), Recursive t, Corecursive t)
=> (Base t (Cofree (Base t) c) -> m c)	algebra
-> (a -> m (Base t a))	coalgebra
-> a
-> m c

dynamorphism on combination variant of ana to histo

codynaM' Source #

Arguments

:: (Monad m, Corecursive c, Traversable (Base c), Traversable (Base t), Recursive t)
=> (Base t (Cofree (Base t) a) -> m a)	algebra
-> (a -> m (Base c a))	coalgebra
-> t
-> m c

codynamorphism on combination variant of histo to ana

dynaM'' Source #

Arguments

:: (Monad m, Traversable t)
=> (t (Cofree t c) -> m c)	algebra
-> (a -> m (t a))	coalgebra
-> a
-> m c

dynamorphism on recursive variant over hylomorphism

codynaM'' Source #

Arguments

:: (Monad m, Traversable t)
=> (t b -> m b)	algebra
-> (a -> m (t (Free t a)))	coalgebra
-> a
-> m b