Safe Haskell	Safe-Inferred
Language	Haskell2010

Data.Functor.Foldable.Monadic

Contents

Folding
Unfolding
Refolding
Generalized Folding
Others

Synopsis

cataM :: (Monad m, Traversable (Base t), Recursive t) => (Base t a -> m a) -> t -> m a
preproM :: (Monad m, Traversable (Base t), Recursive t, Corecursive t) => (Base t t -> m (Base t t)) -> (Base t a -> m a) -> t -> m a
paraM :: (Monad m, Traversable (Base t), Recursive t) => (Base t (t, a) -> m a) -> t -> m a
zygoM :: (Monad m, Traversable (Base t), Recursive t) => (Base t a -> m a) -> (Base t (a, b) -> m b) -> t -> m b
histoM :: (Monad m, Traversable (Base t), Recursive t) => (Base t (Cofree (Base t) a) -> m a) -> t -> m a
histoM' :: (Monad m, Traversable (Base t), Recursive t) => (Base t (Cofree (Base t) a) -> m a) -> t -> m a
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
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
dynaM'' :: (Monad m, Traversable t) => (t (Cofree t c) -> m c) -> (a -> m (t a)) -> a -> m c
anaM :: (Monad m, Traversable (Base t), Corecursive t) => (a -> m (Base t a)) -> a -> m t
postproM :: (Monad m, Traversable (Base t), Recursive t, Corecursive t) => (Base t t -> m (Base t t)) -> (a -> m (Base t a)) -> a -> m t
apoM :: (Monad m, Traversable (Base t), Corecursive t) => (a -> m (Base t (Either t a))) -> a -> m t
cozygoM :: (Monad m, Traversable (Base t), Corecursive t) => (a -> m (Base t a)) -> (b -> m (Base t (Either a b))) -> b -> m t
futuM :: (Monad m, Traversable (Base t), Corecursive t) => (a -> m (Base t (Free (Base t) a))) -> a -> m t
futuM' :: (Monad m, Traversable (Base t), Corecursive t) => (a -> m (Base t (Free (Base t) a))) -> a -> m t
codynaM :: (Monad m, Traversable t) => (t b -> m b) -> (a -> m (t (Free t a))) -> a -> m b
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
codynaM'' :: (Monad m, Traversable t) => (t b -> m b) -> (a -> m (t (Free t a))) -> a -> m b
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
gcataM :: (Monad m, Comonad w, Traversable w, Traversable (Base t), Recursive t, b ~ w a) => (Base t (w b) -> m (w (Base t b))) -> (Base t (w a) -> m a) -> t -> m a
gcataM' :: (Monad m, Comonad w, Traversable w, Traversable (Base t), Recursive t, b ~ w a) => (Base t (w b) -> m (w (Base t b))) -> (Base t (w a) -> m a) -> t -> m a
mutuM :: (Monad m, Traversable (Base t), Recursive t) => (Base t (a, b) -> m b) -> (Base t (a, b) -> m a) -> t -> m b
comutuM :: (Monad m, Traversable (Base t), Corecursive t) => (b -> m (Base t (Either a b))) -> (a -> m (Base t (Either a b))) -> b -> m t
mutuM' :: (Monad m, Traversable (Base t), Recursive t) => (a -> b) -> (Base t a -> m a) -> t -> m b
comutuM' :: (Monad m, Traversable (Base t), Corecursive t) => (b -> a) -> (a -> m (Base t a)) -> b -> m t
cascadeM :: (Monad m, Corecursive (f a), Traversable (Base (f a)), Traversable f, Recursive (f a)) => (a -> m a) -> f a -> m (f a)
iterateM :: (Monad m, Corecursive (f a), Traversable (Base (f a)), Traversable f, Recursive (f a)) => (a -> m a) -> f a -> m (f a)

Folding

cataM Source #

Arguments

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

catamorphism

preproM Source #

Arguments

:: (Monad m, Traversable (Base t), Recursive t, Corecursive t)
=> (Base t t -> m (Base t t))	monadic natural transformation
-> (Base t a -> m a)	algebra
-> t
-> m a

prepromorphism

paraM Source #

Arguments

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

paramorphism

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

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

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

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

dynaM' Source #

Arguments

:: forall m t a c. (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

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

Unfolding

anaM Source #

Arguments

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

anamorphism

postproM Source #

Arguments

:: (Monad m, Traversable (Base t), Recursive t, Corecursive t)
=> (Base t t -> m (Base t t))	monadic natural transformation
-> (a -> m (Base t a))	coalgebra
-> a
-> m t

postpromorphism

apoM Source #

Arguments

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

apomorphism

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

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

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

codynaM Source #

Arguments

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

codynamorphism on recursive variant over chronomorphism

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

codynaM'' Source #

Arguments

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

codynamorphism on recursive variant over hylomorphism

Refolding

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

:: forall m t a b. (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

:: forall m t a b. (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

Generalized Folding

gcataM Source #

Arguments

:: (Monad m, Comonad w, Traversable w, Traversable (Base t), Recursive t, b ~ w a)
=> (Base t (w b) -> m (w (Base t b)))	Distributive (Base t) w b
-> (Base t (w a) -> m a)	algebra
-> t
-> m a

generalized catamorphism

gcataM' Source #

Arguments

:: (Monad m, Comonad w, Traversable w, Traversable (Base t), Recursive t, b ~ w a)
=> (Base t (w b) -> m (w (Base t b)))	Distributive (Base t) w b
-> (Base t (w a) -> m a)	algebra
-> t
-> m a

generalized catamorphism variant

Others

mutuM Source #

Arguments

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

mutumorphism on mutual recursive

comutuM Source #

Arguments

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

comutumorphism on comutual recursive

mutuM' Source #

Arguments

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

mutumorphism on recursive variant over catamorphism

comutuM' Source #

Arguments

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

comutumorphism on recursive variant over anamorphism

cascadeM Source #

Arguments

:: (Monad m, Corecursive (f a), Traversable (Base (f a)), Traversable f, Recursive (f a))
=> (a -> m a)	pre-operator
-> f a
-> m (f a)

cascade (a.k.a supermap)

iterateM Source #

Arguments

:: (Monad m, Corecursive (f a), Traversable (Base (f a)), Traversable f, Recursive (f a))
=> (a -> m a)	post-operator
-> f a
-> m (f a)

iterate