Yaya.Retrofit

This module re-exports a subset of Fold, intended for when you want to define recursion scheme instances for your existing recursive types.

Documentation

class Corecursive c t f | t -> f where

Coinductive (potentially-infinite) structures that guarantee _productivity_ rather than termination.

Methods

ana :: Coalgebra c f a -> a `c` t

Instances

Corecursive ((->) :: Type -> Type -> Type) (Nu f :: Type) (f :: Type -> Type)

Defined in Yaya.Fold

Methods

ana :: Coalgebra (->) f a -> a -> Nu f

Functor f => Corecursive ((->) :: Type -> Type -> Type) (Fix f :: Type) (f :: Type -> Type)

Defined in Yaya.Fold.Native

Methods

ana :: Coalgebra (->) f a -> a -> Fix f

Corecursive ((->) :: Type -> Type -> Type) ([a] :: Type) (XNor a :: Type -> Type)

Defined in Yaya.Fold.Native

Methods

ana :: Coalgebra (->) (XNor a) a0 -> a0 -> [a]

Corecursive ((->) :: Type -> Type -> Type) (NonEmpty a :: Type) (AndMaybe a :: Type -> Type)

Defined in Yaya.Fold.Native

Methods

ana :: Coalgebra (->) (AndMaybe a) a0 -> a0 -> NonEmpty a

Corecursive ((->) :: Type -> Type -> Type) (Maybe a :: Type) (Const (Maybe a) :: Type -> Type)

Defined in Yaya.Fold

Methods

ana :: Coalgebra (->) (Const (Maybe a)) a0 -> a0 -> Maybe a

Corecursive ((->) :: Type -> Type -> Type) (Either a b :: Type) (Const (Either a b) :: Type -> Type)

Defined in Yaya.Fold

Methods

ana :: Coalgebra (->) (Const (Either a b)) a0 -> a0 -> Either a b

Functor f => Corecursive ((->) :: Type -> Type -> Type) (Cofree f a :: Type) (EnvT a f :: Type -> Type)

Defined in Yaya.Fold.Native

Methods

ana :: Coalgebra (->) (EnvT a f) a0 -> a0 -> Cofree f a

Functor f => Corecursive ((->) :: Type -> Type -> Type) (Free f a :: Type) (FreeF f a :: Type -> Type)

Defined in Yaya.Fold.Native

Methods

ana :: Coalgebra (->) (FreeF f a) a0 -> a0 -> Free f a

class Recursive c t f | t -> f where

Inductive structures that can be reasoned about in the way we usually do – with pattern matching.

Methods

cata :: Algebra c f a -> t `c` a

Instances

Recursive ((->) :: Type -> Type -> Type) Natural Maybe

Defined in Yaya.Fold.Native

Methods

cata :: Algebra (->) Maybe a -> Natural -> a

Recursive ((->) :: Type -> Type -> Type) Void Identity

Defined in Yaya.Fold

Methods

cata :: Algebra (->) Identity a -> Void -> a

Recursive ((->) :: Type -> Type -> Type) (Mu f :: Type) (f :: Type -> Type)

Defined in Yaya.Fold

Methods

cata :: Algebra (->) f a -> Mu f -> a

Recursive ((->) :: Type -> Type -> Type) (Maybe a :: Type) (Const (Maybe a) :: Type -> Type)

Defined in Yaya.Fold

Methods

cata :: Algebra (->) (Const (Maybe a)) a0 -> Maybe a -> a0

Recursive ((->) :: Type -> Type -> Type) (Either a b :: Type) (Const (Either a b) :: Type -> Type)

Defined in Yaya.Fold

Methods

cata :: Algebra (->) (Const (Either a b)) a0 -> Either a b -> a0

class Projectable c t f => Steppable c t f | t -> f where

Structures you can walk through step-by-step.

Methods

embed :: Algebra c f t

Instances

Steppable ((->) :: Type -> Type -> Type) Natural Maybe

Defined in Yaya.Fold

Methods

embed :: Algebra (->) Maybe Natural

Steppable ((->) :: Type -> Type -> Type) Void Identity

Defined in Yaya.Fold

Methods

embed :: Algebra (->) Identity Void

Functor f => Steppable ((->) :: Type -> Type -> Type) (Nu f :: Type) (f :: Type -> Type)

Defined in Yaya.Fold

Methods

embed :: Algebra (->) f (Nu f)

Functor f => Steppable ((->) :: Type -> Type -> Type) (Mu f :: Type) (f :: Type -> Type)

Defined in Yaya.Fold

Methods

embed :: Algebra (->) f (Mu f)

Steppable ((->) :: Type -> Type -> Type) (Fix f :: Type) (f :: Type -> Type)

Defined in Yaya.Fold.Native

Methods

embed :: Algebra (->) f (Fix f)

Steppable ((->) :: Type -> Type -> Type) ([a] :: Type) (XNor a :: Type -> Type)

Defined in Yaya.Fold

Methods

embed :: Algebra (->) (XNor a) [a]

Steppable ((->) :: Type -> Type -> Type) (NonEmpty a :: Type) (AndMaybe a :: Type -> Type)

Defined in Yaya.Fold

Methods

embed :: Algebra (->) (AndMaybe a) (NonEmpty a)

Steppable ((->) :: Type -> Type -> Type) (Maybe a :: Type) (Const (Maybe a) :: Type -> Type)

Defined in Yaya.Fold

Methods

embed :: Algebra (->) (Const (Maybe a)) (Maybe a)

Steppable ((->) :: Type -> Type -> Type) (Either a b :: Type) (Const (Either a b) :: Type -> Type)

Defined in Yaya.Fold

Methods

embed :: Algebra (->) (Const (Either a b)) (Either a b)

Steppable ((->) :: Type -> Type -> Type) (Cofree f a :: Type) (EnvT a f :: Type -> Type)

Defined in Yaya.Fold

Methods

embed :: Algebra (->) (EnvT a f) (Cofree f a)

Steppable ((->) :: Type -> Type -> Type) (Free f a :: Type) (FreeF f a :: Type -> Type)

Defined in Yaya.Fold

Methods

embed :: Algebra (->) (FreeF f a) (Free f a)

class Projectable c t f | t -> f where

This type class is lawless on its own, but there exist types that can’t implement the corresponding embed operation. Laws are induced by implementing either Steppable (which extends this) or Corecursive (which doesn’t).

Methods

project :: Coalgebra c f t

Instances

Projectable ((->) :: Type -> Type -> Type) Natural Maybe

Defined in Yaya.Fold

Methods

project :: Coalgebra (->) Maybe Natural

Projectable ((->) :: Type -> Type -> Type) Void Identity

Defined in Yaya.Fold

Methods

project :: Coalgebra (->) Identity Void

Functor f => Projectable ((->) :: Type -> Type -> Type) (Nu f :: Type) (f :: Type -> Type)

Defined in Yaya.Fold

Methods

project :: Coalgebra (->) f (Nu f)

Functor f => Projectable ((->) :: Type -> Type -> Type) (Mu f :: Type) (f :: Type -> Type)

Defined in Yaya.Fold

Methods

project :: Coalgebra (->) f (Mu f)

Projectable ((->) :: Type -> Type -> Type) (Fix f :: Type) (f :: Type -> Type)

Defined in Yaya.Fold.Native

Methods

project :: Coalgebra (->) f (Fix f)

Projectable ((->) :: Type -> Type -> Type) ([a] :: Type) (XNor a :: Type -> Type)

Defined in Yaya.Fold

Methods

project :: Coalgebra (->) (XNor a) [a]

Projectable ((->) :: Type -> Type -> Type) (NonEmpty a :: Type) (AndMaybe a :: Type -> Type)

Defined in Yaya.Fold

Methods

project :: Coalgebra (->) (AndMaybe a) (NonEmpty a)

Projectable ((->) :: Type -> Type -> Type) (Maybe a :: Type) (Const (Maybe a) :: Type -> Type)

Defined in Yaya.Fold

Methods

project :: Coalgebra (->) (Const (Maybe a)) (Maybe a)

Projectable ((->) :: Type -> Type -> Type) (Either a b :: Type) (Const (Either a b) :: Type -> Type)

Defined in Yaya.Fold

Methods

project :: Coalgebra (->) (Const (Either a b)) (Either a b)

Projectable ((->) :: Type -> Type -> Type) (Cofree f a :: Type) (EnvT a f :: Type -> Type)

Defined in Yaya.Fold

Methods

project :: Coalgebra (->) (EnvT a f) (Cofree f a)

Projectable ((->) :: Type -> Type -> Type) (Free f a :: Type) (FreeF f a :: Type -> Type)

Defined in Yaya.Fold

Methods

project :: Coalgebra (->) (FreeF f a) (Free f a)

recursiveEq :: (Recursive (->) t f, Steppable (->) u f, Functor f, Foldable f, Eq1 f) => t -> u -> Bool

An implementation of Eq for any Recursive instance. Note that this is actually more general than Eq, as it can compare between different fixed-point representations of the same functor.

recursiveShowsPrec :: (Recursive (->) t f, Show1 f) => Int -> t -> ShowS

An implementation of Show for any Recursive instance.