Data.Generics.Fixplate.Base

The core types of Fixplate.

Documentation

newtype Mu f

The fixed-point type.

Constructors

Fix

Fields

unFix :: f (Mu f)

Instances

EqF f => Eq (Mu f)

OrdF f => Ord (Mu f)

ReadF f => Read (Mu f)

ShowF f => Show (Mu f)

isAtom :: Foldable f => Mu f -> Bool

We call a tree "atomic" if it has no subtrees.

Annotations

data Ann f a b

Type of annotations

Constructors

Ann

Fields

attr :: a

the annotation

unAnn :: f b

the original functor

Instances

Functor f => Functor (Ann f a)

Foldable f => Foldable (Ann f a)

Traversable f => Traversable (Ann f a)

(Read a, ReadF f) => ReadF (Ann f a)

(Show a, ShowF f) => ShowF (Ann f a)

(Ord a, OrdF f) => OrdF (Ann f a)

NOTE: The OrdF instance for annotations first compares the annotations, and then the functor part. If this is not the desired behaviour (it's not clear to me at the moment what is the good default here), you can use the standard newtype trick to define a new behaviour.

(Eq a, EqF f) => EqF (Ann f a)

NOTE: The EqF instance for annotations compares both the annotations and the original part.

(Eq a, Eq (f b)) => Eq (Ann f a b)

(Ord a, Ord (f b)) => Ord (Ann f a b)

(Show a, Show (f b)) => Show (Ann f a b)

type Attr f a = Mu (Ann f a)

Annotated fixed-point type. Equivalent to CoFree f a

liftAnn :: (f e -> g e) -> Ann f a e -> Ann g a e

Lifting natural transformations to annotations.

Co-annotations

data CoAnn f a b

Categorical dual of Ann.

Constructors

Pure a

CoAnn (f b)

Instances

Functor f => Functor (CoAnn f a)

Foldable f => Foldable (CoAnn f a)

Traversable f => Traversable (CoAnn f a)

(Show a, ShowF f) => ShowF (CoAnn f a)

(Ord a, OrdF f) => OrdF (CoAnn f a)

(Eq a, EqF f) => EqF (CoAnn f a)

(Eq a, Eq (f b)) => Eq (CoAnn f a b)

(Ord a, Ord (f b)) => Ord (CoAnn f a b)

(Show a, Show (f b)) => Show (CoAnn f a b)

type CoAttr f a = Mu (CoAnn f a)

Categorical dual of Attr. Equivalent to Free f a

liftCoAnn :: (f e -> g e) -> CoAnn f a e -> CoAnn g a e

Lifting natural transformations to annotations.

Annotated trees

attribute :: Attr f a -> a

The attribute of the root node.

forget :: Functor f => Attr f a -> Mu f

A function forgetting all the attributes from an annotated tree.

Holes

data Hole

This a data type defined to be a place-holder for childs. It is used in tree drawing, hashing, and Shape.

It is deliberately not made an instance of Show, so that you can choose your preferred style. For example, an acceptable choice is

 instance Show Hole where show _ = "_"

Constructors

Hole

Instances

Eq Hole

Ord Hole

Higher-order type classes

class EqF f where

"Functorised" versions of standard type classes. If you have your a structure functor, for example

 Expr e 
   = Kst Int 
   | Var String 
   | Add e e 
   deriving (Eq,Ord,Read,Show,Functor,Foldable,Traversable)

you should make it an instance of these, so that the fixed-point type Mu Expr can be an instance of Eq, Ord and Show. Doing so is very easy:

 instance EqF   Expr where equalF     = (==)
 instance OrdF  Expr where compareF   = compare
 instance ShowF Expr where showsPrecF = showsPrec

The Read instance depends on whether we are using GHC or not. The Haskell98 version is

 instance ReadF Expr where readsPrecF = readsPrec

while the GHC version is

 instance ReadF Expr where readPrecF  = readPrec

Methods

equalF :: Eq a => f a -> f a -> Bool

Instances

(Eq a, EqF f) => EqF (CoAnn f a)

(Eq a, EqF f) => EqF (Ann f a)

NOTE: The EqF instance for annotations compares both the annotations and the original part.

(Eq hash, EqF f) => EqF (HashAnn hash f)

class EqF f => OrdF f where

Methods

compareF :: Ord a => f a -> f a -> Ordering

Instances

(Ord a, OrdF f) => OrdF (CoAnn f a)

(Ord a, OrdF f) => OrdF (Ann f a)

NOTE: The OrdF instance for annotations first compares the annotations, and then the functor part. If this is not the desired behaviour (it's not clear to me at the moment what is the good default here), you can use the standard newtype trick to define a new behaviour.

(Ord hash, OrdF f) => OrdF (HashAnn hash f)

class ShowF f where

Methods

showsPrecF :: Show a => Int -> f a -> ShowS

Instances

(Show a, ShowF f) => ShowF (CoAnn f a)

(Show a, ShowF f) => ShowF (Ann f a)

(ShowF f, Show hash) => ShowF (HashAnn hash f)

class ReadF f where

Methods

readPrecF :: Read a => ReadPrec (f a)

Instances

(Read a, ReadF f) => ReadF (Ann f a)

showF :: (ShowF f, Show a) => f a -> String

showsF :: (ShowF f, Show a) => f a -> ShowS

Attrib (cofree comonad)

newtype Attrib f a

A newtype wrapper around Attr f a so that we can make Attr f an instance of Functor, Foldable and Traversable (and Comonad). This is necessary since Haskell does not allow partial application of type synonyms.

Equivalent to the co-free comonad.

Constructors

Attrib

Fields

unAttrib :: Attr f a

Instances

Functor f => Functor (Attrib f)

Foldable f => Foldable (Attrib f)

Traversable f => Traversable (Attrib f)

(ShowF f, Show a) => Show (Attrib f a)

CoAttrib (free monad)

newtype CoAttrib f a

Categorial dual of Attrib. Equivalent to the free monad.

Constructors

CoAttrib

Fields

unCoAttrib :: CoAttr f a

Instances

Functor f => Monad (CoAttrib f)

Functor f => Functor (CoAttrib f)

Foldable f => Foldable (CoAttrib f)

Traversable f => Traversable (CoAttrib f)

(ShowF f, Show a) => Show (CoAttrib f a)