fixplate-0.1.5: Uniplate-style generic traversals for optionally annotated fixed-point types.

Safe HaskellSafe-Infered

Data.Generics.Fixplate

Description

This library provides Uniplate-style generic traversals and other recursion schemes for fixed-point types. There are many advantages of using fixed-point types instead of explicit recursion:

  • we can easily add attributes to the nodes of an existing tree;
  • there is no need for a custom type class, we can build everything on the top of Functor, Foldable and Traversable, for which GHC can derive the instances for us;
  • we can provide interesting recursion schemes
  • some operations can retain the structure of the tree, instead flattening it into a list;
  • it is relatively straightforward to provide generic implementations of the zipper, tries, tree drawing, hashing, etc...

The main disadvantage is that it does not work well for mutually recursive data types, and that pattern matching becomes more tedious (but there are partial solutions for the latter).

Consider as an example the following simple expression language, encoded by a recursive algebraic data type: 

 data Expr 
   = Kst Int 
   | Var String 
   | Add Expr Expr
   deriving (Eq,Show)

We can open up the recursion, and obtain a functor instead: 

 data Expr1 e 
   = Kst Int 
   | Var String 
   | Add e e 
   deriving (Eq,Show,Functor,Foldable,Traversable)

The fixed-point type Mu Expr1 is isomorphic to Expr. However, we can also add some attributes to the nodes: The type Attr Expr1 a = Mu (Ann Expr1 a) is the type of with the same structure, but with each node having an extra field of type a.

The functions in this library work on types like that: Mu f, where f is a functor, and sometimes explicitely on Attr f a.

The organization of the modules (excluding Util.*) is the following:

This module re-exports the most common functionality present in the library (but not for example the zipper, tries, hashing).

The library itself should be fully Haskell98 compatible; no language extensions are used. Note: to obtain Eq, Ord, Show, Read and other instances for fixed point types like Mu Expr1, consult the documentation of the EqF type class (cf. the related OrdF, ShowF and ReadF classes)

Synopsis

Documentation

module Data.Generics.Fixplate.Base

module Data.Generics.Fixplate.Traversals

module Data.Generics.Fixplate.Morphisms

module Data.Generics.Fixplate.Attributes

module Data.Generics.Fixplate.Draw

class Functor f where

The Functor class is used for types that can be mapped over. Instances of Functor should satisfy the following laws: 

 fmap id  ==  id
 fmap (f . g)  ==  fmap f . fmap g

The instances of Functor for lists, Maybe and IO satisfy these laws.

Methods

fmap :: (a -> b) -> f a -> f b

Instances

Functor [] 
Functor IO 
Functor ZipList 
Functor ReadPrec 
Functor ReadP 
Functor Maybe 
Functor Id 
Functor ((->) r) 
Functor (Either a) 
Functor ((,) a) 
Ix i => Functor (Array i) 
Functor (Const m) 
Monad m => Functor (WrappedMonad m) 
Functor (Map k) 
Functor (StateR s) 
Functor (StateL s) 
Functor f => Functor (CoAttrib f) 
Functor f => Functor (Attrib f) 
Arrow a => Functor (WrappedArrow a b) 
Functor f => Functor (CoAnn f a) 
Functor f => Functor (Ann f a) 
Functor f => Functor (HashAnn hash f) 

class Foldable t where

Data structures that can be folded.

Minimal complete definition: foldMap or foldr.

For example, given a data type 

 data Tree a = Empty | Leaf a | Node (Tree a) a (Tree a)

a suitable instance would be 

 instance Foldable Tree where
    foldMap f Empty = mempty
    foldMap f (Leaf x) = f x
    foldMap f (Node l k r) = foldMap f l `mappend` f k `mappend` foldMap f r

This is suitable even for abstract types, as the monoid is assumed to satisfy the monoid laws. Alternatively, one could define foldr: 

 instance Foldable Tree where
    foldr f z Empty = z
    foldr f z (Leaf x) = f x z
    foldr f z (Node l k r) = foldr f (f k (foldr f z r)) l

Methods

fold :: Monoid m => t m -> m

Combine the elements of a structure using a monoid.

foldMap :: Monoid m => (a -> m) -> t a -> m

Map each element of the structure to a monoid, and combine the results.

foldr :: (a -> b -> b) -> b -> t a -> b

Right-associative fold of a structure. 

foldr f z = foldr f z . toList

foldl :: (a -> b -> a) -> a -> t b -> a

Left-associative fold of a structure. 

foldl f z = foldl f z . toList

foldr1 :: (a -> a -> a) -> t a -> a

A variant of foldr that has no base case, and thus may only be applied to non-empty structures. 

foldr1 f = foldr1 f . toList

foldl1 :: (a -> a -> a) -> t a -> a

A variant of foldl that has no base case, and thus may only be applied to non-empty structures. 

foldl1 f = foldl1 f . toList

Instances

class (Functor t, Foldable t) => Traversable t where

Functors representing data structures that can be traversed from left to right.

Minimal complete definition: traverse or sequenceA.

Instances are similar to Functor, e.g. given a data type 

 data Tree a = Empty | Leaf a | Node (Tree a) a (Tree a)

a suitable instance would be 

 instance Traversable Tree where
    traverse f Empty = pure Empty
    traverse f (Leaf x) = Leaf <$> f x
    traverse f (Node l k r) = Node <$> traverse f l <*> f k <*> traverse f r

This is suitable even for abstract types, as the laws for <*> imply a form of associativity.

The superclass instances should satisfy the following:

Methods

traverse :: Applicative f => (a -> f b) -> t a -> f (t b)

Map each element of a structure to an action, evaluate these actions from left to right, and collect the results.

sequenceA :: Applicative f => t (f a) -> f (t a)

Evaluate each action in the structure from left to right, and collect the results.

mapM :: Monad m => (a -> m b) -> t a -> m (t b)

Map each element of a structure to a monadic action, evaluate these actions from left to right, and collect the results.

sequence :: Monad m => t (m a) -> m (t a)

Evaluate each monadic action in the structure from left to right, and collect the results.

Instances