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--- |
--- Module : Data.Traversable
--- Copyright : Conor McBride and Ross Paterson 2005
--- License : BSD-style (see the LICENSE file in the distribution)
---
--- Maintainer : ross@soi.city.ac.uk
--- Stability : experimental
--- Portability : portable
---
--- Class of data structures that can be traversed from left to right,
--- performing an action on each element.
---
--- See also
---
--- * /Applicative Programming with Effects/,
--- by Conor McBride and Ross Paterson, online at
--- <http://www.soi.city.ac.uk/~ross/papers/Applicative.html>.
---
--- * /The Essence of the Iterator Pattern/,
--- by Jeremy Gibbons and Bruno Oliveira,
--- in /Mathematically-Structured Functional Programming/, 2006, and online at
--- <http://web.comlab.ox.ac.uk/oucl/work/jeremy.gibbons/publications/#iterator>.
---
--- Note that the functions 'mapM' and 'sequence' generalize "Prelude"
--- functions of the same names from lists to any 'Traversable' functor.
--- To avoid ambiguity, either import the "Prelude" hiding these names
--- or qualify uses of these function names with an alias for this module.
-
-module Data.Traversable (
- Traversable(..),
- for,
- forM,
- fmapDefault,
- foldMapDefault,
- ) where
-
-import Prelude hiding (mapM, sequence, foldr)
-import qualified Prelude (mapM, foldr)
-import Control.Applicative
-import Data.Foldable (Foldable())
-import Data.Monoid (Monoid)
-import Data.Array
-
--- | 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
--- > 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:
---
--- * In the 'Functor' instance, 'fmap' should be equivalent to traversal
--- with the identity applicative functor ('fmapDefault').
---
--- * In the 'Foldable' instance, 'Data.Foldable.foldMap' should be
--- equivalent to traversal with a constant applicative functor
--- ('foldMapDefault').
---
-class (Functor t, Foldable t) => Traversable t where
- -- | Map each element of a structure to an action, evaluate
- -- these actions from left to right, and collect the results.
- traverse :: Applicative f => (a -> f b) -> t a -> f (t b)
- traverse f = sequenceA . fmap f
-
- -- | Evaluate each action in the structure from left to right,
- -- and collect the results.
- sequenceA :: Applicative f => t (f a) -> f (t a)
- sequenceA = traverse id
-
- -- | Map each element of a structure to a monadic action, evaluate
- -- these actions from left to right, and collect the results.
- mapM :: Monad m => (a -> m b) -> t a -> m (t b)
- mapM f = unwrapMonad . traverse (WrapMonad . f)
-
- -- | Evaluate each monadic action in the structure from left to right,
- -- and collect the results.
- sequence :: Monad m => t (m a) -> m (t a)
- sequence = mapM id
-
--- instances for Prelude types
-
-instance Traversable Maybe where
- traverse f Nothing = pure Nothing
- traverse f (Just x) = Just <$> f x
-
-instance Traversable [] where
- traverse f = Prelude.foldr cons_f (pure [])
- where cons_f x ys = (:) <$> f x <*> ys
-
- mapM = Prelude.mapM
-
-instance Ix i => Traversable (Array i) where
- traverse f arr = listArray (bounds arr) <$> traverse f (elems arr)
-
--- general functions
-
--- | 'for' is 'traverse' with its arguments flipped.
-for :: (Traversable t, Applicative f) => t a -> (a -> f b) -> f (t b)
-{-# INLINE for #-}
-for = flip traverse
-
--- | 'forM' is 'mapM' with its arguments flipped.
-forM :: (Traversable t, Monad m) => t a -> (a -> m b) -> m (t b)
-{-# INLINE forM #-}
-forM = flip mapM
-
--- | This function may be used as a value for `fmap` in a `Functor` instance.
-fmapDefault :: Traversable t => (a -> b) -> t a -> t b
-fmapDefault f = getId . traverse (Id . f)
-
--- | This function may be used as a value for `Data.Foldable.foldMap`
--- in a `Foldable` instance.
-foldMapDefault :: (Traversable t, Monoid m) => (a -> m) -> t a -> m
-foldMapDefault f = getConst . traverse (Const . f)
-
--- local instances
-
-newtype Id a = Id { getId :: a }
-
-instance Functor Id where
- fmap f (Id x) = Id (f x)
-
-instance Applicative Id where
- pure = Id
- Id f <*> Id x = Id (f x)
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