Copyright	(c) Ross Paterson 2010
License	BSD-style (see the file LICENSE)
Maintainer	R.Paterson@city.ac.uk
Stability	experimental
Portability	portable
Safe Haskell	Safe
Language	Haskell98

Control.Applicative.Lift

Contents

Lifting an applicative
Collecting errors

Description

Adding a new kind of pure computation to an applicative functor.

Synopsis

data Lift f a
- = Pure a
- | Other (f a)
unLift :: Applicative f => Lift f a -> f a
mapLift :: (f a -> g a) -> Lift f a -> Lift g a
elimLift :: (a -> r) -> (f a -> r) -> Lift f a -> r
type Errors e = Lift (Constant e)
runErrors :: Errors e a -> Either e a
failure :: e -> Errors e a
eitherToErrors :: Either e a -> Errors e a

Lifting an applicative

data Lift f a Source #

Applicative functor formed by adding pure computations to a given applicative functor.

Constructors

Pure a
Other (f a)

Instances

Functor f => Functor (Lift f) #
Instance details Methods fmap :: (a -> b) -> Lift f a -> Lift f b Source # (<$) :: a -> Lift f b -> Lift f a Source #
Applicative f => Applicative (Lift f) #	A combination is `Pure` only if both parts are.
Instance details Methods pure :: a -> Lift f a Source # (<>) :: Lift f (a -> b) -> Lift f a -> Lift f b Source # liftA2 :: (a -> b -> c) -> Lift f a -> Lift f b -> Lift f c Source # (>) :: Lift f a -> Lift f b -> Lift f b Source # (<*) :: Lift f a -> Lift f b -> Lift f a Source #
Foldable f => Foldable (Lift f) #
Instance details Methods fold :: Monoid m => Lift f m -> m Source # foldMap :: Monoid m => (a -> m) -> Lift f a -> m Source # foldr :: (a -> b -> b) -> b -> Lift f a -> b Source # foldr' :: (a -> b -> b) -> b -> Lift f a -> b Source # foldl :: (b -> a -> b) -> b -> Lift f a -> b Source # foldl' :: (b -> a -> b) -> b -> Lift f a -> b Source # foldr1 :: (a -> a -> a) -> Lift f a -> a Source # foldl1 :: (a -> a -> a) -> Lift f a -> a Source # toList :: Lift f a -> [a] Source # null :: Lift f a -> Bool Source # length :: Lift f a -> Int Source # elem :: Eq a => a -> Lift f a -> Bool Source # maximum :: Ord a => Lift f a -> a Source # minimum :: Ord a => Lift f a -> a Source # sum :: Num a => Lift f a -> a Source # product :: Num a => Lift f a -> a Source #
Traversable f => Traversable (Lift f) #
Instance details Methods traverse :: Applicative f0 => (a -> f0 b) -> Lift f a -> f0 (Lift f b) Source # sequenceA :: Applicative f0 => Lift f (f0 a) -> f0 (Lift f a) Source # mapM :: Monad m => (a -> m b) -> Lift f a -> m (Lift f b) Source # sequence :: Monad m => Lift f (m a) -> m (Lift f a) Source #
Eq1 f => Eq1 (Lift f) #
Instance details Methods liftEq :: (a -> b -> Bool) -> Lift f a -> Lift f b -> Bool Source #
Ord1 f => Ord1 (Lift f) #
Instance details Methods liftCompare :: (a -> b -> Ordering) -> Lift f a -> Lift f b -> Ordering Source #
Read1 f => Read1 (Lift f) #
Instance details Methods liftReadsPrec :: (Int -> ReadS a) -> ReadS [a] -> Int -> ReadS (Lift f a) Source # liftReadList :: (Int -> ReadS a) -> ReadS [a] -> ReadS [Lift f a] Source # liftReadPrec :: ReadPrec a -> ReadPrec [a] -> ReadPrec (Lift f a) Source # liftReadListPrec :: ReadPrec a -> ReadPrec [a] -> ReadPrec [Lift f a] Source #
Show1 f => Show1 (Lift f) #
Instance details Methods liftShowsPrec :: (Int -> a -> ShowS) -> ([a] -> ShowS) -> Int -> Lift f a -> ShowS Source # liftShowList :: (Int -> a -> ShowS) -> ([a] -> ShowS) -> [Lift f a] -> ShowS Source #
Alternative f => Alternative (Lift f) #	A combination is `Pure` only either part is.
Instance details Methods empty :: Lift f a Source # (<\|>) :: Lift f a -> Lift f a -> Lift f a Source # some :: Lift f a -> Lift f [a] Source # many :: Lift f a -> Lift f [a] Source #
(Eq1 f, Eq a) => Eq (Lift f a) #
Instance details Methods (==) :: Lift f a -> Lift f a -> Bool # (/=) :: Lift f a -> Lift f a -> Bool #
(Ord1 f, Ord a) => Ord (Lift f a) #
Instance details Methods compare :: Lift f a -> Lift f a -> Ordering # (<) :: Lift f a -> Lift f a -> Bool # (<=) :: Lift f a -> Lift f a -> Bool # (>) :: Lift f a -> Lift f a -> Bool # (>=) :: Lift f a -> Lift f a -> Bool # max :: Lift f a -> Lift f a -> Lift f a # min :: Lift f a -> Lift f a -> Lift f a #
(Read1 f, Read a) => Read (Lift f a) #
Instance details Methods readsPrec :: Int -> ReadS (Lift f a) Source # readList :: ReadS [Lift f a] Source # readPrec :: ReadPrec (Lift f a) Source # readListPrec :: ReadPrec [Lift f a] Source #
(Show1 f, Show a) => Show (Lift f a) #
Instance details Methods showsPrec :: Int -> Lift f a -> ShowS Source # show :: Lift f a -> String Source # showList :: [Lift f a] -> ShowS Source #

unLift :: Applicative f => Lift f a -> f a Source #

Projection to the other functor.

mapLift :: (f a -> g a) -> Lift f a -> Lift g a Source #

Apply a transformation to the other computation.

elimLift :: (a -> r) -> (f a -> r) -> Lift f a -> r Source #

Eliminator for Lift.

```
elimLift f g . pure = f
```
```
elimLift f g . Other = g
```

Collecting errors

type Errors e = Lift (Constant e) Source #

An applicative functor that collects a monoid (e.g. lists) of errors. A sequence of computations fails if any of its components do, but unlike monads made with ExceptT from Control.Monad.Trans.Except, these computations continue after an error, collecting all the errors.

```
pure f <*> pure x = pure (f x)
```
```
pure f <*> failure e = failure e
```
```
failure e <*> pure x = failure e
```

failure e1 <*> failure e2 = failure (e1 <> e2)

runErrors :: Errors e a -> Either e a Source #

Extractor for computations with accumulating errors.

```
runErrors (pure x) = Right x
```
```
runErrors (failure e) = Left e
```

failure :: e -> Errors e a Source #

Report an error.

eitherToErrors :: Either e a -> Errors e a Source #

Convert from Either to Errors (inverse of runErrors).