1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
86
87
88
89
90
91
92
93
94
95
96
97
98
99
100
101
102
103
104
105
106
107
108
109
110
111
112
113
114
115
116
117
118
119
120
121
122
123
124
125
126
127
128
129
130
131
132
133
134
|
{-# LANGUAGE AutoDeriveTypeable #-}
{-# LANGUAGE DeriveGeneric #-}
{-# LANGUAGE NoImplicitPrelude #-}
{-# LANGUAGE Trustworthy #-}
-----------------------------------------------------------------------------
-- |
-- Module : Control.Applicative
-- Copyright : Conor McBride and Ross Paterson 2005
-- License : BSD-style (see the LICENSE file in the distribution)
--
-- Maintainer : libraries@haskell.org
-- Stability : experimental
-- Portability : portable
--
-- This module describes a structure intermediate between a functor and
-- a monad (technically, a strong lax monoidal functor). Compared with
-- monads, this interface lacks the full power of the binding operation
-- '>>=', but
--
-- * it has more instances.
--
-- * it is sufficient for many uses, e.g. context-free parsing, or the
-- 'Data.Traversable.Traversable' class.
--
-- * instances can perform analysis of computations before they are
-- executed, and thus produce shared optimizations.
--
-- This interface was introduced for parsers by Niklas Röjemo, because
-- it admits more sharing than the monadic interface. The names here are
-- mostly based on parsing work by Doaitse Swierstra.
--
-- For more details, see
-- <http://www.soi.city.ac.uk/~ross/papers/Applicative.html Applicative Programming with Effects>,
-- by Conor McBride and Ross Paterson.
module Control.Applicative (
-- * Applicative functors
Applicative(..),
-- * Alternatives
Alternative(..),
-- * Instances
Const(..), WrappedMonad(..), WrappedArrow(..), ZipList(..),
-- * Utility functions
(<$>), (<$), (<**>),
liftA, liftA2, liftA3,
optional,
) where
import Control.Category
import Control.Arrow
import Data.Maybe
import Data.Tuple
import Data.Eq
import Data.Ord
import Data.Foldable (Foldable(..))
import Data.Functor ((<$>))
import GHC.Base hiding ((.), id)
import GHC.Generics
import GHC.List (repeat, zipWith)
import GHC.Read (Read)
import GHC.Show (Show)
newtype Const a b = Const { getConst :: a }
deriving (Generic, Generic1)
instance Foldable (Const m) where
foldMap _ _ = mempty
instance Functor (Const m) where
fmap _ (Const v) = Const v
-- Added in base-4.7.0.0
instance Monoid a => Monoid (Const a b) where
mempty = Const mempty
mappend (Const a) (Const b) = Const (mappend a b)
instance Monoid m => Applicative (Const m) where
pure _ = Const mempty
Const f <*> Const v = Const (f `mappend` v)
newtype WrappedMonad m a = WrapMonad { unwrapMonad :: m a }
deriving (Generic, Generic1)
instance Monad m => Functor (WrappedMonad m) where
fmap f (WrapMonad v) = WrapMonad (liftM f v)
instance Monad m => Applicative (WrappedMonad m) where
pure = WrapMonad . return
WrapMonad f <*> WrapMonad v = WrapMonad (f `ap` v)
-- Added in base-4.7.0.0 (GHC Trac #8218)
instance Monad m => Monad (WrappedMonad m) where
return = WrapMonad . return
a >>= f = WrapMonad (unwrapMonad a >>= unwrapMonad . f)
instance MonadPlus m => Alternative (WrappedMonad m) where
empty = WrapMonad mzero
WrapMonad u <|> WrapMonad v = WrapMonad (u `mplus` v)
newtype WrappedArrow a b c = WrapArrow { unwrapArrow :: a b c }
deriving (Generic, Generic1)
instance Arrow a => Functor (WrappedArrow a b) where
fmap f (WrapArrow a) = WrapArrow (a >>> arr f)
instance Arrow a => Applicative (WrappedArrow a b) where
pure x = WrapArrow (arr (const x))
WrapArrow f <*> WrapArrow v = WrapArrow (f &&& v >>> arr (uncurry id))
instance (ArrowZero a, ArrowPlus a) => Alternative (WrappedArrow a b) where
empty = WrapArrow zeroArrow
WrapArrow u <|> WrapArrow v = WrapArrow (u <+> v)
-- | Lists, but with an 'Applicative' functor based on zipping, so that
--
-- @f '<$>' 'ZipList' xs1 '<*>' ... '<*>' 'ZipList' xsn = 'ZipList' (zipWithn f xs1 ... xsn)@
--
newtype ZipList a = ZipList { getZipList :: [a] }
deriving (Show, Eq, Ord, Read, Generic, Generic1)
instance Functor ZipList where
fmap f (ZipList xs) = ZipList (map f xs)
instance Applicative ZipList where
pure x = ZipList (repeat x)
ZipList fs <*> ZipList xs = ZipList (zipWith id fs xs)
-- extra functions
-- | One or none.
optional :: Alternative f => f a -> f (Maybe a)
optional v = Just <$> v <|> pure Nothing
|
