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
135
136
137
138
139
140
141
142
143
144
145
146
147
148
149
150
151
152
153
154
155
156
157
158
159
160
161
162
163
164
165
166
167
168
169
170
171
172
173
174
175
176
177
178
179
180
181
182
183
184
185
186
187
188
189
190
191
192
193
194
195
196
197
198
199
200
201
202
203
204
205
206
207
208
209
210
211
212
213
214
215
216
217
218
219
220
221
222
223
224
225
226
227
228
229
230
231
232
233
234
235
236
237
238
239
240
241
242
243
244
245
246
247
248
249
250
251
252
253
254
255
256
257
258
259
|
{-# LANGUAGE CPP #-}
#if __GLASGOW_HASKELL__ >= 700
{-# LANGUAGE DeriveDataTypeable #-}
#endif
#if __GLASGOW_HASKELL__ >= 702
{-# LANGUAGE DeriveGeneric #-}
{-# LANGUAGE Trustworthy #-}
#endif
#if __GLASGOW_HASKELL__ >= 706
{-# LANGUAGE PolyKinds #-}
#endif
#if __GLASGOW_HASKELL__ >= 708
{-# LANGUAGE AutoDeriveTypeable #-}
{-# LANGUAGE DataKinds #-}
#endif
#if MIN_VERSION_base(4,7,0)
-- We need to implement bitSize for the Bits instance, but it's deprecated.
{-# OPTIONS_GHC -fno-warn-deprecations #-}
#endif
-----------------------------------------------------------------------------
-- |
-- Module : Data.Functor.Identity
-- Copyright : (c) Andy Gill 2001,
-- (c) Oregon Graduate Institute of Science and Technology 2001
-- License : BSD-style (see the file LICENSE)
--
-- Maintainer : ross@soi.city.ac.uk
-- Stability : experimental
-- Portability : portable
--
-- The identity functor and monad.
--
-- This trivial type constructor serves two purposes:
--
-- * It can be used with functions parameterized by functor or monad classes.
--
-- * It can be used as a base monad to which a series of monad
-- transformers may be applied to construct a composite monad.
-- Most monad transformer modules include the special case of
-- applying the transformer to 'Identity'. For example, @State s@
-- is an abbreviation for @StateT s 'Identity'@.
-----------------------------------------------------------------------------
module Data.Functor.Identity (
Identity(..),
) where
import Data.Bits
import Control.Applicative
import Control.Arrow (Arrow((***)))
import Control.Monad.Fix
#if MIN_VERSION_base(4,4,0)
import Control.Monad.Zip (MonadZip(mzipWith, munzip))
#endif
import Data.Foldable (Foldable(foldMap))
import Data.Monoid (Monoid(mempty, mappend))
import Data.String (IsString(fromString))
import Data.Traversable (Traversable(traverse))
#if __GLASGOW_HASKELL__ >= 700
import Data.Data
#endif
import Data.Ix (Ix(..))
import Foreign (Storable(..), castPtr)
#if __GLASGOW_HASKELL__ >= 702
import GHC.Generics
#endif
-- | Identity functor and monad. (a non-strict monad)
newtype Identity a = Identity { runIdentity :: a }
deriving ( Eq, Ord
#if __GLASGOW_HASKELL__ >= 700
, Data, Typeable
#endif
#if __GLASGOW_HASKELL__ >= 702
, Generic
#endif
#if __GLASGOW_HASKELL__ >= 706
, Generic1
#endif
)
instance (Bits a) => Bits (Identity a) where
Identity x .&. Identity y = Identity (x .&. y)
Identity x .|. Identity y = Identity (x .|. y)
xor (Identity x) (Identity y) = Identity (xor x y)
complement (Identity x) = Identity (complement x)
shift (Identity x) i = Identity (shift x i)
rotate (Identity x) i = Identity (rotate x i)
setBit (Identity x) i = Identity (setBit x i)
clearBit (Identity x) i = Identity (clearBit x i)
shiftL (Identity x) i = Identity (shiftL x i)
shiftR (Identity x) i = Identity (shiftR x i)
rotateL (Identity x) i = Identity (rotateL x i)
rotateR (Identity x) i = Identity (rotateR x i)
testBit (Identity x) i = testBit x i
bitSize (Identity x) = bitSize x
isSigned (Identity x) = isSigned x
bit i = Identity (bit i)
#if MIN_VERSION_base(4,5,0)
unsafeShiftL (Identity x) i = Identity (unsafeShiftL x i)
unsafeShiftR (Identity x) i = Identity (unsafeShiftR x i)
popCount (Identity x) = popCount x
#endif
#if MIN_VERSION_base(4,7,0)
zeroBits = Identity zeroBits
bitSizeMaybe (Identity x) = bitSizeMaybe x
#endif
instance (Bounded a) => Bounded (Identity a) where
minBound = Identity minBound
maxBound = Identity maxBound
instance (Enum a) => Enum (Identity a) where
succ (Identity x) = Identity (succ x)
pred (Identity x) = Identity (pred x)
toEnum i = Identity (toEnum i)
fromEnum (Identity x) = fromEnum x
enumFrom (Identity x) = map Identity (enumFrom x)
enumFromThen (Identity x) (Identity y) = map Identity (enumFromThen x y)
enumFromTo (Identity x) (Identity y) = map Identity (enumFromTo x y)
enumFromThenTo (Identity x) (Identity y) (Identity z) =
map Identity (enumFromThenTo x y z)
#if MIN_VERSION_base(4,7,0)
instance (FiniteBits a) => FiniteBits (Identity a) where
finiteBitSize (Identity x) = finiteBitSize x
#endif
instance (Floating a) => Floating (Identity a) where
pi = Identity pi
exp (Identity x) = Identity (exp x)
log (Identity x) = Identity (log x)
sqrt (Identity x) = Identity (sqrt x)
sin (Identity x) = Identity (sin x)
cos (Identity x) = Identity (cos x)
tan (Identity x) = Identity (tan x)
asin (Identity x) = Identity (asin x)
acos (Identity x) = Identity (acos x)
atan (Identity x) = Identity (atan x)
sinh (Identity x) = Identity (sinh x)
cosh (Identity x) = Identity (cosh x)
tanh (Identity x) = Identity (tanh x)
asinh (Identity x) = Identity (asinh x)
acosh (Identity x) = Identity (acosh x)
atanh (Identity x) = Identity (atanh x)
Identity x ** Identity y = Identity (x ** y)
logBase (Identity x) (Identity y) = Identity (logBase x y)
instance (Fractional a) => Fractional (Identity a) where
Identity x / Identity y = Identity (x / y)
recip (Identity x) = Identity (recip x)
fromRational r = Identity (fromRational r)
instance (IsString a) => IsString (Identity a) where
fromString s = Identity (fromString s)
instance (Ix a) => Ix (Identity a) where
range (Identity x, Identity y) = map Identity (range (x, y))
index (Identity x, Identity y) (Identity i) = index (x, y) i
inRange (Identity x, Identity y) (Identity e) = inRange (x, y) e
rangeSize (Identity x, Identity y) = rangeSize (x, y)
instance (Integral a) => Integral (Identity a) where
quot (Identity x) (Identity y) = Identity (quot x y)
rem (Identity x) (Identity y) = Identity (rem x y)
div (Identity x) (Identity y) = Identity (div x y)
mod (Identity x) (Identity y) = Identity (mod x y)
quotRem (Identity x) (Identity y) = (Identity *** Identity) (quotRem x y)
divMod (Identity x) (Identity y) = (Identity *** Identity) (divMod x y)
toInteger (Identity x) = toInteger x
instance (Monoid a) => Monoid (Identity a) where
mempty = Identity mempty
mappend (Identity x) (Identity y) = Identity (mappend x y)
instance (Num a) => Num (Identity a) where
Identity x + Identity y = Identity (x + y)
Identity x - Identity y = Identity (x - y)
Identity x * Identity y = Identity (x * y)
negate (Identity x) = Identity (negate x)
abs (Identity x) = Identity (abs x)
signum (Identity x) = Identity (signum x)
fromInteger n = Identity (fromInteger n)
instance (Real a) => Real (Identity a) where
toRational (Identity x) = toRational x
instance (RealFloat a) => RealFloat (Identity a) where
floatRadix (Identity x) = floatRadix x
floatDigits (Identity x) = floatDigits x
floatRange (Identity x) = floatRange x
decodeFloat (Identity x) = decodeFloat x
exponent (Identity x) = exponent x
isNaN (Identity x) = isNaN x
isInfinite (Identity x) = isInfinite x
isDenormalized (Identity x) = isDenormalized x
isNegativeZero (Identity x) = isNegativeZero x
isIEEE (Identity x) = isIEEE x
significand (Identity x) = significand (Identity x)
scaleFloat s (Identity x) = Identity (scaleFloat s x)
encodeFloat m n = Identity (encodeFloat m n)
atan2 (Identity x) (Identity y) = Identity (atan2 x y)
instance (RealFrac a) => RealFrac (Identity a) where
properFraction (Identity x) = (id *** Identity) (properFraction x)
truncate (Identity x) = truncate x
round (Identity x) = round x
ceiling (Identity x) = ceiling x
floor (Identity x) = floor x
instance (Storable a) => Storable (Identity a) where
sizeOf (Identity x) = sizeOf x
alignment (Identity x) = alignment x
peekElemOff p i = fmap Identity (peekElemOff (castPtr p) i)
pokeElemOff p i (Identity x) = pokeElemOff (castPtr p) i x
peekByteOff p i = fmap Identity (peekByteOff p i)
pokeByteOff p i (Identity x) = pokeByteOff p i x
peek p = fmap runIdentity (peek (castPtr p))
poke p (Identity x) = poke (castPtr p) x
-- These instances would be equivalent to the derived instances of the
-- newtype if the field were removed.
instance (Read a) => Read (Identity a) where
readsPrec d = readParen (d > 10) $ \ r ->
[(Identity x,t) | ("Identity",s) <- lex r, (x,t) <- readsPrec 11 s]
instance (Show a) => Show (Identity a) where
showsPrec d (Identity x) = showParen (d > 10) $
showString "Identity " . showsPrec 11 x
-- ---------------------------------------------------------------------------
-- Identity instances for Functor and Monad
instance Functor Identity where
fmap f m = Identity (f (runIdentity m))
instance Foldable Identity where
foldMap f (Identity x) = f x
instance Traversable Identity where
traverse f (Identity x) = Identity <$> f x
instance Applicative Identity where
pure a = Identity a
Identity f <*> Identity x = Identity (f x)
instance Monad Identity where
return a = Identity a
m >>= k = k (runIdentity m)
instance MonadFix Identity where
mfix f = Identity (fix (runIdentity . f))
#if MIN_VERSION_base(4,4,0)
instance MonadZip Identity where
mzipWith f (Identity x) (Identity y) = Identity (f x y)
munzip (Identity (a, b)) = (Identity a, Identity b)
#endif
|
