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
|
module Exercises where
import Test.QuickCheck
import Test.QuickCheck.Checkers
--- 1
data Pair a = Pair a a deriving (Show, Eq)
instance Functor Pair where
fmap f (Pair x y) = Pair (f x) (f y)
instance Applicative Pair where
pure f = Pair f f
(Pair f f') <*> (Pair x y) = Pair (f x) (f' y)
instance Arbitrary a => Arbitrary (Pair a) where
arbitrary = do
x <- arbitrary
y <- arbitrary
return $ Pair x y
instance Eq a => EqProp (Pair a) where
(=-=) = eq
--- 2
data Two a b = Two a b deriving (Show, Eq)
instance Functor (Two a) where
fmap f (Two x y) = Two x (f y)
instance Monoid a => Applicative (Two a) where
pure x = Two mempty $ x
(Two f f') <*> (Two x y) = Two (mappend f x) (f' y)
instance (Arbitrary a, Arbitrary b) => Arbitrary (Two a b) where
arbitrary = do
x <- arbitrary
y <- arbitrary
return $ Two x y
instance (Eq a, Eq b) => EqProp (Two a b) where
(=-=) = eq
--- 3
data Three a b c = Three a b c deriving (Show, Eq)
instance Functor (Three a b) where
fmap f (Three x y z) = Three x y (f z)
instance (Monoid a, Monoid b) => Applicative (Three a b) where
pure x = Three mempty mempty x
(Three f f' f'') <*> (Three x y z) = Three (mappend f x) (mappend f' y) (f'' z)
instance (Arbitrary a, Arbitrary b, Arbitrary c) => Arbitrary (Three a b c) where
arbitrary = do
x <- arbitrary
y <- arbitrary
z <- arbitrary
return $ Three x y z
instance (Eq a, Eq b, Eq c) => EqProp (Three a b c) where
(=-=) = eq
--- 4
data Three' a b = Three' a b b deriving (Show, Eq)
instance Functor (Three' a) where
fmap f (Three' x y z) = Three' x (f y) (f z)
instance (Monoid a) => Applicative (Three' a) where
pure x = Three' mempty x x
(Three' f f' f'') <*> (Three' x y z) = Three' (mappend f x) (f' y) (f'' z)
instance (Arbitrary a, Arbitrary b) => Arbitrary (Three' a b) where
arbitrary = do
x <- arbitrary
y <- arbitrary
z <- arbitrary
return $ Three' x y z
instance (Eq a, Eq b) => EqProp (Three' a b) where
(=-=) = eq
--- 5
data Four a b c d = Four a b c d deriving (Show, Eq)
instance Functor (Four a b c) where
fmap f (Four x y z t) = Four x y z (f t)
instance (Monoid a, Monoid b, Monoid c) => Applicative (Four a b c) where
pure x = Four mempty mempty mempty x
(Four f f' f'' f''') <*> (Four x y z t) = Four (mappend f x) (mappend f' y) (mappend f'' z) (f''' t)
instance (Arbitrary a, Arbitrary b, Arbitrary c, Arbitrary d) => Arbitrary (Four a b c d) where
arbitrary = do
x <- arbitrary
y <- arbitrary
z <- arbitrary
t <- arbitrary
return $ Four x y z t
instance (Eq a, Eq b, Eq c, Eq d) => EqProp (Four a b c d) where
(=-=) = eq
--- 5
data Four' a b = Four' a a a b deriving (Show, Eq)
instance Functor (Four' a) where
fmap f (Four' x y z t) = Four' x y z (f t)
instance (Monoid a) => Applicative (Four' a) where
pure x = Four' mempty mempty mempty x
(Four' f f' f'' f''') <*> (Four' x y z t) = Four' (mappend f x) (mappend f' y) (mappend f'' z) (f''' t)
instance (Arbitrary a, Arbitrary b) => Arbitrary (Four' a b) where
arbitrary = do
x <- arbitrary
y <- arbitrary
z <- arbitrary
t <- arbitrary
return $ Four' x y z t
instance (Eq a, Eq b) => EqProp (Four' a b) where
(=-=) = eq
|
