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comparison exercises/src/Exercise_6.hs @ 14:0d15fb5d5ade

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week 6
author Markus Kaiser <markus.kaiser@in.tum.de>
date Wed, 21 Nov 2012 19:45:54 +0100
parents
children bef891fc07b4
comparison
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13:8cc37c82619c 14:0d15fb5d5ade
1 module Exercise_6 where
2 import Data.Char
3 import Test.QuickCheck
4
5 {- Library DO NOT CHANGE -}
6 type PairList = [(Int,Int)]
7 {- End Library -}
8
9
10 {---------------------------------------------------------------------}
11 {- Aufgabe G6.1 -}
12
13 instance Num b => Num (a -> b) where
14 f + g = undefined
15 f - g = undefined
16 f * g = undefined
17 negate f = undefined
18 abs f = undefined
19 signum f = undefined
20 fromInteger x = undefined
21
22
23
24 {---------------------------------------------------------------------}
25 {- Aufgabe G6.2 -}
26
27 foldl' f z [] = z
28 foldl' f z ( x : xs ) = foldl' f ( f z x ) xs
29
30 foldr' f z [] = z
31 foldr' f z ( x : xs ) = f x ( foldr' f z xs )
32
33
34 ffoldl = foldl' . foldl'
35
36 oo = (.).(.)
37
38
39
40 {---------------------------------------------------------------------}
41 {- Aufgabe G6.3 -}
42
43
44 a1 = (div 5)
45 a2 = (`div` 5)
46
47 b1 = (+ 7)
48 b2 = ((+) 7)
49
50 c1 = map (:[])
51 c2 = map ([]:)
52
53 d1 = flip . flip
54 d2 = id
55
56 e1 x y z = [x, y, z]
57 e2 x y z = x : y : z
58
59
60
61 {---------------------------------------------------------------------}
62 {- Aufgabe G6.4 -}
63
64 {-
65 Lemma: reverse = foldl (\xs x -> x : xs) []
66
67 Base case:
68 To show:
69
70 Induction step:
71 IH:
72 To show:
73 -}
74
75
76
77 {---------------------------------------------------------------------}
78 {- Aufgabe G6.5 -}
79
80 f1 xs = map (\x -> x + 1) xs
81
82 f2 xs = map (\x -> 2 * x) (map (\x -> x + 1) xs)
83
84 f3 xs = filter (\x -> x > 1) (map (\x -> x + 1) xs)
85
86 f4 f g x = f (g x)
87
88 f5 f g x y = f (g x y)
89
90 f6 f g x y z = f (g x y z)
91
92 f7 f g h x = g (h (f x))
93
94
95
96 {---------------------------------------------------------------------}
97 {- Aufgabe H6.1 -}
98
99 wellformed :: PairList -> Bool
100 wellformed = undefined
101
102
103 empty :: PairList
104 empty = undefined
105
106
107 member :: Int -> PairList -> Bool
108 member = undefined
109
110
111 insert :: Int -> PairList -> PairList
112 insert = undefined
113
114
115 union :: PairList -> PairList -> PairList
116 union = undefined
117
118
119 delete :: Int -> PairList -> PairList
120 delete = undefined
121
122
123
124 {---------------------------------------------------------------------}
125 {- Aufgabe H6.2 -}
126
127 {-WETT-}
128 anonymize :: String -> String
129 anonymize = undefined
130 {-TTEW-}