|
14
|
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-} |
