-
Notifications
You must be signed in to change notification settings - Fork 0
/
Tema_8.hs
236 lines (193 loc) · 7.07 KB
/
Tema_8.hs
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
-- Tema_8.hs
-- Tema 8: Razonamiento sobre programas.
-- José A. Alonso Jiménez https://jaalonso.github.com
-- =====================================================================
module Tema_8 where
-- ---------------------------------------------------------------------
-- Importaciones --
-- ---------------------------------------------------------------------
import Prelude hiding ( (++)
, drop
, length
, null
, replicate
, sum
, take
)
import Test.QuickCheck
-- (longitud xs) es el número de elementos de xs. Por ejemplo,
-- longitud [2,3,1] == 3
longitud :: [a] -> Int
longitud [] = 0 -- longitud.1
longitud (_:xs) = 1 + longitud xs -- longitud.2
-- (intercambia p) es el par obtenido intercambiando las componentes del
-- par p. Por ejemplo,
-- intercambia (2,5) == (5,2)
intercambia :: (a,b) -> (b,a)
intercambia (x,y) = (y,x) -- intercambia
-- Propiedad: La función intercambia es idempotente
prop_intercambia :: Int -> Int -> Bool
prop_intercambia x y =
intercambia (intercambia (x,y)) == (x,y)
-- Comprobación:
-- λ> quickCheck prop_intercambia
-- +++ OK, passed 100 tests.
-- (inversa xs) es la inversa de la lista xs. Por ejemplo,
-- inversa [3,2,5] == [5,2,3]
inversa :: [a] -> [a]
inversa [] = [] -- inversa.1
inversa (x:xs) = inversa xs ++ [x] -- inversa.2
-- Propiedad: La inversa de una lista unitaria es ella misma.
prop_inversa_unitaria :: [Int] -> Bool
prop_inversa_unitaria x =
inversa [x] == [x]
-- Comprobación:
-- λ> quickCheck prop_inversa_unitaria
-- +++ OK, passed 100 tests.
-- (no x) es la negación de x.
no :: Bool -> Bool
no False = True
no True = False
-- Propiedad: La negación es idempotente.
prop_doble_negacion :: Bool -> Bool
prop_doble_negacion x =
no (no x) == x
-- Comprobación:
-- λ> quickCheck prop_doble_negacion
-- +++ OK, passed 100 tests.
-- (replicate n x) es la lista formda por `n` elementos iguales a
-- x. Por ejemplo,
-- replicate 3 5 == [5,5,5]
replicate :: Int -> a -> [a]
replicate 0 _ = []
replicate n x = x : replicate (n-1) x
-- Propiedad: La longitud de (replicate n x) es n.
prop_length_replicate :: Int -> Int -> Bool
prop_length_replicate n xs =
length (replicate m xs) == m
where m = abs n
-- Comprobación
-- λ> quickCheck prop_length_replicate
-- OK, passed 100 tests.
-- (xs ++ ys) es la concatenación de xs e ys.
(++) :: [a] -> [a] -> [a]
[] ++ ys = ys -- ++.1
(x:xs) ++ ys = x : (xs ++ ys) -- ++.2
-- Propiedad: La concatenación es asociativa.
prop_asociativa_conc :: [Int] -> [Int] -> [Int] -> Bool
prop_asociativa_conc xs ys zs =
xs ++ (ys ++ zs)==(xs ++ ys) ++ zs
-- Comprobación:
-- λ> quickCheck prop_asociativa_conc
-- OK, passed 100 tests.
-- Propiedad: xs ++ [] = xs
prop_identidad_concatenacion :: [Int] -> Bool
prop_identidad_concatenacion xs = xs ++ [] == xs
-- Comprobación:
-- λ> quickCheck prop_identidad_concatenacion
-- OK, passed 100 tests.
-- (length xs) es el número de elementos de xs.
length :: [a] -> Int
length [] = 0 -- length.1
length (_:xs) = 1 + length xs -- length.2
-- Propiedad: length(xs ++ ys) = (length xs) + (length ys)
prop_length_append :: [Int] -> [Int] -> Bool
prop_length_append xs ys =
length(xs ++ ys)==(length xs)+(length ys)
-- Comprobación:
-- λ> quickCheck prop_length_append
-- OK, passed 100 tests.
-- (take n xs) es la lista formada por los n primeros elementos de xs.
take :: Int -> [a] -> [a]
take 0 _ = [] -- take.1
take _ [] = [] -- take.2
take n (x:xs) = x : take (n-1) xs -- take.3
-- (drop n xs) es la lista obtenida eliminando los n primeros elementos
-- de xs.
drop :: Int -> [a] -> [a]
drop 0 xs = xs -- drop.1
drop _ [] = [] -- drop,2
drop n (_:xs) = drop (n-1) xs -- drop.3
-- Propiedad: take n xs ++ drop n xs = xs
prop_take_drop :: Int -> [Int] -> Property
prop_take_drop n xs =
n >= 0 ==> take n xs ++ drop n xs == xs
-- Comprobación:
-- λ> quickCheck prop_take_drop
-- OK, passed 100 tests.
-- (null xs) se verifica si xs no tiene elementos.
null :: [a] -> Bool
null [] = True -- null.1
null (_:_) = False -- null.2
-- Propiedad: xs no tiene elementos syss (xs ++ xs) no los tiene.
prop_null :: [Int] -> Bool
prop_null xs =
null xs == null (xs ++ xs)
-- Comprobación
-- λ> quickCheck prop_null
-- +++ OK, passed 100 tests.
-- (inversa1 xs) es la inversa de xs.
inversa1 :: [a] -> [a]
inversa1 [] = [] -- inversa1.1
inversa1 (x:xs) = inversa1 xs ++ [x] -- inversa1.2
-- (inversa2 xs) es la inversa de xs definida con un acumulador.
inversa2 :: [a] -> [a]
inversa2 xs = inversa2Aux xs [] -- inversa2.1
where inversa2Aux [] ys = ys -- inversa2Aux.1
inversa2Aux (x:xs') ys = inversa2Aux xs' (x:ys) -- inversa2Aux.2
-- Propiedad: La funciones inversa1 e inversa2 son equivalentes.
prop_equiv_inversa :: [Int] -> Bool
prop_equiv_inversa xs = inversa1 xs == inversa2 xs
-- Comprobación
-- λ> quickCheck prop_equiv_inversa
-- +++ OK, passed 100 tests.
-- (sum xs) es la suma de los elementos de xs.
sum :: [Int] -> Int
sum [] = 0
sum (x:xs) = x + sum xs
-- Propiedad: sum (map (2*) xs) = 2 * sum xs
prop_sum_map :: [Int] -> Bool
prop_sum_map xs = sum (map (2*) xs) == 2 * sum xs
-- Comprobación:
-- λ> quickCheck prop_sum_map
-- +++ OK, passed 100 tests.
-- Propiedad La aplicación de una función a los elementos de una lista
-- conserva su longitud:
prop_map_length :: Fun Int Int -> [Int] -> Bool
prop_map_length (Fun _ f) xs =
length (map f xs) == length xs
-- Comprobación
-- λ> quickCheck prop_map_length
-- +++ OK, passed 100 tests.
-- ---------------------------------------------------------------------
-- § Verificación de propiedades --
-- ---------------------------------------------------------------------
-- Las propiedades son
verifica_Tema_8 :: IO ()
verifica_Tema_8 = do
quickCheck prop_intercambia
quickCheck prop_inversa_unitaria
quickCheck prop_doble_negacion
quickCheck prop_length_replicate
quickCheck prop_asociativa_conc
quickCheck prop_identidad_concatenacion
quickCheck prop_length_append
quickCheck prop_take_drop
quickCheck prop_null
quickCheck prop_equiv_inversa
quickCheck prop_sum_map
quickCheck prop_map_length
-- Su verificación es
-- λ> verifica_Tema_8
-- +++ OK, passed 100 tests.
-- +++ OK, passed 100 tests.
-- +++ OK, passed 100 tests.
-- +++ OK, passed 100 tests.
-- +++ OK, passed 100 tests.
-- +++ OK, passed 100 tests.
-- +++ OK, passed 100 tests.
-- +++ OK, passed 100 tests; 105 discarded.
-- +++ OK, passed 100 tests.
-- +++ OK, passed 100 tests.
-- +++ OK, passed 100 tests.
-- +++ OK, passed 100 tests.