aboutsummaryrefslogtreecommitdiff
path: root/stdlib/source/test/lux/data/number/nat.lux
blob: 6e027eab1413bc3d33b985357cc397aaf3786ec0 (plain)
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
(.module:
  [lux #*
   ["_" test (#+ Test)]
   [abstract
    [monad (#+ do)]
    {[0 #spec]
     [/
      ["$." equivalence]
      ["$." order]
      ["$." enum]
      ["$." interval]
      ["$." monoid]
      ["$." codec]]}]
   [data
    ["." bit ("#\." equivalence)]
    [number
     ["f" frac]
     ["." i64 ("#\." hash)]]]
   [math
    ["." random]]]
  {1
   ["." /]})

(def: signature
  Test
  (`` ($_ _.and
          (_.with-cover [/.equivalence /.=]
            ($equivalence.spec /.equivalence random.nat))
          (_.with-cover [/.order /.<]
            ($order.spec /.order random.nat))
          (_.with-cover [/.enum]
            ($enum.spec /.enum random.nat))
          (_.with-cover [/.interval]
            ($interval.spec /.interval random.nat))
          (~~ (template [<compose> <monoid>]
                [(_.with-cover [<monoid> <compose>]
                   ($monoid.spec /.equivalence <monoid> random.nat))]
                
                [/.+ /.addition]
                [/.* /.multiplication]

                [/.min /.minimum]
                [/.max /.maximum]
                ))
          (~~ (template [<codec>]
                [(_.with-cover [<codec>]
                   ($codec.spec /.equivalence <codec> random.nat))]

                [/.binary] [/.octal] [/.decimal] [/.hex]
                ))
          )))

(def: predicate
  Test
  (do {! random.monad}
    [sample random.nat]
    ($_ _.and
        (_.cover [/.even? /.odd?]
                 (bit\= (/.even? sample)
                        (not (/.odd? sample))))
        )))

(def: #export test
  Test
  (<| (_.covering /._)
      (_.with-cover [.Nat])
      ($_ _.and
          (do random.monad
            [sample random.nat]
            ($_ _.and
                (_.cover [/.-]
                         (and (/.= 0 (/.- sample sample))
                              (/.= sample (/.- 0 sample))))
                (_.cover [/./]
                         (and (/.= 1 (/./ sample sample))
                              (/.= sample (/./ 1 sample))))
                ))
          (do random.monad
            [left random.nat
             right random.nat]
            ($_ _.and
                (_.cover [/.>]
                         (bit\= (/.> left right)
                                (/.< right left)))
                (_.cover [/.<= /.>=]
                         (bit\= (/.<= left right)
                                (/.>= right left)))
                ))
          (do random.monad
            [left (random.filter (|>> (/.= 0) not)
                                 random.nat)
             right random.nat]
            ($_ _.and
                (_.cover [/.%]
                         (let [rem (/.% left right)
                               div (|> right (/.- rem) (/./ left))]
                           (/.= right
                                (|> div (/.* left) (/.+ rem)))))
                (_.cover [/./%]
                         (let [[div rem] (/./% left right)]
                           (and (/.= div (/./ left right))
                                (/.= rem (/.% left right)))))
                ))
          (do {! random.monad}
            [#let [random (\ ! map (|>> (/.% 1,000) inc) random.nat)]
             left random
             right random]
            ($_ _.and
                (_.cover [/.gcd]
                         (let [gcd (/.gcd left right)]
                           (and (/.= 0 (/.% gcd left))
                                (/.= 0 (/.% gcd right)))))
                (_.cover [/.lcm]
                         (let [lcm (/.lcm left right)]
                           (and (/.= 0 (/.% left lcm))
                                (/.= 0 (/.% right lcm)))))
                ))
          (do {! random.monad}
            [expected (\ ! map (/.% 1,000,000) random.nat)]
            (_.cover [/.frac]
                     (|> expected /.frac f.nat (/.= expected))))
          (do random.monad
            [sample random.nat]
            (_.cover [/.hash]
                     (i64\= (i64\hash sample)
                            (\ /.hash hash sample))))

          ..predicate
          ..signature
          )))