blob: bc1b643f237796c5e86cd31916928e7a4d993344 (
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
|
(.module:
[library
[lux #*
["_" test (#+ Test)]
[math
["." random]
[number
["n" nat]]]]]
[\\library
["." / (#+ do)]]
[//
[functor (#+ Injection Comparison)]])
(def: (left_identity injection comparison (^open "_//."))
(All [f] (-> (Injection f) (Comparison f) (/.Monad f) Test))
(do {! random.monad}
[sample random.nat
morphism (\ ! map (function (_ diff)
(|>> (n.+ diff) _//wrap))
random.nat)]
(_.test "Left identity."
((comparison n.=)
(|> (injection sample) (_//map morphism) _//join)
(morphism sample)))))
(def: (right_identity injection comparison (^open "_//."))
(All [f] (-> (Injection f) (Comparison f) (/.Monad f) Test))
(do random.monad
[sample random.nat]
(_.test "Right identity."
((comparison n.=)
(|> (injection sample) (_//map _//wrap) _//join)
(injection sample)))))
(def: (associativity injection comparison (^open "_//."))
(All [f] (-> (Injection f) (Comparison f) (/.Monad f) Test))
(do {! random.monad}
[sample random.nat
increase (\ ! map (function (_ diff)
(|>> (n.+ diff) _//wrap))
random.nat)
decrease (\ ! map (function (_ diff)
(|>> (n.- diff) _//wrap))
random.nat)]
(_.test "Associativity."
((comparison n.=)
(|> (injection sample) (_//map increase) _//join (_//map decrease) _//join)
(|> (injection sample) (_//map (|>> increase (_//map decrease) _//join)) _//join)))))
(def: #export (spec injection comparison monad)
(All [f] (-> (Injection f) (Comparison f) (/.Monad f) Test))
(<| (_.for [/.Monad])
($_ _.and
(..left_identity injection comparison monad)
(..right_identity injection comparison monad)
(..associativity injection comparison monad)
)))
|