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|
(.module:
[lux #*
["_" test (#+ Test)]
[abstract
[equivalence (#+ Equivalence)]
[monad (#+ do)]]
[control
["." function]]
[math
["." random]
[number
["n" nat]]]]
[\\
["." / (#+ Functor)]])
(type: #export (Injection f)
(All [a] (-> a (f a))))
(type: #export (Comparison f)
(All [a]
(-> (Equivalence a)
(Equivalence (f a)))))
(def: (identity injection comparison (^open "@//."))
(All [f] (-> (Injection f) (Comparison f) (Functor f) Test))
(do {! random.monad}
[sample (\ ! map injection random.nat)]
(_.test "Identity."
((comparison n.=)
(@//map function.identity sample)
sample))))
(def: (homomorphism injection comparison (^open "@//."))
(All [f] (-> (Injection f) (Comparison f) (Functor f) Test))
(do {! random.monad}
[sample random.nat
increase (\ ! map n.+ random.nat)]
(_.test "Homomorphism."
((comparison n.=)
(@//map increase (injection sample))
(injection (increase sample))))))
(def: (composition injection comparison (^open "@//."))
(All [f] (-> (Injection f) (Comparison f) (Functor f) Test))
(do {! random.monad}
[sample (\ ! map injection random.nat)
increase (\ ! map n.+ random.nat)
decrease (\ ! map n.- random.nat)]
(_.test "Composition."
((comparison n.=)
(|> sample (@//map increase) (@//map decrease))
(|> sample (@//map (|>> increase decrease)))))))
(def: #export (spec injection comparison functor)
(All [f] (-> (Injection f) (Comparison f) (Functor f) Test))
(<| (_.for [/.Functor])
($_ _.and
(..identity injection comparison functor)
(..homomorphism injection comparison functor)
(..composition injection comparison functor)
)))
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