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(.module:
[lux #*
["_" test (#+ Test)]
data/text/format
["r" math/random]
[abstract
[equivalence (#+ Equivalence)]
[monad (#+ do)]]
[control
["." function]]]
{1
["." / (#+ 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 r.monad
[sample (:: @ map injection r.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 r.monad
[sample r.nat
increase (:: @ map n/+ r.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 r.monad
[sample (:: @ map injection r.nat)
increase (:: @ map n/+ r.nat)
decrease (:: @ map n/- r.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))
(_.context (%name (name-of /.Functor))
($_ _.and
(..identity injection comparison functor)
(..homomorphism injection comparison functor)
(..composition injection comparison functor)
)))
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