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|
(.using
[library
[lux (.except)
["_" test (.only Test)]
[abstract
[equivalence (.only Equivalence)]
[monad (.only do)]]
[control
["[0]" function]]
[math
["[0]" random]
[number
["n" nat]]]]]
[\\library
["[0]" / (.only Functor)]])
(type: .public (Injection f)
(All (_ a) (-> a (f a))))
(type: .public (Comparison f)
(All (_ a)
(-> (Equivalence a)
(Equivalence (f a)))))
(def: (identity injection comparison (open "@//[0]"))
(All (_ f) (-> (Injection f) (Comparison f) (Functor f) Test))
(do [! random.monad]
[sample (at ! each injection random.nat)]
(_.property "Identity."
((comparison n.=)
(@//each function.identity sample)
sample))))
(def: (homomorphism injection comparison (open "@//[0]"))
(All (_ f) (-> (Injection f) (Comparison f) (Functor f) Test))
(do [! random.monad]
[sample random.nat
increase (at ! each n.+ random.nat)]
(_.property "Homomorphism."
((comparison n.=)
(@//each increase (injection sample))
(injection (increase sample))))))
(def: (composition injection comparison (open "@//[0]"))
(All (_ f) (-> (Injection f) (Comparison f) (Functor f) Test))
(do [! random.monad]
[sample (at ! each injection random.nat)
increase (at ! each n.+ random.nat)
decrease (at ! each n.- random.nat)]
(_.property "Composition."
((comparison n.=)
(|> sample (@//each increase) (@//each decrease))
(|> sample (@//each (|>> increase decrease)))))))
(def: .public (spec injection comparison functor)
(All (_ f) (-> (Injection f) (Comparison f) (Functor f) Test))
(<| (_.for [/.Functor])
(all _.and
(..identity injection comparison functor)
(..homomorphism injection comparison functor)
(..composition injection comparison functor)
)))
|
