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(.using
[library
[lux (.except)
["_" test (.only Test)]
["[0]" type]
[abstract
[monad (.only do)]]
[control
["[0]" function]]
[math
["[0]" random (.only Random)]
[number
["n" nat]]]]]
[\\library
["[0]" / (.only Apply)]]
[//
[functor (.only Injection Comparison)]])
(def (identity injection comparison (open "/#[0]"))
(All (_ f) (-> (Injection f) (Comparison f) (Apply f) Test))
(do [! random.monad]
[sample (at ! each injection random.nat)]
(_.property "Identity."
((comparison n.=)
(/#on sample (injection function.identity))
sample))))
(def (homomorphism injection comparison (open "/#[0]"))
(All (_ f) (-> (Injection f) (Comparison f) (Apply f) Test))
(do [! random.monad]
[sample random.nat
increase (at ! each n.+ random.nat)]
(_.property "Homomorphism."
((comparison n.=)
(/#on (injection sample) (injection increase))
(injection (increase sample))))))
(def (interchange injection comparison (open "/#[0]"))
(All (_ f) (-> (Injection f) (Comparison f) (Apply f) Test))
(do [! random.monad]
[sample random.nat
increase (at ! each n.+ random.nat)]
(_.property "Interchange."
((comparison n.=)
(/#on (injection sample) (injection increase))
(/#on (injection increase) (injection (is (-> (-> Nat Nat) Nat)
(function (_ f) (f sample)))))))))
(def (composition injection comparison (open "/#[0]"))
(All (_ f) (-> (Injection f) (Comparison f) (Apply f) Test))
(type.let [:$/1: (-> Nat Nat)]
(do [! random.monad]
[sample random.nat
increase (is (Random :$/1:)
(at ! each n.+ random.nat))
decrease (is (Random :$/1:)
(at ! each n.- random.nat))]
(_.property "Composition."
((comparison n.=)
(|> (injection (is (-> :$/1: :$/1: :$/1:)
function.composite))
(/#on (injection increase))
(/#on (injection decrease))
(/#on (injection sample)))
(/#on (/#on (injection sample)
(injection increase))
(injection decrease)))))))
(def .public (spec injection comparison apply)
(All (_ f) (-> (Injection f) (Comparison f) (Apply f) Test))
(_.for [/.Apply]
(all _.and
(..identity injection comparison apply)
(..homomorphism injection comparison apply)
(..interchange injection comparison apply)
(..composition injection comparison apply)
)))
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