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|
(.module:
[library
[lux "*"
["_" test {"+" [Test]}]
[abstract
[monad {"+" [do]}]]
[math
["[0]" random]
[number
["n" nat]]]]]
[\\library
["[0]" / {"+" [CoMonad]}]]
[//
[functor {"+" [Injection Comparison]}]])
(def: (left_identity injection (^open "_//[0]"))
(All (_ f) (-> (Injection f) (CoMonad f) Test))
(do [! random.monad]
[sample random.nat
morphism (# ! each (function (_ diff)
(|>> _//out (n.+ diff)))
random.nat)
.let [start (injection sample)]]
(_.test "Left identity."
(n.= (morphism start)
(|> start _//disjoint (_//each morphism) _//out)))))
(def: (right_identity injection comparison (^open "_//[0]"))
(All (_ f) (-> (Injection f) (Comparison f) (CoMonad f) Test))
(do random.monad
[sample random.nat
.let [start (injection sample)
== (comparison n.=)]]
(_.test "Right identity."
(== start
(|> start _//disjoint (_//each _//out))))))
(def: (associativity injection comparison (^open "_//[0]"))
(All (_ f) (-> (Injection f) (Comparison f) (CoMonad f) Test))
(do [! random.monad]
[sample random.nat
increase (# ! each (function (_ diff)
(|>> _//out (n.+ diff)))
random.nat)
decrease (# ! each (function (_ diff)
(|>> _//out(n.- diff)))
random.nat)
.let [start (injection sample)
== (comparison n.=)]]
(_.test "Associativity."
(== (|> start _//disjoint (_//each (|>> _//disjoint (_//each increase) decrease)))
(|> start _//disjoint (_//each increase) _//disjoint (_//each decrease))))))
(def: .public (spec injection comparison subject)
(All (_ f) (-> (Injection f) (Comparison f) (CoMonad f) Test))
(<| (_.for [/.CoMonad])
($_ _.and
(..left_identity injection subject)
(..right_identity injection comparison subject)
(..associativity injection comparison subject)
)))
|
