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(.module:
[library
[lux "*"
["_" test {"+" [Test]}]
[data
["[0]" identity {"+" [Identity]}]
[collection
["[0]" list ("[1]\[0]" functor mix)]]]
[math
["[0]" random]
[number
["n" nat]]]]]
[\\library
["[0]" / {"+" [Monad do]}]])
(def: .public test
Test
(do random.monad
[mono random.nat
poly (random.list 10 random.nat)]
(<| (_.covering /._)
($_ _.and
(_.cover [/.do]
(n.= (++ mono)
(: (Identity Nat)
(/.do identity.monad
[sample (in mono)]
(in (++ sample))))))
(_.cover [/.then]
(n.= (++ mono)
(: (Identity Nat)
(/.then identity.monad
(|>> ++ (\ identity.monad in))
(\ identity.monad in mono)))))
(_.cover [/.all]
(\ (list.equivalence n.equivalence) =
(list\each ++ poly)
(|> poly
(list\each (|>> ++ (\ identity.monad in)))
(: (List (Identity Nat)))
(/.all identity.monad)
(: (Identity (List Nat))))))
(_.cover [/.each]
(\ (list.equivalence n.equivalence) =
(list\each ++ poly)
(|> poly
(/.each identity.monad (|>> ++ (\ identity.monad in)))
(: (Identity (List Nat))))))
(_.cover [/.only]
(\ (list.equivalence n.equivalence) =
(list.only n.even? poly)
(|> poly
(/.only identity.monad (|>> n.even? (\ identity.monad in)))
(: (Identity (List Nat))))))
(_.cover [/.mix]
(n.= (list\mix n.+ 0 poly)
(|> poly
(/.mix identity.monad
(function (_ part whole)
(\ identity.monad in
(n.+ part whole)))
0)
(: (Identity Nat)))))
))))
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