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(.module:
[lux #*]
[//
[functor (#+ Contravariant)]])
(signature: #export (Equivalence a)
{#.doc "Equivalence for a type's instances."}
(: (-> a a Bit)
=))
(def: #export (product left right)
(All [l r] (-> (Equivalence l) (Equivalence r) (Equivalence [l r])))
(structure
(def: (= [a b] [x y])
(and (:: left = a x)
(:: right = b y)))))
(def: #export (sum left right)
(All [l r] (-> (Equivalence l) (Equivalence r) (Equivalence (| l r))))
(structure
(def: (= reference sample)
(case [reference sample]
[(#.Left reference) (#.Left sample)]
(:: left = reference sample)
[(#.Right reference) (#.Right sample)]
(:: right = reference sample)
_
false))))
(def: #export (rec sub)
(All [a] (-> (-> (Equivalence a) (Equivalence a)) (Equivalence a)))
(structure
(def: (= left right)
(sub (rec sub) left right))))
(structure: #export contravariant
(Contravariant Equivalence)
(def: (map-1 f equivalence)
(structure
(def: (= reference sample)
(:: equivalence = (f reference) (f sample))))))
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