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(.module:
[lux #*
[control
[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: (= a|b x|y)
(case [a|b x|y]
[(0 a) (0 x)]
(:: left = a x)
[(1 b) (1 y)]
(:: right = b y)
_
#0))))
(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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