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(.module: lux)
(signature: #export (Equivalence a)
{#.doc "Equivalence for a type's instances."}
(: (-> a a Bool)
=))
(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)
_
false))))
(def: #export (rec sub)
(All [a] (-> (-> (Equivalence a) (Equivalence a)) (Equivalence a)))
(structure (def: (= left right)
(sub (rec sub) left right))))
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