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oisdk/free-quant.hs

Created March 19, 2018 15:42
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free-quant.hs
newtype Free c a = Free { runFree ∷ ∀ b. c b ⇒ (a → b) → b }
type (a ∷ k → Constraint) ⊨ (b ∷ k → Constraint) = (∀ x. a x ⇒ b x ∷ Constraint)
instance (Monoid ⊨ c) ⇒ Foldable (Free c) where
foldMap = flip runFree
ala ∷ (∀ x. c x ⇒ c (f x), ∀ x. Coercible x (f x)) ⇒ Free c a → (∀ x. x → f x) → Free c a
ala xs to = Free (\k → coerce (runFree xs (to #. k)))
reverse ∷ Free Monoid a → Free Monoid a
reverse xs = xs `ala` Dual
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