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cronokirby/nat.hs

Created August 8, 2020 20:14
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nat.hs
{-# LANGUAGE RankNTypes #-}
newtype Nat = Nat { unNat :: forall m. Monoid m => m -> m }
instance Num Nat where
Nat f + Nat g = Nat (\m -> f m <> g m)
Nat f * Nat g = Nat (\m -> f (g m))
abs = id
negate _ = error "negate @Nat"
signum (Nat f) = if f [()] == [] then 0 else 1
fromInteger 0 = Nat (const mempty)
fromInteger x = Nat (\m -> m <> unNat (fromInteger (x - 1)) m)
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