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{-# LANGUAGE ImpredicativeTypes, RankNTypes, ScopedTypeVariables, TypeApplications #-}
module Church1 where
-- Church numerals w/o extra type constructors
type CNat = forall a. (a->a) -> a -> a
n0 :: CNat
n0 = \f z -> z
n1 :: CNat
n1 = \f z -> f z
nsucc :: CNat -> CNat
nsucc n = \f z -> f (n f z)
add, mul :: CNat -> CNat -> CNat
add m n = \f -> \a -> m f (n f a)
mul m n = \f -> \a -> m (n f) a
-- already works with GHC 6.4
exp0 :: CNat -> CNat -> CNat
exp0 m n = n m
exp1 :: CNat -> CNat -> CNat
exp1 m n = n (mul m) n1
foldNat :: CNat -> (a -> a) -> a -> a
foldNat n = n
idC :: CNat -> CNat
idC x = foldNat @CNat x (\y -> nsucc y) n0
inc :: CNat -> CNat
inc x = foldNat x nsucc n1
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