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{-# LANGUAGE RankNTypes #-}
module Church2 where
-- Church numerals w/o extra type constructors: Should fail
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
-- should fail!
exp2 :: CNat -> CNat -> CNat
exp2 m n = n (mul m) n1
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