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I've got anamorphism defined as follows:

-- Fixed point of a Functor 
newtype Fix f = In (f (Fix f))

deriving instance (Eq (f (Fix f))) => Eq (Fix f)
deriving instance (Ord (f (Fix f))) => Ord (Fix f)
deriving instance (Show (f (Fix f))) => Show (Fix f)

out :: Fix f -> f (Fix f)
out (In f) = f

-- Anamorphism
type Coalgebra f a = a -> f a

ana :: (Functor f) => Coalgebra f a -> a -> Fix f
ana f = In . fmap (ana f) . f

I currently have to write a Coalgebra like this:

appendListCoAlg :: (ListF' a, ListF' a) -> ListF a (ListF' a, ListF' a)
appendListCoAlg (In (ConsF a as), listb) = ConsF a (as, listb)
appendListCoAlg (In NilF, In (ConsF b bs)) = ConsF b (In NilF, bs)
appendListCoAlg (In NilF, In NilF) = NilF

Here, an anamorphism has to be constructed from the "base case" (NilF).

I'm interested in whether it is possible to write ana such that I can do something list this:

appendListCoAlg :: (ListF' a, ListF' a) -> ?
appendListCoAlg (In (ConsF a as), listb) = ConsF a (as, listb)
appendListCoAlg (In NilF, **bs**) = **bs**
appendListCoAlg (In NilF, In NilF) = NilF

where I can return a value of type I'm constructing "early".

Noughtmare
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cocorudeboy
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1 Answers1

2

ana does not let you do that. You can use apo instead (although it's still not as neat as it could be; the Either should really be outside).

apo :: Corecursive t => (a -> Base t (Either t a)) -> a -> t

appendListCoAlg :: [a] -> [a] -> ListF a (Either [a] [a])
appendListCoAlg listb (a : as) = ConsF a (Right as)  -- Right: continue unfolding
appendListCoAlg listb [] = Left <$> project listb    -- Left: stop unfolding

append :: [a] -> [a] -> [a]
append lista listb = apo (appendListCoAlg listb) lista
Li-yao Xia
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