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nat2.hs
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nat2.hs
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{-# language FlexibleInstances #-}
{-# language MultiParamTypeClasses #-}
{-# language FunctionalDependencies #-}
{-# LANGUAGE DeriveFunctor #-}
import Data.Fix
data Nat2 a = ZeroF | SuccF a
deriving Functor
toIntF :: Nat2 Int -> Int
toIntF ZeroF = 0
toIntF (SuccF n) = n + 1
toInt :: Fix Nat2 -> Int
toInt = cata $ toIntF
toNat2 :: Int -> Fix Nat2
toNat2 = ana $ \x -> case x of
0 -> ZeroF
n -> SuccF (pred n)
fiboF :: (Nat2 (Int,Int)) -> (Int,Int)
fiboF ZeroF = (1,0)
fiboF (SuccF (n,m)) = (n+m,n)
fibo :: Fix Nat2 -> Int
fibo = fst . (cata $ fiboF)
coalg :: Int -> Nat2 Int
coalg 0 = ZeroF
coalg n = SuccF (pred n)
main = do
let f0 = fibo (Fix ZeroF)
let f1 = fibo (Fix (SuccF (Fix ZeroF)))
let f2 = fibo (Fix (SuccF (Fix (SuccF (Fix ZeroF)))))
let f3 = fibo (Fix (SuccF (Fix (SuccF (Fix (SuccF (Fix ZeroF)))))))
let f4 = fibo (Fix (SuccF (Fix (SuccF (Fix (SuccF (Fix (SuccF (Fix ZeroF)))))))))
let f5 = fibo (Fix (SuccF (Fix (SuccF (Fix (SuccF (Fix (SuccF (Fix (SuccF (Fix ZeroF)))))))))))
print f0
print f1
print f2
print f3
print f4
print f5