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February 29, 2020 04:55
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hylomorphism.hs
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{-# LANGUAGE GADTs, TypeFamilies, DeriveFunctor, LambdaCase #-} | |
module Hylo | |
where | |
import Data.Functor.Foldable | |
import Data.List | |
data TreeF a r = Leaf | Node a r r deriving (Functor, Show) | |
{- | |
lf = Leaf | |
leaf a = Node a Leaf Leaf | |
node a l r = Node a l r | |
d1 = node 4 (leaf 7) (node 3 (leaf 7) lf) | |
-} | |
split :: Ord a => [a] -> TreeF a [a] | |
split [] = Leaf | |
split (a:as) = Node a l r | |
where (l, r) = partition (<a) as | |
{- | |
> split [4,5,3,6,2,8,1] | |
Node 4 [3,2,1] [5,6,8] <----- one step | |
it :: (Ord a, Num a) => TreeF a [a] | |
-} | |
join :: TreeF a [a] -> [a] | |
join Leaf = [] | |
join (Node a l r) = l ++ [a] ++ r | |
{- | |
> join $ Node 4 [3,2,1] [5,6,8] | |
[3,2,1,4,5,6,8] <----- one step | |
it :: Num a => [a] | |
-} | |
qsort :: Ord a => [a] -> [a] | |
qsort = hylo join split | |
{- | |
> qsort [4,5,3,6,2,8,1] | |
[1,2,3,4,5,6,8] | |
it :: (Ord a, Num a) => [a] | |
-} |
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