From: Ramakrishnan Muthukrishnan Date: Tue, 23 Dec 2014 13:02:46 +0000 (+0530) Subject: lecture 7: folds and monoids X-Git-Url: https://git.rkrishnan.org/%5B/%5D%20/file/URI:LIT:krugkidfnzsc4/%22file:/%3C?a=commitdiff_plain;h=ed2eed0f94eb01dbb95ad6d14317f41196c74a3f;p=yorgey.git lecture 7: folds and monoids --- diff --git a/misc/monoids.hs b/misc/monoids.hs new file mode 100644 index 0000000..848dab9 --- /dev/null +++ b/misc/monoids.hs @@ -0,0 +1,48 @@ +module Monoids where + +import Data.Monoid + +data Tree a = Empty + | Node (Tree a) a (Tree a) + deriving (Eq, Show) + +leaf :: a -> Tree a +leaf x = Node Empty x Empty + +treeSize :: Tree a -> Integer +treeSize Empty = 0 +treeSize (Node l _ r) = 1 + treeSize l + treeSize r + +treeSum :: Tree Integer -> Integer +treeSum Empty = 0 +treeSum (Node l x r) = x + treeSum l + treeSum r + +treeDepth :: Tree a -> Integer +treeDepth Empty = 0 +treeDepth (Node l _ r) = 1 + max (treeDepth l) (treeDepth r) + +flatten :: Tree a -> [a] +flatten Empty = [] +flatten (Node l x r) = flatten l ++ [x] ++ flatten r + +-- treeFold +-- 0. empty case value +-- 1. type of the return value. +-- 2. how to combine the recursive calls. + +treeFold :: b -> (b -> a -> b -> b) -> Tree a -> b +treeFold e _ Empty = e +treeFold e f (Node l x r) = f (treeFold e f l) x (treeFold e f r) + +treeSize' :: Tree a -> Integer +treeSize' = treeFold 0 (\l _ r -> 1 + l + r) + +treeSum' :: Tree Integer -> Integer +treeSum' = treeFold 0 (\l x r -> x + l + r) + +treeDepth' :: Tree a -> Integer +treeDepth' = treeFold 0 (\l _ r -> 1 + max l r) + +flatten' :: Tree a -> [a] +flatten' = treeFold [] (\l x r -> l ++ [x] ++ r) +