3. u
n
unfoldr
f
o
l
d
structure
unfold fold
Value
4. u
n
unfoldr
f
o
l
d
seed seed seed seed ...
element element element
[ a , b , c ...
5. u
n
unfoldr
f
o
l
d
seed new list
seed
element seed
> unfoldr :: (a -> Maybe (b,a)) -> a -> [b]
> unfoldr g a = case g a of
> Nothing -> []
> Just (b,a') -> b : unfoldr g a'
6. u
n
unfoldr
f
o
l
d
> uncons :: [a] -> Maybe (a, [a])
> uncons [] = Nothing
> uncons (x:xs) = Just (x,xs)
> id’ = unfoldr uncons
> app :: (a -> b) -> [a] -> Maybe (b, [a])
> app f [] = Nothing
> app f (x:xs) = Just (f x,xs)
> map’ f = unfoldr (app f)
7. L
o
o
loopless
p
l
e
s
s
[ abcde,
abcde bacde,
permutation bcade,
bcdae,
bcdea,
.....]
8. L
o
o
loopless
p
l
e
s
s
g [ pattern1, f0
structure
pattern2,
f1
pattern3,
f2
pattern4,
f3
.....]
9. L
o
o
loopless
p
l
e
s
s
O(n) O(1)
g [ pattern1, f0
structure
pattern2,
f1
pattern3,
f2
pattern4,
f3
.....]
10. L
o
o
loopless
p
l
e
s
s
> loopless :: (c -> a) ->
> (a -> Maybe (b,a)) ->
> c -> [b]
> loopless prolog step = unfoldr step . prolog
O(1) O(n)
11. L
o
o
Example
p
l
e
s
s
> id’ :: [a] -> [a]
> id’ = unfoldr uncons . id
> reverse’ :: [a] -> [a]
> reverse’ = unfoldr uncons . rv
> where rv = foldl (flip (:)) []
12. L
o
o
Example (concat)
p
l
e
s
s
> cat :: [[a]] -> [a]
> cat = loopless prolog uncons
> where prolog [] = []
> prolog (xs:xss) = xs ++ prolog xss
> cat :: [[a]] -> [a]
> cat = loopless (filter (not.null)) step
> where step [] = Nothing
> step ((x:[]):zs) = Just (x, zs)
> step ((x:xs):zs) = Just (x, xs : zs)
13. L
o
o
Example (RoseT)
p
l
e
s
s
Preorder Traversal
> type Forest a = [Rose a]
> data Rose a = Rose a (Forest a)
a a
[ , , ..... ]
subtree subtree
14. L
o
o
Example (RoseT)
p
l
e
s
s
Preorder Traversal
> type Forest a = [Rose a]
> data Rose a = Rose a (Forest a)
a a
[ , ..... ]
forest subtree
15. L
o
o
Example (RoseT)
p
l
e
s
s
Preorder Traversal
> type Forest a = [Rose a]
> data Rose a = Rose a (Forest a)
a a
++ [ , ..... ]
forest subtree
16. L
o
o
Example (RoseT)
p
l
e
s
s
Preorder Traversal
> type Forest a = [Rose a]
> data Rose a = Rose a (Forest a)
> pre :: Forest a -> [a]
> pre [] = []
> pre (Rose a ts : rs) = a : pre (ts ++ rs)
17. L
o
o
Example (RoseT)
p
l
e
s
s
Preorder Traversal
> type Forest a = [Rose a]
> data Rose a = Rose a (Forest a)
> preorder' = loopless id step
> where step :: Forest a ->
> Maybe (a, Forest a)
> step [] = Nothing
> step (Rose a ts : rs) =
> Just (a, ts ++ rs)
18. L
o
o
Example (RoseT)
p
l
e
s
s
Preorder Traversal
> type Forest a = [Rose a]
> data Rose a = Rose a (Forest a)
> (+:) xs xss = if null xs then xss else xs : xss
> preorder = loopless (a->[a]) step where
> step :: [Forest a] -> Maybe (a, [Forest a])
> step [] = Nothing
> step ((Rose a ts : rs) : fs) =
> Just (a, ts +: rs +: fs)
19. L
o
o
Example (BinT)
p
l
e
s
s
Inorder Traversal
> data Bin a = Nil
> | Bin a (Bin a) (Bin a)
a
l r
20. L
o
o
Example (BinT)
p
l
e
s
s
Inorder Traversal
a a
[ subtree , ... ]
l r
=
Inorder Preorder
Traversal Traversal
21. L
o
o
Example (BinT)
p
l
e
s
s
Inorder Traversal
+ 1 +
1 - = 2 -
2 3 3
22. L
o
o
Example (BinT)
p
l
e
s
s
Inorder Traversal
+ 1 +
1 - 2 -
2 3 3
N EL
S PI
23. L
o
o
Example (BinT)
p
l
e
s
s
Inorder Traversal
+ 1 - +
99 ! 7 - *
- *
50 13 4
1 ! - 4
99 50 7 13
N EL
S PI
24. L
o
o
Example (BinT)
p
l
e
s
s
Inorder Traversal
+ 1 - +
99 ! 7 - *
- *
50 13 4
1 ! - 4
99 50 7 13
N EL
S PI
25. L
o
o
Example (BinT)
p
l
e
s
s
Inorder Traversal
+ 1 - +
99 ! 7 - *
- *
50 13 4
1 ! - 4
99 50 7 13
N EL
S PI
26. L
o
o
Example (BinT)
p
l
e
s
s
Inorder Traversal
> data Bin a = Nil
> | Bin a (Bin a) (Bin a)
> spinel :: Bin a -> Forest a
> spinel Nil = []
> spinel (Bin a l r) =
> (spinel l) ++ [Rose a (spinel r)]
27. L
o
o
Example (BinT)
p
l
e
s
s
Inorder Traversal
> data Bin a = Nil
> | Bin a (Bin a) (Bin a)
> spinel :: Bin a -> Forest a
> spinel Nil = []
> spinel (Bin a l r) =
> (spinel l) ++ [Rose a (spinel r)]
> Rose a (spinel r) : (spinel l)
28. L
o
o
Example (BinT)
p
l
e
s
s
Inorder Traversal
> data Bin a = Nil
> | Bin a (Bin a) (Bin a)
> spinel :: Bin a -> Forest a
> spinel Nil = []
> spinel (Bin a l r) =
> Rose a (spinel r) : (spinel l)
> inorder = preorder . reverse . spines
29. 0
END
• unfold THANK YOU
• loopless
• Concat
• Preorder Traversal (RoseT)
• Inorder Traversal (BinT)
