# Difference between revisions of "Blow your mind"

From HaskellWiki

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(added sieve of eratosthenes... may not be appropriate) |
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unfoldr sieve [2..] where |
unfoldr sieve [2..] where |
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sieve (p:x) = Just(p, [ n | n <- x, n `mod` p > 0 ]) |
sieve (p:x) = Just(p, [ n | n <- x, n `mod` p > 0 ]) |
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+ | |||

+ | -- or if you want to use the Sieve of Eratosthenes.. |
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+ | diff [] l = l |
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+ | diff l [] = l |
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+ | diff xl@(x:xs) yl@(y:ys) | x < y = x:diff xs yl |
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+ | | x > y = diff xl ys |
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+ | | otherwise = diff xs ys |
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+ | esieve [] = [] |
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+ | esieve (p:ps) = p:esieve (diff ps (iterate (+p) p)) |
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+ | eprimes = esieve [2..] |
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-- enumerating the rationals (see [1]) |
-- enumerating the rationals (see [1]) |

## Revision as of 00:48, 3 June 2006

Useful Idioms that will blow your mind (unless you already know them :)

This collection is supposed to be comprised of short, useful, cool, magical examples, which should incite the reader's curiosity and (hopefully) lead him to a deeper understanding of advanced Haskell concepts. At a later time I might add explanations to the more obscure solutions. I've also started providing several alternatives to give more insight into the interrelations of solutions.

More examples are always welcome, especially "obscure" monadic ones.

## List/String Operations

```
-- split at whitespace
-- "hello world" -> ["hello","world"]
words
takeWhile (not . null) . unfoldr (Just . (second $ drop 1) . break (==' '))
fix (\f l -> if null l then [] else let (s,e) = break (==' ') l in s:f (drop 1 e))
-- splitting in two (alternating)
-- "1234567" -> ("1357", "246")
foldr (\a (x,y) -> (a:y,x)) ([],[])
(map snd *** map snd) . partition (even . fst) . zip [0..]
transpose . unfoldr (\a -> if null a then Nothing else Just $ splitAt 2 a)
-- this one uses the solution to the next problem in a nice way :)
-- splitting into lists of length N
-- "1234567" -> ["12", "34", "56", "7"]
unfoldr (\a -> if null a then Nothing else Just $ splitAt 2 a)
takeWhile (not . null) . unfoldr (Just . splitAt 2)
-- sorting by a custom function
-- length -> ["abc", "ab", "a"] -> ["a", "ab", "abc"]
comparing f x y = compare (f x) (f y)
sortBy (comparing length)
map snd . sortBy (comparing fst) . map (length &&& id)
-- the so called "Schwartzian Transform" for computationally more expensive
-- functions.
-- comparing adjacent elements
rises xs = zipWith (<) xs (drop 1 xs)
-- lazy substring search
-- "ell" -> "hello" -> True
substr a b = any (a `isPrefixOf`) $ tails b
```

## Mathematical Series, etc

```
-- factorial
-- 6 -> 720
product [1..6]
foldl1 (*) [1..6]
(!!6) $ scanl (*) 1 [1..]
fix (\f n -> if n <= 0 then 1 else n * f (n-1))
-- powers of two series
iterate (*2) 1
unfoldr (\z -> Just (z,2*z)) 1
-- fibonacci series
unfoldr (\(f1,f2) -> Just (f1,(f2,f1+f2))) (0,1)
fibs = 0:1:zipWith (+) fibs (tail fibs)
fib = 0:scanl (+) 1 fib
-- pascal triangle
pascal = iterate (\row -> zipWith (+) ([0] ++ row) (row ++ [0])) [1]
-- prime numbers
-- example of a memoising caf (??)
primes = sieve [2..] where
sieve (p:x) = p : sieve [ n | n <- x, n `mod` p > 0 ]
unfoldr sieve [2..] where
sieve (p:x) = Just(p, [ n | n <- x, n `mod` p > 0 ])
-- or if you want to use the Sieve of Eratosthenes..
diff [] l = l
diff l [] = l
diff xl@(x:xs) yl@(y:ys) | x < y = x:diff xs yl
| x > y = diff xl ys
| otherwise = diff xs ys
esieve [] = []
esieve (p:ps) = p:esieve (diff ps (iterate (+p) p))
eprimes = esieve [2..]
-- enumerating the rationals (see [1])
rats :: [Rational]
rats = iterate next 1 where
next x = recip (fromInteger n+1-y) where (n,y) = properFraction x
```

[1] Gibbons, Lest, Bird - Enumerating the Rationals

## Monad Magic

```
-- all combinations of a list of lists.
-- these solutions are all pretty much equivalent in that they run
-- in the List Monad. the "sequence" solution has the advantage of
-- scaling to N sublists.
-- "12" -> "45" -> ["14", "15", "24", "25"]
sequence ["12", "45"]
[[x,y] | x <- "12", y <- "45"]
do { x <- "12"; y <- "45"; return [x,y] }
"12" >>= \a -> "45" >>= \b -> return [a,b]
-- all combinations of letters
(inits . repeat) ['a'..'z'] >>= sequence
-- apply a list of functions to an argument
-- even -> odd -> 4 -> [True,False]
map ($4) [even,odd]
sequence [even,odd] 4
-- apply a function to two other function the same argument
-- (lifting to the Function Monad (->))
-- even 4 && odd 4 -> False
liftM2 (&&) even odd 4
liftM2 (>>) putStrLn return "hello"
-- forward function concatenation
(*3) >>> (+1) $ 2
foldl1 (flip (.)) [(+1),(*2)] 500
-- perform functions in/on a monad, lifting
fmap (+2) (Just 2)
liftM2 (+) (Just 4) (Just 2)
-- [still to categorize]
(id >>= (+) >>= (+) >>= (+)) 3 -- (3+3)+(3+3) = 12
(join . liftM2) (*) (+3) 5 -- 64
mapAccumL (\acc n -> (acc+n,acc+n)) 0 [1..10] -- interesting for fac, fib, ...
do f <- [not, not]; d <- [True, False]; return (f d) -- [False,True,False,True]
do { Just x <- [Nothing, Just 5, Nothing, Just 6, Just 7, Nothing]; return x }
```

## Other

```
-- simulating lisp's cond
case () of () | 1 > 2 -> True
| 3 < 4 -> False
| otherwise -> True
-- match a constructor
-- this is better than applying all the arguments, because this way the
-- data type can be changed without touching the code (ideally).
case a of Just{} -> True
_ -> False
{-
TODO, IDEAS:
more fun with monad, monadPlus (liftM, ap, guard, when)
fun with arrows (second, first, &&&, ***)
liftM, ap
lazy search (searching as traversal of lazy structures)
innovative data types (i.e. having fun with Maybe sequencing)
LINKS:
bananas, envelopes, ... (generic traversal)
why functional fp matters (lazy search, ...)
-}
```