# Haskell programming tips

### From HaskellWiki

(more transforms of logic expressions) |
(Avoid redundancy in data types) |

## Revision as of 20:34, 7 December 2010

## Contents |

## 1 Preface

This page shows several examples of how code can be improved. We try to derive general rules from them, though they cannot be applied deterministically and are a matter of taste. We all know this, please don't add "this is disputable" to each item!

Instead, you can now add "this is disputable" on /Discussion and change this page only when some sort of consensus is reached.

## 2 Be concise

### 2.1 Don't reinvent the wheel

The standard libraries are full of useful functions, possibly too full. If you rewrite an existing function, the reader wonders what the difference to the standard function is. But if you use a standard function, the reader may learn something new and useful. If you have problems finding an appropriate list function, try this guide:

http://www.cs.chalmers.se/Cs/Grundutb/Kurser/d1pt/d1pta/ListDoc/

### 2.2 Avoid explicit recursion

Explicit recursion is not generally bad, but you should spend some time trying to find a more declarative implementation using higher order functions.

Don't define

raise :: Num a => a -> [a] -> [a] raise _ [] = [] raise x (y:ys) = x+y : raise x ys

because it is hard for the reader to find out how much of the list is processed and on which values the elements of the output list depend. Just write

raise x ys = map (x+) ys

or even

raise x = map (x+)

and the reader knows that the complete list is processed and that each output element depends only on the corresponding input element.

If you don't find appropriate functions in the standard library, extract a general function. This helps you and others understand the program. Haskell is **very** good at factoring out parts of the code.
If you find it very general, put it in a separate module and re-use it. It may appear in the standard libraries later, or you may later find that it is already there.

*Could this be stated more generally? It seems to me this is a special case of the general principle of separating concerns: iteration over a collection vs operating on elements of a collection should apply. If you can write the loop over a data structure (list, tree, whatever) once and debug it, then you don't need to duplicate that code over and over (at least in haskell), so your code can follow the principle of Wiki:OnceAndOnlyOnce ; Wiki:OnceAndOnlyOnce is a lot harder in languages that don't provide a certain level of functional programming support (i.e. Java requires copy and paste programming, the delegate C# syntax is clumsy but workable - using it is almost Wiki:GoldPlating).*

Another example:

which fulfill a certain property,

i.e. the elements for which the predicateI found the following code (but convoluted in a more specific function) in a Haskell program

count :: (a -> Bool) -> [a] -> Int count _ [] = 0 count p (x:xs) | p x = 1 + count p xs | otherwise = count p xs

which you won't like after you become aware of

count p = length . filter p

.

### 2.3 Only introduce identifiers you need

Here is some advice that is useful for every language, including scientific prose
(http://www.cs.utexas.edu/users/EWD/transcriptions/EWD09xx/EWD993.html):
Introduce only identifiers you use.
The compiler will check this for you if you pass an option like `-Wall`

to GHC.

In an expression like

[a | i <- [1..m]]

replicate m a

is certainly better here.

### 2.4 Remember the zero

Don't forget that zero is a natural number. Recursive definitions become more complicated if the recursion anchor is not chosen properly. For example the function*DMV-Mitteilungen 2004/12-3, Jürgen Bokowski: Haskell, ein gutes Werkzeug der Diskreten Mathematik*(Haskell, a good tool for discrete mathematics). This is also a good example of how to avoid guards.

tuples :: Int -> [a] -> [[a]] tuples r l | r == 1 = [[el] | el <- l] | length l == r = [l] | otherwise = (map ([head l] ++) (tuples (r-1) (tail l))) ++ tuples r (tail l)

Do you have an idea what it does?

Let's strip the guards and forget about list comprehension.

tuples :: Int -> [a] -> [[a]] tuples 1 l = map (:[]) l tuples r l = if r == length l then [l] else let t = tail l in map (head l :) (tuples (r-1) t) ++ tuples r t

What about tuples with zero elements? We can add the pattern

tuples 0 _ = [[]]

but then we can also omit the pattern for 1-tuples.

tuples :: Int -> [a] -> [[a]] tuples 0 _ = [[]] tuples r l = if r == length l then [l] else let t = tail l in map (head l :) (tuples (r-1) t) ++ tuples r t

tuples :: Int -> [a] -> [[a]] tuples 0 _ = [[]] tuples r l = if r > length l then [] else let t = tail l in map (head l :) (tuples (r-1) t) ++ tuples r t

tuples :: Int -> [a] -> [[a]] tuples 0 _ = [[]] tuples _ [] = [] tuples r (x:xs) = map (x :) (tuples (r-1) xs) ++ tuples r xs

*Eliminating thelength test can worsen performance dramatically in some cases, like tuples 24 [1..25]. We could also use null (drop (r-1) l) instead of length l < r, which works for infinite lists. See also below.*

You can even save one direction of recursion

by explicit computation of the list of all suffixes provided byYou can do this with do notation

tuples :: Int -> [a] -> [[a]] tuples 0 _ = [[]] tuples r xs = do y:ys <- tails xs map (y:) (tuples (r-1) ys)

tuples :: Int -> [a] -> [[a]] tuples 0 _ = [[]] tuples r xs = concatMap (\(y:ys) -> map (y:) (tuples (r-1) ys)) (init (tails xs))

but this ends with a "Prelude.tail: empty list".

*More generally, Base cases and identities*

### 2.5 Don't overuse lambdas

Like explicit recursion, using explicit lambdas isn't a universally bad idea, but a better solution often exists. For example, Haskell is quite good at currying. Don't write

zipWith (\x y -> f x y) map (\x -> x + 42)

instead, write

zipWith f map (+42)

also, instead of writing

-- sort a list of strings case insensitively sortBy (\x y -> compare (map toLower x) (map toLower y))

write

comparing p x y = compare (p x) (p y) sortBy (comparing (map toLower))

which is both clearer and re-usable.

Actually, starting with GHC-6.6 you do not need to definehttp://www.haskell.org/ghc/dist/current/docs/libraries/base/Data-Ord.html

(Just a remark for this special example: We can avoid multiple evaluations of the conversions with a function that is present in GHC.Exts of GHC 6.10:

sortWith :: (Ord b) => (a -> b) -> [a] -> [a] sortWith f x = map snd (sortBy (comparing fst) (zip (map f x) x))

)

As a rule of thumb, once your expression becomes too long to easily be point-freed, it probably deserves a name anyway. Lambdas are occasionally appropriate however, e.g. for control structures in monadic code (in this example, a control-structure "foreach2" which most languages don't even support.):

foreach2 xs ys f = zipWithM_ f xs ys linify :: [String] -> IO () linify lines = foreach2 [1..] lines $ \lineNr line -> do unless (null line) $ putStrLn $ shows lineNr $ showString ": " $ show line

### 2.6 Bool is a regular type

Logic expressions are not restricted to guards and Avoid verbosity like in

isEven n | mod n 2 == 0 = True | otherwise = False

since it is the same as

isEven n = mod n 2 == 0

.

The definitions

hasSpace (a:as) | isSpace a = True | otherwise = hasSpace as

and

hasSpace (a:as) = if isSpace a then True else hasSpace as

can be shortened to

hasSpace (a:as) = isSpace a || hasSpace as

(I just wanted to show the logic transform.

In the particular example you would writeThe same way

allPrintable (a:as) | isSpace a = False | otherwise = allPrintable as

and

allPrintable (a:as) = if isSpace a then False else allPrintable as

can be shortened to

allPrintable (a:as) = not (isSpace a) && allPrintable as

## 3 Use syntactic sugar wisely

People who employ syntactic sugar extensively argue that it makes their code more readable. The following sections show several examples where less syntactic sugar is more readable.

It is argued that a special notation is often more intuitive than a purely functional expression. But the term "intuitive notation" is always a matter of habit. You can also develop an intuition for analytic expressions that don't match your habits at the first glance. So why not making a habit of less sugar sometimes?

### 3.1 List comprehension

List comprehension lets you remain in imperative thinking, that is it lets you think in variables rather than transformations. Open your mind, discover the flavour of the pointfree style!

Instead of

[toUpper c | c <- s]

write

`map toUpper s`

.

Consider

[toUpper c | s <- strings, c <- s]

where it takes some time for the reader to discover which value depends on what other value and it is not so clear how many times

the interim valuesIn contrast to that

map toUpper (concat strings)

can't be clearer.

Compare

map (1+) list

and

mapSet (1+) set

.

If there were a standard instance for theyou could use the code

fmap (1+) pool

for both choices.

If you are not used to higher order functions for list processing you may feel you need parallel list comprehension. This is unfortunately supported by GHC now,

but it is arguably superfluous since various flavours of

### 3.2 do notation

do notation is useful to express the imperative nature (e.g. a hidden state or an order of execution) of a piece of code.

Nevertheless it's sometimes useful to remember that theInstead of

do text <- readFile "foo" writeFile "bar" text

one can write

readFile "foo" >>= writeFile "bar"

.

The code

do text <- readFile "foo" return text

can be simplified to

readFile "foo"

by a law that each Monad must fulfill.

You certainly also agree that

do text <- readFile "foobar" return (lines text)

is more complicated than

liftM lines (readFile "foobar")

.

By the way, the*Be aware that "more complicated" does not imply "worse". If your do-expression was longer than this, then mixing do-notation andfmap might be precisely the wrong thing to do, because it adds one more thing to think about. Be natural. Only change it if you gain something by changing it. -- AndrewBromage*

### 3.3 Guards

*Disclaimer: This section is NOT advising you to avoid guards. It is advising you to prefer pattern matching to guards when both are appropriate. -- AndrewBromage*

Guards look like

-- Bad implementation: fac :: Integer -> Integer fac n | n == 0 = 1 | n /= 0 = n * fac (n-1)

which implements a factorial function. This example, like a lot of uses of guards, has a number of problems.

The first problem is that it's nearly impossible for the compiler to check whether guards like this are exhaustive, as the guard conditions may be arbitrarily complex (GHC will warn you if you use the`-Wall`

option). To avoid this problem and potential bugs through non exhaustive patterns you should use an -- Slightly improved implementation: fac :: Integer -> Integer fac n | n == 0 = 1 | otherwise = n * fac (n-1)

-- Less sugar (though the verbosity of if-then-else can also be considered as sugar :-) fac :: Integer -> Integer fac n = if n == 0 then 1 else n * fac (n-1)

But in this special case, the same can be done even more easily with pattern matching:

-- Good implementation: fac :: Integer -> Integer fac 0 = 1 fac n = n * fac (n-1)

Actually, in this case there is an even more easier to read version, which (see above) doesn't use Explicit Recursion:

-- Excellent implementation: fac :: Integer -> Integer fac n = product [1..n]

Note however, that there is a difference between this version and the previous ones: When given a negative number, the previous versions do not terminate (until StackOverflow-time), while the last implementation returns 1.

Guards don't always make code clearer.
Compare

foo xs | not (null xs) = bar (head xs)

and

foo (x:_) = bar x

or compare the following example using the advanced pattern guards

parseCmd ln | Left err <- parse cmd "Commands" ln = BadCmd $ unwords $ lines $ show err | Right x <- parse cmd "Commands" ln = x

with this one with no pattern guards:

parseCmd ln = case parse cmd "Commands" ln of Left err -> BadCmd $ unwords $ lines $ show err Right x -> x

parseCmd :: -- add an explicit type signature, as this is now a pattern binding parseCmd = either (BadCmd . unwords . lines . show) id . parse cmd "Commands"

data Foo = Foo deriving (Eq, Show) instance Num Foo where fromInteger = error "forget it" f :: Foo -> Bool f 42 = True f _ = False

*Main> f 42 *** Exception: forget it

Only use guards when you need to. In general, you should stick to pattern matching whenever possible.

### 3.4 n+k patterns

In order to allow pattern matching against numerical types, Haskell 98 provides so-called n+k patterns, as in

take :: Int -> [a] -> [a] take (n+1) (x:xs) = x: take n xs take _ _ = []

However, they are often criticized for hiding computational complexity and producing ambiguities, see /Discussion for details. They are subsumed by the more general Views proposal, which has unfortunately never been implemented despite being around for quite some time now.

## 4 Efficiency and infinity

A rule of thumb is: If a function makes sense for an infinite data structure but the implementation at hand fails for an infinite amount of data, then the implementation is probably also inefficient for finite data.

### 4.1 Don't ask for the length of a list when you don't need it

Don't write

length x == 0

In contrast

x == []

The best thing to do is

`null x`

*at least*a certain length, and not a specific length. Thus use of

`length`

atLeast :: Int -> [a] -> Bool atLeast 0 _ = True atLeast _ [] = False atLeast n (_:ys) = atLeast (n-1) ys

atLeast :: Int -> [a] -> Bool atLeast n x = n == length (take n x)

or non-recursive but fairly efficient

atLeast :: Int -> [a] -> Bool atLeast n = if n>0 then not . null . drop (n-1) else const True

or

atLeast :: Int -> [a] -> Bool atLeast 0 = const True atLeast n = not . null . drop (n-1)

The same problem arises if you want to shorten a list to the length of another one by

take (length x) y

So, instead

zipWith const y x

works well.

It should be noted thatwhich allow the usage of Peano numbers.

### 4.2 Don't ask for the minimum when you don't need it

The functionisLowerLimit :: Ord a => a -> [a] -> Bool isLowerLimit x ys = x <= minimum ys

Compare it with

isLowerLimit x = all (x<=)

### 4.3 Use sharing

If you want a list of lists with increasing length and constant content, don't write

map (flip replicate x) [0..]

because this needs quadratic space and run-time. If you code

iterate (x:) []

then the lists will share their suffixes and thus need only linear space and run-time for creation.

### 4.4 Choose the appropriate fold

See "Stack overflow" or "Foldr Foldl Foldl'" for advice on which fold is appropriate for your situation.

## 5 Choose types properly

### 5.1 Lists are not good for everything

#### 5.1.1 Lists are not arrays

Lists are not arrays, so don't treat them as such.

Frequent use ofThis is very inefficient.

If you access the elements progressively, as in

[x !! i - i | i <- [0..n]]

you should try to get rid of indexing, as in

zipWith (-) x [0..n]

.

If you really need random access, as in the Fourier Transform, you should switch to Arrays.

#### 5.1.2 Lists are not sets

If you manage data sets where each object can occur only once and the order is irrelevant, if you use list functions like

frequently, you should think about switching to sets. If you need multi-sets, i.e. data sets with irrelevant order but multiple occurrences of objects,

you can use a

#### 5.1.3 Lists are not finite maps

Similarly, lists are not finite maps, as mentioned in efficiency hints.

### 5.2 Reduce type class constraints

#### 5.2.1 Eq type class

When using functions likeExample:

The following function takes the input listClear what it does? No? The code is probably more understandable

removeEach :: (Eq a) => [a] -> [[a]] removeEach xs = map (flip List.delete xs) xs

but it should be replaced by

removeEach :: [a] -> [[a]] removeEach xs = zipWith (++) (List.inits xs) (tail (List.tails xs))

### 5.3 Don't use Int when you don't consider integers

Before using integers for each and everything (C style) think of more specialised types.

If only the valuesIf there are more but predefined choices and numeric operations aren't needed try an enumeration.

Instead of

type Weekday = Int

write

data Weekday = Monday | Tuesday | Wednesday | Thursday | Friday | Saturday | Sunday deriving (Eq, Ord, Enum)

You cannot accidentally mix up weekdays with numbers and the signature of a function with weekday parameter clearly states what kind of data is expected.

If an enumeration is not appropriate

you can define aE.g. if you want to associate objects with a unique identifier,

you may want to choose the typenewtype Identifier = Identifier Int deriving Eq

### 5.4 Avoid redundancy in data types

I often see data types with redundant fields, e.g.

data XML = Element Position [Attribute] [XML] | Comment Position String | Text Position String

since this lets you handle the text position the same way for all XML parts.

data XML = XML Position Part data Part = Element [Attribute] [XML] | Comment String | Text String

## 6 Miscellaneous

### 6.1 Separate IO and data processing

It's not good to use the IO Monad everywhere, much of the data processing can be done without IO interaction. You should separate data processing and IO because pure data processing can be done purely functionally, that is you don't have to specify an order of execution and you don't have to worry about what computations are actually necessary. Useful techniques are described in Avoiding IO.

### 6.2 Forget about quot and rem

They complicate handling of negative dividends.

a == b * div a b + mod a b mod a b < b mod a b >= 0

This seems to be more an issue of experience rather than one of a superior reason. You might argue, that the sign of the dividend is more important for you, than that of the divisor. However, I have never seen such an application,

but many uses ofExamples:

- Conversion from a continuously counted tone pitch to the pitch class, like C, D, E etc.: mod p 12

- Pad a list to a multiple ofxsnumber of elements:mxs ++ replicate (mod (- length xs) m) pad

- Conversion from a day counter to a week day: mod n 7

- Pacman runs out of the screen and re-appears at the opposite border: mod x screenWidth

See

- Daan Leijen: Division and Modulus for Computer Scientists
- Haskell-Cafe: default for quotRem in terms of divMod?

### 6.3 Partial functions like fromJust and head

Avoid functions that fail for certain input values like They raise errors that can only be detected at runtime. Think about how they can be avoided by different program organization or by choosing more specific types.

Instead of

if i == Nothing then deflt else fromJust i

write

fromMaybe deflt i

See also #Reduce type class constraints.

If it is not possible to avoidfromMaybe (error "Function bla: The list does always contains the searched value") (lookup key dict)

(See remark.)