Haskell programming tips

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 deterministicly 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.

Be concise

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/

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.

Decomposing a problem this way also has the advantage that you can debug more easily. If the last implementation of raise does not show the expected behaviour, you can inspect map (I hope it is correct :-) ) and the invoked instance of (+) separately.

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: The function count counts the number of elements which fulfill a certain property, i.e. the elements for which the predicate p is True.

I 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

.

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]]

where a might be a horrible complex expression it is not easy to see, that a really does not depend on i.

replicate m a

is certainly better here.

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 tupel presented in 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

What about the case r > length l? Sure, no reason to let head fail - in that case there is no tuple, thus we return an empty list. Again, this saves us one special case.

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

We have learnt above that length is evil! What about

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

? It is no longer necessary to compute the length of l again and again. The code is easier to read and it covers all special cases, including tuples (-1) [1,2,3]!

Eliminating the length 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 by tails. You 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)

Since (=<<) in the list monad is concatMap, we can also write this as follows. Where in the previous version the pattern y:ys filtered out the last empty suffix we have to do this manually now with init.

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

The list of all suffixes could be generated with iterate tail but this ends with a "Prelude.tail: empty list". tails generates the suffixes in the same order but aborts properly.

More generally, Base cases and identities

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 define comparing, since it is already in module Data.Ord. http://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.

sortKey :: (Ord b) => (a -> b) -> [a] -> [a]
sortKey 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

Bool is a regular type

Logic expressions are not restricted to guards and if statements. 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

.

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?

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 values s and c are used. In contrast to that

map toUpper (concat strings)

can't be clearer.

When using higher order functions you can switch more easily from List to other data structures.

Compare

map (1+) list

and

mapSet (1+) set

. If there were a standard instance for the Functor class you 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 zip already do a great job.

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 the do notation is explained in terms of functions.

Instead 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 Functor class method fmap and the Monad based function liftM are the same (as long as both are defined, as they should be).

Be aware that "more complicated" does not imply "worse". If your do-expression was longer than this, then mixing do-notation and fmap 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

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 otherwise guard, that will match for all remaining cases:

-- Slightly improved implementation:
fac :: Integer -> Integer
fac n | n == 0    = 1
      | otherwise = n * fac (n-1)

Another reason to prefer this one is its greater readability for humans and optimizability for compilers. Though it may not matter much in a simple case like this, when seeing an otherwise it's immediately clear that it's used whenever the previous guard fails, which isn't true if the "negation of the previous test" is spelled out. The same applies to the compiler: It probably will be able to optimize an otherwise (which is a synonym for True) away but cannot do that for most expressions.

This can be done with even less sugar using if,

-- 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)

Note that if has its own set of problems, for example in connection with the layout rule or that nested ifs are difficult to read. See Case how to avoid nested ifs.

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]

This may also be more efficient as product might be optimized by the library-writer... In GHC, when compiling with optimizations turned on, this version runs in O(1) stack-space, whereas the previous versions run in O(n) stack-space.

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 implemenation 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

or, if you expect your readers to be familiar with the either function:

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

Incidentally, compilers often also have problems with numerical patterns. For example, the pattern 0 in fact means fromInteger 0; thus it involves a computation, which is uncommon for function parameter patterns. To illustrate this, consider the following example:

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.

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 criticised 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.

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.

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

Don't write

length x == 0

to find out if the list x is empty. If you write it, you force Haskell to create all list nodes. It fails on an infinite list although the expression should be evaluated to False in this case. (Nevertheless the content of the list elements may not be evaluated.)

In contrast

x == []

is faster but it requires the list x to be of type [a] where a is a type of class Eq.

The best thing to do is

null x

Additionally, many uses of the length function are overspecifying the problem: one may only need to check that a list is at least a certain length, and not a specific length. Thus use of

length

could be replaced with an atLeast function that only checks to see that a list is greater than the required minimum length.

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

or non-recursive, but less efficient because both length and take must count

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

since this is inefficient for large lists x and fails for infinite ones. But this can be useful to extract a finite prefix from an infinite list. So, instead

zipWith const y x

works well.

It should be noted that length, take can be replaced by genericLength, genericTake et.al., which allow the usage of Peano numbers.

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

The function isLowerLimit checks if a number is a lower limit to a sequence.

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

It certainly fails if ys is infinite. Is this a problem?

Compare it with

isLowerLimit x = all (x<=)

This definition terminates for infinite lists, if x is not a lower limit. It aborts immediately if an element is found which is below x. Thus it is also faster for finite lists. Even more: It also works for empty lists.

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.

Choose the appropriate fold

See Stack overflow for advice on which fold is appropriate for your situation.

Choose types properly

Lists are not good for everything

Lists are not arrays

Lists are not arrays, so don't treat them as such. Frequent use of (!!) should alarm you. Accessing the nth list element involves traversing through the first n nodes of the list. This 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.

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 sort, nub, union, elem, delete, (\\) 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 Data.Map.Map a Int.

Lists are not finite maps

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

Reduce type class constraints

Eq type class

When using functions like delete, (\\), nub, and so on you should be aware that they need types of the Eq class. There are two problems: The routines might not work as expected if a processed list contains multiple equal elements and the element type of the list may not be comparable, like functions.

Example: The following function takes the input list xs and removes each element of xs once from xs. Clear 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))

since this works perfectly for function types a and for equal elements in xs.

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 values 0 and 1 are of interest, try the type Bool instead. If 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)

It allows all sensible operations like ==, <, succ and forbids all nonsensical ones like +, *. 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 a newtype carrying the type that is closest to what you need. E.g. if you want to associate objects with a unique identifier, you may want to choose the type Int. But you don't need arithmetic and you can make this type distinct from real Ints by defining

newtype Identifier = Identifier Int deriving Eq

Miscellaneous

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. You can easily benefit from lazy evaluation if you process data purely functionally and output it by a short IO interaction.

-- import Control.Monad (replicateM_)
replicateM_ 10 (putStr "foo")

is certainly worse than

putStr (concat $ replicate 10 "foo")

Similarly,

do
  h <- openFile "foo" WriteMode
  replicateM_ 10 (hPutStr h "bar")
  hClose h

can be shortened to

writeFile "foo" (concat $ replicate 10 "bar")

which also ensures proper closing of the handle h in case of failure.

A function which computes a random value with respect to a custom distribution (distInv is the inverse of the distribution function) can be defined via IO

randomDist :: (Random a, Num a) => (a -> a) -> IO a
randomDist distInv = liftM distInv (randomRIO (0,1))

but there is no need to do so. You don't need the state of the whole world just for remembering the state of a random number generator. What about

randomDist :: (RandomGen g, Random a, Num a) => (a -> a) -> State g a
randomDist distInv = liftM distInv (State (randomR (0,1)))

? You can get actual values by running the State as follows:

evalState (randomDist distInv) (mkStdGen an_arbitrary_seed)

Forget about quot and rem

They complicate handling of negative dividends. div and mod are almost always the better choice. If b > 0 then it always holds

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

The first equation is true also for quot and rem, but the two others are true only for mod, but not for rem. That is, mod a b always wraps a to an element from [0..(b-1)], whereas the sign of rem a b depends on the sign of a.

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 of quot and rem where div and mod were clearly superior.

Examples:

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

• Pad a list xs to a multiple of m number of elements: xs ++ 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?

Partial functions like fromJust and head

Avoid functions that fail for certain input values like fromJust and head. 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

Please note, that (==) also requires an Eq class instance for the type of i, which fromMaybe does not require because it employs pattern matching. See also #Reduce type class constraints.

If it is not possible to avoid fromJust this way, then use fromMaybe anyway and document with an error why you think that the value must be always Just in your situation.

fromMaybe (error "Function bla: The list does always contains the searched value")
          (lookup key dict)

The function head can be avoided by checking with types, that it is never empty. There is also a function which returns an existing first list element in terms of Maybe: maybeToList (See remark.)

Related Links

Common Mistakes and Incorrect Beliefs By Haskell Beginners

• Common Misunderstandings

Some Common (and not so common!) Hugs Errors

• Some common Hugs error messages