Difference between revisions of "Haskell programming tips"
m (English corrections) 
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==Preface== 
==Preface== 

−  This page shows several examples of how code can be improved. We try to derive general rules from them, though they 
+  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. 
Instead, you can now add "this is disputable" on [[/Discussion]] and change this page only when some sort of consensus is reached. 

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===Don't reinvent the wheel=== 
===Don't reinvent the wheel=== 

−  The standard libraries are full of useful 
+  The standard libraries are full of useful, welltuned functions. If you rewrite an existing library function, the reader of your code might spend a minute trying to figure out why you've done that. But if you use a standard function, the reader will either immediately understand what you've done, or can learn something new. 
−  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=== 
===Avoid explicit recursion=== 

−  Explicit recursion is not generally bad, but you should spend some time 
+  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 
Don't define 

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and the reader knows that the complete list is processed and that each output element depends only on the corresponding input element. 
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 
+  If you don't find appropriate functions in the standard library, extract a general function. 
−  +  This helps you and others understand the program. 

+  Thanks to [[higher order function]]s Haskell gives you '''very''' many opportunities to factor out parts of the code. 

+  If you find the function very general, put it in a separate module and reuse it. It may appear in the standard libraries later, or you may later find that it is already there in an even more general way. 

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

+  ''This is a special case of the general principle of [[separation of concernsseparating concerns]]. If you can write the loop over a data structure once and debug it, then there's no need to duplicate that code.'' 

−  Another example: 

⚫  
−  The function <hask>count</hask> counts the number of elements 

−  which fulfill a certain property, 

⚫  
I found the following code (but convoluted in a more specific function) in a Haskell program 
I found the following code (but convoluted in a more specific function) in a Haskell program 

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 otherwise = count p xs 
 otherwise = count p xs 

</haskell> 
</haskell> 

−  which you won't like 
+  which you won't like after you become aware of 
<haskell> 
<haskell> 

count p = length . filter p 
count p = length . filter p 

</haskell> 
</haskell> 

. 
. 

−  
===Only introduce identifiers you need=== 
===Only introduce identifiers you need=== 

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(http://www.cs.utexas.edu/users/EWD/transcriptions/EWD09xx/EWD993.html): 
(http://www.cs.utexas.edu/users/EWD/transcriptions/EWD09xx/EWD993.html): 

Introduce only identifiers you use. 
Introduce only identifiers you use. 

−  The compiler will check 
+  The compiler will check this for you if you pass an option like <code>Wall</code> to GHC. 
In an expression like 
In an expression like 

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===Remember the zero=== 
===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. 
+  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 <hask>tupel</hask> presented in ''DMVMitteilungen 2004/123, 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. 
<haskell> 
<haskell> 

tuples :: Int > [a] > [[a]] 
tuples :: Int > [a] > [[a]] 

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</haskell> 
</haskell> 

−  We 
+  We will learn below that <hask>length</hask> can be evil! What about 
<haskell> 
<haskell> 

tuples :: Int > [a] > [[a]] 
tuples :: Int > [a] > [[a]] 

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

−  ''Eliminating the <hask>length</hask> test can worsen performance dramatically in some cases, like <hask>tuples 24 [1..25]</hask>. We could also use <hask>null (drop (r1) l)</hask> instead of <hask>length l < r</hask>, which works for infinite lists. See also [[ 
+  ''Eliminating the <hask>length</hask> test can worsen performance dramatically in some cases, like <hask>tuples 24 [1..25]</hask>. We could also use <hask>null (drop (r1) l)</hask> instead of <hask>length l < r</hask>, which works for infinite lists. See also [[#Don't ask for the length of a list, if you don't need itbelow]].'' 
You can even save one direction of recursion 
You can even save one direction of recursion 

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which is both clearer and reusable. 
which is both clearer and reusable. 

Actually, starting with GHC6.6 you do not need to define <hask>comparing</hask>, since it is already in module <hask>Data.Ord</hask>. 
Actually, starting with GHC6.6 you do not need to define <hask>comparing</hask>, since it is already in module <hask>Data.Ord</hask>. 

−  http:// 
+  http://hackage.haskell.org/packages/archive/base/latest/doc/html/DataOrd.html 
(Just a remark for this special example: 
(Just a remark for this special example: 

−  We can avoid multiple evaluations of the conversions 
+  We can avoid multiple evaluations of the conversions 
+  with a function that is present in GHC.Exts of GHC 6.10: 

<haskell> 
<haskell> 

−  +  sortWith :: (Ord b) => (a > b) > [a] > [a] 

−  +  sortWith f x = map snd (sortBy (comparing fst) (zip (map f x) x)) 

</haskell> 
</haskell> 

) 
) 

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putStrLn $ shows lineNr $ showString ": " $ show line 
putStrLn $ shows lineNr $ showString ": " $ show line 

</haskell> 
</haskell> 

−  
===<hask>Bool</hask> is a regular type=== 
===<hask>Bool</hask> is a regular type=== 

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. 
. 

+  The definitions 

⚫  
+  hasSpace (a:as) 

+   isSpace a = True 

+   otherwise = hasSpace as 

⚫  
+  and 

+  <haskell> 

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

+  </haskell> 

⚫  
+  <haskell> 

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

+  </haskell> 

+  (I just wanted to show the logic transform. 

+  In the particular example you would write <hask>any isSpace</hask>, of course.) 

+  The same way 

+  <haskell> 

+  allPrintable (a:as) 

+   isSpace a = False 

+   otherwise = allPrintable as 

+  </haskell> 

+  and 

+  <haskell> 

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

+  </haskell> 

+  can be shortened to 

+  <haskell> 

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

+  </haskell> 

+  (but <hask>all (not . isSpace)</hask> is even better in this particular example.) 

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People who employ [[syntactic sugar]] extensively 
People who employ [[syntactic sugar]] extensively 

−  argue that their code 
+  argue that it makes their code more readable. 
The following sections show several examples 
The following sections show several examples 

where less syntactic sugar is more readable. 
where less syntactic sugar is more readable. 

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===List comprehension=== 
===List comprehension=== 

−  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 
Instead of 

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</haskell> 
</haskell> 

where it takes some time for the reader 
where it takes some time for the reader 

−  to 
+  to discover which value depends on what other value 
and it is not so clear how many times 
and it is not so clear how many times 

the interim values <hask>s</hask> and <hask>c</hask> are used. 
the interim values <hask>s</hask> and <hask>c</hask> are used. 

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−  When using higher order functions you can switch 
+  When using higher order functions you can switch more easily from <hask>List</hask> to other data structures. 
−  data structures different from <hask>List</hask>. 

Compare 
Compare 

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If you are not used to higher order functions for list processing 
If you are not used to higher order functions for list processing 

−  you may feel 
+  you may feel you need parallel list comprehension. 
This is unfortunately supported by GHC now, 
This is unfortunately supported by GHC now, 

but it is arguably superfluous since various flavours of <hask>zip</hask> already do a great job. 
but it is arguably superfluous since various flavours of <hask>zip</hask> already do a great job. 

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===<hask>do</hask> notation=== 
===<hask>do</hask> notation=== 

−  +  [[Do notation considered harmfuldo 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 <hask>do</hask> notation is explained in terms of functions. 
Nevertheless it's sometimes useful to remember that the <hask>do</hask> notation is explained in terms of functions. 

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</haskell> 
</haskell> 

. 
. 

−  By the way, 
+  By the way, the <hask>Functor</hask> class method <hask>fmap</hask> and the <hask>Monad</hask> based function <hask>liftM</hask> are the same (as long as both are defined, as they should be). 
''Be aware that "more complicated" does not imply "worse". If your doexpression was longer than this, then mixing donotation and <hask>fmap</hask> 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'' 
''Be aware that "more complicated" does not imply "worse". If your doexpression was longer than this, then mixing donotation and <hask>fmap</hask> 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=== 
===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 
Guards look like 

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which implements a factorial function. This example, like a lot of uses of guards, has a number of problems. 
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 
+  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 <code>Wall</code> option). To avoid this problem and potential bugs through non exhaustive patterns you should use an <hask>otherwise</hask> guard, that will match for all remaining cases: 
<haskell> 
<haskell> 

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else n * fac (n1) 
else n * fac (n1) 

</haskell> 
</haskell> 

−  Note that <hask>if</hask> has its own set of problems, for example in connection with the layout rule or that nested <hask>if</hask>s are difficult to read. See [ 
+  Note that <hask>if</hask> has its own set of [[Ifthenelseproblems]], for example in connection with the layout rule or that nested <hask>if</hask>s are difficult to read. See [[Case]] how to avoid nested <hask>if</hask>s. 
But in this special case, the same can be done even more easily with pattern matching: 
But in this special case, the same can be done even more easily with pattern matching: 

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This may also be more efficient as <hask>product</hask> might be optimized by the librarywriter... In GHC, when compiling with optimizations turned on, this version runs in O(1) stackspace, whereas the previous versions run in O(n) stackspace. 
This may also be more efficient as <hask>product</hask> might be optimized by the librarywriter... In GHC, when compiling with optimizations turned on, this version runs in O(1) stackspace, whereas the previous versions run in O(n) stackspace. 

−  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 StackOverflowtime), while the last 
+  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 StackOverflowtime), while the last implementation returns 1. 
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or compare the following example using the advanced [[pattern guard]]s 
or compare the following example using the advanced [[pattern guard]]s 

−  (http://www.haskell.org/ghc/docs/latest/html/users_guide/syntaxextns.html#PATTERNGUARDS) 

<haskell> 
<haskell> 

parseCmd ln 
parseCmd ln 

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take _ _ = [] 
take _ _ = [] 

</haskell> 
</haskell> 

−  However, they are often 
+  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. 
+  The <hask>n+k</hask> patterns are not in the [[Haskell 2010]] standard. 

==Efficiency and infinity== 
==Efficiency and infinity== 

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−  ===Choose the 
+  ===Choose the appropriate fold=== 
−  See [[Stack overflow]] for advice on which fold is appropriate for your situation. 
+  See "[[Stack overflow]]" or "[[Foldr Foldl Foldl']]" for advice on which fold is appropriate for your situation. 
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If you really need random access, as in the Fourier Transform, 
If you really need random access, as in the Fourier Transform, 

−  you should switch to 
+  you should switch to [[Arrays]]. 
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====Lists are not finite maps==== 
====Lists are not finite maps==== 

−  Similarly, lists are not finite maps, as mentioned in [[efficiency hints]]. 
+  Similarly, lists are not finite maps, as mentioned in [[Efficiency_hints#Data.Sequence_vs._lists  efficiency hints]]. 
−  
===Reduce type class constraints=== 
===Reduce type class constraints=== 

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+  ===Avoid redundancy in data types=== 

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

+  <haskell> 

+  data XML = 

+  Element Position Name [Attribute] [XML] 

+   Comment Position String 

+   Text Position String 

+  </haskell> 

+  
+  I suggest to factor out the common field <hask>Position</hask> 

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

+  <haskell> 

+  data XML = XML Position Part 

+  
+  data Part = 

+  Element Name [Attribute] [XML] 

+   Comment String 

+   Text String 

+  </haskell> 

==Miscellaneous== 
==Miscellaneous== 

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that is you don't have to specify an order of execution 
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. 
and you don't have to worry about what computations are actually necessary. 

−  You can easily benefit from lazy evaluation 

+  Useful techniques are described in [[Avoiding IO]]. 

−  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 

−  <haskell> 

−  putStr (concat $ replicate 10 "foo") 

−  </haskell> 

−  
−  Similarly, 

−  <haskell> 

−  do 

−  h < openFile "foo" WriteMode 

−  replicateM_ 10 (hPutStr h "bar") 

−  hClose h 

−  </haskell> 

⚫  
−  <haskell> 

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

−  </haskell> 

−  which also ensures proper closing of the handle <hask>h</hask> 

−  in case of failure. 

−  
−  A function which computes a random value 

−  with respect to a custom distribution 

−  (<hask>distInv</hask> is the inverse of the distribution function) 

−  can be defined via IO 

−  <haskell> 

−  randomDist :: (Random a, Num a) => (a > a) > IO a 

−  randomDist distInv = liftM distInv (randomRIO (0,1)) 

−  </haskell> 

−  but [[Humor/Erlkönigthere 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 

−  <haskell> 

−  randomDist :: (RandomGen g, Random a, Num a) => (a > a) > State g a 

−  randomDist distInv = liftM distInv (State (randomR (0,1))) 

−  </haskell> 

−  ? 

===Forget about quot and rem=== 
===Forget about quot and rem=== 

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

−  If <hask>b > 0</hask> then it always holds 

<haskell> 
<haskell> 

a == b * div a b + mod a b 
a == b * div a b + mod a b 

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</haskell> 
</haskell> 

The first equation is true also for <hask>quot</hask> and <hask>rem</hask>, 
The first equation is true also for <hask>quot</hask> and <hask>rem</hask>, 

−  but the two others are true only for <hask>mod</hask>, but not for <hask>rem</hask>. 
+  but the two others are true only for <hask>mod</hask>, but not for <hask>rem</hask>. That is, <hask>mod a b</hask> always wraps <hask>a</hask> to an element from <hask>[0..(b1)]</hask>, whereas the sign of <hask>rem a b</hask> depends on the sign of <hask>a</hask>. 
−  That is, <hask>mod a b</hask> always wraps <hask>a</hask> to an element from <hask>[0..(b1)]</hask>, 

−  whereas the sign of <hask>rem a b</hask> depends on the sign of <hask>a</hask>. 

−  This seems to be more an issue of experience rather than one of a superior reason. 

+  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 <hask>quot</hask> and <hask>rem</hask> where <hask>div</hask> and <hask>mod</hask> were clearly superior. 

−  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 <hask>quot</hask> and <hask>rem</hask> where <hask>div</hask> and <hask>mod</hask> were clearly superior. 

Examples: 
Examples: 

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* Pacman runs out of the screen and reappears at the opposite border: <hask>mod x screenWidth</hask> 
* Pacman runs out of the screen and reappears at the opposite border: <hask>mod x screenWidth</hask> 

+  See 

+  * Daan Leijen: [http://www.cs.uu.nl/~daan/download/papers/divmodnoteletter.pdf Division and Modulus for Computer Scientists] 

+  * HaskellCafe: [http://www.haskell.org/pipermail/haskellcafe/2007August/030394.html default for quotRem in terms of divMod?] 

===Partial functions like <hask>fromJust</hask> and <hask>head</hask>=== 
===Partial functions like <hask>fromJust</hask> and <hask>head</hask>=== 

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There is also a function which returns an existing first list element in terms of <hask>Maybe</hask>: 
There is also a function which returns an existing first list element in terms of <hask>Maybe</hask>: 

<hask>maybeToList</hask> 
<hask>maybeToList</hask> 

−  (See [http://www.haskell.org/pipermail/haskellcafe/2007March/023391.html remark]. 
+  (See [http://www.haskell.org/pipermail/haskellcafe/2007March/023391.html remark]. 
+  See also "[[Avoiding partial functions]]".) 

+  
+  == Related Links == 

+  
+  === Common Mistakes and Incorrect Beliefs By Haskell Beginners === 

+  
+  * [[Common Misunderstandings]] 

+  
+  === Some Common (and not so common!) Hugs Errors === 

+  
+  * [http://www.cs.kent.ac.uk/people/staff/sjt/craft2e/errors/allErrors.html Some common Hugs error messages] 

Latest revision as of 12:36, 4 May 2021
Contents
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.
Be concise
Don't reinvent the wheel
The standard libraries are full of useful, welltuned functions. If you rewrite an existing library function, the reader of your code might spend a minute trying to figure out why you've done that. But if you use a standard function, the reader will either immediately understand what you've done, or can learn something new.
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. Thanks to higher order functions Haskell gives you very many opportunities to factor out parts of the code. If you find the function very general, put it in a separate module and reuse it. It may appear in the standard libraries later, or you may later find that it is already there in an even more general way.
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.
This is a special case of the general principle of separating concerns. If you can write the loop over a data structure once and debug it, then there's no need to duplicate that code.
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 DMVMitteilungen 2004/123, 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 (r1) (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 (r1) 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 1tuples.
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 (r1) 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 (r1) t)
++ tuples r t
We will learn below that length
can be evil! What about
tuples :: Int > [a] > [[a]]
tuples 0 _ = [[]]
tuples _ [] = []
tuples r (x:xs) =
map (x :) (tuples (r1) 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 (r1) 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 (r1) 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 (r1) 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 reusable.
Actually, starting with GHC6.6 you do not need to define comparing
, since it is already in module Data.Ord
.
http://hackage.haskell.org/packages/archive/base/latest/doc/html/DataOrd.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 pointfreed, it probably deserves a name anyway. Lambdas are occasionally appropriate however, e.g. for control structures in monadic code (in this example, a controlstructure "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
.
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 write any isSpace
, of course.)
The 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
(but all (not . isSpace)
is even better in this particular example.)
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 doexpression was longer than this, then mixing donotation 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 (n1)
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 (n1)
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 ifthenelse can also be considered as sugar :)
fac :: Integer > Integer
fac n = if n == 0
then 1
else n * fac (n1)
Note that if
has its own set of problems, for example in connection with the layout rule or that nested if
s are difficult to read. See Case how to avoid nested if
s.
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 (n1)
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 librarywriter... In GHC, when compiling with optimizations turned on, this version runs in O(1) stackspace, whereas the previous versions run in O(n) stackspace.
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 StackOverflowtime), 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
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 socalled 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.
The n+k
patterns are not in the Haskell 2010 standard.
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
length
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 (n1) ys
or nonrecursive, but less efficient because both length
and take
must count
atLeast :: Int > [a] > Bool
atLeast n x = n == length (take n x)
or nonrecursive but fairly efficient
atLeast :: Int > [a] > Bool
atLeast n =
if n>0
then not . null . drop (n1)
else const True
or
atLeast :: Int > [a] > Bool
atLeast 0 = const True
atLeast n = not . null . drop (n1)
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 runtime. If you code
iterate (x:) []
then the lists will share their suffixes and thus need only linear space and runtime for creation.
Choose the appropriate fold
See "Stack overflow" or "Foldr Foldl Foldl'" 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 n
th 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 multisets,
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 Int
s by defining
newtype Identifier = Identifier Int deriving Eq
Avoid redundancy in data types
I often see data types with redundant fields, e.g.
data XML =
Element Position Name [Attribute] [XML]
 Comment Position String
 Text Position String
I suggest to factor out the common field Position
since this lets you handle the text position the same way for all XML parts.
data XML = XML Position Part
data Part =
Element Name [Attribute] [XML]
 Comment String
 Text String
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. Useful techniques are described in Avoiding IO.
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..(b1)]
, 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 ofm
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 reappears at the opposite border:
mod x screenWidth
See
 Daan Leijen: Division and Modulus for Computer Scientists
 HaskellCafe: 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.
See also "Avoiding partial functions".)