# Difference between revisions of "Haskell programming tips"

(→Avoid explicit recursion: no factoring functions out is actually not done by GHC, but must be done by the programmer, but Haskell is expressive enough to allow it in awfully many cases) |
ConradParker (talk | contribs) m (→Forget about quot and rem: Formatting) |
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===Forget about quot and rem=== |
===Forget about quot and rem=== |
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− | 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. |
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− | If <hask>b > 0</hask> then it always holds |
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<haskell> |
<haskell> |
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a == b * div a b + mod a b |
a == b * div a b + mod a b |
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Line 763: | Line 763: | ||

</haskell> |
</haskell> |
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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>, |
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− | 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..(b-1)]</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..(b-1)]</hask>, |
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− | whereas the sign of <hask>rem a b</hask> depends on the sign of <hask>a</hask>. |
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− | This seems to be more an issue of experience rather than one of a superior reason. |
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+ | 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. |
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− | You might argue, that the sign of the dividend is more important for you, than that of the divisor. |
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− | However, I have never seen such an application, |
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− | but many uses of <hask>quot</hask> and <hask>rem</hask> where <hask>div</hask> and <hask>mod</hask> were clearly superior. |
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Examples: |
Examples: |
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Line 783: | Line 780: | ||

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

* Haskell-Cafe: [http://www.haskell.org/pipermail/haskell-cafe/2007-August/030394.html default for quotRem in terms of divMod?] |
* Haskell-Cafe: [http://www.haskell.org/pipermail/haskell-cafe/2007-August/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>=== |

## Revision as of 02:44, 16 May 2011

## 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, well-tuned 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 is likely to 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** much opportunities to factor out parts of the code.
If you find the function 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 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 *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 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
```

`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 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 `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 (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 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 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.

## 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
```

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

```
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 (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" 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 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 `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..(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.)