[Haskell-cafe] How do you rewrite your code?

[Sean Leather]

There are numerous threads on the Haskell Café involving rewriting,
refactoring, refining, and in general improving code (for some definition of
improve). I am interested in seeing examples of how Haskell code can be
rewritten to make it better. Some general examples are:

   - Eta-reduce
   - Make more pointfree
   - Introduce monadic operators or do-notation
      - e.g. for Maybe, lists, State
      - Eliminate monadic operators or do-notation
   - Generalize types
      - e.g. change map to fmap, (++) to mappend
      - Use instances of Functor, Applicative, Alternative, Category, Arrow,
   Monoid, Traversable, etc.
   - Use library functions from Data.List, Data.Map, Data.Set, etc.
   - Use some form of generic programming (e.g. SYB, Uniplate, EMGM, Alloy)
   - Use other libraries not included in the Platform


My question is simple:

   *How do you rewrite your code to improve it?*

You can answer this in any way you like, but I think the most useful answer
is to show a reasonably small, concrete example of what your code looked
like before and after. Also, please describe how you think the rewrite
improves such code.

   - Is it better style? More useful? More efficient?
   - Are the types (before and after) the same?
   - Are the semantics the same?
   - How did you prove or test equivalence? (e.g. Can you use equational
   reasoning to confirm the rewrite is valid? Did you use QuickCheck?)


Here is an example that I find myself doing occasionally.

For all x, f:

x >>= return . f
-->
fmap f x
or
f <$> x -- requires importing Control.Applicative

I think the right-hand side (RHS) is more concise and simpler. The types
here do change: the type constructor has a Monad constraint in the left-hand
side and a Functor constraint in the RHS. Types that are Monad instances are
generally also Functor instances, so this is often possible. I'm convinced
the semantics are preserved, though I haven't proven it.

What's an example of a rewrite that you've encountered?

Thanks,
Sean
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