Documentation

Focus on a key in an indexed set.

Given an IxSet of people:

 people = fromList [ Person (FirstName "Edward A.") (LastName "Kmett")
                   , Person (FirstName "Simon") (LastName "P. Jones")
                   ]

We can now work with indices as lenses and fix Simon's last name:

 people' = lastName . ixLens (FirstName "Simon") ^= (LastName "Peyton-Jones") people

Perhaps more commonly you're working with an IxSet from inside a state monad such as with acid-state. In that case usage is even easier:

 changeLastName = lastName . ixLens (FirstName "Simon") %= LastName "Peyton-Jones"

Feels backwards? Lens composition uses Category so we can flip it around more intuitively using the composition arrows instead:

 changeLastName' = ixLens (FirstName "Simon") >>> lastName %= LastName "Peyton-Jones"

Here's the missing boilerplate:

 {-# LANGUAGE DeriveDataTypeable #-}
 {-# LANGUAGE TemplateHaskell #-}

 import Prelude hiding ((.))
 import Control.Category
 import Data.Data

 import Data.Lens
 import Data.Lens.Template
 import Data.IxSet

 data Person = Person { _firstName :: FirstName
                      , _lastName  :: LastName
                      } deriving (Show, Eq, Ord, Data, Typeable)

 mkLens ''Person

 newtype FirstName = FirstName String
   deriving (Show, Eq, Ord, Data, Typeable)

 newtype LastName = LastName String
   deriving (Show, Eq, Ord, Data, Typeable)

 instance Indexable Person where
   empty = ixSet [ ixGen (Proxy :: Proxy FirstName)
                 , ixGen (Proxy :: Proxy LastName)
                 ]