Documentation

Focus on a key in an indexed set, much like with mapLens.

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 using lenses and fix Simon's last name:

people' = ixLens (FirstName "Simon") ^%= fmap (lastName ^= LastName "Peyton-Jones") $ people

>>> people'
fromList [Person {_firstName = FirstName "Edward A.", _lastName = LastName "Kmett"}
         ,Person {_firstName = FirstName "Simon", _lastName = LastName "Peyton-Jones"}]
>>> (firstName ^$) <$> people' ^. ixLens (LastName "Peyton-Jones")
Just (FirstName "Simon")
>>> ixLens (LastName "Peyton-Jones") ^$ people
Nothing

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

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

Here's the missing boilerplate, which also needs the packages data-lens-fd and data-lens-template:

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

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

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

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

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

makeLens ''Person

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