Enumerator and iteratee

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An enumerator is something that knows how to generate a list and an iteratee is something that does one step in processing another piece of the big list. E.g. to sum up all elements of a list, we do <pre-haskell> foldl (+) 0 xs </pre-haskell> Then <code-haskell>foldl</code-haskell> is the enumerator and <code-haskell>((+),0)</code-haskell> is the iteratee.

Clearly the function that sums the current element with the accumulator, <code-haskell>(+)</code-haskell>, doesn't know or care from which collection the elements are coming from. The initial seed, <code-haskell>0</code-haskell>, is again unaware of the collection. That achieves the separation of concerns: fold (aka, enumerator) has the intimate knowledge of the collection and how to get to the next element; iteratee knows what to do with the current element.

Definition

Do not rely on the <code-haskell>foldl</code-haskell> analogy too firmly, it is misleading. <code-haskell>((+),0)</code-haskell> is an F-algebra and <code-haskell>foldl (+) 0</code-haskell> is a catamorphism. But iteratee is different, it is an automaton. From this point of view, the enumerator sends elements of a list sequentially, from head to tail, as input messages to the iteratee. If the iteratee finishes, it outputs an accumulator. If the iteratee continues, it outputs nothing (i.e., <code-haskell>()</code-haskell>).

So, a set of states of iteratee is divided into subsets "Done" and "Next". Done-state means that automaton finished consuming a list, i.e., the automaton is dead. Next-state means that you can give an input message and obtain the same automaton in a new state. <pre-haskell> data Iteratee i o

 = Done o
 | Next (i -> Iteratee i o)

</pre-haskell>

<code-haskell>i</code-haskell> is the type of the iteratee's input messages (or list elements) and <code-haskell>o</code-haskell> is a type of the output message (an accumulator). Precisely speaking, <code-haskell>Iteratee</code-haskell> stores not an automaton, but an automaton in some state, an automaton with distinguished state. As you see, if an <code-haskell>Iteratee</code-haskell> is in the <code-haskell>Next</code-haskell> state, then we have a function that takes an input message and returns a new <code-haskell>Iteratee</code-haskell>.

The distinct feature of iteratee is that it can say after which list element an iteratee finishes. An iteratee says this by sending "Done" to an enumerator. Then the enumerator can, for example, close a file or a socket (a stream) where a list of characters is read from. Lazy I/O, which uses lazy lists, closes a stream only when the stream is exhausted.

The drawback is that an enumerator can not tell an iteratee that an input is exhausted — an <code-haskell>Iteratee</code-haskell> consumes only infinite lists. You can remedy this by assuming <pre-haskell> i == Maybe i' </pre-haskell> where <code-haskell>i'</code-haskell> is a type of list elements. <code-haskell>Nothing</code-haskell> given to iteratee signals that the list is exhausted.

Here is a sample enumerator that takes input messages from a file: <pre-haskell> enumerator :: FilePath -> Iteratee (Maybe Char) o -> IO o enumerator file it = withFile file ReadMode

 $ \h -> fix (\rc it -> case it of
   Done o -> return o
   Next f -> do
     eof <- hIsEOF h
     case eof of
       False -> do
         c <- hGetChar h
         rc (f (Just c))
       True -> rc (f Nothing)
   ) it

</pre-haskell>

Functions

You can compose iteratees sequentially in time. This is done by <code-haskell>(>>)</code-haskell>. <code-haskell>it0 >> it1</code-haskell> means that when <code-haskell>it0</code-haskell> finishes, <code-haskell>it1</code-haskell> starts. Generally speaking, <code-haskell>Iteratee i</code-haskell> is a <code-haskell>Monad</code-haskell>, and it works exactly like a monadic parser. <pre-haskell> {- s = state -} instance Functor (Iteratee input) where

 fmap f = fix $ \rc s -> case s of
   Done o -> Done (f o)
   Next g -> Next (rc . g)

instance Monad (Iteratee input) where

 return = Done
 it0 >>= it1 = fix (\rc s -> case s of
   Done o -> it1 o
   Next g -> Next (rc . g)
   ) it0

</pre-haskell>

You can also compose iteratees sequentially in space. <code-haskell>it0</code-haskell>'s output messages become <code-haskell>it1</code-haskell>'s input messages, so <code-haskell>it0</code-haskell> and <code-haskell>it1</code-haskell> work in parallel. Their composition is denoted <code-haskell>it1 . it0</code-haskell>. If <code-haskell>it0</code-haskell> finishes, it is resurrected to its original state. If <code-haskell>it1</code-haskell> finishes, <code-haskell>it1 . it0</code-haskell> finishes — The main feature here is that <code-haskell>it0</code-haskell> is restarted, as this is used for repetitive parsing. <pre-haskell> arr0 f = Next $ \i -> Done (f i) instance Category Iteratee where

 id = arr0 id
 it1 . it0 = fix (\rc1 it1 -> case it1 of
   Done c -> Done c
   Next f1 -> fix (\rc0 it0 -> case it0 of
     Done b -> rc1 (f1 b)
     Next f0 -> Next (rc0 . f0)
     ) it0
   ) it1

</pre-haskell>

Generalization

You may note that <code-haskell>Iteratee</code-haskell> is a final coalgebra. Other kinds of automata can be described with other F-coalgebras. In practice such automata can handle network protocols or interactive user input. See for example papers by Bart Jacobs for theoretical discussion.

See also