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Enumerator and iteratee

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An enumerator is something that knows how to process a data structure and an iteratee is something that does one step in processing another piece of the big data structure. E.g. to sum up all elements of Data.Map, we do
+
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
<haskell>
+
<pre-haskell>
Map.fold (+) 0 mp
+
foldl (+) 0 xs
</haskell>
+
</pre-haskell>
  +
Then <code-haskell>foldl</code-haskell> is the enumerator and <code-haskell>((+),0)</code-haskell> is the iteratee.
   
to sum up all elements of a set we do
+
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
<haskell>
 
Set.fold (+) 0 st
 
</haskell>
 
 
Then <hask>fold</hask> is the enumerator and <hask>(+)</hask> and <hask>0</hask> are the iteratee.
 
 
Ditto for any other foldable data structure. Clearly the function that
 
sums the current element with the accumulator, (+), doesn't know or
 
care from which collection the elements are coming from. The initial
 
seed, 0, is again unaware of the collection.
 
 
Iteratee is indeed the function that you pass to fold (combined with
 
the seed for practical reasons). One may conceptually consider
 
iteratee to be a pair of the function to feed to fold, and the initial
 
seed (the accumulator in the above example). That achieves the
 
 
[[separation of concerns]]: fold (aka, enumerator) has the intimate knowledge
 
[[separation of concerns]]: fold (aka, enumerator) has the intimate knowledge
 
of the collection and how to get to the next element; iteratee knows
 
of the collection and how to get to the next element; iteratee knows
 
what to do with the current element.
 
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-coalgebra]]s. In practice such automata can handle network protocols or interactive user input. See for example [http://www.cs.ru.nl/~bart/PAPERS/index.html papers] by Bart Jacobs for theoretical discussion.
   
 
== See also ==
 
== See also ==
   
  +
* Oleg Kiselyov: "[http://okmij.org/ftp/Haskell/Iteratee/describe.pdf Iteratees]" - FLOPS 2012 paper
  +
* [http://www.mew.org/~kazu/proj/enumerator/ A tutorial on the enumerator library]
 
* Haskell-Cafe on [http://www.haskell.org/pipermail/haskell-cafe/2008-December/052181.html understanding enumerator/iteratee]
 
* Haskell-Cafe on [http://www.haskell.org/pipermail/haskell-cafe/2008-December/052181.html understanding enumerator/iteratee]
* Oleg Kiselyov: "[http://okmij.org/ftp/Haskell/Iteratee/DEFUN08-talk-notes.pdf Incremental multi-level input processing with left-fold enumerator] - predictable, high-performance, safe, and elegant"
+
* Haskell-Cafe on [http://www.haskell.org/pipermail/haskell-cafe/2009-February/056816.html Left fold enumerator - a real pearl overlooked?]
  +
* John Lato's cabalized [http://inmachina.net/~jwlato/haskell/iteratee/ package] of Oleg's code
  +
* [[Iteratee I/O]]
  +
* The Yesod book's [http://www.yesodweb.com/book/enumerator appendix on the Enumerator package]
   
 
[[Category:Idioms]]
 
[[Category:Idioms]]

Latest revision as of 03:59, 3 July 2012

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

foldl (+) 0 xs

Then foldl is the enumerator and ((+),0) is the iteratee.

Clearly the function that sums the current element with the accumulator, (+), doesn't know or care from which collection the elements are coming from. The initial seed, 0, 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.

Contents

[edit] 1 Definition

Do not rely on the foldl analogy too firmly, it is misleading. ((+),0) is an F-algebra and foldl (+) 0 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., ()).

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.

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

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

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 Iteratee consumes only infinite lists. You can remedy this by assuming

i == Maybe i'

where i' is a type of list elements. Nothing given to iteratee signals that the list is exhausted.

Here is a sample enumerator that takes input messages from a file:

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

[edit] 2 Functions

You can compose iteratees sequentially in time. This is done by (>>). it0 >> it1 means that when it0 finishes, it1 starts. Generally speaking, Iteratee i is a Monad, and it works exactly like a monadic parser.

{- 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

You can also compose iteratees sequentially in space. it0's output messages become it1's input messages, so it0 and it1 work in parallel. Their composition is denoted it1 . it0. If it0 finishes, it is resurrected to its original state. If it1 finishes, it1 . it0 finishes — The main feature here is that it0 is restarted, as this is used for repetitive parsing.

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

[edit] 3 Generalization

You may note that Iteratee 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.

[edit] 4 See also