[] is my favorite iterator, and the most common in Haskell. In many languages, iterators delay the tail of the sequence, so that the entire sequence does not need to be stored in memory. In Haskell, laziness is pervasive; lists benefit without any extra code. This makes lists in Haskell much more useful than singly linked lists in most strict languages. Pattern matching on (x:xs) is equivalent to your `next`. `tail` is your `rest`. `unpack` for ByteString and Text, and Data.Foldable.toList for many other types, produce a list. Did I miss any important operations on iterators? cheers, bergey On 2016-05-18 at 17:53, Silvio Frischknecht wrote:

Hello,

We know about Foldable, but sometimes you just want more functionality like: give me the rest of the string! Or a function to build pieces back together. I've been experimenting a bit and come up with 6 flavors of Iterators that do the same thing. Of course they all work for containers like ByteStrings, Text.

1) Haskell98 version (I like)

data Iterator98 list ele = Iterator98 { next98 :: Maybe (ele, Iterator98 list ele), ... rest98 :: list, concat98 :: [list] -> list }

-- How we can create an Iterator98 listIter98 :: [a] -> Iterator98 [a] a

-- How the sum type looks sum98 :: (Num n) => Iterator98 listN n -> n

Performance: *3

I'll also usually give the type of the constructor and sum functions. I also benchmarked the sum functions for [] and compared them to the best sum function I could come up with (which is significantly faster than the sum in Prelude!!! because it's strict. Whoever came up with the idea of making it non-strict, must have been drunk at the time :)).

I like how handy and simple typed the Haskell98 version is. There are absolutely no superfluous Types or Contexts. However, *3 is quite a heavy penalty and it might even get worse when more functions are added.

2) Haskell98 Explicit (ambivalent)

data IteratorExplicit98 iter list ele = IteratorExplicit98 { iterExplicit98 :: iter, nextExplicit98 :: iter -> Maybe (ele, iter) ... restExplicit98 :: iter -> list }

listIterExplicit98 :: [a] -> IteratorExplicit98 [a] [a] a

sumExplicit98 :: (Num n) => IteratorExplicit98 it list n -> n

Performance: *1

It is explicit and it is still quite nice to use. There is however always that extra argument. Note: `iter` and `list` could potentially be different (in all examples). They are in Haskell however usually the same. Performance could be different, if you create and destroy a lot of data of type IteratorExplicit98. However, that won't usually be the case.

3) TypeFamilies (I don't like)

class IteratorTF i where type ListTF i type ElemTF i nextTF :: i -> Maybe (ElemTF i, i) ... restTF :: i -> ListTF i

instance IteratorTF2Class [ele] ele where ...

sumTF :: (Num n, IteratorTF it, ElemTF it ~ n) => it -> n

Performance: *1

I used to like type families. But now I'm a bit fed up with ~ contexts. This would be the "Rust" version. Interesting point: List and Elem functions could be separated into two classes. I.e. Note that no list type exists in the type of "sum".

4) TypeFamilies2 (ambivalent)

class IteratorTF2Class list ele where data IteratorTF2 list ele nextTF2 :: IteratorTF2 list ele -> Maybe (ele, IteratorTF2 list ele) ... restTF2 :: IteratorTF2 list ele -> list

instance IteratorTF2Class [ele] ele where data IteratorTF2 [ele] ele = ListIterTF2 [ele]

sumTF2 :: (Num n, IteratorTF2Class list n) => IteratorTF2 list n -> n

Performance: *1

Better than the last. However, IteratorTF2Class, IteratorTF2 are two Type-ish things where one would be preferred. This is my preferred method where all functions are carried in the type.

5) MultiParameterTypeClasses and Functional Dependencies (ambivalent)

class IteratorMPTC iter list ele | iter -> list, iter -> ele where nextMPTC :: iter -> Maybe (ele, iter) ... restMPTC :: iter -> list

instance IteratorMPTC [a] [a] a where

sumMPTC :: (Num n, IteratorMPTC it list n) => it -> n

Performance: *1

About the same as 3). The user will still be exposed to various individual types ":: it". That is not as bad as it is in "Rust", since (as already stated) in Haskell usually "list == it". This is similar to the parsec approach.

class (Monad m) => Stream iter m ele | iter -> ele

Parsec has no "rest" function so the "list" type is not needed. But they have an additional monad type.

6) Existential Quantification (my favorite)

data IteratorEQ list ele = forall iter . IteratorEQ { iterEQ :: iter, nextEQ :: iter -> Maybe (ele, iter) ... restEQ :: iter -> list }

listIterEQ :: [a] -> IteratorEQ [a] a

sumEQ :: (Num n) => IteratorEQ list n -> n

Performance: *1

Looks as nice as Haskell98 and is as fast as Haskell98Explicit. Btw. This is probably how It would be done in "C" with iter = void*.

Additional thoughts:

* Do we really need the "list" type. Couldn't we simply return iterators instead of the original "list" type. In 3) and 5), they will *usually* be the same anyway.

* In 3) and 5) the typeclasses could be split to separate ele and list.

* On the other hand combining Iterators will be very annoying for 3) and 5)

data ZipIterator ... instance IteratorMPTC (ZipIterator (?) (elem, elem')) ? (elem, elem') where zip :: (IteratorMPTC iter list elem, IteratorMPTC iter' list' elem') -> ZipIterator ? (elem, elem')

Which is your favorite? Why? Did I forget any good ones?

Cheers

Silvio {-# LANGUAGE FlexibleInstances #-} {-# LANGUAGE TypeFamilies #-} {-# LANGUAGE ExistentialQuantification #-} {-# LANGUAGE MultiParamTypeClasses #-} {-# LANGUAGE FunctionalDependencies #-} {-# LANGUAGE FlexibleContexts #-} import Criterion.Main import Data.Foldable import Data.Word import qualified Data.ByteString as BS

listNext :: [a] -> Maybe (a,[a]) listNext (a:as) = Just (a,as) listNext [] = Nothing

data Iterator98 list ele = Iterator98 { next98 :: Maybe (ele, Iterator98 list ele) }

listIter98 :: [a] -> Iterator98 [a] a listIter98 (x:xs) = Iterator98 $ Just (x, listIter98 xs) listIter98 [] = Iterator98 $ Nothing

sum98 :: (Num n) => Iterator98 listN n -> n sum98 iter = rec iter 0 where rec (Iterator98 iter') sum' = case iter' of (Just (ele,rest)) -> rec rest $! (sum' + ele) Nothing -> sum'

data IteratorExplicit98 iter list ele = IteratorExplicit98 { iterExplicit98 :: iter, nextExplicit98 :: iter -> Maybe (ele, iter) }

listIterExplicit98 :: [a] -> IteratorExplicit98 [a] [a] a listIterExplicit98 list = IteratorExplicit98 list listNext

sumExplicit98 :: (Num n) => IteratorExplicit98 it list n -> n sumExplicit98 (IteratorExplicit98 iter nextF) = rec iter 0 where rec iter' sum' = case nextF iter' of (Just (ele,rest)) -> rec rest $! (sum' + ele) Nothing -> sum'

class IteratorTF i where type ListTF i type ElemTF i nextTF :: i -> Maybe (ElemTF i, i)

instance IteratorTF [a] where type ListTF [a] = [a] type ElemTF [a] = a nextTF (c:str) = Just (c,str) nextTF [] = Nothing

sumTF :: (Num n, IteratorTF it, ElemTF it ~ n) => it -> n sumTF it' = rec it' 0 where rec it sum' = case nextTF it of (Just (c,n)) -> rec n $! (sum' + c) Nothing -> sum'

class IteratorTF2Class list ele where data IteratorTF2 list ele nextTF2 :: IteratorTF2 list ele -> Maybe (ele, IteratorTF2 list ele)

instance IteratorTF2Class [ele] ele where data IteratorTF2 [ele] ele = ListIterTF2 [ele] nextTF2 (ListIterTF2 []) = Nothing nextTF2 (ListIterTF2 (x:xs)) = Just (x, ListIterTF2 xs)

sumTF2 :: (Num n, IteratorTF2Class list n) => IteratorTF2 list n -> n sumTF2 it' = rec it' 0 where rec it sum' = case nextTF2 it of (Just (c,n)) -> rec n $! (sum' + c) Nothing -> sum'

class IteratorMPTC iter list ele | iter -> list, iter -> ele where nextMPTC :: iter -> Maybe (ele, iter)

instance IteratorMPTC [a] [a] a where nextMPTC (c:str) = Just (c,str) nextMPTC [] = Nothing

sumMPTC :: (Num n, IteratorMPTC it list n) => it -> n sumMPTC it' = rec it' 0 where rec it sum' = case nextMPTC it of (Just (c,n)) -> rec n $! (sum' + c) Nothing -> sum'

data IteratorEQ list ele = forall iter . IteratorEQ { iterEQ :: iter, nextEQ :: iter -> Maybe (ele, iter) }

listIterEQ :: [a] -> IteratorEQ [a] a listIterEQ list = IteratorEQ list listNext

sumEQ :: (Num n) => IteratorEQ list n -> n sumEQ (IteratorEQ iter nextF) = rec iter 0 where rec iter' sum' = case nextF iter' of (Just (c,n)) -> rec n $! (sum' + c) Nothing -> sum'

explicitSum :: (Num n) => [n] -> n explicitSum l' = rec l' 0 where rec (c:n) s = rec n $! (s + c) rec [] s = s

n = 1000000 l = replicate n 5 bs = BS.pack l

main = do last l `seq` return () defaultMain [ bgroup "list" [ bench "Prelude sum" $ whnf sum l, bench "Prelude foldl'" $ whnf (foldl' (+) 0) l, bench "explicit sum" $ whnf explicitSum l, bench "Iterator 98" $ whnf (sum98 . listIter98) l, bench "Iterator explicit 98" $ whnf (sumExplicit98 . listIterExplicit98) l, bench "Iterator type families" $ whnf sumTF l, bench "Iterator type families 2" $ whnf (sumTF2 . ListIterTF2) l, bench "Iterator multiparameter typeclasse" $ whnf sumMPTC l, bench "Iterator Existential Quantification" $ whnf (sumEQ . listIterEQ) l ], bgroup "bytestring" [ bench "foldl'" $ whnf (BS.foldl' (+) 0) bs ] ] _______________________________________________ Haskell-Cafe mailing list Haskell-Cafe@haskell.org http://mail.haskell.org/cgi-bin/mailman/listinfo/haskell-cafe