Writing Iterators in Julia 0.7

This post originally appeared on the Invenia blog.

With the upcoming 0.7 release, Julia has simplified its iteration interface. The 0.7-beta release is available for download. This was a huge undertaking which mostly fell to the prolific Keno Fischer, who wrote an entirely new optimizer for the language to accomplish it! As the most active maintainer of the IterTools package, I decided to spend a week rewriting its iterators for the new interface. I’d like to share that experience with you to introduce the new interface and assist in transitioning to Julia 0.7.

Iteration in Julia 0.6

Previously, Julia’s iteration interface consisted of three methods: start, next, and done. A good way to demonstrate how these work together is to show the transformation from a for loop to the equivalent while loop using those functions. I’ve taken this from the Julia Interfaces documentation, written by Matt Bauman and others.

A simple for loop like this:

for element in iterable
    # body
end

was equivalent to this while loop:

state = start(iterable)
while !done(iterable, state)
    (element, state) = next(iterable, state)
    # body
end

A simple example is a range iterator which yields every nth element up to some number of elements:

julia> struct EveryNth
           n::Int
           start::Int
           length::Int
       end

julia> Base.start(iter::EveryNth) = (iter.start, 0)

julia> function Base.next(iter::EveryNth, state)
           element, count = state
           return (element, (element + iter.n, count + 1))
       end

julia> function Base.done(iter::EveryNth, state)
           _, count = state
           return count >= iter.length
       end

julia> Base.length(iter::EveryNth) = iter.length

julia> Base.eltype(iter::EveryNth) = Int

Then we can iterate:

julia> for element in EveryNth(2, 0, 10)
           println(element)
       end
0
2
4
6
8
10
12
14
16
18

Which is equivalent to:

julia> let iterable = EveryNth(2, 0, 10), state = start(iterable)
           while !done(iterable, state)
               (element, state) = next(iterable, state)
               println(element)
           end
       end
0
2
4
6
8
10
12
14
16
18

Notice that our EveryNth struct is immutable and we never mutate the state information.

As an aside, the length and eltype method definitions are not necessary. Instead, we could use the IteratorSize and IteratorEltype traits to say that we don’t implement those functions and Julia’s Base functions will not try to call them when iterating. collect is notable for specializing on both of these traits to provide optimizations for different kinds of iterators.

Iteration in Julia 0.7

In Julia 0.7, the iteration interface is now just one function: iterate. The while loop above would now be written as:

iter_result = iterate(iterable)
while iter_result !== nothing
    (element, state) = iter_result
    # body
    iter_result = iterate(iterable, state)
end

The iterate function has two methods. The first is called once, to begin iteration (like the old start) and also perform the first iteration step. The second is called repeatedly to iterate, like next in Julia 0.6.

The EveryNth example now looks like this:

julia> struct EveryNth
           n::Int
           start::Int
           length::Int
       end

julia> function Base.iterate(iter::EveryNth, state=(iter.start, 0))
           element, count = state

           if count >= iter.length
               return nothing
           end

           return (element, (element + iter.n, count + 1))
       end

julia> Base.length(iter::EveryNth) = iter.length

julia> Base.eltype(iter::EveryNth) = Int

In our iterate function we define a default value for state which is used when iterate is called with one argument. 1

This is already less code than the old interface required, but we can reduce it further using another new feature of Julia 0.7.

function Base.iterate(it::EveryNth, (el, i)=(it.start, 0))
	return i >= it.length ? nothing : (el, (el + it.n, i + 1))
end

I personally prefer verbosity when it increases readability, but some people prefer shorter code, and that’s easier than ever to achieve.

A Note on Compatibility

To assist with transitioning between versions, Julia 0.7 includes fallback definitions of iterate which call start, next, and done. If you want code to work on both 0.6 and 0.7, I recommend keeping your iterators defined in those terms, as there isn’t a good way to use the iterate interface on Julia 0.6. Julia 1.0 will remove those fallback definitions and all usage of the old iteration interface.

Common Strategies

The above example was constructed to be as straightforward as possible, but not all iteration is that easy to express. Luckily, the new interface was designed to assist with situations which were previously difficult or inefficient, and in some cases (like the EveryNth example) reduces the amount of code necessary. While updating IterTools.jl, I came across a few patterns which repeatedly proved useful.

Wrapping Another Iterable

In many cases, the iterable we want to create is a transformation applied to a caller-supplied iterable. Many of the useful patterns apply specifically to this situation.

Early Return

When wrapping an iterable, we usually want to terminate when the wrapped iterable terminates, i.e., return nothing when the wrapped call to iterate returns nothing. If the call to iterate doesn’t return nothing, we want to apply some operations before returning. This pattern was common and simple enough to justify a macro which in IterTools I’ve called @ifsomething2:

macro ifsomething(ex)
    quote
        result = $(esc(ex))
        result === nothing && return nothing
        result
    end
end

Putting this code in a multiline macro allows us to simplify code which would usually require multiple lines. This code:

iter = iterate(wrapped, wrapped_state)

if iter === nothing
    return nothing
end

val, wrapped_state = iter

# continue processing

becomes this:

val, wrapped_state = @ifsomething iterate(wrapped, wrapped_state)

Conveniently (since it would otherwise error), the value returned from iterate will only be unpacked if it’s not nothing.

Slurping and Splatting

The iteration interface requires two methods of iterate, but it’s handy to use default arguments1 to only write out one function. However, sometimes there is no clear initial value for state, e.g., if it requires you to start iterating over the wrapped iterable. In this case it’s helpful to use “slurping” and “splatting”3 to refer to either zero or one function argument—the presence or absence of the state argument.

A simple example is the TakeNth iterator from IterTools.jl. Its implementation of the iterate function looks like this:

function iterate(it::TakeNth, state...)
    xs_iter = nothing

    for i = 1:it.interval
        xs_iter = @ifsomething iterate(it.xs, state...)
        state = Base.tail(xs_iter)
    end

    return xs_iter
end

When you first call iterate(::TakeNth), state starts out as an empty tuple. Splatting this empty tuple into iterate produces the call iterate(it.xs). In all further calls, the actual state returned from iterating over the wrapped iterable will be wrapped in a 1-tuple, and unwrapped in each call.

One of the other tools we use here is the unexported function Base.tail(::Tuple). This function performs the equivalent of slurping on tuples, or xs_iter[2:end]. No matter the size of the input tuple, it will always return at least an empty tuple. This is especially useful in the next, slightly more complicated example.

For TakeNth, we were only passing around the wrapped iterable’s state, but sometimes we need to carry some state of our own as well. For the TakeStrict iterator from IterTools.jl we want to iterate over exactly n elements from the wrapped iterable, so we need to carry a counter as well.

function iterate(it::TakeStrict, state=(it.n,))
    n, xs_state = first(state), Base.tail(state)
    n <= 0 && return nothing
    xs_iter = iterate(it.xs, xs_state...)

    if xs_iter === nothing
        throw(ArgumentError("In takestrict(xs, n), xs had fewer than n items to take."))
    end

    v, xs_state = xs_iter
    return v, (n - 1, xs_state)
end

Here we use Base.tail to slurp the rest of the input after our counter, so xs_state is either an empty tuple (on the initial iterate call) or a 1-tuple containing the state for the wrapped iterable.

Look-ahead Iterators

Occasionally we may want to write an iterable that requires advancing the wrapped iterable before returning a value, such as some kind of generic Fibonnaci iterator, or the simplest example, a “peekable” iterator that can look ahead to the next value. This exists in IterTools.jl as PeekIter.

function iterate(pit::PeekIter, state=iterate(pit.it))
    val, it_state = @ifsomething state
    return (val, iterate(pit.it, it_state))
end

In this case, the work needed for the initial iterate call is just a superset of the regular iterate call, so it’s very simple to implement. In general, the code for look-ahead iterators is just as easy to write in Julia 0.7, but usually more compact.

Piecewise Development Approach

Having to write many new iterate methods led me to discover some helpful strategies for writing iterate methods when unsure of the best approach. The most helpful thing I did was to write the two-argument method for iterate first, then write the one-argument method, then try to simplify them into a single method. Remember that the one-argument method is a combination of the start and next methods from the old iteration interface. I also realized that it was sometimes easier to apply patterns like the ones above in order to translate from the old to the new iteration interface without attempting to understand the initial version completely.

Let’s look at one of the more complicated iterators in IterTools.jl: Partition. Something that immediately jumps out about the original is this pattern:

if done(it.xs, s)
    break
end
(x, s) = next(it.xs, s)

If there are more items, this advances the wrapped iterable, otherwise it breaks out of the surrounding loop. In the new interface this requires just one call instead of two:

iter = iterate(it.xs, s)
iter === nothing && break
(x, s) = iter

Then this pattern can be applied by rote wherever it appears. Applying this and writing two iterate methods results in this4:

function iterate(it::Partition{I, N}, state) where {I, N}
    (xs_state, result) = state
    # this @ifsomething call handles the 0.6 situation
    # where `done` is always called before `next`
    result[end], xs_state = @ifsomething iterate(it.xs, xs_state)

    p = similar(result)
    overlap = max(0, N - it.step)
    p[1:overlap] .= result[it.step .+ (1:overlap)]

    # when step > n, skip over some elements
    for i in 1:max(0, it.step - N)
        xs_iter = iterate(it.xs, xs_state)
        xs_iter === nothing && break
        _, xs_state = xs_iter
    end

    for i in (overlap + 1):(N - 1)
        xs_iter = iterate(it.xs, xs_state)
        xs_iter === nothing && break

        p[i], xs_state = xs_iter
    end

    return (tuple(result...), (xs_state, p))
end

function iterate(it::Partition{I, N}) where {I, N}
    result = Vector{eltype(I)}(undef, N)

    result[1], xs_state = @ifsomething iterate(it.xs)

    for i in 2:(N - 1)
        result[i], xs_state = @ifsomething iterate(it.xs, xs_state)
    end

    return iterate(it, (xs_state, result))
end

This works for almost every case, except when N == 1! In that case, we do need to start with iterate(it.xs), but we have to return the first item before calling iterate again, so we have to skip the first iteration in the two-argument method. It would be nice to have the methods be this simple chain, but it looks like we need to combine them.

Previously, we’ve been able to come up with a sensible default state (or a tuple we can splat) for the combined method. We can’t5 do that here, as we need to have conditional behaviour for both cases. Luckily, we can add nothing as a sentinel and Julia will compile the check away. Making this change results in the version which appears in IterTool 1.0:

function iterate(it::Partition{I, N}, state=nothing) where {I, N}
    if state === nothing
        result = Vector{eltype(I)}(undef, N)

        result[1], xs_state = @ifsomething iterate(it.xs)

        for i in 2:N
            result[i], xs_state = @ifsomething iterate(it.xs, xs_state)
        end
    else
        (xs_state, result) = state
        result[end], xs_state = @ifsomething iterate(it.xs, xs_state)
    end

    p = similar(result)
    overlap = max(0, N - it.step)
    p[1:overlap] .= result[it.step .+ (1:overlap)]

    # when step > n, skip over some elements
    for i in 1:max(0, it.step - N)
        xs_iter = iterate(it.xs, xs_state)
        xs_iter === nothing && break
        _, xs_state = xs_iter
    end

    for i in (overlap + 1):(N - 1)
        xs_iter = iterate(it.xs, xs_state)
        xs_iter === nothing && break

        p[i], xs_state = xs_iter
    end

    return (tuple(result...)::eltype(Partition{I, N}), (xs_state, p))
end

Conclusion

These are the techniques that helped me in my work, but I’d like to hear about more! I’m also curious which patterns improve or harm performance and why. IterTools will definitely accept pull requests, and I’m interested in feedback on Slack and Discourse.

  1. In Julia, this actually defines two methods of iterate, as described in the Julia docs 2

  2. This name is definitely up for debate! 

  3. Slurping refers to how using args... in a function definition “slurps” up the trailing arguments, and splatting is the inverse operation. The Julia docs say more on this. 

  4. All other changes here are renaming or respelling something that appears in the original, for clarity’s sake. 

  5. We could, but we’d need to do something different depending on the length of the tuple, which would add another conditional check in addition to the splatting. 

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