1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
86
87
88
89
90
91
92
93
94
95
96
97
98
99
100
101
102
103
104
105
106
107
108
109
110
111
112
113
114
115
116
117
118
119
120
121
122
123
124
125
126
127
128
129
130
131
132
133
134
135
136
137
138
139
140
141
142
143
144
145
146
147
148
149
150
151
152
153
154
155
156
157
158
159
160
161
162
163
164
165
166
167
168
169
170
171
172
173
174
175
176
177
178
179
180
181
182
183
184
185
186
187
188
189
190
191
192
193
194
195
196
197
198
199
200
201
202
203
204
205
206
207
208
209
210
211
212
213
214
215
216
217
218
219
220
221
222
223
224
225
226
227
228
229
230
231
232
233
234
235
236
237
238
239
240
241
242
243
244
245
246
247
248
249
250
251
252
253
254
255
256
257
258
259
260
261
262
263
264
265
266
267
268
269
270
271
272
273
274
275
276
277
278
279
280
281
282
283
284
285
286
287
288
289
290
291
292
293
294
295
296
297
298
299
300
301
302
303
304
305
306
307
308
309
310
311
312
313
314
315
316
317
318
319
320
321
322
323
324
325
326
327
328
329
330
331
332
333
334
335
336
337
338
339
340
341
342
343
344
345
346
347
348
349
350
351
352
353
354
355
356
357
358
359
360
361
362
363
364
365
366
367
368
369
370
371
372
373
374
375
376
377
378
379
380
381
382
383
384
385
386
387
388
389
390
391
392
393
394
395
396
397
398
399
400
401
402
403
404
405
406
407
408
409
410
411
412
413
414
415
416
417
418
419
420
421
422
423
424
425
426
427
428
429
430
431
432
433
434
435
436
437
438
439
440
441
442
443
444
445
446
447
448
449
450
451
452
453
454
455
456
457
458
459
460
461
462
463
464
465
466
467
468
469
470
471
472
473
474
475
476
477
478
479
480
481
482
483
484
485
486
487
488
489
490
491
492
493
494
495
496
497
498
499
500
501
502
503
504
505
506
507
508
509
510
511
512
513
514
515
516
517
518
519
520
521
522
523
524
525
526
527
528
529
530
531
532
533
534
535
536
537
538
539
540
541
542
543
544
545
546
547
548
549
550
551
552
553
554
555
556
557
558
559
560
561
562
563
564
565
566
567
568
569
570
571
572
573
574
575
576
577
578
579
580
581
582
583
584
585
586
587
588
589
590
591
592
593
594
595
596
597
598
599
600
601
602
603
604
605
606
607
608
609
610
611
612
613
614
615
616
617
618
619
620
621
622
623
624
625
626
627
628
629
630
631
632
633
634
635
//! Arranges a collection into a re-usable trace structure.
//!
//! The `arrange` operator applies to a differential dataflow `Collection` and returns an `Arranged`
//! structure, provides access to both an indexed form of accepted updates as well as a stream of
//! batches of newly arranged updates.
//!
//! Several operators (`join`, `reduce`, and `count`, among others) are implemented against `Arranged`,
//! and can be applied directly to arranged data instead of the collection. Internally, the operators
//! will borrow the shared state, and listen on the timely stream for shared batches of data. The
//! resources to index the collection---communication, computation, and memory---are spent only once,
//! and only one copy of the index needs to be maintained as the collection changes.
//!
//! The arranged collection is stored in a trace, whose append-only operation means that it is safe to
//! share between the single `arrange` writer and multiple readers. Each reader is expected to interrogate
//! the trace only at times for which it knows the trace is complete, as indicated by the frontiers on its
//! incoming channels. Failing to do this is "safe" in the Rust sense of memory safety, but the reader may
//! see ill-defined data at times for which the trace is not complete. (All current implementations
//! commit only completed data to the trace).

use timely::dataflow::operators::{Enter, Map};
use timely::order::PartialOrder;
use timely::dataflow::{Scope, Stream, StreamCore};
use timely::dataflow::operators::generic::Operator;
use timely::dataflow::channels::pact::{ParallelizationContract, Pipeline, Exchange};
use timely::progress::Timestamp;
use timely::progress::Antichain;
use timely::dataflow::operators::Capability;

use crate::{Data, ExchangeData, Collection, AsCollection, Hashable};
use crate::difference::Semigroup;
use crate::lattice::Lattice;
use crate::trace::{self, Trace, TraceReader, Batch, BatchReader, Batcher, Builder, Cursor};
use crate::trace::implementations::{KeySpine, ValSpine};

use trace::wrappers::enter::{TraceEnter, BatchEnter,};
use trace::wrappers::enter_at::TraceEnter as TraceEnterAt;
use trace::wrappers::enter_at::BatchEnter as BatchEnterAt;
use trace::wrappers::filter::{TraceFilter, BatchFilter};

use super::TraceAgent;

/// An arranged collection of `(K,V)` values.
///
/// An `Arranged` allows multiple differential operators to share the resources (communication,
/// computation, memory) required to produce and maintain an indexed representation of a collection.
pub struct Arranged<G: Scope, Tr>
where
    G::Timestamp: Lattice+Ord,
    Tr: TraceReader+Clone,
{
    /// A stream containing arranged updates.
    ///
    /// This stream contains the same batches of updates the trace itself accepts, so there should
    /// be no additional overhead to receiving these records. The batches can be navigated just as
    /// the batches in the trace, by key and by value.
    pub stream: Stream<G, Tr::Batch>,
    /// A shared trace, updated by the `Arrange` operator and readable by others.
    pub trace: Tr,
    // TODO : We might have an `Option<Collection<G, (K, V)>>` here, which `as_collection` sets and
    // returns when invoked, so as to not duplicate work with multiple calls to `as_collection`.
}

impl<G, Tr> Clone for Arranged<G, Tr>
where
    G: Scope<Timestamp=Tr::Time>,
    Tr: TraceReader + Clone,
{
    fn clone(&self) -> Self {
        Arranged {
            stream: self.stream.clone(),
            trace: self.trace.clone(),
        }
    }
}

use ::timely::dataflow::scopes::Child;
use ::timely::progress::timestamp::Refines;
use timely::Container;
use timely::container::PushInto;

impl<G, Tr> Arranged<G, Tr>
where
    G: Scope<Timestamp=Tr::Time>,
    Tr: TraceReader + Clone,
{
    /// Brings an arranged collection into a nested scope.
    ///
    /// This method produces a proxy trace handle that uses the same backing data, but acts as if the timestamps
    /// have all been extended with an additional coordinate with the default value. The resulting collection does
    /// not vary with the new timestamp coordinate.
    pub fn enter<'a, TInner>(&self, child: &Child<'a, G, TInner>)
        -> Arranged<Child<'a, G, TInner>, TraceEnter<Tr, TInner>>
        where
            TInner: Refines<G::Timestamp>+Lattice+Timestamp+Clone,
    {
        Arranged {
            stream: self.stream.enter(child).map(|bw| BatchEnter::make_from(bw)),
            trace: TraceEnter::make_from(self.trace.clone()),
        }
    }

    /// Brings an arranged collection into a nested region.
    ///
    /// This method only applies to *regions*, which are subscopes with the same timestamp
    /// as their containing scope. In this case, the trace type does not need to change.
    pub fn enter_region<'a>(&self, child: &Child<'a, G, G::Timestamp>)
        -> Arranged<Child<'a, G, G::Timestamp>, Tr> {
        Arranged {
            stream: self.stream.enter(child),
            trace: self.trace.clone(),
        }
    }

    /// Brings an arranged collection into a nested scope.
    ///
    /// This method produces a proxy trace handle that uses the same backing data, but acts as if the timestamps
    /// have all been extended with an additional coordinate with the default value. The resulting collection does
    /// not vary with the new timestamp coordinate.
    pub fn enter_at<'a, TInner, F, P>(&self, child: &Child<'a, G, TInner>, logic: F, prior: P)
        -> Arranged<Child<'a, G, TInner>, TraceEnterAt<Tr, TInner, F, P>>
        where
            TInner: Refines<G::Timestamp>+Lattice+Timestamp+Clone+'static,
            F: FnMut(Tr::Key<'_>, Tr::Val<'_>, Tr::TimeGat<'_>)->TInner+Clone+'static,
            P: FnMut(&TInner)->Tr::Time+Clone+'static,
        {
        let logic1 = logic.clone();
        let logic2 = logic.clone();
        Arranged {
            trace: TraceEnterAt::make_from(self.trace.clone(), logic1, prior),
            stream: self.stream.enter(child).map(move |bw| BatchEnterAt::make_from(bw, logic2.clone())),
        }
    }

    /// Filters an arranged collection.
    ///
    /// This method produces a new arrangement backed by the same shared
    /// arrangement as `self`, paired with user-specified logic that can
    /// filter by key and value. The resulting collection is restricted
    /// to the keys and values that return true under the user predicate.
    ///
    /// # Examples
    ///
    /// ```
    /// use differential_dataflow::input::Input;
    /// use differential_dataflow::operators::arrange::ArrangeByKey;
    ///
    /// ::timely::example(|scope| {
    ///
    ///     let arranged =
    ///     scope.new_collection_from(0 .. 10).1
    ///          .map(|x| (x, x+1))
    ///          .arrange_by_key();
    ///
    ///     arranged
    ///         .filter(|k,v| k == v)
    ///         .as_collection(|k,v| (*k,*v))
    ///         .assert_empty();
    /// });
    /// ```
    pub fn filter<F>(&self, logic: F)
        -> Arranged<G, TraceFilter<Tr, F>>
        where
            F: FnMut(Tr::Key<'_>, Tr::Val<'_>)->bool+Clone+'static,
    {
        let logic1 = logic.clone();
        let logic2 = logic.clone();
        Arranged {
            trace: TraceFilter::make_from(self.trace.clone(), logic1),
            stream: self.stream.map(move |bw| BatchFilter::make_from(bw, logic2.clone())),
        }
    }
    /// Flattens the stream into a `Collection`.
    ///
    /// The underlying `Stream<G, BatchWrapper<T::Batch>>` is a much more efficient way to access the data,
    /// and this method should only be used when the data need to be transformed or exchanged, rather than
    /// supplied as arguments to an operator using the same key-value structure.
    pub fn as_collection<D: Data, L>(&self, mut logic: L) -> Collection<G, D, Tr::Diff>
        where
            L: FnMut(Tr::Key<'_>, Tr::Val<'_>) -> D+'static,
    {
        self.flat_map_ref(move |key, val| Some(logic(key,val)))
    }

    /// Extracts elements from an arrangement as a collection.
    ///
    /// The supplied logic may produce an iterator over output values, allowing either
    /// filtering or flat mapping as part of the extraction.
    pub fn flat_map_ref<I, L>(&self, logic: L) -> Collection<G, I::Item, Tr::Diff>
        where
            I: IntoIterator,
            I::Item: Data,
            L: FnMut(Tr::Key<'_>, Tr::Val<'_>) -> I+'static,
    {
        Self::flat_map_batches(&self.stream, logic)
    }

    /// Extracts elements from a stream of batches as a collection.
    ///
    /// The supplied logic may produce an iterator over output values, allowing either
    /// filtering or flat mapping as part of the extraction.
    ///
    /// This method exists for streams of batches without the corresponding arrangement.
    /// If you have the arrangement, its `flat_map_ref` method is equivalent to this.
    pub fn flat_map_batches<I, L>(stream: &Stream<G, Tr::Batch>, mut logic: L) -> Collection<G, I::Item, Tr::Diff>
    where
        I: IntoIterator,
        I::Item: Data,
        L: FnMut(Tr::Key<'_>, Tr::Val<'_>) -> I+'static,
    {
        stream.unary(Pipeline, "AsCollection", move |_,_| move |input, output| {
            input.for_each(|time, data| {
                let mut session = output.session(&time);
                for wrapper in data.iter() {
                    let batch = &wrapper;
                    let mut cursor = batch.cursor();
                    while let Some(key) = cursor.get_key(batch) {
                        while let Some(val) = cursor.get_val(batch) {
                            for datum in logic(key, val) {
                                cursor.map_times(batch, |time, diff| {
                                    session.give((datum.clone(), time.into_owned(), diff.into_owned()));
                                });
                            }
                            cursor.step_val(batch);
                        }
                        cursor.step_key(batch);
                    }
                }
            });
        })
        .as_collection()
    }
}


use crate::difference::Multiply;
// Direct join implementations.
impl<G, T1> Arranged<G, T1>
where
    G: Scope<Timestamp=T1::Time>,
    T1: TraceReader + Clone + 'static,
{
    /// A direct implementation of the `JoinCore::join_core` method.
    pub fn join_core<T2,I,L>(&self, other: &Arranged<G,T2>, mut result: L) -> Collection<G,I::Item,<T1::Diff as Multiply<T2::Diff>>::Output>
    where
        T2: for<'a> TraceReader<Key<'a>=T1::Key<'a>,Time=T1::Time>+Clone+'static,
        T1::Diff: Multiply<T2::Diff>,
        <T1::Diff as Multiply<T2::Diff>>::Output: Semigroup+'static,
        I: IntoIterator,
        I::Item: Data,
        L: FnMut(T1::Key<'_>,T1::Val<'_>,T2::Val<'_>)->I+'static
    {
        let result = move |k: T1::Key<'_>, v1: T1::Val<'_>, v2: T2::Val<'_>, t: &G::Timestamp, r1: &T1::Diff, r2: &T2::Diff| {
            let t = t.clone();
            let r = (r1.clone()).multiply(r2);
            result(k, v1, v2).into_iter().map(move |d| (d, t.clone(), r.clone()))
        };
        self.join_core_internal_unsafe(other, result)
    }
    /// A direct implementation of the `JoinCore::join_core_internal_unsafe` method.
    pub fn join_core_internal_unsafe<T2,I,L,D,ROut> (&self, other: &Arranged<G,T2>, mut result: L) -> Collection<G,D,ROut>
    where
        T2: for<'a> TraceReader<Key<'a>=T1::Key<'a>, Time=T1::Time>+Clone+'static,
        D: Data,
        ROut: Semigroup+'static,
        I: IntoIterator<Item=(D, G::Timestamp, ROut)>,
        L: FnMut(T1::Key<'_>, T1::Val<'_>,T2::Val<'_>,&G::Timestamp,&T1::Diff,&T2::Diff)->I+'static,
    {
        use crate::operators::join::join_traces;
        join_traces::<_, _, _, _, crate::consolidation::ConsolidatingContainerBuilder<_>>(
            self,
            other,
            move |k, v1, v2, t, d1, d2, c| {
                for datum in result(k, v1, v2, t, d1, d2) {
                    c.give(datum);
                }
            }
        )
            .as_collection()
    }
}

use crate::trace::cursor::IntoOwned;

// Direct reduce implementations.
use crate::difference::Abelian;
impl<G, T1> Arranged<G, T1>
where
    G: Scope<Timestamp = T1::Time>,
    T1: TraceReader + Clone + 'static,
{
    /// A direct implementation of `ReduceCore::reduce_abelian`.
    pub fn reduce_abelian<L, K, V, T2>(&self, name: &str, mut logic: L) -> Arranged<G, TraceAgent<T2>>
    where
        for<'a> T1::Key<'a>: IntoOwned<'a, Owned = K>,
        T2: for<'a> Trace<Key<'a>= T1::Key<'a>, Time=T1::Time>+'static,
        K: Ord + 'static,
        V: Data,
        for<'a> T2::Val<'a> : IntoOwned<'a, Owned = V>,
        T2::Diff: Abelian,
        T2::Batch: Batch,
        <T2::Builder as Builder>::Input: Container + PushInto<((K, V), T2::Time, T2::Diff)>,
        L: FnMut(T1::Key<'_>, &[(T1::Val<'_>, T1::Diff)], &mut Vec<(V, T2::Diff)>)+'static,
    {
        self.reduce_core::<_,K,V,T2>(name, move |key, input, output, change| {
            if !input.is_empty() {
                logic(key, input, change);
            }
            change.extend(output.drain(..).map(|(x,mut d)| { d.negate(); (x, d) }));
            crate::consolidation::consolidate(change);
        })
    }

    /// A direct implementation of `ReduceCore::reduce_core`.
    pub fn reduce_core<L, K, V, T2>(&self, name: &str, logic: L) -> Arranged<G, TraceAgent<T2>>
    where
        for<'a> T1::Key<'a>: IntoOwned<'a, Owned = K>,
        T2: for<'a> Trace<Key<'a>=T1::Key<'a>, Time=T1::Time>+'static,
        K: Ord + 'static,
        V: Data,
        for<'a> T2::Val<'a> : IntoOwned<'a, Owned = V>,
        T2::Batch: Batch,
        <T2::Builder as Builder>::Input: Container + PushInto<((K, V), T2::Time, T2::Diff)>,
        L: FnMut(T1::Key<'_>, &[(T1::Val<'_>, T1::Diff)], &mut Vec<(V, T2::Diff)>, &mut Vec<(V, T2::Diff)>)+'static,
    {
        use crate::operators::reduce::reduce_trace;
        reduce_trace::<_,_,_,_,V,_>(self, name, logic)
    }
}


impl<'a, G, Tr> Arranged<Child<'a, G, G::Timestamp>, Tr>
where
    G: Scope<Timestamp=Tr::Time>,
    Tr: TraceReader + Clone,
{
    /// Brings an arranged collection out of a nested region.
    ///
    /// This method only applies to *regions*, which are subscopes with the same timestamp
    /// as their containing scope. In this case, the trace type does not need to change.
    pub fn leave_region(&self) -> Arranged<G, Tr> {
        use timely::dataflow::operators::Leave;
        Arranged {
            stream: self.stream.leave(),
            trace: self.trace.clone(),
        }
    }
}

/// A type that can be arranged as if a collection of updates.
pub trait Arrange<G, C>
where
    G: Scope,
    G::Timestamp: Lattice,
{
    /// Arranges updates into a shared trace.
    fn arrange<Tr>(&self) -> Arranged<G, TraceAgent<Tr>>
    where
        Tr: Trace<Time=G::Timestamp> + 'static,
        Tr::Batch: Batch,
        Tr::Batcher: Batcher<Input=C>,
    {
        self.arrange_named("Arrange")
    }

    /// Arranges updates into a shared trace, with a supplied name.
    fn arrange_named<Tr>(&self, name: &str) -> Arranged<G, TraceAgent<Tr>>
    where
        Tr: Trace<Time=G::Timestamp> + 'static,
        Tr::Batch: Batch,
        Tr::Batcher: Batcher<Input=C>,
    ;
}

impl<G, K, V, R> Arrange<G, Vec<((K, V), G::Timestamp, R)>> for Collection<G, (K, V), R>
where
    G: Scope,
    G::Timestamp: Lattice,
    K: ExchangeData + Hashable,
    V: ExchangeData,
    R: ExchangeData + Semigroup,
{
    fn arrange_named<Tr>(&self, name: &str) -> Arranged<G, TraceAgent<Tr>>
    where
        Tr: Trace<Time=G::Timestamp> + 'static,
        Tr::Batch: Batch,
        Tr::Batcher: Batcher<Input=Vec<((K, V), G::Timestamp, R)>>,
    {
        let exchange = Exchange::new(move |update: &((K,V),G::Timestamp,R)| (update.0).0.hashed().into());
        arrange_core(&self.inner, exchange, name)
    }
}

/// Arranges a stream of updates by a key, configured with a name and a parallelization contract.
///
/// This operator arranges a stream of values into a shared trace, whose contents it maintains.
/// It uses the supplied parallelization contract to distribute the data, which does not need to
/// be consistently by key (though this is the most common).
pub fn arrange_core<G, P, Tr>(stream: &StreamCore<G, <Tr::Batcher as Batcher>::Input>, pact: P, name: &str) -> Arranged<G, TraceAgent<Tr>>
where
    G: Scope,
    G::Timestamp: Lattice,
    P: ParallelizationContract<G::Timestamp, <Tr::Batcher as Batcher>::Input>,
    Tr: Trace<Time=G::Timestamp>+'static,
    Tr::Batch: Batch,
    <Tr::Batcher as Batcher>::Input: timely::Container,
{
    // The `Arrange` operator is tasked with reacting to an advancing input
    // frontier by producing the sequence of batches whose lower and upper
    // bounds are those frontiers, containing updates at times greater or
    // equal to lower and not greater or equal to upper.
    //
    // The operator uses its batch type's `Batcher`, which accepts update
    // triples and responds to requests to "seal" batches (presented as new
    // upper frontiers).
    //
    // Each sealed batch is presented to the trace, and if at all possible
    // transmitted along the outgoing channel. Empty batches may not have
    // a corresponding capability, as they are only retained for actual data
    // held by the batcher, which may prevents the operator from sending an
    // empty batch.

    let mut reader: Option<TraceAgent<Tr>> = None;

    // fabricate a data-parallel operator using the `unary_notify` pattern.
    let reader_ref = &mut reader;
    let scope = stream.scope();

    let stream = stream.unary_frontier(pact, name, move |_capability, info| {

        // Acquire a logger for arrange events.
        let logger = {
            let register = scope.log_register();
            register.get::<crate::logging::DifferentialEvent>("differential/arrange")
        };

        // Where we will deposit received updates, and from which we extract batches.
        let mut batcher = Tr::Batcher::new(logger.clone(), info.global_id);

        // Capabilities for the lower envelope of updates in `batcher`.
        let mut capabilities = Antichain::<Capability<G::Timestamp>>::new();

        let activator = Some(scope.activator_for(info.address.clone()));
        let mut empty_trace = Tr::new(info.clone(), logger.clone(), activator);
        // If there is default exertion logic set, install it.
        if let Some(exert_logic) = scope.config().get::<trace::ExertionLogic>("differential/default_exert_logic").cloned() {
            empty_trace.set_exert_logic(exert_logic);
        }

        let (reader_local, mut writer) = TraceAgent::new(empty_trace, info, logger);

        *reader_ref = Some(reader_local);

        // Initialize to the minimal input frontier.
        let mut prev_frontier = Antichain::from_elem(<G::Timestamp as Timestamp>::minimum());

        move |input, output| {

            // As we receive data, we need to (i) stash the data and (ii) keep *enough* capabilities.
            // We don't have to keep all capabilities, but we need to be able to form output messages
            // when we realize that time intervals are complete.

            input.for_each(|cap, data| {
                capabilities.insert(cap.retain());
                batcher.push_container(data);
            });

            // The frontier may have advanced by multiple elements, which is an issue because
            // timely dataflow currently only allows one capability per message. This means we
            // must pretend to process the frontier advances one element at a time, batching
            // and sending smaller bites than we might have otherwise done.

            // Assert that the frontier never regresses.
            assert!(PartialOrder::less_equal(&prev_frontier.borrow(), &input.frontier().frontier()));

            // Test to see if strict progress has occurred, which happens whenever the new
            // frontier isn't equal to the previous. It is only in this case that we have any
            // data processing to do.
            if prev_frontier.borrow() != input.frontier().frontier() {
                // There are two cases to handle with some care:
                //
                // 1. If any held capabilities are not in advance of the new input frontier,
                //    we must carve out updates now in advance of the new input frontier and
                //    transmit them as batches, which requires appropriate *single* capabilites;
                //    Until timely dataflow supports multiple capabilities on messages, at least.
                //
                // 2. If there are no held capabilities in advance of the new input frontier,
                //    then there are no updates not in advance of the new input frontier and
                //    we can simply create an empty input batch with the new upper frontier
                //    and feed this to the trace agent (but not along the timely output).

                // If there is at least one capability not in advance of the input frontier ...
                if capabilities.elements().iter().any(|c| !input.frontier().less_equal(c.time())) {

                    let mut upper = Antichain::new();   // re-used allocation for sealing batches.

                    // For each capability not in advance of the input frontier ...
                    for (index, capability) in capabilities.elements().iter().enumerate() {

                        if !input.frontier().less_equal(capability.time()) {

                            // Assemble the upper bound on times we can commit with this capabilities.
                            // We must respect the input frontier, and *subsequent* capabilities, as
                            // we are pretending to retire the capability changes one by one.
                            upper.clear();
                            for time in input.frontier().frontier().iter() {
                                upper.insert(time.clone());
                            }
                            for other_capability in &capabilities.elements()[(index + 1) .. ] {
                                upper.insert(other_capability.time().clone());
                            }

                            // Extract updates not in advance of `upper`.
                            let batch = batcher.seal::<Tr::Builder>(upper.clone());

                            writer.insert(batch.clone(), Some(capability.time().clone()));

                            // send the batch to downstream consumers, empty or not.
                            output.session(&capabilities.elements()[index]).give(batch);
                        }
                    }

                    // Having extracted and sent batches between each capability and the input frontier,
                    // we should downgrade all capabilities to match the batcher's lower update frontier.
                    // This may involve discarding capabilities, which is fine as any new updates arrive
                    // in messages with new capabilities.

                    let mut new_capabilities = Antichain::new();
                    for time in batcher.frontier().iter() {
                        if let Some(capability) = capabilities.elements().iter().find(|c| c.time().less_equal(time)) {
                            new_capabilities.insert(capability.delayed(time));
                        }
                        else {
                            panic!("failed to find capability");
                        }
                    }

                    capabilities = new_capabilities;
                }
                else {
                    // Announce progress updates, even without data.
                    let _batch = batcher.seal::<Tr::Builder>(input.frontier().frontier().to_owned());
                    writer.seal(input.frontier().frontier().to_owned());
                }

                prev_frontier.clear();
                prev_frontier.extend(input.frontier().frontier().iter().cloned());
            }

            writer.exert();
        }
    });

    Arranged { stream, trace: reader.unwrap() }
}

impl<G: Scope, K: ExchangeData+Hashable, R: ExchangeData+Semigroup> Arrange<G, Vec<((K, ()), G::Timestamp, R)>> for Collection<G, K, R>
where
    G::Timestamp: Lattice+Ord,
{
    fn arrange_named<Tr>(&self, name: &str) -> Arranged<G, TraceAgent<Tr>>
    where
        Tr: Trace<Time=G::Timestamp> + 'static,
        Tr::Batch: Batch,
        Tr::Batcher: Batcher<Input=Vec<((K, ()), G::Timestamp, R)>>,
    {
        let exchange = Exchange::new(move |update: &((K,()),G::Timestamp,R)| (update.0).0.hashed().into());
        arrange_core(&self.map(|k| (k, ())).inner, exchange, name)
    }
}

/// Arranges something as `(Key,Val)` pairs according to a type `T` of trace.
///
/// This arrangement requires `Key: Hashable`, and uses the `hashed()` method to place keys in a hashed
/// map. This can result in many hash calls, and in some cases it may help to first transform `K` to the
/// pair `(u64, K)` of hash value and key.
pub trait ArrangeByKey<G: Scope, K: Data+Hashable, V: Data, R: Ord+Semigroup+'static>
where G::Timestamp: Lattice+Ord {
    /// Arranges a collection of `(Key, Val)` records by `Key`.
    ///
    /// This operator arranges a stream of values into a shared trace, whose contents it maintains.
    /// This trace is current for all times completed by the output stream, which can be used to
    /// safely identify the stable times and values in the trace.
    fn arrange_by_key(&self) -> Arranged<G, TraceAgent<ValSpine<K, V, G::Timestamp, R>>>;

    /// As `arrange_by_key` but with the ability to name the arrangement.
    fn arrange_by_key_named(&self, name: &str) -> Arranged<G, TraceAgent<ValSpine<K, V, G::Timestamp, R>>>;
}

impl<G: Scope, K: ExchangeData+Hashable, V: ExchangeData, R: ExchangeData+Semigroup> ArrangeByKey<G, K, V, R> for Collection<G, (K,V), R>
where
    G::Timestamp: Lattice+Ord
{
    fn arrange_by_key(&self) -> Arranged<G, TraceAgent<ValSpine<K, V, G::Timestamp, R>>> {
        self.arrange_by_key_named("ArrangeByKey")
    }

    fn arrange_by_key_named(&self, name: &str) -> Arranged<G, TraceAgent<ValSpine<K, V, G::Timestamp, R>>> {
        self.arrange_named(name)
    }
}

/// Arranges something as `(Key, ())` pairs according to a type `T` of trace.
///
/// This arrangement requires `Key: Hashable`, and uses the `hashed()` method to place keys in a hashed
/// map. This can result in many hash calls, and in some cases it may help to first transform `K` to the
/// pair `(u64, K)` of hash value and key.
pub trait ArrangeBySelf<G: Scope, K: Data+Hashable, R: Ord+Semigroup+'static>
where
    G::Timestamp: Lattice+Ord
{
    /// Arranges a collection of `Key` records by `Key`.
    ///
    /// This operator arranges a collection of records into a shared trace, whose contents it maintains.
    /// This trace is current for all times complete in the output stream, which can be used to safely
    /// identify the stable times and values in the trace.
    fn arrange_by_self(&self) -> Arranged<G, TraceAgent<KeySpine<K, G::Timestamp, R>>>;

    /// As `arrange_by_self` but with the ability to name the arrangement.
    fn arrange_by_self_named(&self, name: &str) -> Arranged<G, TraceAgent<KeySpine<K, G::Timestamp, R>>>;
}


impl<G: Scope, K: ExchangeData+Hashable, R: ExchangeData+Semigroup> ArrangeBySelf<G, K, R> for Collection<G, K, R>
where
    G::Timestamp: Lattice+Ord
{
    fn arrange_by_self(&self) -> Arranged<G, TraceAgent<KeySpine<K, G::Timestamp, R>>> {
        self.arrange_by_self_named("ArrangeBySelf")
    }

    fn arrange_by_self_named(&self, name: &str) -> Arranged<G, TraceAgent<KeySpine<K, G::Timestamp, R>>> {
        self.map(|k| (k, ()))
            .arrange_named(name)
    }
}