improvise/context/code/zset.md

zset: the reasoning

crates/zset is ADR 009 step 1 (improvise-tk51, epic improvise-bw4p): the Z-set group, first and alone. Nothing depends on it yet, so it changes no behaviour. The decisions are the ADR's (context/adr/009-incremental-evaluation.md, clause 1). This file records how the crate reads them, where the ADR left a choice open, and the evidence discipline. The evidence for each test is in context/test-evidence/zset.md.

The shape

item	what it is
ZSet<K: Ord>	a map from K to a non-zero i64 weight; an abelian group within i64 (interpretation 5)
+, -, unary -, * i64, scale	the group operations and scalar multiplication
new, singleton, insert, FromIterator, Extend	construction; weights of equal keys sum
weight, is_zero, len, iter, IntoIterator	reads; iteration is ascending by key
map, filter, distinct	the three per-element operators
integrate, differentiate	the stream operators, over a slice

There are no dependencies: not serde (clause 9 keeps the wire form in improvise-protocol), not even the workspace's own crates. The crate is wasm32-clean by construction and is in nix/ci.nix's wasmCrates.

Canonical form

A key with weight zero is never stored. insert removes a key whose sum reaches zero, and singleton(k, 0) is the zero Z-set. Two Z-sets are therefore == exactly when every key has the same weight, so the derived PartialEq, Hash and Ord are the group's equality. The clause 9 correction target - held relies on it: a correct state gives == the zero Z-set, and is_zero is len() == 0, not a scan.

The representation is a BTreeMap. Iteration order is the key order, the same in every process and for every insertion order, which clause 3 needs (eager folds in CellKey order) and which a HashMap would give up (context/code/core.md, gotcha 18's argument).

Interpretations

The ADR is one paragraph on the crate, and says more about what it is for than what it is. These are the readings this step takes.

1. Clause 1 lists a Circuit and more operators; step 1 built the pure part, and "The circuit" below built the rest (improvise-bw4p.1). The ADR's list is delay, integrate, differentiate, map, filter, flat_map, index_by, join_indexed, distinct and aggregate, run by a synchronous Circuit, plus resumable rebuilds and a trace interface. Step 1 as ticketed is the group and the operators that are functions of a Z-set or of a stream of them: map, filter, distinct, integrate, differentiate. The rest needs the circuit (a clock, state held between steps), or a second key type (index_by, join_indexed, aggregate), and is left to the steps that use it rather than designed without a caller. flat_map is map into several images and has no user yet either.

2. integrate and differentiate are slice functions, not circuit nodes. integrate(&[d_0, d_1, ..]) is the running sums d_0 + .. + d_i; differentiate is its inverse, s_0 then s_i - s_(i-1). The state before the first element is zero, as in DBSP. delay is not provided: over a slice it is a shift, and a circuit gives it meaning.

3. distinct is not linear, and is not a group homomorphism. It keeps weight 1 on the keys whose weight is positive and drops every other key, negative included. That is the set-semantics operator of DBSP. The ADR says nothing about negative weights; dropping them is the standard reading, and the one that makes distinct idempotent.

4. Operators are methods on &self, group operations are std::ops traits. K: Clone is required only where a result copies keys (filter, distinct, scale, the borrowed operators); map and the by-value operators need only Ord.

5. Overflow. Neither clause 1 nor clause 8 states a policy for weights (clause 8 is about f64 drift, which wrapping integers do not have). The crate currently uses checked_* on every weight operation, for the reason given below, and panics with zset: weight overflow in <op>, in debug and in release (checked_* does not depend on overflow-checks). The operations are add (including insert, Extend, FromIterator), sub, neg (so i64::MIN panics when it has to be negated) and scale. Scaling by zero cannot overflow and returns the zero Z-set. A panic, not a Result: Result does not belong in the majority of the code (AGENTS.md), and a weight near i64::MAX is a defect in the caller, not an input to recover from. The weights clause 3 produces are small (one per cell).

   The group is partial, and that is the stated reading. The ADR calls a Z-set an abelian group. With i64 weights and no wrapping, the laws hold wherever no weight, intermediate ones included, leaves i64; outside that, an operation panics rather than return a different value. So associativity is order-dependent at the boundary: (MAX + 1) + (-1) panics where MAX + (1 + (-1)) is MAX. The result is never wrong, only sometimes refused. Wrapping arithmetic would make the type a true group (the integers mod 2^64), and (w + x) - x == w would still hold exactly, so a retraction does cancel its insertion under wrapping. (An earlier version of this paragraph said otherwise; that was wrong.) What wrapping breaks is the intermediate reads. MAX + 1 stores i64::MIN, so distinct drops a key whose true weight is positive and weight() has the wrong sign. A true weight of 2^64 stores as 0 (by the add path; a scale product of 2^64 would store a zero too, which breaks canonical form), so the key vanishes and is_zero, len and == report a set that does not exist. Those are wrong answers returned silently, which is why the crate panics instead. A wider weight (i128) moves the boundary and does not remove it. The ADR's "abelian group" wording needs amending whichever policy is chosen: checked-and-panic gives a group only within range, wrapping gives a group whose reads can be wrong, and i128 is partial too. Which one is a ruling for the user, not for this step; the crate currently panics, and overflow_depends_on_the_order_of_evaluation_and_never_gives_a_wrong_value states it. sub is checked directly against the held weight, so a - a is zero for every a, i64::MIN included, and only an absent key's 0 - w can overflow (w is i64::MIN).

6. Stable error text. The panic message names the operation and both operands, so a failure in a long-running host is diagnosable from the log.

What the tests are

crates/zset/tests/properties.rs holds one checker per property, parameterised by an Alg trait. The property's test runs it on ZSet. A companion runs it on Model(Fault::None), a second implementation over a sorted vector, so the checker is shown not to reject a correct implementation that is not ZSet. Each rival is Model(Fault::X), run through the same checker with a deterministic seed, and the failure message must carry the property's tag ([inverse], [map], ..). A rival that fails for another reason does not count. The group laws, canonical form, scalar distributivity, the map homomorphism, filter linearity, distinct's definition, iteration order, the clause 9 correction identity and the integrate/differentiate inverses are all properties; each runs at the default 256 cases over keys from a range of six, so collisions and cancelling pairs are the common case. Weights come from -3..=3, an explicit zero, and ±2^40, so sums of three cannot wrap.

The overflow policy is not a property over the generators (they cannot reach it by design) and is tested by example in src/lib.rs, with should_panic(expected = ..).

The circuit (improvise-bw4p.1)

Clause 1's deferred scope, built without ADR 008. The ADR is not edited; this is how the crate reads it.

item	what it is
Circuit	creation-order list of boxed nodes; step() runs each once
Input<K>, Stream<ZSet<K>>, Output<K>	push a delta in; the value on an edge; a sink that sums every step's delta until take()
delay, integrate, differentiate, plus	the stream operators as nodes
map, filter, flat_map, index_by	linear, per-element
distinct	incremental, state is the integrated input (DistinctState)
join_indexed, join_indexed_in	bilinear delta join of two ZSet<(K, _)> (JoinState)
aggregate, aggregate_in	group-by, re-folds only touched keys (AggregateState)
Trace, MemTrace	operator state behind lookup, range, apply
Rebuild, Progress	a snapshot loaded as a resumable job

Decisions, where the ADR left a choice:

1. Wiring is apart from logic. circuit.rs is the only file with Rc, RefCell and Box<dyn Node>. ops.rs holds each stateful operator as a plain struct with a pure step(delta) -> delta, testable and usable without a circuit.
2. Scheduling is creation order. A node is built from streams that already exist, so creation order is a topological order, and the circuit has no cycles: the ADR has no recursion operator, and integrate is its own stateful node, not a delayed feedback loop. delay is a node with one held Z-set. Not Send; one thread per circuit (clause 1).
3. Incremental means the integral of the output is the operator of the integral of the input. That is the property every operator is tested against, over random delta streams. distinct and aggregate are not linear, so they keep the integrated input and emit the difference of the operator at the touched keys only.
4. index_by is map to (key, element). A keyed stream is a ZSet<(K, V)>; there is no separate indexed collection type, so the join and the aggregate read the same shape.
5. The join is da x b_prev + a_prev x db + da x db, computed as da against the right trace, da applied to the left, then db against the updated left (which holds the cross term), then db applied. Output weights are products and panic on i64 overflow like every weight (interpretation 5). f(&K, &A, &B) -> O builds the output key.
6. aggregate's fold gets the key and the group's (value, weight) pairs (owned, because a paged trace cannot lend references) and returns Option<R>; None means the group has no row (an empty group, or a Min of nothing). Sum, count, min and max are closures; text unanimity and the ADR's ExactSum belong to the caller (clause 4, 8), not this crate.
7. The trace interface is apply(k, v, w), lookup(k) and range(lo, hi), returning owned vectors. MemTrace is a BTreeMap<K, ZSet<V>>; the _in constructors take any Trace, which is the seam for paging or compression. An empty or inverted range reads nothing (BTreeMap::range would panic).
8. The resumable step takes a predicate, not an Instant. Rebuild::step(circuit, expired) loads chunk keys per circuit step and stops when expired() is true, always running at least one chunk first, so every call progresses. Instant::now() panics on wasm32 (web-time is a dependency this crate refuses), so the host closes over its own clock. Outputs of the chunks sum to what one delta would give, which the test states. Buffering live deltas during a rebuild (clause 7) is the host's: push them to the same input after the job is done, or to a second input merged with plus.
9. Not built: Circuit does not own a job runner (ADR 008's), and nothing here is serialised (clause 9, improvise-protocol).

The tests are crates/zset/tests/circuit.rs; the rivals and where they failed are in context/test-evidence/zset.md.