lazily

Lazy reactive primitives for Python — the Cell kernel (Source / Computed cells, plus Effect) with automatic dependency tracking and cache invalidation, plus the language-agnostic lazily-spec wire protocol for mirroring graph state across processes and languages.

Overview

lazily is the Python port of the Cell kernel (#lzcellkernel): two value kinds — Source and Computed — plus the value-less Effect sink. Cell is the value node the Source handle is bound to.

• Source — a value written from outside (set / merge); the writable kind. Construct with source / cell (handle Source, native class Cell, slot SourceSlot / CellSlot). A MergeCell is a Source whose write folds under a non-KeepLatest policy (Cell ≡ Source(KeepLatest)).
• Computed — a value computed from upstream, via a compute function. Construct with computed(ctx, f). Guarded by default and lazy by default.
• Effect — a value-less sink outside the hierarchy; nothing can depend on it.

A Computed is lazy by default: dependents are marked dirty on invalidation but only recompute when accessed. When you need eager push-style semantics — recompute immediately, observe v1 → v2 with no unset window — make it eager: computed(ctx, f).eager(). Going eager attaches a scheduled puller Effect over the backing memo (eagerness is graph state — an _eager bit plus a side table — not a distinct type), so N writes inside one batch re-materialize the computed once, at the flush. Every cell is guarded — an equal recompute is suppressed by the PartialEq guard (matching TC39 Signal.Computed), so unchanged values never cascade downstream work. There is no unguarded derived mode: computed is the guarded derived constructor, and the former separate memo construction is retired.

Migration note (v2 Cell kernel, #lzcellkernel). The v1 value vocabulary is removed: Signal / signal / signal_def, formula / formula_def / FormulaCell, SourceCell / SourceCellSlot, and the .drive() / .undrive() / is_driven / is_active methods are gone. Use the v2 spelling instead — an eager Computed is computed(ctx, f).eager(); the lifecycle is .eager() / .lazy() / .is_eager(). The construction sugar cell / cell_def is deprecated in favour of source / source_def, and the derived-value slot decorator is deprecated in favour of the guarded computed (slot_def remains as the storage-sense factory). Python has no compile-time read/write split (see the design's §4): the split is a convention — a Source has set / merge, a Computed does not — not a runtime gate.

There is no dedicated Context class — a plain dict is the context, so the Rust reference's ctx.computed(f) is spelled computed(ctx, f) here. Slot is retained as the storage position that holds a node: a Slot uses itself as the dictionary key that caches its value, so any dict works as the reactive "world" (lazily-spec §5.0 "Slot-as-storage"). It is the Python analog of lazily-rs's surviving storage-sense Slot; construct it directly with Slot(callable=…) when a raw storage node is genuinely needed.

Feature coverage

The full lazily capability set across every binding. Legend: ✅ shipped · ~ partial · — absent or not applicable. The canonical matrix with per-cell notes and platform carve-outs lives in lazily-spec § Cross-Language Coverage.

Installation

pip install lazily

Example usage

from lazily import CellSlot, cell, slot

# Cells hold a value that can be updated.
name = CellSlot[dict, dict, str]()


# Slots are functions that depend on cells and other slots.
@slot
def greeting(ctx: dict) -> str:
    print("Calculating greeting...")
    return f"Hello, {name(ctx).value}!"


# A CellSlot can also have a default value.
@cell
def response(ctx: dict) -> str:
    return "How are you?"


@slot
def greeting_and_response(ctx: dict) -> str:
    print("Calculating greeting_and_response...")
    return f"{greeting(ctx)} {response(ctx).value}"


ctx = {}

name(ctx).value = "World"

# First access: runs the function
print(greeting(ctx))
# Calculating greeting...
# 'Hello, World!'

# Second access: uses cache (no print)
print(greeting(ctx))
# 'Hello, World!'

# Dependencies also access cached values
print(greeting_and_response(ctx))
# Calculating greeting_and_response...
# 'Hello, World! How are you?'

# Dependencies also cached
print(greeting_and_response(ctx))
# 'Hello, World! How are you?'

# Update cell: invalidates cache
name(ctx).value = "Lazily"

# Access again: re-runs the function
print(greeting_and_response(ctx))
# Calculating greeting_and_response...
# Calculating greeting...
# 'Hello, Lazily! How are you?'

# Another access: uses cache
print(greeting_and_response(ctx))
# 'Hello, Lazily! How are you?'

Core Concepts

Context

A plain dict is the context. It owns all cached Slot values; Slots store their cache under themselves as keys. The current implementation is single-threaded — create one dict per reactive graph.

Slot

A Slot wraps a compute function (ctx) -> T; the result is cached after first access. Dependencies are discovered automatically via a global slot_stack — any Slot or Cell read during computation becomes a dependency and re-subscribes on every recompute, so conditional branches update the dependency graph with no manual cleanup. When a dependency invalidates, the Slot only marks its cache dirty; it does not recompute until called again.

Source cell

A Source cell (native class Cell) holds a mutable value. Reading cell.value inside a Computed or Effect auto-subscribes that reader; assigning cell.value = x (or cell.set(x)) compares old and new via != and, only if changed, cascades invalidation to dependents. Construct with source (the v1 cell name is deprecated).

Eager Computed

An eager Computed — computed(ctx, f).eager() — is the counterpart to a lazy Computed. Where a lazy cell marks itself dirty on invalidation and recomputes on the next read, an eager one recomputes the instant a dependency is invalidated, before the mutating call returns. The value is always materialized, so observers never see an intermediate unset value.

from lazily import CellSlot, computed

n = CellSlot[dict, dict, int]()

ctx: dict = {}
n(ctx).value = 1

doubled = computed(ctx, lambda c: n(c).value * 2).eager()  # eager: materialized now
print(doubled.value)   # 2

n(ctx).value = 5       # doubled recomputes immediately
print(doubled.value)   # 10 — already current, no lazy read needed

An eager Computed is composed from existing primitives, not a parallel engine: a memoized backing Slot supplies glitch-free, guarded recomputation, and a small puller Effect re-materializes it after every invalidation to supply the eagerness. It inherits the guard (an equal recompute suppresses the downstream cascade). .lazy() (or .dispose()) removes the eager puller — the value stays readable but reverts to lazy (recompute-on-read) behavior.

StateMachine

StateMachine[S, E] is a finite state machine backed by a reactive Cell, so its state participates in dependency tracking like any other reactive value. Construct it with StateMachine(ctx, initial, transition) where transition is a pure (state, event) -> next_state | None (returning None rejects the event). send(event) returns whether the transition was accepted; a self-transition to an equal state is accepted but suppressed by the Cell's PartialEq guard.

Reactive collections, async, and thread-safe contexts

lazily-py also implements the lazily-spec compute-layer MUSTs, each ported from its Lean formal model in lazily-formal:

• ReactiveMap / SourceMap / ComputedMap / SourceTree — keyed reactive collections (#reactivemap) with independent value/membership/order signals and atomic move. One generic ReactiveMap over a handle kind; SourceMap (input cells, adds set + eager entry) and ComputedMap (derived slots, lazy get_or_insert_with + eager materialize_all) are its specializations.
• QueueCell — a reactive FIFO queue (SPSC primitive with an MPSC-via-batch usage rule) with a pluggable QueueStorage backend. Reader-kind invalidation (head/len/is_empty/is_full/closed), bounded reactive backpressure via is_full, and the closure lifecycle (drain / Closed-distinct-from-Empty / idempotent).
• reconcile_ops — move-minimized keyed reconciliation (LIS kernel).
• AsyncSlot / AsyncEffect — the async slot lifecycle with stale-completion discard, and cleanup-before-body effect scheduling.
• ThreadSafeContext — a lock-serialized batch boundary that coalesces writes into one invalidation pass.
• lazily.ffi — the C-ABI FFI boundary (LazilyFfiStatus, LazilyFfiMessageKind incl. CrdtSync = 3, LazilyFfiBytes).

The test suite gates on lazily-formal's lake build (every theorem checks) and mirrors the named Lean theorems as property tests. See SPEC.md for the full compliance surface.

Reactive queue — lazily.queue

QueueCell is a FIFO collection composed of reactive cells — not a new cell kind — that adds queue semantics (push to tail, pop from head) to the reactive graph. It is an SPSC primitive; MPSC is a usage rule on the same primitive — multiple producers push inside one batch, which serializes the pushes into a deterministic order. The reactive shell wraps a pluggable QueueStorage backend (default VecDequeStorage); the shell owns the reader-kind version cells and invalidates by reader kind — a push to a non-empty queue does NOT invalidate the head reader, a pop does.

from lazily import QueueCell, QueuePopError, batch

ctx = {}
q: QueueCell[str] = QueueCell(ctx)

q.try_push("a")
q.try_push("b")
assert q.head() == "a"
assert q.len() == 2
assert q.try_pop() == "a"

# Bounded queue → reactive backpressure via is_full.
bq = QueueCell[int].with_capacity(ctx, 2)
bq.try_push(1)
bq.try_push(2)
assert bq.is_full()
assert bq.try_push(3).label == "Full"   # reject at capacity
assert bq.try_pop() == 1
assert not bq.is_full()                  # pop freed a slot → is_full reader invalidated

# MPSC: multiple producers push inside one batch → one invalidation pass.
batch(lambda: (q.try_push("p1"), q.try_push("p2")))

# Closure: pop on closed+empty returns Closed (distinct from Empty).
q.close()
assert q.is_closed()
assert q.try_push("x").label == "Closed"

Competing-consumer work queue

WorkQueueCell provides exclusive FIFO claims with visibility deadlines, worker-scoped acknowledgements, tail retries, and bounded dead-letter handling. Item ids survive retries while each claim gets a fresh delivery id.

from lazily import WorkQueueCell

work = WorkQueueCell[str](ctx, visibility_timeout=10, max_deliveries=3)
work.push("job")
delivery = work.claim("worker-a", 100)
assert delivery is not None
assert work.ack("worker-a", delivery.delivery_id)

The reader-kind independence law (a push to a non-empty queue does not change head, so the head reader is not invalidated) comes for free from the Cell != (PartialEq) guard: after each op the shell re-derives each reader-kind cell from storage and writes it back, and a cell whose value did not change is not invalidated.

IPC — the lazily-spec wire protocol

lazily.ipc implements the language-agnostic lazily-spec wire protocol, so a Python graph's state can be mirrored to remote observers across processes and languages. The JSON encoding is byte-compatible with the Rust (lazily-rs), Zig (lazily-zig), and TypeScript (@lazily/signaling) bindings, and is validated against the canonical lazily-spec/conformance fixtures (vendored under tests/conformance/).

Two message kinds flow over any transport (WebSocket text, WebRTC data, FFI buffer):

• Snapshot — the full graph state at an epoch (nodes, edges, roots).
• Delta — an ordered batch of the 7 DeltaOp variants (CellSet, SlotValue, Invalidate, NodeAdd, NodeRemove, EdgeAdd, EdgeRemove) applied with epoch sequencing and fail-closed resync.

from lazily import (
    Snapshot, NodeSnapshot, EdgeSnapshot, ShmBlobRef,
    Delta, DeltaOp, IpcMessage,
)

# Build and serialize a snapshot — encode_json() returns transport-agnostic bytes.
snap = Snapshot(
    epoch=7,
    nodes=[
        NodeSnapshot.payload(1, "i32", bytes([1, 2, 3])),
        NodeSnapshot.opaque(2, "opaque-type"),
        NodeSnapshot.shared_blob(3, "text/plain", ShmBlobRef(0, 16, 1, 7, 999)),
    ],
    edges=[EdgeSnapshot(2, 1), EdgeSnapshot(3, 1)],
    roots=[1, 2],
)
wire = IpcMessage.of_snapshot(snap).encode_json()
assert IpcMessage.decode_json(wire).snapshot == snap

# An incremental delta carrying mutations.
delta = Delta.next(40, [
    DeltaOp.cell_set(1, bytes([10])),
    DeltaOp.invalidate(3),
])
IpcMessage.of_delta(delta).encode_json()

A PeerPermissions boundary gates what is shared: it is default-deny, so only nodes a peer is explicitly allowed to read are serialized into a snapshot or delta — non-allowlisted nodes are omitted entirely.

Shared-memory blobs — ShmBlobArena

ShmBlobArena lets a Python process host blob payloads (not just carry ShmBlobRef descriptors). It is a bytearray-backed, append-only arena with a 40-byte header (LZSH magic + FNV-1a-64 checksum) and wraparound, ported from the lazily-rs ShmBlobArena<B> and byte-compatible with the Rust and Zig arenas. The module exports ShmBlobArena, ShmBlobArenaError (with its variant subclasses), and SHM_BLOB_HEADER_LEN.

Lossless tree CRDT — lazily.lossless_tree_crdt

LosslessTreeCrdt (#lzlosstree) is a single rooted concrete-syntax tree whose leaves own every rendered byte — render(tree) == source_text for valid, invalid, and unknown source alike. Where TextCrdt is a flat lossless floor, this is the structured tree that can itself be the wire authority. Element nodes own structure only; all text lives in leaf nodes tagged Token / Trivia / Raw / Error, so unknown/invalid spans round-trip exactly as Raw/Error leaves rather than being discarded.

from lazily import LeafKind, LosslessTreeCrdt, SeedElement, SeedLeaf
from lazily.lossless_tree_crdt import ROOT

tree = LosslessTreeCrdt(peer=1)
heading = tree.create_node(ROOT, None, SeedElement("heading"))
tree.create_node(heading, None, SeedLeaf(LeafKind.TOKEN, "# "))
title = tree.create_node(heading, None, SeedLeaf(LeafKind.RAW, "Título"))
assert tree.render() == "# Título"

# Op-based delta sync: fork, diverge, converge through a dotted frontier.
other = tree.fork(peer=2)
other.edit_leaf(title, 0, 0, "X")
tree.apply_update(other.diff(tree.frontier()))
assert tree.render() == other.render()

Leaf text embeds TextCrdt wholesale; child order is a fractional index (key_between); the clock is a Lamport TreeOpId. Anti-entropy is op-based over a dotted, non-contiguous version frontier (TreeVersionFrontier) — a dot set (contiguous prefix + sparse holes), never a per-peer max, so a missing interior op stays representable and re-requestable. Leaf-local wire offsets are UTF-8 bytes (byte_to_char). The wire codec (tree_update_to_wire / tree_update_from_wire) validates against lazily-spec's lossless-tree-delta.json, and all nine conformance/lossless-tree/ fixtures replay.

Command / RPC message plane — lazily.command

command-plane-v1 is an additive sibling to Snapshot / Delta / CrdtSync: four evented frames (CommandSubmit / CommandCancel / CommandEvents / CommandProjection) that carry command traffic, not cell state. lazily owns the envelope; the namespace owns the IpcValue payload, which lazily never decodes.

The single hard rule: terminal authority is the causal receipt. A command is terminal only when a terminal CausalReceipt for its command_id folds in (applied, or rejected — including the cancelled / superseded / timed_out reasons). observed / accepted / started events are progress only; a transport ACK is never terminal.

from lazily import (
    CommandPolicy, CommandRpcClient, CommandSubmit, DedupePolicy,
    applied_receipt,
)
from lazily.ipc import IpcValue

class Transport:
    def __init__(self):
        self.sent = []

    def send(self, message):
        self.sent.append(message)

client = CommandRpcClient(Transport())
cmd_id = client.submit(CommandSubmit(
    command_id="cmd-1", causation_id="cmd-1", source="plugin",
    target="controller", namespace="agent-doc", name="editor_route",
    authority_generation=1, idempotency_key="doc:run", deadline_ms=0,
    policy=CommandPolicy(DedupePolicy.SAME_IDEMPOTENCY_KEY, False, True),
    payload_type="agent-doc.editor_route.v1", payload_hash="sha256:…",
    payload=IpcValue.of(b"{…}"),
    required_features=["command-plane-v1"],
))
# `call` resolves ONLY on a terminal receipt — never an ACK or `accepted`.
client.ingest_receipt(applied_receipt("rcpt-1", cmd_id, "controller", 1))
assert client.poll_call(cmd_id).kind.value == "resolved"

CommandProjection is the pure reducer (generation guards, idempotency, cancel-before-terminal-only, terminal-conflict-fails-closed, reconnect equivalence); CommandRpcClient is the derived RPC facade. The wire codec validates against lazily-spec's message-passing.json, and all eight conformance/message-passing/ fixtures replay.

Benchmarks

Wall-clock benchmarks live in BENCHMARKS.md, covering both the in-library micro-suite (reactive core, keyed reconciliation, SourceMap, TextCrdt, CRDT plane) and a large spreadsheet-shaped scale suite that mirrors the lazily-rs / lazily-go scale groups (N input cells + N formula slots, formula[i] = input[i] + input[i-1]). The scale suite is measured up to a full 10,000,000-cell Google Sheets workbook (N = 5,000,000); a one-cell edit plus a 1,000-cell viewport read stays in the ~75 µs range regardless of sheet size, because the lazy pull model recomputes only the ~2 formulas that read the edited input.

make bench          # micro-suite
make bench-scale    # scale suite (default N = 1,000,000)

# or directly, with a custom size:
uv run python -m lazily.benchmarks
LAZILY_SCALE_N=5000000 uv run python -m lazily.scale_bench   # 10M-cell workbook

See BENCHMARKS.md for the full results, hardware, and honest notes on CPython's per-node overhead.

The lazily family

lazily-py is one binding in a cross-language reactive family that shares the lazily-spec wire protocol:

See lazily-spec for the canonical Snapshot/Delta schemas, the IPC Lean proofs of the epoch/memo/batch invariants, and the conformance fixtures every IPC-capable binding validates against. The language-agnostic formal model — the flat FSM kernel and the full Harel state chart — lives in lazily-formal.

Development

This project uses uv. Run the local CI-equivalent suite — type-check (ty), lint (ruff), the runnable README example, and the test suite — with:

uv run poe precommit

SPEC.md is the authoritative specification for the Python primitives and the lazily-spec compliance notes.