Execution model

This notation describes the execution model. It is not a proof of implementation correctness. Replay assumes deterministic reducers, compatible definitions, and available event history or a compatible snapshot.

1. The Canonical Run Log#

A Run $R$ is a tuple consisting of a globally unique run identity $r$ and an ordered, append-only sequence of immutable events $L$:

Every agent, DAG workflow, child thread, external signal, and observable effect outcome participates in this single, canonical event stream.

2. Thread Universe & Parent Relation#

The units of computation participating in Run $R$ form a thread universe $X_R$ with a partial parent relation:

The root thread $x_0$ has $\text{parent}(x_0) = \bot$. Every child thread references its parent, inducing a strict tree hierarchy over threads within the run.

3. State Transition Function#

Each thread kind $k$ (e.g. agent, workflow, or a custom module kind) defines a pure, deterministic state transition function:

Given current state $s_t^x \in S_k$ and incoming event $e_t \in E$, the reducer deterministically computes next state $s_{t+1}^x$ and an ordered sequence of requested effects $\Phi_t^x \in F^*$.

4. Projections as Folds#

Compute state and read models by folding over the event log:

With persisted snapshot checkpoints at event sequence $m \le n$, state reconstruction is accelerated:

5. Causal Ordering vs. Structural Hierarchy#

Log order records when events were appended. Causation IDs record which event caused each one:

Events from concurrent threads can interleave in the log while retaining their causal links.

6. Replay & Durability Invariant#

Let $\pi_x(L)$ denote the projection filtering events relevant to thread $x$. The state at logical step $t$ is reproducible under those assumptions:

During historical replay, the effect stream $\Phi$ is ignored by the runtime kernel. Recovery also resumes unfinished work, which may retry external calls. Safe retries require idempotency or reconciliation at the external boundary.