Concurrent Process Algebra for AI Agents

CPA Agents for OpenClaw

Version: 2.0.0

Use concurrent process algebra for practical multi-agent orchestration in OpenClaw. This skill is focused on production workflows: parallel execution, branch-fix loops, model fan-out, and session status introspection.

Install

1) Install library dependency

npm install cpa-agents

2) Create skill entrypoint

import { createOpenClawSkill } from "cpa-agents/adapters/openclaw";
export default createOpenClawSkill();

3) Runtime prerequisites

OpenClaw Gateway is running and reachable.

Skill host supports async command handlers.

Session context provides appendEvent for trace streaming.

Advanced operators

Use these when you need stronger control over failures, rollback, and data lineage.

Undo / rollback (invertible + saga)

invertible(forward, undo) defines a step plus compensating action.

saga([...steps]) executes steps in order; on failure, runs undo in reverse order.

Best for workflows with side effects (branch creation, file writes, merges, etc.).

Pattern:

import { invertible, saga } from "cpa-agents";
const workflow = saga([
  invertible(createBranch, deleteBranch),
  invertible(writeCode, revertCode),
  invertible(runValidation, cleanupValidation),
]);

Provenance (converse)

converse(R, inverseFn) is relational provenance, not operational undo.

Use it to answer: "which input(s) could have produced this output?"

Keep this separate from rollback logic (invertible/saga).

Pattern:

import { rel, converse } from "cpa-agents";
const generate = rel("generate", async (prompt: string) => [prompt + "-out"]);
const provenance = converse(generate, async (output: string) => [output.replace("-out", "")]);

Guarded flow (guard, guardValue, ifThenElse)

Use guard(...) to block unsafe execution.

Use guardValue(...) when a required value must exist.

Combine with ifThenElse(...) for conditional routing.

Reliability (retryWithBackoff, timeout, or)

retryWithBackoff for transient failures.

timeout(ms, process) to bound execution.

or(primary, fallback) for fallback routing when primary fails.

Practical guidance: undo vs converse

Use undo (invertible + saga) when you must reverse side effects.

Use converse for provenance/audit and lineage queries.

Typical production setup uses both:

- saga during execution - converse for post-run explainability

Commands

parallel

Run independent tasks concurrently.

{
  "tasks": [
    "analyze failing tests",
    "draft fix proposal",
    "write migration notes"
  ],
  "timeout": 300000
}

branch-fix

Run one task, and if errors are returned, branch into fix flow and continue.

{
  "task": "implement auth middleware and resolve lint issues",
  "timeout": 300000
}

fan-out

Run the same task across multiple models and merge outputs.

{
  "task": "propose API surface for agent orchestration",
  "models": ["model-a", "model-b"],
  "timeout": 300000
}

status

Return the current CPA process tree/status for the session.

{}

Recommended prompts

"Run parallel: audit security risks, propose patch plan, generate tests"

"Branch-fix this refactor until no type errors remain"

"Fan-out this architecture question across two models and compare"

"Show cpa status"

"Execute as saga: create branch, patch files, validate, rollback on failure"

"Show provenance: what input likely produced this output?"

Troubleshooting

Gateway not connected:

- Start OpenClaw Gateway and retry.

Unknown command:

- Use one of: parallel, branch-fix, fan-out, status.

Timeout:

- Increase timeout in command args.

Missing session events:

- Ensure session context is present and appendEvent is enabled.

Rollback did not occur:

- Verify steps are wrapped with invertible(...) and executed with saga(...).

Provenance unclear:

- Provide an explicit inverseFn when defining converse(...).

Gateway not connected:

- Start OpenClaw Gateway and retry.

Unknown command:

- Use one of: parallel, branch-fix, fan-out, status.

Timeout:

- Increase timeout in command args.

Missing session events:

- Ensure session context is present and appendEvent is enabled.

Rollback did not occur:

- Verify steps are wrapped with invertible(...) and executed with saga(...).

Provenance unclear:

- Provide an explicit inverseFn when defining converse(...).