Concurrent Process Algebra for AI Agents

Manage AI agent workflows using concurrent process algebra patterns like parallel tasks, branch-fix loops, fan-out comparisons, and session status tracking.

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

bash

npm install cpa-agents

2) Create skill entrypoint

ts

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:

ts

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:

ts

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.

json

{
  "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.

json

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

fan-out

Run the same task across multiple models and merge outputs.

json

{
  "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.

json

{}

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(...).