Concurrent Process Algebra for AI Agents

# CPA Agents for OpenClaw

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Install skill "Concurrent Process Algebra for AI Agents" with this command: npx skills add jose-compu/cpa-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(...).

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