How does it differ from traditional unit testing?

While unit testing checks specific inputs and outputs, Temporal Coalgebra uses bisimulation to prove that two systems are observationally identical across all possible infinite execution paths.

Can I use this for game logic verification?

Yes, the skill includes specialized gadgets for three-match integration, allowing you to verify that attacker and defender strategies remain consistent with defined rules.

What is the primary purpose of the Temporal Coalgebra skill?

It provides a formal framework to observe system behaviors and verify if two systems are equivalent (bisimilar) by analyzing their derivation streams, even if those streams are infinite.

What is a 'distinguishing trace' in this context?

If the BisimulationChecker finds that two systems are not equivalent, it produces a distinguishing trace—a specific sequence of moves or states that serves as a witness to their difference.

Temporal Coalgebra Verification

Name: Temporal Coalgebra Verification
Author: plurigrid

byplurigrid

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Security & Testing

Verifies infinite system behaviors and observational equivalence using coalgebraic bisimulation and stream analysis.

Temporal Coalgebra is a specialized verification skill designed for the observation and validation of complex, potentially infinite system behaviors. Unlike traditional algebraic methods that focus on construction, this skill employs the dual approach of coalgebra to observe derivation streams and establish behavioral equivalence. By implementing final coalgebra bisimulation, it allows developers to prove that two systems are observationally indistinguishable, making it an essential tool for formal verification, game semantics, and validating infinite data structures like streams and trees.

Key Features

01Final Coalgebra (νF) implementation for maximal bisimulation checking

02Infinite stream observation with lazy evaluation of derivation traces

03Automated identification of distinguishing traces for non-equivalent systems

04Observation functor mapping for transforming derivations into observable states

057 GitHub stars

06Three-match integration for game-theoretic strategy verification

Use Cases

01Verifying that a refactored protocol maintains the same observable behavior as the original

02Analyzing infinite data streams for correct-by-construction behavior

03Proving strategy equivalence in game development via bisimulation games

What are Skills?·How to Install

Install with 🐟 Skill.Fish

npx skillfish add plurigrid/asi temporal-coalgebra

For use in Claude.ai and ChatGPT

Download Skill