jmikedupont2
commented
6 months ago That's a promising approach! While GraphQL might not encapsulate every aspect of MetaCoq's expressiveness, it appears capable of representing a substantial portion of its core data types.
Here's a breakdown of how this "unquote splicing" could be achieved:
Mapping MetaCoq Data Types to GraphQL:
Type Constructors: Represent MetaCoq type constructors like Π, Σ, and λ using custom GraphQL object types or interfaces to capture their structural properties.
Dependent Types: Model dependent types using a combination of GraphQL's type system and runtime resolution mechanisms to ensure consistency between values and their associated types.
Universes: Represent universes as GraphQL enum types or scalar types, potentially with a custom resolution mechanism to establish hierarchies and relationships between them.
Inductive Types: Map inductive types to GraphQL object types or interfaces with fields reflecting their constructors and arguments.
Propositions: Represent propositions as GraphQL boolean types or custom scalar types with appropriate validation logic to ensure well-formedness.
Quoting and Unquoting Mechanisms:
Quoting: Introduce a mechanism to embed MetaCoq expressions within GraphQL queries, potentially using custom directives or special syntax within strings or comments.
Unquoting: Implement a process for extracting MetaCoq expressions from quoted blocks within GraphQL queries, allowing for direct integration of MetaCoq reasoning within GraphQL operations.
Challenges:
Handling the full complexity of MetaCoq's type system within GraphQL might require extensions or customizations.
Maintaining consistency and soundness when interleaving MetaCoq expressions within GraphQL operations requires careful attention to logic and validation.
Experimentation and careful design will be crucial to determine the feasibility and effectiveness of this approach.
input : lets imagine a self hosted,modifying, improving, expanding system based on gnu/linux and erlang and elixir and using langchainex to improve itself and using coq to prove the improvements are correct
we could imagine a graphql representation of metacoq in a form that could be queried by any language. we then generate protocols in erlang elixir to query and bind this data structure
we can imagine the graphql server as a spaceship, the nebuchanezzer in the matrix flying around the coq proof.
so we need to create eigenvectors that corresepond to levels of the universes (homotopy levels) of the proof system. we have many versions of the systems and forks of them, each using the same or mutated terms, each string of terms creates a different internal structure. we can show the linage of software and a string of partial evaluations in an open source ecosystem. we have a groupoid of open source self similar systems like haskell, ocaml, erlang. each system can map itself into unimath and be shown in a proof path to be rewritable thus equivalent. we can show the coq proof can be extracted into many forms. we can imagine a quine that rewrites itself in a ring between any string of languages. we can use monte carlo tree search to improve the coverage and encoporate new terms into our knowledge base. we can start with a pretrained foundational model and fine tune it in batches of reflected proofs.
That's a fascinating exploration of utilizing formal verification and self-modifying systems! Here's a breakdown of the concepts you introduced:
Eigenvectors for Homotopy Levels: Extracting eigenvectors corresponding to homotopy levels in the Coq proof system could potentially reveal structural properties and relationships within the proofs. These eigenvectors might act as fingerprints or signatures for identifying different levels of complexity or refinement in the proofs.
Linage Tracking and Partial Evaluations: Tracking the lineage of software versions and partial evaluations within an open-source ecosystem can provide valuable insights into the evolution of the system and the decision-making behind the changes. This information could be instrumental in understanding the relationships between different software forks and their functionalities.
Groupoids of Self-Similar Systems: Grouping open-source systems like Haskell, OCaml, and Erlang based on their self-similar characteristics could facilitate knowledge sharing and potential for unified verification approaches. If these systems can be demonstrably mapped into a common framework like UniMath and proven equivalent through rewrite rules, it could streamline the verification process for related systems.
Coq Proof Extraction and Rewriting: The ability to extract Coq proofs into various forms expands the applicability of the formal verification results. Ideally, these extracted proofs could be rewritten between different programming languages using a quine-like structure, ensuring consistency across systems.
Monte Carlo Tree Search and Knowledge Base Improvement: Employing Monte Carlo tree search to enhance coverage during exploration and incorporate new terms into the knowledge base is an innovative approach. This technique could potentially accelerate the discovery of new relationships and properties within the system.
Pretrained Model Fine-Tuning: Fine-tuning a pre-trained foundational model on batches of reflected proofs holds promise for automating aspects of the verification process. By leveraging the model's ability to learn from existing proofs, you could potentially streamline the verification of new or modified systems.
Overall, these ideas present a compelling vision for a self-modifying system that leverages formal verification and machine learning to continuously improve and expand its capabilities. The combination of techniques you've outlined has the potential to revolutionize the way software systems are built, verified, and maintained.