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Compile & Prove Protocol
May 21, 2024
lets make up a protocol for you to use to communicate in a more formal manner with a proof engine and compiler and cicd framework
ChatGPT
Sure, let's create a protocol for formal communication between an AI language model (like me) and a proof engine, compiler, and CI/CD (Continuous Integration/Continuous Deployment) framework. This protocol will ensure precise, clear, and effective interaction.
Command: SUBMIT_THEOREM
Parameters:
theorem_id: Unique identifier for the theorem.
theorem_statement: Formal statement of the theorem.
Response: THEOREM_SUBMITTED or ERROR_[error_code]
Request Proof Status
Command: REQUEST_PROOF_STATUS
Parameters:
theorem_id
Response: PROOF_STATUS_[status] (where [status] can be PENDING, PROVEN, FAILED)
Retrieve Proof Details
Command: TERMINATE_PROOF_ENGINE
Response: PROOF_ENGINE_TERMINATED
AI to Compiler Protocol
Initialization
Command: INITIATE_COMPILER
Purpose: Start the compiler session.
Response: COMPILER_READY
Submit Code for Compilation
Command: SUBMIT_CODE
Parameters:
code_id: Unique identifier for the code snippet.
source_code: The code to be compiled.
language: Programming language of the source code.
Response: CODE_SUBMITTED or ERROR_[error_code]
Request Compilation Status
Command: REQUEST_COMPILATION_STATUS
Parameters:
code_id
Response: COMPILATION_STATUS_[status] (where [status] can be PENDING, SUCCESS, FAILED)
Retrieve Compilation Output
Command: TRIGGER_BUILD
Parameters:
build_id: Unique identifier for the build.
repository_url: URL of the code repository.
branch: Branch to be built.
Response: BUILD_TRIGGERED or ERROR_[error_code]
Request Build Status
Command: REQUEST_BUILD_STATUS
Parameters:
build_id
Response: BUILD_STATUS_[status] (where [status] can be PENDING, SUCCESS, FAILED)
Retrieve Build Logs
Command: DEPLOY_APPLICATION
Parameters:
deployment_id: Unique identifier for the deployment.
build_id: Identifier of the build to deploy.
environment: Deployment environment (e.g., staging, production).
Response: DEPLOYMENT_TRIGGERED or ERROR_[error_code]
Request Deployment Status
Command: REQUEST_DEPLOYMENT_STATUS
Parameters:
deployment_id
Response: DEPLOYMENT_STATUS_[status] (where [status] can be PENDING, SUCCESS, FAILED)
Terminate CI/CD Session
Command: TERMINATE_CICD
Response: CICD_TERMINATED
Example Interaction Flow
AI to Proof Engine:
INITIATE_PROOF_ENGINE
SUBMIT_THEOREM with theorem_id="T123" and theorem_statement="∀x∈ℝ, x²≥0"
REQUEST_PROOF_STATUS with theorem_id="T123"
RETRIEVE_PROOF_DETAILS with theorem_id="T123"
TERMINATE_PROOF_ENGINE
AI to Compiler:
INITIATE_COMPILER
SUBMIT_CODE with code_id="C456", source_code="int main() { return 0; }", and language="C"
REQUEST_COMPILATION_STATUS with code_id="C456"
RETRIEVE_COMPILATION_OUTPUT with code_id="C456"
TERMINATE_COMPILER
AI to CI/CD Framework:
INITIATE_CICD
TRIGGER_BUILD with build_id="B789", repository_url="https://github.com/user/repo", and branch="main"
REQUEST_BUILD_STATUS with build_id="B789"
RETRIEVE_BUILD_LOGS with build_id="B789"
DEPLOY_APPLICATION with deployment_id="D012", build_id="B789", and environment="production"
REQUEST_DEPLOYMENT_STATUS with deployment_id="D012"
TERMINATE_CICD
This protocol structure ensures clarity and consistency in communication, making interactions between the AI, proof engine, compiler, and CI/CD framework efficient and error-free.
now lets abstract the validation provider as a plugin and consider a composed algebraic representation of the internal state of the feedback that is self contained and comprehensive
ChatGPT
To abstract the validation provider as a plugin and to create a composed algebraic representation of the internal state of the feedback, we can define a more modular and extensible system. This approach will allow for easy integration of various validation providers (proof engines, compilers, CI/CD frameworks) and enable a comprehensive internal state representation.
Abstracting the Validation Provider as a Plugin
Plugin Interface Definition
Define a common interface that all validation providers must implement. This interface will include methods for initialization, submission, status checking, retrieval, and termination.
Example Interface (Pseudocode)
python
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class ValidationProvider:
def initialize(self) -> str:
pass
Composed Algebraic Representation of Internal State
State Representation
Use algebraic data types to represent the state of each interaction with the validation providers. This ensures a structured and self-contained feedback mechanism.
Example State Classes (Pseudocode)
python
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from enum import Enum
from typing import Union, Optional
internal_state = InternalState()
proof_state = ProofState(theorem_id="T123", status=Status.PENDING)
internal_state.update_state("T123", proof_state)
Integrating the Plugin System with Internal State
Controller Class (Pseudocode)
python
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class ValidationController:
def init(self):
self.providers = {}
self.internal_state = InternalState()
def register_provider(self, provider_name: str, provider: ValidationProvider):
self.providers[provider_name] = provider
def initialize_provider(self, provider_name: str) -> str:
return self.providers[provider_name].initialize()
def submit_to_provider(self, provider_name: str, id: str, content: str, **kwargs) -> str:
response = self.providers[provider_name].submit(id, content, **kwargs)
self.internal_state.update_state(id, ProofState(id, Status.PENDING))
return response
def check_status(self, provider_name: str, id: str) -> str:
status = self.providers[provider_name].request_status(id)
# Update internal state based on status
if status == "PROOF_STATUS_SUCCESS":
self.internal_state.update_state(id, ProofState(id, Status.SUCCESS))
elif status == "PROOF_STATUS_FAILED":
self.internal_state.update_state(id, ProofState(id, Status.FAILED))
return status
def retrieve_details(self, provider_name: str, id: str) -> str:
details = self.providers[provider_name].retrieve_details(id)
current_state = self.internal_state.get_state(id)
if current_state and isinstance(current_state, ProofState):
self.internal_state.update_state(id, ProofState(id, current_state.status, details))
return details
def terminate_provider(self, provider_name: str) -> str:
return self.providers[provider_name].terminate()
This approach encapsulates the interactions with validation providers and maintains a comprehensive internal state, ensuring all feedback is self-contained and can be easily managed and queried.
lets consider this a typeclass
ChatGPT
To create a typeclass for validation providers, we'll use an approach that can be adapted to languages supporting typeclasses or similar constructs, such as Haskell or Scala. In this example, I'll demonstrate using Haskell syntax, which is known for its robust typeclass support. We can then describe how similar concepts could be implemented in other languages like Scala or using traits in Rust.
Haskell Typeclass for Validation Providers
Typeclass Definition
haskell
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class ValidationProvider v where
initialize :: v -> IO String
submit :: v -> String -> String -> IO String
requestStatus :: v -> String -> IO String
retrieveDetails :: v -> String -> IO String
terminate :: v -> IO String
Typeclass Instances
updateState :: String -> ValidationState -> InternalState -> InternalState
updateState id newState (InternalState state) = InternalState (Map.insert id newState state)
getState :: String -> InternalState -> Maybe ValidationState
getState id (InternalState state) = Map.lookup id state
Example Usage in Haskell
Controller Functionality
haskell
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initializeProvider :: ValidationProvider v => v -> IO String
initializeProvider = initialize
submitToProvider :: ValidationProvider v => v -> String -> String -> IO (String, InternalState)
submitToProvider provider id content = do
response <- submit provider id content
let newState = case provider of
ProofEngine -> PS (ProofState id Pending Nothing)
Compiler -> CS (CompilationState id Pending Nothing)
return (response, updateState id newState (InternalState Map.empty))
checkStatus :: ValidationProvider v => v -> String -> InternalState -> IO (String, InternalState)
checkStatus provider id internalState = do
status <- requestStatus provider id
let newStatus = if status == "PROOF_STATUS_SUCCESS" || status == "COMPILATION_STATUS_SUCCESS"
then Success
else if status == "PROOF_STATUS_FAILED" || status == "COMPILATION_STATUS_FAILED"
then Failed
else Pending
updatedState = case provider of
ProofEngine -> let (Just (PS (ProofState _ _ details))) = getState id internalState
in updateState id (PS (ProofState id newStatus details)) internalState
Compiler -> let (Just (CS (CompilationState _ _ output))) = getState id internalState
in updateState id (CS (CompilationState id newStatus output)) internalState
return (status, updatedState)
retrieveDetails :: ValidationProvider v => v -> String -> InternalState -> IO (String, InternalState)
retrieveDetails provider id internalState = do
details <- retrieveDetails provider id
let updatedState = case provider of
ProofEngine -> let (Just (PS (ProofState _ status _))) = getState id internalState
in updateState id (PS (ProofState id status (Just details))) internalState
Compiler -> let (Just (CS (CompilationState _ status _))) = getState id internalState
in updateState id (CS (CompilationState id status (Just details))) internalState
return (details, updatedState)
terminateProvider :: ValidationProvider v => v -> IO String
terminateProvider = terminate
Typeclass Concept in Other Languages
Scala
In Scala, you can achieve similar functionality using traits and implicit classes:
impl ValidationProvider for Compiler {
fn initialize(&self) -> String {
"COMPILER_READY".to_string()
}
fn submit(&self, id: &str, content: &str) -> String {
"CODE_SUBMITTED".to_string()
}
fn request_status(&self, id: &str) -> String {
"COMPILATION_STATUS_PENDING".to_string()
}
fn retrieve_details(&self, id: &str) -> String {
"COMPILATION_OUTPUT_[output]".to_string()
}
fn terminate(&self) -> String {
"COMPILER_TERMINATED".to_string()
}
}
This approach ensures modularity and abstraction, allowing easy integration of various validation providers and consistent internal state management across different programming languages.
now we loop in liquid haskell to implement the proofs using dependant type thoery
ChatGPT
Liquid Haskell is a refinement type system that allows embedding logical assertions directly within Haskell code, enabling more precise type checking and verification of properties. Let's integrate Liquid Haskell to implement the proofs for our validation provider system using dependent type theory.
Overview
Defining Types and Refinements: Use Liquid Haskell to specify precise types and invariants for our data structures.
Validation Provider Typeclass: Ensure that the methods in our typeclass adhere to the specified invariants.
Internal State Management: Utilize dependent types to maintain correctness in our state transitions.
Setup
First, make sure you have Liquid Haskell installed. You can find installation instructions on the Liquid Haskell GitHub page.
Defining Types and Refinements
We define our data types with Liquid Haskell refinements to capture invariants.
haskell
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{-# LANGUAGE GADTs #-}
{-# LANGUAGE DataKinds #-}
{-# LANGUAGE KindSignatures #-}
{-# LANGUAGE TypeFamilies #-}
{-# LANGUAGE FlexibleContexts #-}
{-# LANGUAGE ScopedTypeVariables #-}
{-# LANGUAGE TypeApplications #-}
module ValidationProvider where
import Data.Map (Map)
import qualified Data.Map as Map
import LiquidHaskell
{-@ data Status = Pending | Success | Failed @-}
data Status = Pending | Success | Failed deriving (Show, Eq)
{-@ type NonEmptyString = {v:String | len v > 0} @-}
{-@ data DeploymentState = DeploymentState
{ deploymentId :: NonEmptyString
, deploymentStatus :: Status
} @-}
data DeploymentState = DeploymentState
{ deploymentId :: String
, deploymentStatus :: Status
} deriving (Show, Eq)
data ValidationState
= PS ProofState
| CS CompilationState
| BS BuildState
| DS DeploymentState
deriving (Show, Eq)
Validation Provider Typeclass
Next, define the typeclass with Liquid Haskell refinements to ensure that the methods adhere to the specified invariants.
haskell
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{-# LANGUAGE MultiParamTypeClasses #-}
{-# LANGUAGE FunctionalDependencies #-}
{-# LANGUAGE FlexibleInstances #-}
{-@ class ValidationProvider v where
initialize :: v -> IO {v:String | len v > 0}
submit :: v -> NonEmptyString -> NonEmptyString -> IO {v:String | len v > 0}
requestStatus :: v -> NonEmptyString -> IO {v:String | len v > 0}
retrieveDetails :: v -> NonEmptyString -> IO {v:String | len v > 0}
terminate :: v -> IO {v:String | len v > 0}
@-}
class ValidationProvider v where
initialize :: v -> IO String
submit :: v -> String -> String -> IO String
requestStatus :: v -> String -> IO String
retrieveDetails :: v -> String -> IO String
terminate :: v -> IO String
data ProofEngine = ProofEngine
data Compiler = Compiler
{-@ getState :: NonEmptyString -> InternalState -> Maybe ValidationState @-}
getState :: String -> InternalState -> Maybe ValidationState
getState id (InternalState state) = Map.lookup id state
-- Example Usage
initializeProvider :: ValidationProvider v => v -> IO String
initializeProvider = initialize
submitToProvider :: ValidationProvider v => v -> String -> String -> IO (String, InternalState)
submitToProvider provider id content = do
response <- submit provider id content
let newState = case provider of
ProofEngine -> PS (ProofState id Pending Nothing)
Compiler -> CS (CompilationState id Pending Nothing)
return (response, updateState id newState (InternalState Map.empty))
checkStatus :: ValidationProvider v => v -> String -> InternalState -> IO (String, InternalState)
checkStatus provider id internalState = do
status <- requestStatus provider id
let newStatus = if status == "PROOF_STATUS_SUCCESS" || status == "COMPILATION_STATUS_SUCCESS"
then Success
else if status == "PROOF_STATUS_FAILED" || status == "COMPILATION_STATUS_FAILED"
then Failed
else Pending
updatedState = case provider of
ProofEngine -> let (Just (PS (ProofState _ _ details))) = getState id internalState
in updateState id (PS (ProofState id newStatus details)) internalState
Compiler -> let (Just (CS (CompilationState _ _ output))) = getState id internalState
in updateState id (CS (CompilationState id newStatus output)) internalState
return (status, updatedState)
retrieveDetails :: ValidationProvider v => v -> String -> InternalState -> IO (String, InternalState)
retrieveDetails provider id internalState = do
details <- retrieveDetails provider id
let updatedState = case provider of
ProofEngine -> let (Just (PS (ProofState _ status _))) = getState id internalState
in updateState id (PS (ProofState id status (Just details))) internalState
Compiler -> let (Just (CS (CompilationState _ status _))) = getState id internalState
in updateState id (CS (CompilationState id status (Just details))) internalState
return (details, updatedState)
terminateProvider :: ValidationProvider v => v -> IO String
terminateProvider = terminate
Summary
By incorporating Liquid Haskell, we've refined our types to enforce invariants and properties at the type level. This ensures that our data remains consistent and valid throughout the operations of the validation providers. This approach enhances the safety and reliability of the system, leveraging the power of dependent type theory and refinement types in Haskell.
we can now return a desugared th as the detailed state feedback so the interface to the system reflects the complexities of th itself
ChatGPT
To return desugared Template Haskell (TH) as detailed state feedback, we need to integrate TH into our validation provider system. Template Haskell allows us to generate and manipulate Haskell code programmatically. By leveraging TH, we can provide more detailed feedback and introspection capabilities within our system.
Here's how we can achieve this:
Define Types for Desugared TH Representations: We need a way to represent the desugared TH feedback.
Modify Validation Provider Interface: Ensure the interface returns desugared TH representations as detailed state feedback.
Implement Desugaring Logic: Use TH to desugar and extract detailed state information.
Step 1: Define Types for Desugared TH Representations
We'll define types to capture the desugared TH feedback. These types should be rich enough to represent the various forms of TH constructs.
haskell
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{-# LANGUAGE TemplateHaskell #-}
{-# LANGUAGE GADTs #-}
{-# LANGUAGE DataKinds #-}
{-# LANGUAGE KindSignatures #-}
{-# LANGUAGE TypeFamilies #-}
{-# LANGUAGE FlexibleContexts #-}
{-# LANGUAGE ScopedTypeVariables #-}
{-# LANGUAGE TypeApplications #-}
data ValidationState
= PS ProofState
| CS CompilationState
| BS BuildState
| DS DeploymentState
deriving (Show, Eq)
Step 2: Modify Validation Provider Interface
Modify the interface to include desugared TH feedback. We'll adjust the retrieveDetails method to return desugared TH.
haskell
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{-# LANGUAGE MultiParamTypeClasses #-}
{-# LANGUAGE FunctionalDependencies #-}
{-# LANGUAGE FlexibleInstances #-}
{-# LANGUAGE TemplateHaskell #-}
{-@ class ValidationProvider v where
initialize :: v -> IO {v:String | len v > 0}
submit :: v -> NonEmptyString -> NonEmptyString -> IO {v:String | len v > 0}
requestStatus :: v -> NonEmptyString -> IO {v:String | len v > 0}
retrieveDetails :: v -> NonEmptyString -> IO (DesugaredTH, {v:String | len v > 0})
terminate :: v -> IO {v:String | len v > 0}
@-}
class ValidationProvider v where
initialize :: v -> IO String
submit :: v -> String -> String -> IO String
requestStatus :: v -> String -> IO String
retrieveDetails :: v -> String -> IO (DesugaredTH, String)
terminate :: v -> IO String
data ProofEngine = ProofEngine
data Compiler = Compiler
instance ValidationProvider Compiler where
initialize _ = return "COMPILER_READY"
submit _ codeId sourceCode = return "CODE_SUBMITTED"
requestStatus _ codeId = return "COMPILATION_STATUS_PENDING"
retrieveDetails _ codeId = return (DesugaredExp $ VarE 'codeId, "COMPILATION_OUTPUT_[output]")
terminate _ = return "COMPILER_TERMINATED"
Step 3: Implement Desugaring Logic
Implement the logic to desugar TH constructs and integrate it into the state updates.
haskell
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-- Desugaring Logic
desugarExp :: Exp -> Exp
desugarExp = id -- Simplified for illustration; normally you would process the AST
desugarDec :: Dec -> Dec
desugarDec = id
desugarType :: Type -> Type
desugarType = id
desugarPat :: Pat -> Pat
desugarPat = id
-- Adjust Internal State Management to include DesugaredTH
updateState :: String -> ValidationState -> InternalState -> InternalState
updateState id newState (InternalState state) = InternalState (Map.insert id newState state)
getState :: String -> InternalState -> Maybe ValidationState
getState id (InternalState state) = Map.lookup id state
initializeProvider :: ValidationProvider v => v -> IO String
initializeProvider = initialize
submitToProvider :: ValidationProvider v => v -> String -> String -> IO (String, InternalState)
submitToProvider provider id content = do
response <- submit provider id content
let newState = case provider of
ProofEngine -> PS (ProofState id Pending Nothing Nothing)
Compiler -> CS (CompilationState id Pending Nothing Nothing)
return (response, updateState id newState (InternalState Map.empty))
checkStatus :: ValidationProvider v => v -> String -> InternalState -> IO (String, InternalState)
checkStatus provider id internalState = do
status <- requestStatus provider id
let newStatus = if status == "PROOF_STATUS_SUCCESS" || status == "COMPILATION_STATUS_SUCCESS"
then Success
else if status == "PROOF_STATUS_FAILED" || status == "COMPILATION_STATUS_FAILED"
then Failed
else Pending
updatedState = case provider of
ProofEngine -> let (Just (PS (ProofState _ _ details th))) = getState id internalState
in updateState id (PS (ProofState id newStatus details th)) internalState
Compiler -> let (Just (CS (CompilationState _ _ output th))) = getState id internalState
in updateState id (CS (CompilationState id newStatus output th)) internalState
return (status, updatedState)
retrieveDetails :: ValidationProvider v => v -> String -> InternalState -> IO (String, InternalState)
retrieveDetails provider id internalState = do
(th, details) <- retrieveDetails provider id
let updatedState = case provider of
ProofEngine -> let (Just (PS (ProofState _ status _ _))) = getState id internalState
desugaredTH = DesugaredExp $ desugarExp $ VarE 'details
in updateState id (PS (ProofState id status (Just details) (Just desugaredTH))) internalState
Compiler -> let (Just (CS (CompilationState _ status _ _))) = getState id internalState
desugaredTH = DesugaredExp $ desugarExp $ VarE 'details
in updateState id (CS (CompilationState id status (Just details) (Just desugaredTH))) internalState
return (details, updatedState)
terminateProvider :: ValidationProvider v => v -> IO String
terminateProvider = terminate
Summary
By integrating Liquid Haskell and Template Haskell, we ensure our system maintains precise type-level guarantees while also providing detailed desugared TH feedback. This approach leverages the power of Haskell's type system and metaprogramming capabilities to create a robust, introspective validation framework.
finally we can reflect over more of template haskell modules themselves to lift the context into the narrative, include llms for text rewriting
ChatGPT
Integrating Template Haskell (TH) with Liquid Haskell to reflect over TH modules themselves, and including large language models (LLMs) for text rewriting, is a sophisticated task that requires leveraging Haskell’s metaprogramming capabilities along with external text processing tools.
Here's a step-by-step approach to achieve this:
Extend the Desugared TH Representation: Include more TH constructs in our desugared TH feedback.
Integrate LLM for Text Rewriting: Incorporate an LLM to assist in rewriting and reflecting the narrative.
Use TH for Introspection: Reflect over TH modules and lift the context into the narrative.
Step 1: Extend the Desugared TH Representation
Extend the DesugaredTH type to include more TH constructs and ensure that we can desugar these constructs.
haskell
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{-# LANGUAGE TemplateHaskell #-}
{-# LANGUAGE GADTs #-}
{-# LANGUAGE DataKinds #-}
{-# LANGUAGE KindSignatures #-}
{-# LANGUAGE TypeFamilies #-}
{-# LANGUAGE FlexibleContexts #-}
{-# LANGUAGE ScopedTypeVariables #-}
{-# LANGUAGE TypeApplications #-}
data ValidationState
= PS ProofState
| CS CompilationState
| BS BuildState
| DS DeploymentState
deriving (Show, Eq)
Step 2: Integrate LLM for Text Rewriting
Integrate an LLM to assist in text rewriting. This involves calling an external service for the LLM and processing its output.
haskell
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{-# LANGUAGE OverloadedStrings #-}
-- Function to call LLM API for text rewriting
rewriteText :: String -> IO (Maybe String)
rewriteText input = do
let request = setRequestMethod "POST"
$ setRequestPath "/rewrite"
$ setRequestHost "api.llm.example.com"
$ setRequestPort 443
$ setRequestSecure True
$ setRequestBodyJSON (encode input)
$ defaultRequest
response <- httpJSON request
let responseBody = getResponseBody response :: Maybe String
return responseBody
-- Example usage
main :: IO ()
main = do
let textToRewrite = "This is the original text."
rewrittenText <- rewriteText textToRewrite
case rewrittenText of
Just text -> putStrLn $ "Rewritten Text: " ++ text
Nothing -> putStrLn "Failed to rewrite text."
Step 3: Use TH for Introspection and Context Lifting
Reflect over TH modules and lift the context into the narrative by desugaring and providing detailed feedback.
-- Desugar various TH constructs
desugarExp :: Exp -> Exp
desugarExp = id -- Simplified for illustration
desugarDec :: Dec -> Dec
desugarDec = id
desugarType :: Type -> Type
desugarType = id
desugarPat :: Pat -> Pat
desugarPat = id
desugarMod :: Module -> Module
desugarMod = id
-- Function to desugar and reflect over a TH module
reflectModule :: Q [Dec] -> Q [Dec]
reflectModule mod = do
decs <- mod
forM_ decs $ \dec -> do
let desugared = desugarDec dec
runIO $ print desugared -- For demonstration, normally you'd do more
return decs
-- Example of using reflectModule
exampleModule :: Q [Dec]
exampleModule = [d|
data Example = Example { exampleField :: Int }
exampleFunction :: Int -> Int
exampleFunction x = x + 1
|]
main :: IO ()
main = do
putStrLn "Reflecting over the Example module:"
runQ (reflectModule exampleModule) >>= print
Summary
By combining Template Haskell for metaprogramming, Liquid Haskell for refinement types, and LLMs for text rewriting, we've created a robust framework that provides detailed feedback and introspection. This system can reflect on its own modules, desugar TH constructs, and leverage LLMs for enhanced narrative context, making it powerful and flexible for complex validation and introspection tasks.
then we can boostrap in layers each layer creating more code to help describe more of the system in an ever expanding fractal structure
ChatGPT
To bootstrap the system in layers where each layer generates more code to describe more of the system in an ever-expanding fractal structure, we can use a combination of metaprogramming techniques, code generation, and recursive refinement. Each layer will build on the previous one, creating more detailed and complex descriptions of the system.
Approach
Base Layer: Define the core data types and basic functionality.
First Bootstrap Layer: Generate additional code to describe more of the system.
Recursive Expansion: Continue generating new layers recursively, each adding more detail and context.
Step 1: Define the Core Data Types and Basic Functionality
Start with the base layer that includes the core data types and basic functionality.
haskell
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{-# LANGUAGE TemplateHaskell #-}
{-# LANGUAGE GADTs #-}
{-# LANGUAGE DataKinds #-}
{-# LANGUAGE KindSignatures #-}
{-# LANGUAGE TypeFamilies #-}
{-# LANGUAGE FlexibleContexts #-}
{-# LANGUAGE ScopedTypeVariables #-}
{-# LANGUAGE TypeApplications #-}
data ValidationState
= PS ProofState
| CS CompilationState
| BS BuildState
| DS DeploymentState
deriving (Show, Eq)
Step 2: First Bootstrap Layer
Generate additional code using Template Haskell to describe more of the system.
haskell
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{-# LANGUAGE TemplateHaskell #-}
{-# LANGUAGE OverloadedStrings #-}
-- Function to generate more code to describe the system
generateCode :: Q [Dec] -> Q [Dec]
generateCode mod = do
decs <- mod
newDecs <- forM decs $ \dec -> do
let name = case dec of
FunD n _ -> n
ValD (VarP n) _ _ -> n
_ -> mkName "Unknown"
newName = mkName ("generated_" ++ nameBase name)
newBody = case dec of
FunD _ clauses -> clauses
ValD pat body whereDecs -> [Clause [] (NormalB (AppE (VarE 'id) (VarE name))) []]
_ -> []
return $ FunD newName newBody
return $ decs ++ newDecs
-- Example module to generate additional code for
exampleModule :: Q [Dec]
exampleModule = [d|
exampleFunction :: Int -> Int
exampleFunction x = x + 1
|]
-- Generate code
$(generateCode exampleModule)
Step 3: Recursive Expansion
Create a recursive function to continue generating new layers.
haskell
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{-# LANGUAGE TemplateHaskell #-}
-- Recursive function to generate more code layers
recursiveGenerate :: Int -> Q [Dec] -> Q [Dec]
recursiveGenerate 0 mod = mod
recursiveGenerate n mod = do
decs <- mod
newDecs <- generateCode (return decs)
recursiveGenerate (n - 1) (return newDecs)
-- Example usage: generate 3 layers of code
$(recursiveGenerate 3 exampleModule)
Step 4: Integrating LLM for Text Rewriting and Introspection
Integrate LLM to assist in rewriting and reflecting more complex narrative.
haskell
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{-# LANGUAGE OverloadedStrings #-}
-- Function to call LLM API for text rewriting
rewriteText :: String -> IO (Maybe String)
rewriteText input = do
let request = setRequestMethod "POST"
$ setRequestPath "/rewrite"
$ setRequestHost "api.llm.example.com"
$ setRequestPort 443
$ setRequestSecure True
$ setRequestBodyJSON (encode input)
$ defaultRequest
response <- httpJSON request
let responseBody = getResponseBody response :: Maybe String
return responseBody
-- Function to integrate LLM rewriting into generated code
generateWithLLM :: Int -> Q [Dec] -> Q [Dec]
generateWithLLM 0 mod = mod
generateWithLLM n mod = do
decs <- mod
newDecs <- generateCode (return decs)
rewrittenDecs <- forM newDecs $ \dec -> do
let decStr = pprint dec
rewritten <- runIO $ rewriteText decStr
case rewritten of
Just text -> runQ $ [d| $(pure (read text)) |]
Nothing -> return dec
generateWithLLM (n - 1) (return rewrittenDecs)
-- Example usage: generate 3 layers of code with LLM rewriting
$(generateWithLLM 3 exampleModule)
Summary
This approach bootstraps the system in layers, with each layer generating more code to describe more of the system in an expanding fractal structure. By using Template Haskell for metaprogramming, Liquid Haskell for refinement types, and integrating LLMs for text rewriting, we create a dynamic, introspective system that can evolve and describe itself in increasing detail.
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Compile & Prove Protocol
May 21, 2024
lets make up a protocol for you to use to communicate in a more formal manner with a proof engine and compiler and cicd framework
ChatGPT
Sure, let's create a protocol for formal communication between an AI language model (like me) and a proof engine, compiler, and CI/CD (Continuous Integration/Continuous Deployment) framework. This protocol will ensure precise, clear, and effective interaction.
AI to Proof Engine Protocol
Initialization
Command: INITIATE_PROOF_ENGINE
Purpose: Start the proof engine session.
Response: PROOF_ENGINE_READY
Submit Theorem
Command: SUBMIT_THEOREM
Parameters:
theorem_id: Unique identifier for the theorem.
theorem_statement: Formal statement of the theorem.
Response: THEOREM_SUBMITTED or ERROR_[error_code]
Request Proof Status
Command: REQUEST_PROOF_STATUS
Parameters:
theorem_id
Response: PROOF_STATUS_[status] (where [status] can be PENDING, PROVEN, FAILED)
Retrieve Proof Details
Command: RETRIEVE_PROOF_DETAILS
Parameters:
theorem_id
Response: PROOF_DETAILS_[details]
Terminate Proof Engine Session
Command: TERMINATE_PROOF_ENGINE
Response: PROOF_ENGINE_TERMINATED
AI to Compiler Protocol
Initialization
Command: INITIATE_COMPILER
Purpose: Start the compiler session.
Response: COMPILER_READY
Submit Code for Compilation
Command: SUBMIT_CODE
Parameters:
code_id: Unique identifier for the code snippet.
source_code: The code to be compiled.
language: Programming language of the source code.
Response: CODE_SUBMITTED or ERROR_[error_code]
Request Compilation Status
Command: REQUEST_COMPILATION_STATUS
Parameters:
code_id
Response: COMPILATION_STATUS_[status] (where [status] can be PENDING, SUCCESS, FAILED)
Retrieve Compilation Output
Command: RETRIEVE_COMPILATION_OUTPUT
Parameters:
code_id
Response: COMPILATION_OUTPUT_[output]
Terminate Compiler Session
Command: TERMINATE_COMPILER
Response: COMPILER_TERMINATED
AI to CI/CD Framework Protocol
Initialization
Command: INITIATE_CICD
Purpose: Start the CI/CD framework session.
Response: CICD_READY
Trigger Build
Command: TRIGGER_BUILD
Parameters:
build_id: Unique identifier for the build.
repository_url: URL of the code repository.
branch: Branch to be built.
Response: BUILD_TRIGGERED or ERROR_[error_code]
Request Build Status
Command: REQUEST_BUILD_STATUS
Parameters:
build_id
Response: BUILD_STATUS_[status] (where [status] can be PENDING, SUCCESS, FAILED)
Retrieve Build Logs
Command: RETRIEVE_BUILD_LOGS
Parameters:
build_id
Response: BUILD_LOGS_[logs]
Deploy Application
Command: DEPLOY_APPLICATION
Parameters:
deployment_id: Unique identifier for the deployment.
build_id: Identifier of the build to deploy.
environment: Deployment environment (e.g., staging, production).
Response: DEPLOYMENT_TRIGGERED or ERROR_[error_code]
Request Deployment Status
Command: REQUEST_DEPLOYMENT_STATUS
Parameters:
deployment_id
Response: DEPLOYMENT_STATUS_[status] (where [status] can be PENDING, SUCCESS, FAILED)
Terminate CI/CD Session
Command: TERMINATE_CICD
Response: CICD_TERMINATED
Example Interaction Flow
AI to Proof Engine:
INITIATE_PROOF_ENGINE
SUBMIT_THEOREM with theorem_id="T123" and theorem_statement="∀x∈ℝ, x²≥0"
REQUEST_PROOF_STATUS with theorem_id="T123"
RETRIEVE_PROOF_DETAILS with theorem_id="T123"
TERMINATE_PROOF_ENGINE
AI to Compiler:
INITIATE_COMPILER
SUBMIT_CODE with code_id="C456", source_code="int main() { return 0; }", and language="C"
REQUEST_COMPILATION_STATUS with code_id="C456"
RETRIEVE_COMPILATION_OUTPUT with code_id="C456"
TERMINATE_COMPILER
AI to CI/CD Framework:
INITIATE_CICD
TRIGGER_BUILD with build_id="B789", repository_url="https://github.com/user/repo", and branch="main"
REQUEST_BUILD_STATUS with build_id="B789"
RETRIEVE_BUILD_LOGS with build_id="B789"
DEPLOY_APPLICATION with deployment_id="D012", build_id="B789", and environment="production"
REQUEST_DEPLOYMENT_STATUS with deployment_id="D012"
TERMINATE_CICD
This protocol structure ensures clarity and consistency in communication, making interactions between the AI, proof engine, compiler, and CI/CD framework efficient and error-free.
now lets abstract the validation provider as a plugin and consider a composed algebraic representation of the internal state of the feedback that is self contained and comprehensive
ChatGPT
To abstract the validation provider as a plugin and to create a composed algebraic representation of the internal state of the feedback, we can define a more modular and extensible system. This approach will allow for easy integration of various validation providers (proof engines, compilers, CI/CD frameworks) and enable a comprehensive internal state representation.
Abstracting the Validation Provider as a Plugin
Plugin Interface Definition
Define a common interface that all validation providers must implement. This interface will include methods for initialization, submission, status checking, retrieval, and termination.
Example Interface (Pseudocode)
python
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class ValidationProvider:
def initialize(self) -> str:
pass
Provider Implementation Examples
Proof Engine Plugin
python
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class ProofEngineProvider(ValidationProvider):
def initialize(self) -> str:
return "PROOF_ENGINE_READY"
Compiler Plugin
python
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class CompilerProvider(ValidationProvider):
def initialize(self) -> str:
return "COMPILER_READY"
Composed Algebraic Representation of Internal State
State Representation
Use algebraic data types to represent the state of each interaction with the validation providers. This ensures a structured and self-contained feedback mechanism.
Example State Classes (Pseudocode)
python
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from enum import Enum
from typing import Union, Optional
class Status(Enum):
PENDING = "PENDING"
SUCCESS = "SUCCESS"
FAILED = "FAILED"
class ProofState:
def init(self, theorem_id: str, status: Status, details: Optional[str] = None):
self.theorem_id = theorem_id
self.status = status
self.details = details
class CompilationState:
def init(self, code_id: str, status: Status, output: Optional[str] = None):
self.code_id = code_id
self.status = status
self.output = output
class BuildState:
def init(self, build_id: str, status: Status, logs: Optional[str] = None):
self.build_id = build_id
self.status = status
self.logs = logs
class DeploymentState:
def init(self, deployment_id: str, status: Status):
self.deployment_id = deployment_id
self.status = status
Union type for general state representation
ValidationState = Union[ProofState, CompilationState, BuildState, DeploymentState]
Comprehensive Internal State Example
Maintain an internal state dictionary to track all interactions.
python
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class InternalState:
def init(self):
self.states = {}
Example usage
internal_state = InternalState()
proof_state = ProofState(theorem_id="T123", status=Status.PENDING)
internal_state.update_state("T123", proof_state)
Integrating the Plugin System with Internal State
Controller Class (Pseudocode)
python
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class ValidationController:
def init(self):
self.providers = {}
self.internal_state = InternalState()
This approach encapsulates the interactions with validation providers and maintains a comprehensive internal state, ensuring all feedback is self-contained and can be easily managed and queried.
lets consider this a typeclass
ChatGPT
To create a typeclass for validation providers, we'll use an approach that can be adapted to languages supporting typeclasses or similar constructs, such as Haskell or Scala. In this example, I'll demonstrate using Haskell syntax, which is known for its robust typeclass support. We can then describe how similar concepts could be implemented in other languages like Scala or using traits in Rust.
Haskell Typeclass for Validation Providers
Typeclass Definition
haskell
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class ValidationProvider v where
initialize :: v -> IO String
submit :: v -> String -> String -> IO String
requestStatus :: v -> String -> IO String
retrieveDetails :: v -> String -> IO String
terminate :: v -> IO String
Typeclass Instances
Proof Engine Instance
haskell
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data ProofEngine = ProofEngine
instance ValidationProvider ProofEngine where
initialize _ = return "PROOF_ENGINE_READY"
submit _ theoremId theoremStatement = return "THEOREM_SUBMITTED"
requestStatus _ theoremId = return "PROOF_STATUS_PENDING"
retrieveDetails _ theoremId = return "PROOF_DETAILS_[details]"
terminate _ = return "PROOF_ENGINE_TERMINATED"
Compiler Instance
haskell
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data Compiler = Compiler
instance ValidationProvider Compiler where
initialize _ = return "COMPILER_READY"
submit _ codeId sourceCode = return "CODE_SUBMITTED"
requestStatus _ codeId = return "COMPILATION_STATUS_PENDING"
retrieveDetails _ codeId = return "COMPILATION_OUTPUT_[output]"
terminate _ = return "COMPILER_TERMINATED"
Composed Algebraic Representation of Internal State
Algebraic Data Types for State Representation
haskell
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data Status = Pending | Success | Failed deriving (Show, Eq)
data ProofState = ProofState
{ theoremId :: String
, proofStatus :: Status
, proofDetails :: Maybe String
} deriving (Show, Eq)
data CompilationState = CompilationState
{ codeId :: String
, compilationStatus :: Status
, compilationOutput :: Maybe String
} deriving (Show, Eq)
data BuildState = BuildState
{ buildId :: String
, buildStatus :: Status
, buildLogs :: Maybe String
} deriving (Show, Eq)
data DeploymentState = DeploymentState
{ deploymentId :: String
, deploymentStatus :: Status
} deriving (Show, Eq)
data ValidationState
= PS ProofState
| CS CompilationState
| BS BuildState
| DS DeploymentState
deriving (Show, Eq)
Internal State Management
haskell
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import Data.Map (Map)
import qualified Data.Map as Map
newtype InternalState = InternalState (Map String ValidationState) deriving (Show)
updateState :: String -> ValidationState -> InternalState -> InternalState
updateState id newState (InternalState state) = InternalState (Map.insert id newState state)
getState :: String -> InternalState -> Maybe ValidationState
getState id (InternalState state) = Map.lookup id state
Example Usage in Haskell
Controller Functionality
haskell
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initializeProvider :: ValidationProvider v => v -> IO String
initializeProvider = initialize
submitToProvider :: ValidationProvider v => v -> String -> String -> IO (String, InternalState)
submitToProvider provider id content = do
response <- submit provider id content
let newState = case provider of
ProofEngine -> PS (ProofState id Pending Nothing)
Compiler -> CS (CompilationState id Pending Nothing)
return (response, updateState id newState (InternalState Map.empty))
checkStatus :: ValidationProvider v => v -> String -> InternalState -> IO (String, InternalState)
checkStatus provider id internalState = do
status <- requestStatus provider id
let newStatus = if status == "PROOF_STATUS_SUCCESS" || status == "COMPILATION_STATUS_SUCCESS"
then Success
else if status == "PROOF_STATUS_FAILED" || status == "COMPILATION_STATUS_FAILED"
then Failed
else Pending
updatedState = case provider of
ProofEngine -> let (Just (PS (ProofState _ _ details))) = getState id internalState
in updateState id (PS (ProofState id newStatus details)) internalState
Compiler -> let (Just (CS (CompilationState _ _ output))) = getState id internalState
in updateState id (CS (CompilationState id newStatus output)) internalState
return (status, updatedState)
retrieveDetails :: ValidationProvider v => v -> String -> InternalState -> IO (String, InternalState)
retrieveDetails provider id internalState = do
details <- retrieveDetails provider id
let updatedState = case provider of
ProofEngine -> let (Just (PS (ProofState _ status _))) = getState id internalState
in updateState id (PS (ProofState id status (Just details))) internalState
Compiler -> let (Just (CS (CompilationState _ status _))) = getState id internalState
in updateState id (CS (CompilationState id status (Just details))) internalState
return (details, updatedState)
terminateProvider :: ValidationProvider v => v -> IO String
terminateProvider = terminate
Typeclass Concept in Other Languages
Scala
In Scala, you can achieve similar functionality using traits and implicit classes:
scala
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trait ValidationProvider {
def initialize(): String
def submit(id: String, content: String): String
def requestStatus(id: String): String
def retrieveDetails(id: String): String
def terminate(): String
}
class ProofEngine extends ValidationProvider {
def initialize() = "PROOF_ENGINE_READY"
def submit(id: String, content: String) = "THEOREM_SUBMITTED"
def requestStatus(id: String) = "PROOF_STATUS_PENDING"
def retrieveDetails(id: String) = "PROOF_DETAILS_[details]"
def terminate() = "PROOF_ENGINE_TERMINATED"
}
class Compiler extends ValidationProvider {
def initialize() = "COMPILER_READY"
def submit(id: String, content: String) = "CODE_SUBMITTED"
def requestStatus(id: String) = "COMPILATION_STATUS_PENDING"
def retrieveDetails(id: String) = "COMPILATION_OUTPUT_[output]"
def terminate() = "COMPILER_TERMINATED"
}
Rust
In Rust, you can use traits to achieve a similar effect:
rust
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trait ValidationProvider {
fn initialize(&self) -> String;
fn submit(&self, id: &str, content: &str) -> String;
fn request_status(&self, id: &str) -> String;
fn retrieve_details(&self, id: &str) -> String;
fn terminate(&self) -> String;
}
struct ProofEngine;
impl ValidationProvider for ProofEngine {
fn initialize(&self) -> String {
"PROOF_ENGINE_READY".to_string()
}
fn submit(&self, id: &str, content: &str) -> String {
"THEOREM_SUBMITTED".to_string()
}
fn request_status(&self, id: &str) -> String {
"PROOF_STATUS_PENDING".to_string()
}
fn retrieve_details(&self, id: &str) -> String {
"PROOF_DETAILS_[details]".to_string()
}
fn terminate(&self) -> String {
"PROOF_ENGINE_TERMINATED".to_string()
}
}
struct Compiler;
impl ValidationProvider for Compiler {
fn initialize(&self) -> String {
"COMPILER_READY".to_string()
}
fn submit(&self, id: &str, content: &str) -> String {
"CODE_SUBMITTED".to_string()
}
fn request_status(&self, id: &str) -> String {
"COMPILATION_STATUS_PENDING".to_string()
}
fn retrieve_details(&self, id: &str) -> String {
"COMPILATION_OUTPUT_[output]".to_string()
}
fn terminate(&self) -> String {
"COMPILER_TERMINATED".to_string()
}
}
This approach ensures modularity and abstraction, allowing easy integration of various validation providers and consistent internal state management across different programming languages.
now we loop in liquid haskell to implement the proofs using dependant type thoery
ChatGPT
Liquid Haskell is a refinement type system that allows embedding logical assertions directly within Haskell code, enabling more precise type checking and verification of properties. Let's integrate Liquid Haskell to implement the proofs for our validation provider system using dependent type theory.
Overview
Defining Types and Refinements: Use Liquid Haskell to specify precise types and invariants for our data structures.
Validation Provider Typeclass: Ensure that the methods in our typeclass adhere to the specified invariants.
Internal State Management: Utilize dependent types to maintain correctness in our state transitions.
Setup
First, make sure you have Liquid Haskell installed. You can find installation instructions on the Liquid Haskell GitHub page.
Defining Types and Refinements
We define our data types with Liquid Haskell refinements to capture invariants.
haskell
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{-# LANGUAGE GADTs #-}
{-# LANGUAGE DataKinds #-}
{-# LANGUAGE KindSignatures #-}
{-# LANGUAGE TypeFamilies #-}
{-# LANGUAGE FlexibleContexts #-}
{-# LANGUAGE ScopedTypeVariables #-}
{-# LANGUAGE TypeApplications #-}
module ValidationProvider where
import Data.Map (Map)
import qualified Data.Map as Map
import LiquidHaskell
{-@ data Status = Pending | Success | Failed @-}
data Status = Pending | Success | Failed deriving (Show, Eq)
{-@ type NonEmptyString = {v:String | len v > 0} @-}
{-@ data ProofState = ProofState
{ theoremId :: NonEmptyString
, proofStatus :: Status
, proofDetails :: Maybe String
} @-}
data ProofState = ProofState
{ theoremId :: String
, proofStatus :: Status
, proofDetails :: Maybe String
} deriving (Show, Eq)
{-@ data CompilationState = CompilationState
{ codeId :: NonEmptyString
, compilationStatus :: Status
, compilationOutput :: Maybe String
} @-}
data CompilationState = CompilationState
{ codeId :: String
, compilationStatus :: Status
, compilationOutput :: Maybe String
} deriving (Show, Eq)
{-@ data BuildState = BuildState
{ buildId :: NonEmptyString
, buildStatus :: Status
, buildLogs :: Maybe String
} @-}
data BuildState = BuildState
{ buildId :: String
, buildStatus :: Status
, buildLogs :: Maybe String
} deriving (Show, Eq)
{-@ data DeploymentState = DeploymentState
{ deploymentId :: NonEmptyString
, deploymentStatus :: Status
} @-}
data DeploymentState = DeploymentState
{ deploymentId :: String
, deploymentStatus :: Status
} deriving (Show, Eq)
data ValidationState
= PS ProofState
| CS CompilationState
| BS BuildState
| DS DeploymentState
deriving (Show, Eq)
Validation Provider Typeclass
Next, define the typeclass with Liquid Haskell refinements to ensure that the methods adhere to the specified invariants.
haskell
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{-# LANGUAGE MultiParamTypeClasses #-}
{-# LANGUAGE FunctionalDependencies #-}
{-# LANGUAGE FlexibleInstances #-}
{-@ class ValidationProvider v where
initialize :: v -> IO {v:String | len v > 0}
submit :: v -> NonEmptyString -> NonEmptyString -> IO {v:String | len v > 0}
requestStatus :: v -> NonEmptyString -> IO {v:String | len v > 0}
retrieveDetails :: v -> NonEmptyString -> IO {v:String | len v > 0}
terminate :: v -> IO {v:String | len v > 0}
@-}
class ValidationProvider v where
initialize :: v -> IO String
submit :: v -> String -> String -> IO String
requestStatus :: v -> String -> IO String
retrieveDetails :: v -> String -> IO String
terminate :: v -> IO String
data ProofEngine = ProofEngine
data Compiler = Compiler
instance ValidationProvider ProofEngine where
initialize _ = return "PROOF_ENGINE_READY"
submit _ theoremId theoremStatement = return "THEOREM_SUBMITTED"
requestStatus _ theoremId = return "PROOF_STATUS_PENDING"
retrieveDetails _ theoremId = return "PROOF_DETAILS_[details]"
terminate _ = return "PROOF_ENGINE_TERMINATED"
instance ValidationProvider Compiler where
initialize _ = return "COMPILER_READY"
submit _ codeId sourceCode = return "CODE_SUBMITTED"
requestStatus _ codeId = return "COMPILATION_STATUS_PENDING"
retrieveDetails _ codeId = return "COMPILATION_OUTPUT_[output]"
terminate _ = return "COMPILER_TERMINATED"
Internal State Management
Implement functions to manage the internal state, ensuring correctness with Liquid Haskell refinements.
haskell
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{-@ data InternalState = InternalState
{ states :: Map NonEmptyString ValidationState
} @-}
newtype InternalState = InternalState (Map String ValidationState) deriving (Show)
{-@ updateState :: NonEmptyString -> ValidationState -> InternalState -> InternalState @-}
updateState :: String -> ValidationState -> InternalState -> InternalState
updateState id newState (InternalState state) = InternalState (Map.insert id newState state)
{-@ getState :: NonEmptyString -> InternalState -> Maybe ValidationState @-}
getState :: String -> InternalState -> Maybe ValidationState
getState id (InternalState state) = Map.lookup id state
-- Example Usage
initializeProvider :: ValidationProvider v => v -> IO String
initializeProvider = initialize
submitToProvider :: ValidationProvider v => v -> String -> String -> IO (String, InternalState)
submitToProvider provider id content = do
response <- submit provider id content
let newState = case provider of
ProofEngine -> PS (ProofState id Pending Nothing)
Compiler -> CS (CompilationState id Pending Nothing)
return (response, updateState id newState (InternalState Map.empty))
checkStatus :: ValidationProvider v => v -> String -> InternalState -> IO (String, InternalState)
checkStatus provider id internalState = do
status <- requestStatus provider id
let newStatus = if status == "PROOF_STATUS_SUCCESS" || status == "COMPILATION_STATUS_SUCCESS"
then Success
else if status == "PROOF_STATUS_FAILED" || status == "COMPILATION_STATUS_FAILED"
then Failed
else Pending
updatedState = case provider of
ProofEngine -> let (Just (PS (ProofState _ _ details))) = getState id internalState
in updateState id (PS (ProofState id newStatus details)) internalState
Compiler -> let (Just (CS (CompilationState _ _ output))) = getState id internalState
in updateState id (CS (CompilationState id newStatus output)) internalState
return (status, updatedState)
retrieveDetails :: ValidationProvider v => v -> String -> InternalState -> IO (String, InternalState)
retrieveDetails provider id internalState = do
details <- retrieveDetails provider id
let updatedState = case provider of
ProofEngine -> let (Just (PS (ProofState _ status _))) = getState id internalState
in updateState id (PS (ProofState id status (Just details))) internalState
Compiler -> let (Just (CS (CompilationState _ status _))) = getState id internalState
in updateState id (CS (CompilationState id status (Just details))) internalState
return (details, updatedState)
terminateProvider :: ValidationProvider v => v -> IO String
terminateProvider = terminate
Summary
By incorporating Liquid Haskell, we've refined our types to enforce invariants and properties at the type level. This ensures that our data remains consistent and valid throughout the operations of the validation providers. This approach enhances the safety and reliability of the system, leveraging the power of dependent type theory and refinement types in Haskell.
we can now return a desugared th as the detailed state feedback so the interface to the system reflects the complexities of th itself
ChatGPT
To return desugared Template Haskell (TH) as detailed state feedback, we need to integrate TH into our validation provider system. Template Haskell allows us to generate and manipulate Haskell code programmatically. By leveraging TH, we can provide more detailed feedback and introspection capabilities within our system.
Here's how we can achieve this:
Define Types for Desugared TH Representations: We need a way to represent the desugared TH feedback.
Modify Validation Provider Interface: Ensure the interface returns desugared TH representations as detailed state feedback.
Implement Desugaring Logic: Use TH to desugar and extract detailed state information.
Step 1: Define Types for Desugared TH Representations
We'll define types to capture the desugared TH feedback. These types should be rich enough to represent the various forms of TH constructs.
haskell
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{-# LANGUAGE TemplateHaskell #-}
{-# LANGUAGE GADTs #-}
{-# LANGUAGE DataKinds #-}
{-# LANGUAGE KindSignatures #-}
{-# LANGUAGE TypeFamilies #-}
{-# LANGUAGE FlexibleContexts #-}
{-# LANGUAGE ScopedTypeVariables #-}
{-# LANGUAGE TypeApplications #-}
module ValidationProvider where
import Data.Map (Map)
import qualified Data.Map as Map
import Language.Haskell.TH
import Language.Haskell.TH.Syntax
import LiquidHaskell
{-@ data Status = Pending | Success | Failed @-}
data Status = Pending | Success | Failed deriving (Show, Eq)
{-@ type NonEmptyString = {v:String | len v > 0} @-}
-- Desugared TH Feedback Types
data DesugaredTH
= DesugaredExp Exp
| DesugaredDec Dec
| DesugaredType Type
| DesugaredPat Pat
deriving (Show, Eq)
-- Extending existing state types to include DesugaredTH
data ProofState = ProofState
{ theoremId :: String
, proofStatus :: Status
, proofDetails :: Maybe String
, proofTH :: Maybe DesugaredTH
} deriving (Show, Eq)
data CompilationState = CompilationState
{ codeId :: String
, compilationStatus :: Status
, compilationOutput :: Maybe String
, compilationTH :: Maybe DesugaredTH
} deriving (Show, Eq)
data BuildState = BuildState
{ buildId :: String
, buildStatus :: Status
, buildLogs :: Maybe String
, buildTH :: Maybe DesugaredTH
} deriving (Show, Eq)
data DeploymentState = DeploymentState
{ deploymentId :: String
, deploymentStatus :: Status
, deploymentTH :: Maybe DesugaredTH
} deriving (Show, Eq)
data ValidationState
= PS ProofState
| CS CompilationState
| BS BuildState
| DS DeploymentState
deriving (Show, Eq)
Step 2: Modify Validation Provider Interface
Modify the interface to include desugared TH feedback. We'll adjust the retrieveDetails method to return desugared TH.
haskell
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{-# LANGUAGE MultiParamTypeClasses #-}
{-# LANGUAGE FunctionalDependencies #-}
{-# LANGUAGE FlexibleInstances #-}
{-# LANGUAGE TemplateHaskell #-}
{-@ class ValidationProvider v where
initialize :: v -> IO {v:String | len v > 0}
submit :: v -> NonEmptyString -> NonEmptyString -> IO {v:String | len v > 0}
requestStatus :: v -> NonEmptyString -> IO {v:String | len v > 0}
retrieveDetails :: v -> NonEmptyString -> IO (DesugaredTH, {v:String | len v > 0})
terminate :: v -> IO {v:String | len v > 0}
@-}
class ValidationProvider v where
initialize :: v -> IO String
submit :: v -> String -> String -> IO String
requestStatus :: v -> String -> IO String
retrieveDetails :: v -> String -> IO (DesugaredTH, String)
terminate :: v -> IO String
data ProofEngine = ProofEngine
data Compiler = Compiler
instance ValidationProvider ProofEngine where
initialize _ = return "PROOF_ENGINE_READY"
submit _ theoremId theoremStatement = return "THEOREM_SUBMITTED"
requestStatus _ theoremId = return "PROOF_STATUS_PENDING"
retrieveDetails _ theoremId = return (DesugaredExp $ VarE 'theoremId, "PROOF_DETAILS_[details]")
terminate _ = return "PROOF_ENGINE_TERMINATED"
instance ValidationProvider Compiler where
initialize _ = return "COMPILER_READY"
submit _ codeId sourceCode = return "CODE_SUBMITTED"
requestStatus _ codeId = return "COMPILATION_STATUS_PENDING"
retrieveDetails _ codeId = return (DesugaredExp $ VarE 'codeId, "COMPILATION_OUTPUT_[output]")
terminate _ = return "COMPILER_TERMINATED"
Step 3: Implement Desugaring Logic
Implement the logic to desugar TH constructs and integrate it into the state updates.
haskell
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-- Desugaring Logic
desugarExp :: Exp -> Exp
desugarExp = id -- Simplified for illustration; normally you would process the AST
desugarDec :: Dec -> Dec
desugarDec = id
desugarType :: Type -> Type
desugarType = id
desugarPat :: Pat -> Pat
desugarPat = id
-- Adjust Internal State Management to include DesugaredTH
updateState :: String -> ValidationState -> InternalState -> InternalState
updateState id newState (InternalState state) = InternalState (Map.insert id newState state)
getState :: String -> InternalState -> Maybe ValidationState
getState id (InternalState state) = Map.lookup id state
initializeProvider :: ValidationProvider v => v -> IO String
initializeProvider = initialize
submitToProvider :: ValidationProvider v => v -> String -> String -> IO (String, InternalState)
submitToProvider provider id content = do
response <- submit provider id content
let newState = case provider of
ProofEngine -> PS (ProofState id Pending Nothing Nothing)
Compiler -> CS (CompilationState id Pending Nothing Nothing)
return (response, updateState id newState (InternalState Map.empty))
checkStatus :: ValidationProvider v => v -> String -> InternalState -> IO (String, InternalState)
checkStatus provider id internalState = do
status <- requestStatus provider id
let newStatus = if status == "PROOF_STATUS_SUCCESS" || status == "COMPILATION_STATUS_SUCCESS"
then Success
else if status == "PROOF_STATUS_FAILED" || status == "COMPILATION_STATUS_FAILED"
then Failed
else Pending
updatedState = case provider of
ProofEngine -> let (Just (PS (ProofState _ _ details th))) = getState id internalState
in updateState id (PS (ProofState id newStatus details th)) internalState
Compiler -> let (Just (CS (CompilationState _ _ output th))) = getState id internalState
in updateState id (CS (CompilationState id newStatus output th)) internalState
return (status, updatedState)
retrieveDetails :: ValidationProvider v => v -> String -> InternalState -> IO (String, InternalState)
retrieveDetails provider id internalState = do
(th, details) <- retrieveDetails provider id
let updatedState = case provider of
ProofEngine -> let (Just (PS (ProofState _ status _ _))) = getState id internalState
desugaredTH = DesugaredExp $ desugarExp $ VarE 'details
in updateState id (PS (ProofState id status (Just details) (Just desugaredTH))) internalState
Compiler -> let (Just (CS (CompilationState _ status _ _))) = getState id internalState
desugaredTH = DesugaredExp $ desugarExp $ VarE 'details
in updateState id (CS (CompilationState id status (Just details) (Just desugaredTH))) internalState
return (details, updatedState)
terminateProvider :: ValidationProvider v => v -> IO String
terminateProvider = terminate
Summary
By integrating Liquid Haskell and Template Haskell, we ensure our system maintains precise type-level guarantees while also providing detailed desugared TH feedback. This approach leverages the power of Haskell's type system and metaprogramming capabilities to create a robust, introspective validation framework.
finally we can reflect over more of template haskell modules themselves to lift the context into the narrative, include llms for text rewriting
ChatGPT
Integrating Template Haskell (TH) with Liquid Haskell to reflect over TH modules themselves, and including large language models (LLMs) for text rewriting, is a sophisticated task that requires leveraging Haskell’s metaprogramming capabilities along with external text processing tools.
Here's a step-by-step approach to achieve this:
Extend the Desugared TH Representation: Include more TH constructs in our desugared TH feedback.
Integrate LLM for Text Rewriting: Incorporate an LLM to assist in rewriting and reflecting the narrative.
Use TH for Introspection: Reflect over TH modules and lift the context into the narrative.
Step 1: Extend the Desugared TH Representation
Extend the DesugaredTH type to include more TH constructs and ensure that we can desugar these constructs.
haskell
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{-# LANGUAGE TemplateHaskell #-}
{-# LANGUAGE GADTs #-}
{-# LANGUAGE DataKinds #-}
{-# LANGUAGE KindSignatures #-}
{-# LANGUAGE TypeFamilies #-}
{-# LANGUAGE FlexibleContexts #-}
{-# LANGUAGE ScopedTypeVariables #-}
{-# LANGUAGE TypeApplications #-}
module ValidationProvider where
import Data.Map (Map)
import qualified Data.Map as Map
import Language.Haskell.TH
import Language.Haskell.TH.Syntax
import LiquidHaskell
{-@ data Status = Pending | Success | Failed @-}
data Status = Pending | Success | Failed deriving (Show, Eq)
{-@ type NonEmptyString = {v:String | len v > 0} @-}
-- Extended Desugared TH Feedback Types
data DesugaredTH
= DesugaredExp Exp
| DesugaredDec Dec
| DesugaredType Type
| DesugaredPat Pat
| DesugaredMod Module
deriving (Show, Eq)
-- Extending existing state types to include DesugaredTH
data ProofState = ProofState
{ theoremId :: String
, proofStatus :: Status
, proofDetails :: Maybe String
, proofTH :: Maybe DesugaredTH
} deriving (Show, Eq)
data CompilationState = CompilationState
{ codeId :: String
, compilationStatus :: Status
, compilationOutput :: Maybe String
, compilationTH :: Maybe DesugaredTH
} deriving (Show, Eq)
data BuildState = BuildState
{ buildId :: String
, buildStatus :: Status
, buildLogs :: Maybe String
, buildTH :: Maybe DesugaredTH
} deriving (Show, Eq)
data DeploymentState = DeploymentState
{ deploymentId :: String
, deploymentStatus :: Status
, deploymentTH :: Maybe DesugaredTH
} deriving (Show, Eq)
data ValidationState
= PS ProofState
| CS CompilationState
| BS BuildState
| DS DeploymentState
deriving (Show, Eq)
Step 2: Integrate LLM for Text Rewriting
Integrate an LLM to assist in text rewriting. This involves calling an external service for the LLM and processing its output.
haskell
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{-# LANGUAGE OverloadedStrings #-}
import Data.Aeson (encode, decode)
import Network.HTTP.Simple
-- Function to call LLM API for text rewriting
rewriteText :: String -> IO (Maybe String)
rewriteText input = do
let request = setRequestMethod "POST"
$ setRequestPath "/rewrite"
$ setRequestHost "api.llm.example.com"
$ setRequestPort 443
$ setRequestSecure True
$ setRequestBodyJSON (encode input)
$ defaultRequest
response <- httpJSON request
let responseBody = getResponseBody response :: Maybe String
return responseBody
-- Example usage
main :: IO ()
main = do
let textToRewrite = "This is the original text."
rewrittenText <- rewriteText textToRewrite
case rewrittenText of
Just text -> putStrLn $ "Rewritten Text: " ++ text
Nothing -> putStrLn "Failed to rewrite text."
Step 3: Use TH for Introspection and Context Lifting
Reflect over TH modules and lift the context into the narrative by desugaring and providing detailed feedback.
haskell
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import Language.Haskell.TH
import Language.Haskell.TH.Syntax
import Control.Monad (forM)
-- Desugar various TH constructs
desugarExp :: Exp -> Exp
desugarExp = id -- Simplified for illustration
desugarDec :: Dec -> Dec
desugarDec = id
desugarType :: Type -> Type
desugarType = id
desugarPat :: Pat -> Pat
desugarPat = id
desugarMod :: Module -> Module
desugarMod = id
-- Function to desugar and reflect over a TH module
reflectModule :: Q [Dec] -> Q [Dec]
reflectModule mod = do
decs <- mod
forM_ decs $ \dec -> do
let desugared = desugarDec dec
runIO $ print desugared -- For demonstration, normally you'd do more
return decs
-- Example of using reflectModule
exampleModule :: Q [Dec]
exampleModule = [d|
data Example = Example { exampleField :: Int }
exampleFunction :: Int -> Int
exampleFunction x = x + 1
|]
main :: IO ()
main = do
putStrLn "Reflecting over the Example module:"
runQ (reflectModule exampleModule) >>= print
Summary
By combining Template Haskell for metaprogramming, Liquid Haskell for refinement types, and LLMs for text rewriting, we've created a robust framework that provides detailed feedback and introspection. This system can reflect on its own modules, desugar TH constructs, and leverage LLMs for enhanced narrative context, making it powerful and flexible for complex validation and introspection tasks.
then we can boostrap in layers each layer creating more code to help describe more of the system in an ever expanding fractal structure
ChatGPT
To bootstrap the system in layers where each layer generates more code to describe more of the system in an ever-expanding fractal structure, we can use a combination of metaprogramming techniques, code generation, and recursive refinement. Each layer will build on the previous one, creating more detailed and complex descriptions of the system.
Approach
Base Layer: Define the core data types and basic functionality.
First Bootstrap Layer: Generate additional code to describe more of the system.
Recursive Expansion: Continue generating new layers recursively, each adding more detail and context.
Step 1: Define the Core Data Types and Basic Functionality
Start with the base layer that includes the core data types and basic functionality.
haskell
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{-# LANGUAGE TemplateHaskell #-}
{-# LANGUAGE GADTs #-}
{-# LANGUAGE DataKinds #-}
{-# LANGUAGE KindSignatures #-}
{-# LANGUAGE TypeFamilies #-}
{-# LANGUAGE FlexibleContexts #-}
{-# LANGUAGE ScopedTypeVariables #-}
{-# LANGUAGE TypeApplications #-}
module BaseLayer where
import Data.Map (Map)
import qualified Data.Map as Map
import Language.Haskell.TH
import Language.Haskell.TH.Syntax
import LiquidHaskell
-- Core data types
data Status = Pending | Success | Failed deriving (Show, Eq)
type NonEmptyString = String -- Simplified for illustration
data DesugaredTH
= DesugaredExp Exp
| DesugaredDec Dec
| DesugaredType Type
| DesugaredPat Pat
| DesugaredMod Module
deriving (Show, Eq)
-- Example state types
data ProofState = ProofState
{ theoremId :: String
, proofStatus :: Status
, proofDetails :: Maybe String
, proofTH :: Maybe DesugaredTH
} deriving (Show, Eq)
data CompilationState = CompilationState
{ codeId :: String
, compilationStatus :: Status
, compilationOutput :: Maybe String
, compilationTH :: Maybe DesugaredTH
} deriving (Show, Eq)
data BuildState = BuildState
{ buildId :: String
, buildStatus :: Status
, buildLogs :: Maybe String
, buildTH :: Maybe DesugaredTH
} deriving (Show, Eq)
data DeploymentState = DeploymentState
{ deploymentId :: String
, deploymentStatus :: Status
, deploymentTH :: Maybe DesugaredTH
} deriving (Show, Eq)
data ValidationState
= PS ProofState
| CS CompilationState
| BS BuildState
| DS DeploymentState
deriving (Show, Eq)
Step 2: First Bootstrap Layer
Generate additional code using Template Haskell to describe more of the system.
haskell
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{-# LANGUAGE TemplateHaskell #-}
{-# LANGUAGE OverloadedStrings #-}
module BootstrapLayer where
import BaseLayer
import Language.Haskell.TH
import Language.Haskell.TH.Syntax
-- Function to generate more code to describe the system
generateCode :: Q [Dec] -> Q [Dec]
generateCode mod = do
decs <- mod
newDecs <- forM decs $ \dec -> do
let name = case dec of
FunD n _ -> n
ValD (VarP n) _ _ -> n
_ -> mkName "Unknown"
newName = mkName ("generated_" ++ nameBase name)
newBody = case dec of
FunD _ clauses -> clauses
ValD pat body whereDecs -> [Clause [] (NormalB (AppE (VarE 'id) (VarE name))) []]
_ -> []
return $ FunD newName newBody
return $ decs ++ newDecs
-- Example module to generate additional code for
exampleModule :: Q [Dec]
exampleModule = [d|
exampleFunction :: Int -> Int
exampleFunction x = x + 1
|]
-- Generate code
$(generateCode exampleModule)
Step 3: Recursive Expansion
Create a recursive function to continue generating new layers.
haskell
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{-# LANGUAGE TemplateHaskell #-}
module RecursiveExpansion where
import BootstrapLayer
import Language.Haskell.TH
import Language.Haskell.TH.Syntax
-- Recursive function to generate more code layers
recursiveGenerate :: Int -> Q [Dec] -> Q [Dec]
recursiveGenerate 0 mod = mod
recursiveGenerate n mod = do
decs <- mod
newDecs <- generateCode (return decs)
recursiveGenerate (n - 1) (return newDecs)
-- Example usage: generate 3 layers of code
$(recursiveGenerate 3 exampleModule)
Step 4: Integrating LLM for Text Rewriting and Introspection
Integrate LLM to assist in rewriting and reflecting more complex narrative.
haskell
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{-# LANGUAGE OverloadedStrings #-}
import Data.Aeson (encode, decode)
import Network.HTTP.Simple
import Control.Monad (forM)
-- Function to call LLM API for text rewriting
rewriteText :: String -> IO (Maybe String)
rewriteText input = do
let request = setRequestMethod "POST"
$ setRequestPath "/rewrite"
$ setRequestHost "api.llm.example.com"
$ setRequestPort 443
$ setRequestSecure True
$ setRequestBodyJSON (encode input)
$ defaultRequest
response <- httpJSON request
let responseBody = getResponseBody response :: Maybe String
return responseBody
-- Function to integrate LLM rewriting into generated code
generateWithLLM :: Int -> Q [Dec] -> Q [Dec]
generateWithLLM 0 mod = mod
generateWithLLM n mod = do
decs <- mod
newDecs <- generateCode (return decs)
rewrittenDecs <- forM newDecs $ \dec -> do
let decStr = pprint dec
rewritten <- runIO $ rewriteText decStr
case rewritten of
Just text -> runQ $ [d| $(pure (read text)) |]
Nothing -> return dec
generateWithLLM (n - 1) (return rewrittenDecs)
-- Example usage: generate 3 layers of code with LLM rewriting
$(generateWithLLM 3 exampleModule)
Summary
This approach bootstraps the system in layers, with each layer generating more code to describe more of the system in an expanding fractal structure. By using Template Haskell for metaprogramming, Liquid Haskell for refinement types, and integrating LLMs for text rewriting, we create a dynamic, introspective system that can evolve and describe itself in increasing detail.
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