def vv_loop(task, max_retries=3):
    """
    Execute task with verification and validation
    """
    for attempt in range(max_retries):
        # Generate
        output = agent.generate(task)

        # Verify (syntactic checks)
        if not verify(output):
            feedback = get_verification_errors(output)
            task = enhance_with_feedback(task, feedback)
            continue

        # Validate (semantic checks)
        if not validate(output, task.constraints):
            feedback = get_validation_errors(output, task)
            task = enhance_with_feedback(task, feedback)
            continue

        # Success
        return output

    # All retries exhausted
    raise ValidationError("Failed to produce valid output")

def ensemble_validation(output, validators):
    """
    Require majority agreement among validators
    """
    votes = [v(output) for v in validators]
    confidence = sum(votes) / len(votes)

    return {
        'valid': confidence >= 0.5,
        'confidence': confidence,
        'disagreements': [i for i, v in enumerate(votes) if not v]
    }

class HierarchicalVV:
    def __init__(self):
        self.checks = [
            ('syntax', fast_syntax_check),
            ('type', type_checker),
            ('logic', expensive_formal_verification),
            ('security', security_scan)
        ]

    def validate(self, output):
        """Run checks in order of cost/speed"""
        for name, check in self.checks:
            if not check(output):
                return False, f"Failed {name} check"
        return True, "All checks passed"

import ast
import subprocess
from typing import Tuple

class CodeValidator:
    def __init__(self, llm):
        self.llm = llm

    def generate_code(self, task: str, max_retries: int = 3) -> str:
        """Generate Python code with V&V loop"""
        prompt = task

        for attempt in range(max_retries):
            # Generate
            code = self.llm.generate(prompt)

            # Verify: Syntax check
            syntax_valid, syntax_error = self._verify_syntax(code)
            if not syntax_valid:
                prompt = f"{task}\n\nPrevious attempt had syntax error:\n{syntax_error}\n\nPlease fix."
                continue

            # Verify: Runs without error
            runtime_valid, runtime_error = self._verify_runtime(code)
            if not runtime_valid:
                prompt = f"{task}\n\nPrevious code raised error:\n{runtime_error}\n\nPlease fix."
                continue

            # Validate: Meets requirements
            semantic_valid, semantic_feedback = self._validate_semantics(code, task)
            if not semantic_valid:
                prompt = f"{task}\n\nCode runs but: {semantic_feedback}\n\nPlease revise."
                continue

            return code

        raise ValueError(f"Failed to generate valid code after {max_retries} attempts")

    def _verify_syntax(self, code: str) -> Tuple[bool, str]:
        """Check if code is syntactically valid Python"""
        try:
            ast.parse(code)
            return True, ""
        except SyntaxError as e:
            return False, str(e)

    def _verify_runtime(self, code: str) -> Tuple[bool, str]:
        """Execute code in sandbox and catch errors"""
        try:
            result = subprocess.run(
                ['python', '-c', code],
                capture_output=True,
                text=True,
                timeout=5
            )
            if result.returncode != 0:
                return False, result.stderr
            return True, ""
        except subprocess.TimeoutExpired:
            return False, "Code execution timed out"

    def _validate_semantics(self, code: str, task: str) -> Tuple[bool, str]:
        """Use LLM to check if code solves the task"""
        validation_prompt = f"""
        Task: {task}

        Generated code:
        ```python
        {code}
        ```

        Does this code correctly solve the task?
        Answer with YES or NO, followed by explanation.
        """

        response = self.llm.generate(validation_prompt)
        valid = response.strip().upper().startswith('YES')
        feedback = response.split('\n', 1)[1] if '\n' in response else ""

        return valid, feedback

# Usage with LangChain
from langchain.chat_models import ChatOpenAI

validator = CodeValidator(ChatOpenAI(model="gpt-4", temperature=0))

task = "Write a function that finds the longest palindromic substring"
code = validator.generate_code(task)
print(code)

from langgraph.graph import StateGraph, END

def create_vv_agent():
    workflow = StateGraph()

    # Nodes
    workflow.add_node("generate", generate_output)
    workflow.add_node("verify", verify_output)
    workflow.add_node("validate", validate_output)
    workflow.add_node("correct", apply_corrections)

    # Edges
    workflow.set_entry_point("generate")
    workflow.add_edge("generate", "verify")

    # Conditional edges
    workflow.add_conditional_edges(
        "verify",
        should_retry,
        {
            "pass": "validate",
            "fail": "correct"
        }
    )

    workflow.add_conditional_edges(
        "validate",
        should_retry,
        {
            "pass": END,
            "fail": "correct"
        }
    )

    workflow.add_edge("correct", "generate")

    return workflow.compile()

def divide(a: float, b: float) -> float:
    # Precondition (verify)
    assert b != 0, "Divisor cannot be zero"

    result = a / b

    # Postcondition (validate)
    assert abs(result * b - a) < 1e-10, "Result failed sanity check"

    return result

import json
from jsonschema import validate, ValidationError

# Your task:
# Write a function that uses an LLM to generate JSON for this schema
# Add verification (valid JSON syntax)
# Add validation (matches schema)
# Implement retry with feedback
# Test with edge cases

schema = {
    "type": "object",
    "properties": {
        "name": {"type": "string"},
        "age": {"type": "integer", "minimum": 0, "maximum": 120},
        "email": {"type": "string", "format": "email"}
    },
    "required": ["name", "age", "email"]
}

task = "Generate profile for a 25-year-old software engineer named Alice"

# Your implementation here
def generate_json_with_vv(task, schema, llm):
    # TODO: Implement V&V loop
    pass

# Test cases to handle:
# - Invalid JSON syntax
# - Missing required fields
# - Type mismatches
# - Constraint violations (age out of range)