torsh_jit/

symbolic_execution.rs

//! Symbolic execution engine for path analysis and constraint solving
//!
//! This module provides symbolic execution capabilities including:
//! - Path-sensitive analysis of computation graphs
//! - Constraint generation and solving
//! - Symbolic value tracking and propagation
//! - Bug detection and verification

use crate::{
    ir::{BasicBlock, Instruction, IrModule, IrOpcode, IrValue, Terminator},
    ComputationGraph, JitError, JitResult, NodeId,
};
use std::collections::{HashMap, HashSet};
use torsh_core::{DType, Shape};

/// Symbolic execution engine for path analysis
pub struct SymbolicExecutionEngine {
    config: SymbolicExecutionConfig,
    constraint_solver: ConstraintSolver,
    path_explorer: PathExplorer,
    symbolic_memory: SymbolicMemory,
    bug_detector: BugDetector,
    verification_engine: VerificationEngine,
}

impl SymbolicExecutionEngine {
    /// Create a new symbolic execution engine
    pub fn new(config: SymbolicExecutionConfig) -> Self {
        Self {
            constraint_solver: ConstraintSolver::new(),
            path_explorer: PathExplorer::new(config.clone()),
            symbolic_memory: SymbolicMemory::new(),
            bug_detector: BugDetector::new(),
            verification_engine: VerificationEngine::new(),
            config,
        }
    }

    /// Execute symbolic analysis on a computation graph
    pub fn execute_graph(
        &mut self,
        graph: &ComputationGraph,
    ) -> JitResult<SymbolicExecutionResult> {
        let mut execution_states = Vec::new();
        let mut path_conditions = Vec::new();
        let mut bugs_found = Vec::new();
        let mut assertions_verified = Vec::new();

        // Convert graph to symbolic representation
        let symbolic_graph = self.convert_to_symbolic(graph)?;

        // Explore all possible execution paths
        let paths = self.path_explorer.explore_paths(&symbolic_graph)?;

        for path in paths {
            let mut state = ExecutionState::new();
            let mut constraints = ConstraintSet::new();

            // Execute path symbolically
            for node_id in &path.nodes {
                if let Some(node) = symbolic_graph.get_node(*node_id) {
                    let step_result =
                        self.execute_symbolic_node(node, &mut state, &mut constraints)?;

                    // Check for bugs at this step
                    if let Some(bug) = self.bug_detector.check_step(&step_result, &state) {
                        bugs_found.push(bug);
                    }

                    // Update state
                    state.merge(step_result.state_changes);
                }
            }

            // Check path constraints for satisfiability
            if self.constraint_solver.is_satisfiable(&constraints)? {
                execution_states.push(state);
                // Verify assertions on this path
                let verification_result =
                    self.verification_engine.verify_path(&path, &constraints)?;
                path_conditions.push(constraints);
                assertions_verified.extend(verification_result.verified_assertions);
            }
        }

        // Analyze results
        let coverage = self.calculate_coverage(&execution_states, graph);
        let complexity = self.analyze_complexity(&symbolic_graph);

        Ok(SymbolicExecutionResult {
            execution_states,
            path_conditions,
            bugs_found,
            assertions_verified,
            coverage,
            complexity,
            statistics: self.collect_statistics(),
            execution_paths: Vec::new(), // Initialize empty for now
        })
    }

    /// Execute symbolic analysis on an IR module
    pub fn execute_ir(&mut self, ir_module: &IrModule) -> JitResult<SymbolicIrResult> {
        let mut function_results = HashMap::new();
        let global_constraints = ConstraintSet::new();

        // Analyze the IR module as a whole since it contains basic blocks, not separate functions
        let ir_result = self.execute_symbolic_ir_module(ir_module)?;
        // Since we're working with the whole module, store the result with the module name
        function_results.insert(ir_module.name.clone(), ir_result);

        // Perform inter-procedural analysis
        let interprocedural_result = self.analyze_interprocedural(&function_results)?;

        Ok(SymbolicIrResult {
            function_results,
            interprocedural_result,
            global_constraints,
        })
    }

    /// Execute symbolic analysis on a single IR module
    fn execute_symbolic_ir_module(
        &mut self,
        ir_module: &IrModule,
    ) -> JitResult<SymbolicFunctionResult> {
        let mut execution_states = Vec::new();
        let mut function_constraints = ConstraintSet::new();

        // Analyze each basic block
        for (&block_id, block) in &ir_module.blocks {
            let mut state = ExecutionState::new();

            // Process each instruction in the block
            for instruction in &block.instructions {
                // Create a symbolic step result for this instruction
                let step_result = self.process_ir_instruction(instruction, &mut state)?;
                function_constraints.merge(&step_result.constraints);
            }

            execution_states.push(state);
        }

        Ok(SymbolicFunctionResult {
            function_name: ir_module.name.clone(),
            execution_paths: execution_states
                .into_iter()
                .enumerate()
                .map(|(i, state)| FunctionExecutionPath {
                    instructions: vec![i],
                    final_state: state,
                    path_constraints: ConstraintSet::new(),
                })
                .collect(),
            function_constraints: ConstraintSet::new(),
            safety_checks: Vec::new(),
        })
    }

    /// Process a single IR instruction symbolically
    fn process_ir_instruction(
        &self,
        instruction: &Instruction,
        state: &mut ExecutionState,
    ) -> JitResult<SymbolicStepResult> {
        let mut constraints = ConstraintSet::new();
        let symbolic_value = match instruction.opcode {
            IrOpcode::Add => Some(SymbolicValue::BinaryOp {
                op: BinaryOperator::Add,
                left: Box::new(SymbolicValue::Symbol("operand0".to_string())),
                right: Box::new(SymbolicValue::Symbol("operand1".to_string())),
            }),
            IrOpcode::Div => {
                // Add non-zero constraint for divisor
                constraints.add_constraint(Constraint::NonZero(SymbolicValue::Symbol(
                    "operand1".to_string(),
                )));
                Some(SymbolicValue::BinaryOp {
                    op: BinaryOperator::Divide,
                    left: Box::new(SymbolicValue::Symbol("operand0".to_string())),
                    right: Box::new(SymbolicValue::Symbol("operand1".to_string())),
                })
            }
            _ => None,
        };

        Ok(SymbolicStepResult {
            symbolic_value,
            constraints,
            state_changes: StateChanges::new(),
            side_effects: Vec::new(),
        })
    }

    /// Convert computation graph to symbolic representation
    fn convert_to_symbolic(&self, graph: &ComputationGraph) -> JitResult<SymbolicGraph> {
        let mut symbolic_graph = SymbolicGraph::new();

        // Convert nodes to symbolic nodes
        for (node_id, node) in graph.nodes() {
            let symbolic_node = self.create_symbolic_node(node_id, node)?;
            symbolic_graph.add_node(node_id, symbolic_node);
        }

        // Convert edges to symbolic constraints
        for (source, target, edge) in graph.edges() {
            let symbolic_edge = self.create_symbolic_edge(edge)?;
            symbolic_graph.add_edge(source, target, symbolic_edge);
        }

        Ok(symbolic_graph)
    }

    /// Create symbolic node from computation node
    fn create_symbolic_node(
        &self,
        node_id: NodeId,
        node: &crate::graph::Node,
    ) -> JitResult<SymbolicNode> {
        let symbolic_value = match node.op.as_str() {
            "add" => SymbolicValue::BinaryOp {
                op: BinaryOperator::Add,
                left: Box::new(SymbolicValue::Input(0)),
                right: Box::new(SymbolicValue::Input(1)),
            },
            "mul" => SymbolicValue::BinaryOp {
                op: BinaryOperator::Multiply,
                left: Box::new(SymbolicValue::Input(0)),
                right: Box::new(SymbolicValue::Input(1)),
            },
            "constant" => SymbolicValue::Constant(SymbolicConstant::Unknown), // Would extract actual value
            "parameter" => SymbolicValue::Symbol(format!("param_{:?}", node_id)),
            _ => SymbolicValue::Symbol(format!("unknown_{:?}", node_id)),
        };

        Ok(SymbolicNode {
            id: node_id,
            operation: format!("{:?}", node.op),
            symbolic_value,
            constraints: Vec::new(),
            type_info: TypeInformation {
                dtype: node.dtype,
                shape: node.output_shape.clone(),
                constraints: Vec::new(),
            },
        })
    }

    /// Create symbolic edge from graph edge
    fn create_symbolic_edge(&self, edge: &crate::graph::Edge) -> JitResult<SymbolicEdge> {
        Ok(SymbolicEdge {
            from: NodeId::new(0),                 // Placeholder
            to: NodeId::new(1),                   // Placeholder
            data_flow: DataFlowConstraint::Equal, // Simplified
            type_constraint: None,
        })
    }

    /// Execute a symbolic node
    fn execute_symbolic_node(
        &mut self,
        node: &SymbolicNode,
        state: &mut ExecutionState,
        constraints: &mut ConstraintSet,
    ) -> JitResult<SymbolicStepResult> {
        let mut state_changes = StateChanges::new();
        let mut new_constraints = Vec::new();

        match &node.symbolic_value {
            SymbolicValue::BinaryOp { op, left, right } => {
                let left_val = self.evaluate_symbolic_value(left, state)?;
                let right_val = self.evaluate_symbolic_value(right, state)?;

                let result = self.apply_binary_op(*op, &left_val, &right_val)?;
                state_changes.add_binding(node.id, result.clone());

                // Generate constraints based on operation
                match op {
                    BinaryOperator::Divide => {
                        // Add non-zero constraint for divisor
                        new_constraints.push(Constraint::NonZero(right_val));
                    }
                    BinaryOperator::Modulo => {
                        // Add non-zero constraint for modulus
                        new_constraints.push(Constraint::NonZero(right_val));
                    }
                    _ => {}
                }
            }
            SymbolicValue::UnaryOp { op, operand } => {
                let operand_val = self.evaluate_symbolic_value(operand, state)?;
                let result = self.apply_unary_op(*op, &operand_val)?;
                state_changes.add_binding(node.id, result);

                // Generate constraints for operations like sqrt
                match op {
                    UnaryOperator::SquareRoot => {
                        new_constraints.push(Constraint::GreaterEqualZero(operand_val));
                    }
                    UnaryOperator::Log => {
                        new_constraints.push(Constraint::GreaterThanZero(operand_val));
                    }
                    _ => {}
                }
            }
            SymbolicValue::Constant(constant) => {
                let value = self.convert_constant(constant)?;
                state_changes.add_binding(node.id, value);
            }
            SymbolicValue::Symbol(name) => {
                if !state.has_binding(name) {
                    // Create fresh symbolic variable
                    let fresh_var =
                        SymbolicValue::Symbol(format!("{}_{}", name, state.get_generation()));
                    state_changes.add_binding(node.id, fresh_var);
                }
            }
            SymbolicValue::Conditional {
                condition,
                true_branch,
                false_branch,
            } => {
                let cond_val = self.evaluate_symbolic_value(condition, state)?;

                // Fork execution for both branches
                let true_result = self.evaluate_symbolic_value(true_branch, state)?;
                let false_result = self.evaluate_symbolic_value(false_branch, state)?;

                // Create conditional result
                let result = SymbolicValue::Conditional {
                    condition: Box::new(cond_val.clone()),
                    true_branch: Box::new(true_result),
                    false_branch: Box::new(false_result),
                };

                state_changes.add_binding(node.id, result);
            }
            _ => {
                // Default handling for unknown operations
                let fresh_var = SymbolicValue::Symbol(format!("unknown_{:?}", node.id));
                state_changes.add_binding(node.id, fresh_var);
            }
        }

        // Add node-specific constraints
        for constraint in &node.constraints {
            new_constraints.push(constraint.clone());
        }

        // Update constraint set
        for constraint in new_constraints {
            constraints.add_constraint(constraint);
        }

        Ok(SymbolicStepResult {
            symbolic_value: state.get_binding(&node.id).cloned(),
            constraints: constraints.clone(),
            state_changes,
            side_effects: Vec::new(),
        })
    }

    /// Execute symbolic analysis on a function (placeholder - IR uses basic blocks, not separate functions)
    fn execute_symbolic_function(
        &mut self,
        ir_module: &IrModule,
    ) -> JitResult<SymbolicFunctionResult> {
        let mut execution_paths = Vec::new();
        let mut function_constraints = ConstraintSet::new();

        // Build control flow graph
        let cfg = self.build_control_flow_graph(ir_module)?;

        // For now, simulate path exploration with basic block iteration
        for (&block_id, block) in &ir_module.blocks {
            let mut state = ExecutionState::new();
            let mut path_constraints = ConstraintSet::new();

            // Execute each instruction in the block
            for instruction in &block.instructions {
                let step_result = self.process_ir_instruction(instruction, &mut state)?;
                path_constraints.merge(&step_result.constraints);

                // Check for potential issues
                self.check_instruction_safety(instruction, &step_result)?;
            }

            execution_paths.push(FunctionExecutionPath {
                instructions: vec![block_id as usize],
                final_state: state,
                path_constraints: path_constraints.clone(),
            });
        }

        // Merge constraints from all paths
        for path in &execution_paths {
            function_constraints.merge(&path.path_constraints);
        }

        Ok(SymbolicFunctionResult {
            function_name: ir_module.name.clone(),
            execution_paths,
            safety_checks: Vec::new(),
            function_constraints,
        })
    }

    /// Execute a symbolic instruction
    fn execute_symbolic_instruction(
        &mut self,
        instruction: &Instruction,
        state: &mut ExecutionState,
        constraints: &mut ConstraintSet,
    ) -> JitResult<SymbolicStepResult> {
        let mut state_changes = StateChanges::new();
        let mut new_constraints = Vec::new();

        match instruction.opcode {
            IrOpcode::Add => {
                if instruction.operands.len() >= 2 {
                    let left_val = self.get_ir_value_symbolic(&instruction.operands[0], state)?;
                    let right_val = self.get_ir_value_symbolic(&instruction.operands[1], state)?;
                    let result = SymbolicValue::BinaryOp {
                        op: BinaryOperator::Add,
                        left: Box::new(left_val),
                        right: Box::new(right_val),
                    };
                    if let Some(result_reg) = instruction.result {
                        state_changes.add_register_binding(result_reg.0, result);
                    }
                }
            }
            IrOpcode::Mul => {
                if instruction.operands.len() >= 2 {
                    let left_val = self.get_ir_value_symbolic(&instruction.operands[0], state)?;
                    let right_val = self.get_ir_value_symbolic(&instruction.operands[1], state)?;
                    let result = SymbolicValue::BinaryOp {
                        op: BinaryOperator::Multiply,
                        left: Box::new(left_val),
                        right: Box::new(right_val),
                    };
                    if let Some(result_reg) = instruction.result {
                        state_changes.add_register_binding(result_reg.0, result);
                    }
                }
            }
            IrOpcode::Const => {
                // For constants, we'll create a placeholder symbolic constant
                // In a real implementation, this would extract the actual constant value from attributes
                let symbolic_const = SymbolicValue::Constant(SymbolicConstant::Unknown);
                if let Some(result_reg) = instruction.result {
                    state_changes.add_register_binding(result_reg.0, symbolic_const);
                }
            }
            IrOpcode::CondBr => {
                if !instruction.operands.is_empty() {
                    let cond_val = self.get_ir_value_symbolic(&instruction.operands[0], state)?;
                    new_constraints.push(Constraint::Boolean(cond_val));
                }
            }
            _ => {
                // Handle other instructions with generic symbolic representation
                if let Some(result_reg) = instruction.result {
                    let symbolic_value = SymbolicValue::Symbol(format!(
                        "op_{:?}_{}",
                        instruction.opcode, result_reg.0
                    ));
                    state_changes.add_register_binding(result_reg.0, symbolic_value);
                }
            }
        }

        // Add new constraints
        for constraint in new_constraints {
            constraints.add_constraint(constraint);
        }

        Ok(SymbolicStepResult {
            symbolic_value: None,
            constraints: constraints.clone(),
            state_changes,
            side_effects: Vec::new(),
        })
    }

    /// Evaluate a symbolic value in the current state
    fn evaluate_symbolic_value(
        &self,
        value: &SymbolicValue,
        state: &ExecutionState,
    ) -> JitResult<SymbolicValue> {
        match value {
            SymbolicValue::Symbol(name) => Ok(state
                .get_symbol_value(name)
                .cloned()
                .unwrap_or_else(|| value.clone())),
            SymbolicValue::Input(index) => Ok(state
                .get_input_value(*index)
                .cloned()
                .unwrap_or_else(|| value.clone())),
            _ => Ok(value.clone()),
        }
    }

    /// Apply binary operation to symbolic values
    fn apply_binary_op(
        &self,
        op: BinaryOperator,
        left: &SymbolicValue,
        right: &SymbolicValue,
    ) -> JitResult<SymbolicValue> {
        // Simplify if both operands are constants
        if let (SymbolicValue::Constant(l), SymbolicValue::Constant(r)) = (left, right) {
            return self.evaluate_constant_binary_op(op, l, r);
        }

        // Apply algebraic simplifications
        match op {
            BinaryOperator::Add => {
                if let SymbolicValue::Constant(SymbolicConstant::Zero) = right {
                    return Ok(left.clone());
                }
                if let SymbolicValue::Constant(SymbolicConstant::Zero) = left {
                    return Ok(right.clone());
                }
            }
            BinaryOperator::Multiply => {
                if let SymbolicValue::Constant(SymbolicConstant::Zero) = right {
                    return Ok(SymbolicValue::Constant(SymbolicConstant::Zero));
                }
                if let SymbolicValue::Constant(SymbolicConstant::Zero) = left {
                    return Ok(SymbolicValue::Constant(SymbolicConstant::Zero));
                }
                if let SymbolicValue::Constant(SymbolicConstant::One) = right {
                    return Ok(left.clone());
                }
                if let SymbolicValue::Constant(SymbolicConstant::One) = left {
                    return Ok(right.clone());
                }
            }
            _ => {}
        }

        Ok(SymbolicValue::BinaryOp {
            op,
            left: Box::new(left.clone()),
            right: Box::new(right.clone()),
        })
    }

    /// Apply unary operation to symbolic value
    fn apply_unary_op(
        &self,
        op: UnaryOperator,
        operand: &SymbolicValue,
    ) -> JitResult<SymbolicValue> {
        // Simplify if operand is constant
        if let SymbolicValue::Constant(c) = operand {
            return self.evaluate_constant_unary_op(op, c);
        }

        Ok(SymbolicValue::UnaryOp {
            op,
            operand: Box::new(operand.clone()),
        })
    }

    /// Evaluate constant binary operation
    fn evaluate_constant_binary_op(
        &self,
        op: BinaryOperator,
        left: &SymbolicConstant,
        right: &SymbolicConstant,
    ) -> JitResult<SymbolicValue> {
        match (left, right, op) {
            (SymbolicConstant::Integer(a), SymbolicConstant::Integer(b), BinaryOperator::Add) => {
                Ok(SymbolicValue::Constant(SymbolicConstant::Integer(a + b)))
            }
            (
                SymbolicConstant::Integer(a),
                SymbolicConstant::Integer(b),
                BinaryOperator::Multiply,
            ) => Ok(SymbolicValue::Constant(SymbolicConstant::Integer(a * b))),
            (SymbolicConstant::Float(a), SymbolicConstant::Float(b), BinaryOperator::Add) => {
                Ok(SymbolicValue::Constant(SymbolicConstant::Float(a + b)))
            }
            (SymbolicConstant::Float(a), SymbolicConstant::Float(b), BinaryOperator::Multiply) => {
                Ok(SymbolicValue::Constant(SymbolicConstant::Float(a * b)))
            }
            _ => Ok(SymbolicValue::BinaryOp {
                op,
                left: Box::new(SymbolicValue::Constant(left.clone())),
                right: Box::new(SymbolicValue::Constant(right.clone())),
            }),
        }
    }

    /// Evaluate constant unary operation
    fn evaluate_constant_unary_op(
        &self,
        op: UnaryOperator,
        operand: &SymbolicConstant,
    ) -> JitResult<SymbolicValue> {
        match (operand, op) {
            (SymbolicConstant::Integer(a), UnaryOperator::Negate) => {
                Ok(SymbolicValue::Constant(SymbolicConstant::Integer(-a)))
            }
            (SymbolicConstant::Float(a), UnaryOperator::Negate) => {
                Ok(SymbolicValue::Constant(SymbolicConstant::Float(-a)))
            }
            (SymbolicConstant::Float(a), UnaryOperator::SquareRoot) => {
                if *a >= 0.0 {
                    Ok(SymbolicValue::Constant(SymbolicConstant::Float(a.sqrt())))
                } else {
                    Err(JitError::AnalysisError(
                        "Square root of negative number".to_string(),
                    ))
                }
            }
            _ => Ok(SymbolicValue::UnaryOp {
                op,
                operand: Box::new(SymbolicValue::Constant(operand.clone())),
            }),
        }
    }

    /// Get symbolic representation of IR value
    fn get_ir_value_symbolic(
        &self,
        value: &IrValue,
        state: &ExecutionState,
    ) -> JitResult<SymbolicValue> {
        // IrValue is just a wrapper around u32, so we'll create a symbolic representation based on the ID
        let value_id = value.0;
        Ok(SymbolicValue::Symbol(format!("value_{}", value_id)))
    }

    /// Convert IR constant to symbolic constant
    fn convert_ir_constant(
        &self,
        value: &crate::partial_evaluation::ConstantValue,
    ) -> JitResult<SymbolicValue> {
        match value {
            crate::partial_evaluation::ConstantValue::Float32(f) => {
                Ok(SymbolicValue::Constant(SymbolicConstant::Float(*f as f64)))
            }
            crate::partial_evaluation::ConstantValue::Float64(f) => {
                Ok(SymbolicValue::Constant(SymbolicConstant::Float(*f)))
            }
            crate::partial_evaluation::ConstantValue::Int32(i) => Ok(SymbolicValue::Constant(
                SymbolicConstant::Integer(*i as i64),
            )),
            crate::partial_evaluation::ConstantValue::Int64(i) => {
                Ok(SymbolicValue::Constant(SymbolicConstant::Integer(*i)))
            }
            crate::partial_evaluation::ConstantValue::Boolean(b) => {
                Ok(SymbolicValue::Constant(SymbolicConstant::Boolean(*b)))
            }
        }
    }

    /// Convert symbolic constant
    fn convert_constant(&self, constant: &SymbolicConstant) -> JitResult<SymbolicValue> {
        Ok(SymbolicValue::Constant(constant.clone()))
    }

    /// Build control flow graph for IR module
    fn build_control_flow_graph(&self, ir_module: &IrModule) -> JitResult<ControlFlowGraph> {
        let mut cfg = ControlFlowGraph::new();

        // Build basic blocks
        let mut current_block = Vec::new();
        let block_id = 0;

        for (&block_id, block) in &ir_module.blocks {
            for (inst_id, instruction) in block.instructions.iter().enumerate() {
                current_block.push(inst_id);

                // Check if this instruction ends a basic block
                if self.is_terminator_instruction(instruction, block) {
                    cfg.add_block(block_id as usize, current_block.clone());
                    current_block.clear();
                }
            }
        }

        // Add final block if non-empty
        if !current_block.is_empty() {
            cfg.add_block(block_id, current_block);
        }

        // Add control flow edges
        self.add_control_flow_edges(ir_module, &mut cfg)?;

        Ok(cfg)
    }

    /// Check if instruction is a terminator
    fn is_terminator_instruction(&self, _instruction: &Instruction, block: &BasicBlock) -> bool {
        // Check if the block has a branch or return terminator
        if let Some(ref terminator) = block.terminator {
            matches!(
                terminator,
                Terminator::Branch { .. } | Terminator::Return { .. }
            )
        } else {
            false
        }
    }

    /// Add control flow edges to CFG
    fn add_control_flow_edges(
        &self,
        _ir_module: &IrModule,
        cfg: &mut ControlFlowGraph,
    ) -> JitResult<()> {
        // Analyze control flow and add edges between basic blocks
        // This is a simplified implementation
        for block_id in 0..cfg.block_count() {
            if block_id + 1 < cfg.block_count() {
                cfg.add_edge(block_id, block_id + 1);
            }
        }
        Ok(())
    }

    /// Check instruction safety
    fn check_instruction_safety(
        &self,
        instruction: &Instruction,
        result: &SymbolicStepResult,
    ) -> JitResult<()> {
        // Check for potential safety issues like division by zero, null pointer dereference, etc.
        match instruction {
            instruction if instruction.opcode == IrOpcode::Div => {
                if let Some(_divisor) = instruction.operands.get(1) {
                    // Check if divisor could be zero
                    if let Some(SymbolicValue::Constant(SymbolicConstant::Zero)) =
                        result.symbolic_value.as_ref()
                    {
                        return Err(JitError::AnalysisError(
                            "Potential division by zero detected".to_string(),
                        ));
                    }
                }
            }
            _ => {}
        }
        Ok(())
    }

    /// Perform interprocedural analysis
    fn analyze_interprocedural(
        &self,
        function_results: &HashMap<String, SymbolicFunctionResult>,
    ) -> JitResult<InterproceduralResult> {
        // Analyze interactions between functions
        let mut call_graph = CallGraph::new();
        let mut global_constraints = ConstraintSet::new();

        // Build call graph
        for (func_name, result) in function_results {
            call_graph.add_function(func_name.clone());
            global_constraints.merge(&result.function_constraints);
        }

        Ok(InterproceduralResult {
            call_graph,
            global_constraints,
            potential_issues: Vec::new(),
        })
    }

    /// Calculate code coverage
    fn calculate_coverage(&self, states: &[ExecutionState], graph: &ComputationGraph) -> Coverage {
        let total_nodes = graph.node_count();
        let mut covered_nodes = HashSet::new();

        for state in states {
            for binding in state.get_node_bindings() {
                covered_nodes.insert(*binding.0);
            }
        }

        Coverage {
            node_coverage: covered_nodes.len() as f64 / total_nodes as f64,
            path_coverage: states.len(),
            total_nodes,
            covered_nodes: covered_nodes.len(),
        }
    }

    /// Analyze complexity
    fn analyze_complexity(&self, graph: &SymbolicGraph) -> ComplexityAnalysis {
        ComplexityAnalysis {
            cyclomatic_complexity: self.calculate_cyclomatic_complexity(graph),
            path_complexity: graph.node_count(),
            constraint_complexity: 0, // Placeholder
        }
    }

    /// Calculate cyclomatic complexity
    fn calculate_cyclomatic_complexity(&self, graph: &SymbolicGraph) -> usize {
        // V(G) = E - N + 2P where E = edges, N = nodes, P = connected components
        let edges = graph.edge_count();
        let nodes = graph.node_count();
        let components = 1; // Assuming single connected component

        if edges >= nodes {
            edges - nodes + 2 * components
        } else {
            1 // Minimum complexity
        }
    }

    /// Collect execution statistics
    fn collect_statistics(&self) -> ExecutionStatistics {
        ExecutionStatistics {
            paths_explored: 0, // Would be tracked during execution
            constraints_generated: 0,
            solver_calls: 0,
            execution_time: std::time::Duration::from_millis(0),
        }
    }

    /// Collect safety checks
    fn collect_safety_checks(&self, paths: &[FunctionExecutionPath]) -> Vec<SafetyCheck> {
        let mut checks = Vec::new();

        for path in paths {
            // Analyze each path for potential safety issues
            checks.push(SafetyCheck {
                check_type: SafetyCheckType::DivisionByZero,
                location: "placeholder".to_string(),
                confidence: 0.8,
                description: "Potential division by zero".to_string(),
            });
        }

        checks
    }
}

// Configuration and data structures

/// Configuration for symbolic execution
#[derive(Debug, Clone)]
pub struct SymbolicExecutionConfig {
    pub max_path_length: usize,
    pub max_paths: usize,
    pub timeout_seconds: u64,
    pub enable_constraint_solving: bool,
    pub enable_bug_detection: bool,
    pub enable_verification: bool,
    pub solver_timeout_ms: u64,
}

impl Default for SymbolicExecutionConfig {
    fn default() -> Self {
        Self {
            max_path_length: 1000,
            max_paths: 100,
            timeout_seconds: 300,
            enable_constraint_solving: true,
            enable_bug_detection: true,
            enable_verification: true,
            solver_timeout_ms: 5000,
        }
    }
}

/// Symbolic representation of values
#[derive(Debug, Clone)]
pub enum SymbolicValue {
    Symbol(String),
    Constant(SymbolicConstant),
    Input(usize),
    BinaryOp {
        op: BinaryOperator,
        left: Box<SymbolicValue>,
        right: Box<SymbolicValue>,
    },
    UnaryOp {
        op: UnaryOperator,
        operand: Box<SymbolicValue>,
    },
    Conditional {
        condition: Box<SymbolicValue>,
        true_branch: Box<SymbolicValue>,
        false_branch: Box<SymbolicValue>,
    },
    Array {
        elements: Vec<SymbolicValue>,
    },
    MemoryLoad {
        address: Box<SymbolicValue>,
        size: usize,
    },
}

/// Symbolic constants
#[derive(Debug, Clone)]
pub enum SymbolicConstant {
    Integer(i64),
    Float(f64),
    Boolean(bool),
    Zero,
    One,
    Unknown,
}

/// Binary operators
#[derive(Debug, Clone, Copy)]
pub enum BinaryOperator {
    Add,
    Subtract,
    Multiply,
    Divide,
    Modulo,
    Equal,
    NotEqual,
    LessThan,
    LessEqual,
    GreaterThan,
    GreaterEqual,
    And,
    Or,
    Xor,
}

/// Unary operators
#[derive(Debug, Clone, Copy)]
pub enum UnaryOperator {
    Negate,
    Not,
    SquareRoot,
    Log,
    Exp,
    Sin,
    Cos,
    Tan,
}

/// Constraints on symbolic values
#[derive(Debug, Clone)]
pub enum Constraint {
    Equal(SymbolicValue, SymbolicValue),
    NotEqual(SymbolicValue, SymbolicValue),
    LessThan(SymbolicValue, SymbolicValue),
    GreaterThan(SymbolicValue, SymbolicValue),
    GreaterEqualZero(SymbolicValue),
    GreaterThanZero(SymbolicValue),
    NonZero(SymbolicValue),
    Boolean(SymbolicValue),
    TypeConstraint(SymbolicValue, DType),
    ShapeConstraint(SymbolicValue, Shape),
}

/// Set of constraints
#[derive(Debug, Clone)]
pub struct ConstraintSet {
    constraints: Vec<Constraint>,
}

impl ConstraintSet {
    pub fn new() -> Self {
        Self {
            constraints: Vec::new(),
        }
    }

    pub fn add_constraint(&mut self, constraint: Constraint) {
        self.constraints.push(constraint);
    }

    pub fn merge(&mut self, other: &ConstraintSet) {
        self.constraints.extend(other.constraints.iter().cloned());
    }

    pub fn is_empty(&self) -> bool {
        self.constraints.is_empty()
    }

    pub fn len(&self) -> usize {
        self.constraints.len()
    }
}

/// Execution state tracking symbolic values
#[derive(Debug, Clone)]
pub struct ExecutionState {
    node_bindings: HashMap<NodeId, SymbolicValue>,
    symbol_bindings: HashMap<String, SymbolicValue>,
    register_bindings: HashMap<u32, SymbolicValue>,
    input_bindings: HashMap<usize, SymbolicValue>,
    generation: usize,
}

impl ExecutionState {
    pub fn new() -> Self {
        Self {
            node_bindings: HashMap::new(),
            symbol_bindings: HashMap::new(),
            register_bindings: HashMap::new(),
            input_bindings: HashMap::new(),
            generation: 0,
        }
    }

    pub fn has_binding(&self, name: &str) -> bool {
        self.symbol_bindings.contains_key(name)
    }

    pub fn get_binding(&self, node_id: &NodeId) -> Option<&SymbolicValue> {
        self.node_bindings.get(node_id)
    }

    pub fn get_symbol_value(&self, name: &str) -> Option<&SymbolicValue> {
        self.symbol_bindings.get(name)
    }

    pub fn get_register_value(&self, reg: &u32) -> Option<SymbolicValue> {
        self.register_bindings.get(reg).cloned()
    }

    pub fn get_input_value(&self, index: usize) -> Option<&SymbolicValue> {
        self.input_bindings.get(&index)
    }

    pub fn get_generation(&self) -> usize {
        self.generation
    }

    pub fn get_node_bindings(&self) -> &HashMap<NodeId, SymbolicValue> {
        &self.node_bindings
    }

    pub fn merge(&mut self, changes: StateChanges) {
        for (node_id, value) in changes.node_changes {
            self.node_bindings.insert(node_id, value);
        }
        for (name, value) in changes.symbol_changes {
            self.symbol_bindings.insert(name, value);
        }
        for (reg, value) in changes.register_changes {
            self.register_bindings.insert(reg, value);
        }
        self.generation += 1;
    }
}

/// Changes to execution state
#[derive(Debug, Clone)]
pub struct StateChanges {
    node_changes: HashMap<NodeId, SymbolicValue>,
    symbol_changes: HashMap<String, SymbolicValue>,
    register_changes: HashMap<u32, SymbolicValue>,
}

impl StateChanges {
    pub fn new() -> Self {
        Self {
            node_changes: HashMap::new(),
            symbol_changes: HashMap::new(),
            register_changes: HashMap::new(),
        }
    }

    pub fn add_binding(&mut self, node_id: NodeId, value: SymbolicValue) {
        self.node_changes.insert(node_id, value);
    }

    pub fn add_symbol_binding(&mut self, name: String, value: SymbolicValue) {
        self.symbol_changes.insert(name, value);
    }

    pub fn add_register_binding(&mut self, reg: u32, value: SymbolicValue) {
        self.register_changes.insert(reg, value);
    }
}

/// Symbolic graph representation
#[derive(Debug)]
pub struct SymbolicGraph {
    nodes: HashMap<NodeId, SymbolicNode>,
    edges: Vec<(NodeId, NodeId, SymbolicEdge)>,
}

impl SymbolicGraph {
    pub fn new() -> Self {
        Self {
            nodes: HashMap::new(),
            edges: Vec::new(),
        }
    }

    pub fn add_node(&mut self, id: NodeId, node: SymbolicNode) {
        self.nodes.insert(id, node);
    }

    pub fn add_edge(&mut self, from: NodeId, to: NodeId, edge: SymbolicEdge) {
        self.edges.push((from, to, edge));
    }

    pub fn get_node(&self, id: NodeId) -> Option<&SymbolicNode> {
        self.nodes.get(&id)
    }

    pub fn node_count(&self) -> usize {
        self.nodes.len()
    }

    pub fn edge_count(&self) -> usize {
        self.edges.len()
    }
}

/// Symbolic node in the graph
#[derive(Debug)]
pub struct SymbolicNode {
    pub id: NodeId,
    pub operation: String,
    pub symbolic_value: SymbolicValue,
    pub constraints: Vec<Constraint>,
    pub type_info: TypeInformation,
}

/// Symbolic edge in the graph
#[derive(Debug)]
pub struct SymbolicEdge {
    pub from: NodeId,
    pub to: NodeId,
    pub data_flow: DataFlowConstraint,
    pub type_constraint: Option<DType>,
}

/// Data flow constraints
#[derive(Debug)]
pub enum DataFlowConstraint {
    Equal,
    Subset,
    Transform(String),
}

/// Type information for symbolic analysis
#[derive(Debug)]
pub struct TypeInformation {
    pub dtype: DType,
    pub shape: Shape,
    pub constraints: Vec<String>,
}

// Supporting components

/// Constraint solver
pub struct ConstraintSolver;

impl ConstraintSolver {
    pub fn new() -> Self {
        Self
    }

    pub fn is_satisfiable(&self, constraints: &ConstraintSet) -> JitResult<bool> {
        // Simplified constraint solving
        // In a real implementation, this would use an SMT solver
        Ok(!constraints.is_empty())
    }
}

/// Path explorer for finding execution paths
pub struct PathExplorer {
    config: SymbolicExecutionConfig,
}

impl PathExplorer {
    pub fn new(config: SymbolicExecutionConfig) -> Self {
        Self { config }
    }

    pub fn explore_paths(&self, graph: &SymbolicGraph) -> JitResult<Vec<ExecutionPath>> {
        // Simplified path exploration
        // In practice, this would use sophisticated path exploration algorithms
        let mut paths = Vec::new();

        // For now, create a single linear path through all nodes
        let node_ids: Vec<NodeId> = graph.nodes.keys().cloned().collect();
        paths.push(ExecutionPath {
            nodes: node_ids,
            conditions: Vec::new(),
        });

        Ok(paths)
    }

    pub fn explore_function_paths(&self, cfg: &ControlFlowGraph) -> JitResult<Vec<FunctionPath>> {
        // Explore paths through function CFG
        let mut paths = Vec::new();

        for block_id in 0..cfg.block_count() {
            if let Some(instructions) = cfg.get_block(block_id) {
                paths.push(FunctionPath {
                    instructions: instructions.clone(),
                });
            }
        }

        Ok(paths)
    }
}

/// Execution path through the graph
#[derive(Debug, Clone)]
pub struct ExecutionPath {
    pub nodes: Vec<NodeId>,
    pub conditions: Vec<Constraint>,
}

/// Function execution path
#[derive(Debug)]
pub struct FunctionPath {
    pub instructions: Vec<usize>,
}

/// Control flow graph
#[derive(Debug)]
pub struct ControlFlowGraph {
    blocks: HashMap<usize, Vec<usize>>,
    edges: Vec<(usize, usize)>,
}

impl ControlFlowGraph {
    pub fn new() -> Self {
        Self {
            blocks: HashMap::new(),
            edges: Vec::new(),
        }
    }

    pub fn add_block(&mut self, id: usize, instructions: Vec<usize>) {
        self.blocks.insert(id, instructions);
    }

    pub fn add_edge(&mut self, from: usize, to: usize) {
        self.edges.push((from, to));
    }

    pub fn block_count(&self) -> usize {
        self.blocks.len()
    }

    pub fn get_block(&self, id: usize) -> Option<&Vec<usize>> {
        self.blocks.get(&id)
    }
}

/// Symbolic memory model
pub struct SymbolicMemory;

impl SymbolicMemory {
    pub fn new() -> Self {
        Self
    }
}

/// Bug detector
pub struct BugDetector;

impl BugDetector {
    pub fn new() -> Self {
        Self
    }

    pub fn check_step(
        &self,
        step_result: &SymbolicStepResult,
        state: &ExecutionState,
    ) -> Option<Bug> {
        // Check for potential bugs in the step result
        None // Placeholder
    }
}

/// Verification engine
pub struct VerificationEngine;

impl VerificationEngine {
    pub fn new() -> Self {
        Self
    }

    pub fn verify_path(
        &self,
        path: &ExecutionPath,
        constraints: &ConstraintSet,
    ) -> JitResult<VerificationResult> {
        Ok(VerificationResult {
            verified_assertions: Vec::new(),
            failed_assertions: Vec::new(),
        })
    }
}

// Result types

/// Result of symbolic execution
#[derive(Debug, Clone)]
pub struct SymbolicExecutionResult {
    pub execution_states: Vec<ExecutionState>,
    pub path_conditions: Vec<ConstraintSet>,
    pub bugs_found: Vec<Bug>,
    pub assertions_verified: Vec<VerifiedAssertion>,
    pub coverage: Coverage,
    pub complexity: ComplexityAnalysis,
    pub statistics: ExecutionStatistics,
    pub execution_paths: Vec<ExecutionPath>,
}

/// Result of symbolic IR execution
#[derive(Debug)]
pub struct SymbolicIrResult {
    pub function_results: HashMap<String, SymbolicFunctionResult>,
    pub interprocedural_result: InterproceduralResult,
    pub global_constraints: ConstraintSet,
}

/// Result of symbolic function execution
#[derive(Debug)]
pub struct SymbolicFunctionResult {
    pub function_name: String,
    pub execution_paths: Vec<FunctionExecutionPath>,
    pub function_constraints: ConstraintSet,
    pub safety_checks: Vec<SafetyCheck>,
}

/// Function execution path with state
#[derive(Debug)]
pub struct FunctionExecutionPath {
    pub instructions: Vec<usize>,
    pub final_state: ExecutionState,
    pub path_constraints: ConstraintSet,
}

/// Result of a symbolic execution step
#[derive(Debug)]
pub struct SymbolicStepResult {
    pub symbolic_value: Option<SymbolicValue>,
    pub constraints: ConstraintSet,
    pub state_changes: StateChanges,
    pub side_effects: Vec<SideEffect>,
}

/// Side effects from execution
#[derive(Debug)]
pub enum SideEffect {
    MemoryWrite(SymbolicValue, SymbolicValue),
    FunctionCall(String, Vec<SymbolicValue>),
    IOOperation(String),
}

/// Interprocedural analysis result
#[derive(Debug)]
pub struct InterproceduralResult {
    pub call_graph: CallGraph,
    pub global_constraints: ConstraintSet,
    pub potential_issues: Vec<String>,
}

/// Call graph
#[derive(Debug)]
pub struct CallGraph {
    functions: HashSet<String>,
    calls: Vec<(String, String)>,
}

impl CallGraph {
    pub fn new() -> Self {
        Self {
            functions: HashSet::new(),
            calls: Vec::new(),
        }
    }

    pub fn add_function(&mut self, name: String) {
        self.functions.insert(name);
    }
}

/// Coverage information
#[derive(Debug, Clone)]
pub struct Coverage {
    pub node_coverage: f64,
    pub path_coverage: usize,
    pub total_nodes: usize,
    pub covered_nodes: usize,
}

/// Complexity analysis
#[derive(Debug, Clone)]
pub struct ComplexityAnalysis {
    pub cyclomatic_complexity: usize,
    pub path_complexity: usize,
    pub constraint_complexity: usize,
}

/// Execution statistics
#[derive(Debug, Clone)]
pub struct ExecutionStatistics {
    pub paths_explored: usize,
    pub constraints_generated: usize,
    pub solver_calls: usize,
    pub execution_time: std::time::Duration,
}

/// Bug found during symbolic execution
#[derive(Debug, Clone)]
pub struct Bug {
    pub bug_type: BugType,
    pub location: String,
    pub description: String,
    pub severity: BugSeverity,
    pub path_condition: ConstraintSet,
}

/// Types of bugs
#[derive(Debug, Clone)]
pub enum BugType {
    DivisionByZero,
    NullPointerDereference,
    ArrayBoundsViolation,
    IntegerOverflow,
    MemoryLeak,
    UseAfterFree,
}

/// Bug severity levels
#[derive(Debug, Clone)]
pub enum BugSeverity {
    Low,
    Medium,
    High,
    Critical,
}

/// Verified assertion
#[derive(Debug, Clone)]
pub struct VerifiedAssertion {
    pub assertion: String,
    pub verified: bool,
    pub counterexample: Option<ConstraintSet>,
}

/// Verification result
#[derive(Debug)]
pub struct VerificationResult {
    pub verified_assertions: Vec<VerifiedAssertion>,
    pub failed_assertions: Vec<VerifiedAssertion>,
}

/// Safety check
#[derive(Debug)]
pub struct SafetyCheck {
    pub check_type: SafetyCheckType,
    pub location: String,
    pub confidence: f64,
    pub description: String,
}

/// Types of safety checks
#[derive(Debug)]
pub enum SafetyCheckType {
    DivisionByZero,
    NullPointer,
    BufferOverflow,
    IntegerOverflow,
    MemoryLeak,
}

#[cfg(test)]
mod tests {
    use super::*;

    #[test]
    fn test_symbolic_execution_config() {
        let config = SymbolicExecutionConfig::default();
        assert_eq!(config.max_path_length, 1000);
        assert_eq!(config.max_paths, 100);
        assert!(config.enable_constraint_solving);
    }

    #[test]
    fn test_symbolic_value_creation() {
        let value = SymbolicValue::Symbol("x".to_string());
        if let SymbolicValue::Symbol(name) = value {
            assert_eq!(name, "x");
        } else {
            panic!("Expected Symbol variant");
        }
    }

    #[test]
    fn test_constraint_set() {
        let mut constraints = ConstraintSet::new();
        assert!(constraints.is_empty());

        constraints.add_constraint(Constraint::NonZero(SymbolicValue::Symbol("x".to_string())));
        assert_eq!(constraints.len(), 1);
    }

    #[test]
    fn test_execution_state() {
        let mut state = ExecutionState::new();
        assert_eq!(state.get_generation(), 0);

        let changes = StateChanges::new();
        state.merge(changes);
        assert_eq!(state.get_generation(), 1);
    }

    #[test]
    fn test_symbolic_graph() {
        let mut graph = SymbolicGraph::new();
        let node_id = NodeId::new(0);

        let node = SymbolicNode {
            id: node_id,
            operation: "add".to_string(),
            symbolic_value: SymbolicValue::Symbol("test".to_string()),
            constraints: Vec::new(),
            type_info: TypeInformation {
                dtype: DType::F32,
                shape: Shape::new(vec![1]),
                constraints: Vec::new(),
            },
        };

        graph.add_node(node_id, node);
        assert_eq!(graph.node_count(), 1);
    }
}