scirs2-autograd 0.3.2

//! Expression simplification optimization
//!
//! This module implements algebraic simplifications for computation graphs,
//! such as x + 0 -> x, x * 1 -> x, x - x -> 0, etc.

use super::{OptimizationError, SimplificationPattern};
use crate::graph::{Graph, TensorID};
use crate::tensor::TensorInternal;
use crate::Float;
use std::collections::HashMap;

/// Type alias for the transform function used in simplification rules.
type TransformFn = Box<dyn Fn(&[TensorID]) -> Result<TensorID, OptimizationError>>;

/// Expression simplifier
pub struct ExpressionSimplifier<F: Float> {
    /// Rules for simplification
    rules: Vec<SimplificationRule<F>>,
    /// Cache of simplified expressions
    cache: HashMap<String, TensorID>,
}

impl<F: Float> ExpressionSimplifier<F> {
    /// Create a new expression simplifier with default rules
    pub fn new() -> Self {
        let mut simplifier = Self {
            rules: Vec::new(),
            cache: HashMap::new(),
        };
        simplifier.load_default_rules();
        simplifier
    }

    /// Load default simplification rules
    fn load_default_rules(&mut self) {
        // Identity rules
        self.add_rule(SimplificationRule::new(
            "add_zero",
            SimplificationPattern::AddZero,
            create_identity_replacement,
        ));

        self.add_rule(SimplificationRule::new(
            "sub_zero",
            SimplificationPattern::SubZero,
            create_identity_replacement,
        ));

        self.add_rule(SimplificationRule::new(
            "mul_one",
            SimplificationPattern::MulOne,
            create_identity_replacement,
        ));

        self.add_rule(SimplificationRule::new(
            "div_one",
            SimplificationPattern::DivOne,
            create_identity_replacement,
        ));

        // Zero rules
        self.add_rule(SimplificationRule::new(
            "mul_zero",
            SimplificationPattern::MulZero,
            |_inputs| create_zero_replacement(),
        ));

        // Self-operation rules
        self.add_rule(SimplificationRule::new(
            "sub_self",
            SimplificationPattern::SubSelf,
            |_inputs| create_zero_replacement(),
        ));

        self.add_rule(SimplificationRule::new(
            "div_self",
            SimplificationPattern::DivSelf,
            |_inputs| create_one_replacement(),
        ));

        // Composite function rules
        self.add_rule(SimplificationRule::new(
            "log_exp",
            SimplificationPattern::LogExp,
            create_inner_replacement,
        ));

        self.add_rule(SimplificationRule::new(
            "exp_log",
            SimplificationPattern::ExpLog,
            create_inner_replacement,
        ));

        // Power rules
        self.add_rule(SimplificationRule::new(
            "pow_one",
            SimplificationPattern::PowOne,
            create_identity_replacement,
        ));

        self.add_rule(SimplificationRule::new(
            "pow_zero",
            SimplificationPattern::PowZero,
            |_inputs| create_one_replacement(),
        ));
    }

    /// Add a simplification rule
    pub fn add_rule(&mut self, rule: SimplificationRule<F>) {
        self.rules.push(rule);
    }

    /// Apply expression simplification to a graph
    pub fn simplify_expressions(
        &mut self,
        _graph: &mut Graph<F>,
    ) -> Result<usize, OptimizationError> {
        let simplified_count = 0;

        // Implementation would:
        // 1. Traverse all nodes in the graph
        // 2. For each node, check if it matches any simplification pattern
        // 3. Apply the corresponding rule to create a simplified version
        // 4. Replace the original node with the simplified version
        // 5. Update all references in the graph

        Ok(simplified_count)
    }

    /// Check if a tensor matches any simplification pattern
    pub(crate) fn find_applicable_rule(
        &self,
        _tensor_internal: &TensorInternal<F>,
    ) -> Option<&SimplificationRule<F>> {
        // Check each rule to see if it applies to this tensor
        self.rules
            .iter()
            .find(|&rule| rule.matches(_tensor_internal))
            .map(|v| v as _)
    }

    /// Apply a specific rule to simplify a tensor
    pub(crate) fn apply_rule(
        &self,
        _rule: &SimplificationRule<F>,
        _tensor_internal: &TensorInternal<F>,
        _graph: &mut Graph<F>,
    ) -> Result<TensorID, OptimizationError> {
        // Apply the rule's transformation to create a new simplified tensor
        Err(OptimizationError::InvalidOperation(
            "Rule application not implemented".to_string(),
        ))
    }

    /// Clear the simplification cache
    pub fn clear_cache(&mut self) {
        self.cache.clear();
    }
}

/// Create an identity replacement (return the first input tensor)
fn create_identity_replacement(inputs: &[TensorID]) -> Result<TensorID, OptimizationError> {
    inputs.first().copied().ok_or_else(|| {
        OptimizationError::InvalidOperation(
            "Identity replacement requires at least one input".to_string(),
        )
    })
}

/// Create a zero replacement tensor
fn create_zero_replacement() -> Result<TensorID, OptimizationError> {
    // Create a constant zero tensor
    Err(OptimizationError::InvalidOperation(
        "Zero replacement not implemented".to_string(),
    ))
}

/// Create a one replacement tensor
fn create_one_replacement() -> Result<TensorID, OptimizationError> {
    // Create a constant one tensor
    Err(OptimizationError::InvalidOperation(
        "One replacement not implemented".to_string(),
    ))
}

/// Create an inner replacement (for patterns like log(exp(x)), return x)
fn create_inner_replacement(inputs: &[TensorID]) -> Result<TensorID, OptimizationError> {
    // For patterns like log(exp(x)), return the inner argument x
    inputs.first().copied().ok_or_else(|| {
        OptimizationError::InvalidOperation(
            "Inner replacement requires at least one input".to_string(),
        )
    })
}

impl<F: Float> Default for ExpressionSimplifier<F> {
    fn default() -> Self {
        Self::new()
    }
}

/// A simplification rule that can be applied to nodes
pub struct SimplificationRule<F: Float> {
    /// Name of this rule
    name: String,
    /// Pattern this rule matches
    pattern: SimplificationPattern,
    /// Function to apply the transformation
    transform: TransformFn,
    /// Phantom data for the Float type parameter
    _phantom: std::marker::PhantomData<F>,
}

impl<F: Float> SimplificationRule<F> {
    /// Create a new simplification rule
    pub fn new<Transform>(name: &str, pattern: SimplificationPattern, transform: Transform) -> Self
    where
        Transform: Fn(&[TensorID]) -> Result<TensorID, OptimizationError> + 'static,
    {
        Self {
            name: name.to_string(),
            pattern,
            transform: Box::new(transform),
            _phantom: std::marker::PhantomData,
        }
    }

    /// Get the name of this rule
    pub fn name(&self) -> &str {
        &self.name
    }

    /// Get the pattern this rule matches
    pub fn pattern(&self) -> SimplificationPattern {
        self.pattern
    }

    /// Check if this rule matches a tensor internal node
    pub(crate) fn matches(&self, _tensor_internal: &TensorInternal<F>) -> bool {
        // Check if the tensor internal's operation and structure matches this rule's pattern
        match self.pattern {
            SimplificationPattern::AddZero => self.matches_add_zero(_tensor_internal),
            SimplificationPattern::SubZero => self.matches_sub_zero(_tensor_internal),
            SimplificationPattern::MulOne => self.matches_mul_one(_tensor_internal),
            SimplificationPattern::DivOne => self.matches_div_one(_tensor_internal),
            SimplificationPattern::MulZero => self.matches_mul_zero(_tensor_internal),
            SimplificationPattern::SubSelf => self.matches_sub_self(_tensor_internal),
            SimplificationPattern::DivSelf => self.matches_div_self(_tensor_internal),
            SimplificationPattern::LogExp => self.matches_log_exp(_tensor_internal),
            SimplificationPattern::ExpLog => self.matches_exp_log(_tensor_internal),
            SimplificationPattern::SqrtSquare => self.matches_sqrt_square(_tensor_internal),
            SimplificationPattern::PowOne => self.matches_pow_one(_tensor_internal),
            SimplificationPattern::PowZero => self.matches_pow_zero(_tensor_internal),
        }
    }

    /// Apply this rule to create a simplified tensor
    pub fn apply(&self, inputs: &[TensorID]) -> Result<TensorID, OptimizationError> {
        (self.transform)(inputs)
    }

    // Pattern matching methods
    fn matches_add_zero(&self, _tensor_internal: &TensorInternal<F>) -> bool {
        // Check if this is an Add operation with one operand being zero
        false
    }

    fn matches_sub_zero(&self, _tensor_internal: &TensorInternal<F>) -> bool {
        // Check if this is a Sub operation with the second operand being zero
        false
    }

    fn matches_mul_one(&self, _tensor_internal: &TensorInternal<F>) -> bool {
        // Check if this is a Mul operation with one operand being one
        false
    }

    fn matches_div_one(&self, _tensor_internal: &TensorInternal<F>) -> bool {
        // Check if this is a Div operation with the second operand being one
        false
    }

    fn matches_mul_zero(&self, _tensor_internal: &TensorInternal<F>) -> bool {
        // Check if this is a Mul operation with one operand being zero
        false
    }

    fn matches_sub_self(&self, _tensor_internal: &TensorInternal<F>) -> bool {
        // Check if this is a Sub operation with both operands being the same
        false
    }

    fn matches_div_self(&self, _tensor_internal: &TensorInternal<F>) -> bool {
        // Check if this is a Div operation with both operands being the same
        false
    }

    fn matches_log_exp(&self, _tensor_internal: &TensorInternal<F>) -> bool {
        // Check if this is a Log operation applied to an Exp operation
        false
    }

    fn matches_exp_log(&self, _tensor_internal: &TensorInternal<F>) -> bool {
        // Check if this is an Exp operation applied to a Log operation
        false
    }

    fn matches_sqrt_square(&self, _tensor_internal: &TensorInternal<F>) -> bool {
        // Check if this is a Sqrt operation applied to a Square operation
        false
    }

    fn matches_pow_one(&self, _tensor_internal: &TensorInternal<F>) -> bool {
        // Check if this is a Pow operation with exponent one
        false
    }

    fn matches_pow_zero(&self, _tensor_internal: &TensorInternal<F>) -> bool {
        // Check if this is a Pow operation with exponent zero
        false
    }
}

/// Algebraic expression analyzer
pub struct AlgebraicAnalyzer<F: Float> {
    _phantom: std::marker::PhantomData<F>,
}

impl<F: Float> AlgebraicAnalyzer<F> {
    /// Create a new algebraic analyzer
    pub fn new() -> Self {
        Self {
            _phantom: std::marker::PhantomData,
        }
    }

    /// Analyze an expression for simplification opportunities
    pub(crate) fn analyze(
        &self,
        _tensor_internal: &TensorInternal<F>,
    ) -> Vec<SimplificationOpportunity> {
        let opportunities = Vec::new();

        // Analyze the tensor and its subgraph for various patterns:
        // - Identity operations (x + 0, x * 1, etc.)
        // - Redundant operations (x - x, x / x, etc.)
        // - Composite functions that can be simplified
        // - Commutative/associative rearrangements

        opportunities
    }

    /// Check for associative rearrangement opportunities
    pub(crate) fn find_associative_opportunities(
        &self,
        _tensor_internal: &TensorInternal<F>,
    ) -> Vec<AssociativityPattern> {
        // Look for patterns like (a + b) + c that can be rearranged
        // for better constant folding or other optimizations
        Vec::new()
    }

    /// Check for commutative rearrangement opportunities
    pub(crate) fn find_commutative_opportunities(
        &self,
        _tensor_internal: &TensorInternal<F>,
    ) -> Vec<CommutativityPattern> {
        // Look for patterns where operands can be reordered
        // to enable other optimizations
        Vec::new()
    }

    /// Check for distributive law opportunities
    pub(crate) fn find_distributive_opportunities(
        &self,
        _tensor_internal: &TensorInternal<F>,
    ) -> Vec<DistributivityPattern> {
        // Look for patterns like a * (b + c) that can be expanded
        // or patterns like a*b + a*c that can be factored
        Vec::new()
    }
}

impl<F: Float> Default for AlgebraicAnalyzer<F> {
    fn default() -> Self {
        Self::new()
    }
}

/// Types of simplification opportunities
#[derive(Debug, Clone)]
pub struct SimplificationOpportunity {
    /// The pattern that was found
    pub pattern: SimplificationPattern,
    /// Description of the opportunity
    pub description: String,
    /// Estimated benefit (higher is better)
    pub benefit: f32,
}

/// Patterns for associative operations
#[derive(Debug, Clone)]
pub struct AssociativityPattern {
    /// The operation that can be rearranged
    pub operation: String,
    /// Description of the rearrangement
    pub description: String,
}

/// Patterns for commutative operations
#[derive(Debug, Clone)]
pub struct CommutativityPattern {
    /// The operation that can have operands reordered
    pub operation: String,
    /// Description of the reordering
    pub description: String,
}

/// Patterns for distributive operations
#[derive(Debug, Clone)]
pub struct DistributivityPattern {
    /// Type of distributive transformation
    pub transformation_type: DistributiveType,
    /// Description of the transformation
    pub description: String,
}

/// Types of distributive transformations
#[derive(Debug, Clone, Copy)]
pub enum DistributiveType {
    /// Factor out common terms: a*b + a*c -> a*(b + c)
    Factor,
    /// Expand: a*(b + c) -> a*b + a*c
    Expand,
}

/// Canonical form converter
pub struct CanonicalFormConverter<F: Float> {
    _phantom: std::marker::PhantomData<F>,
}

impl<F: Float> CanonicalFormConverter<F> {
    /// Create a new canonical form converter
    pub fn new() -> Self {
        Self {
            _phantom: std::marker::PhantomData,
        }
    }

    /// Convert an expression to canonical form
    pub(crate) fn canonicalize(
        &self,
        _tensor_internal: &TensorInternal<F>,
    ) -> Result<TensorID, OptimizationError> {
        // Convert expressions to a standard canonical form:
        // - Sort operands in a consistent order
        // - Normalize associative operations
        // - Apply standard algebraic transformations

        Err(OptimizationError::InvalidOperation(
            "Canonicalization not implemented".to_string(),
        ))
    }

    /// Check if two expressions are equivalent in canonical form
    pub(crate) fn are_equivalent(
        &self,
        _node1: &TensorInternal<F>,
        _node2: &TensorInternal<F>,
    ) -> bool {
        // Compare the canonical forms of two expressions
        false
    }
}

impl<F: Float> Default for CanonicalFormConverter<F> {
    fn default() -> Self {
        Self::new()
    }
}

/// Utility functions for expression simplification
///
/// Create common simplification patterns
#[allow(dead_code)]
pub fn create_standard_rules<F: Float>() -> Vec<SimplificationRule<F>> {
    // This would create the standard set of simplification rules
    // that most users would want
    Vec::new()
}

/// Check if an operation is commutative
#[allow(dead_code)]
pub fn is_commutative(op_name: &str) -> bool {
    matches!(op_name, "Add" | "Mul" | "Min" | "Max")
}

/// Check if an operation is associative
#[allow(dead_code)]
pub fn is_associative(op_name: &str) -> bool {
    matches!(op_name, "Add" | "Mul" | "Min" | "Max")
}

/// Check if an operation has an identity element
#[allow(dead_code)]
pub fn has_identity(op_name: &str) -> bool {
    matches!(op_name, "Add" | "Mul")
}

/// Get the identity element for an operation
#[allow(dead_code)]
pub fn get_identity<F: Float>(op_name: &str) -> Option<F> {
    match op_name {
        "Add" => Some(F::zero()),
        "Mul" => Some(F::one()),
        _ => None,
    }
}

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

    #[test]
    fn test_expression_simplifier_creation() {
        let _simplifier = ExpressionSimplifier::<f32>::new();
    }

    #[test]
    fn test_algebraic_analyzer_creation() {
        let _analyzer = AlgebraicAnalyzer::<f32>::new();
    }

    #[test]
    fn test_canonical_form_converter_creation() {
        let _converter = CanonicalFormConverter::<f32>::new();
    }

    #[test]
    fn test_operation_properties() {
        assert!(is_commutative("Add"));
        assert!(is_commutative("Mul"));
        assert!(!is_commutative("Sub"));
        assert!(!is_commutative("Div"));

        assert!(is_associative("Add"));
        assert!(is_associative("Mul"));
        assert!(!is_associative("Sub"));
        assert!(!is_associative("Div"));

        assert!(has_identity("Add"));
        assert!(has_identity("Mul"));
        assert!(!has_identity("Sub"));
        assert!(!has_identity("Div"));

        assert_eq!(get_identity::<f32>("Add"), Some(0.0));
        assert_eq!(get_identity::<f32>("Mul"), Some(1.0));
        assert_eq!(get_identity::<f32>("Sub"), None);
    }

    #[test]
    fn test_simplification_opportunity() {
        let opportunity = SimplificationOpportunity {
            pattern: SimplificationPattern::AddZero,
            description: "Remove addition of zero".to_string(),
            benefit: 1.0,
        };

        assert!(matches!(
            opportunity.pattern,
            SimplificationPattern::AddZero
        ));
        assert_eq!(opportunity.benefit, 1.0);
    }

    #[test]
    fn test_distributive_patterns() {
        let factor_pattern = DistributivityPattern {
            transformation_type: DistributiveType::Factor,
            description: "Factor out common term".to_string(),
        };

        let expand_pattern = DistributivityPattern {
            transformation_type: DistributiveType::Expand,
            description: "Expand distributive expression".to_string(),
        };

        assert!(matches!(
            factor_pattern.transformation_type,
            DistributiveType::Factor
        ));
        assert!(matches!(
            expand_pattern.transformation_type,
            DistributiveType::Expand
        ));
    }
}