//! Formal verification contracts for tropical algebra
//!
//! This module provides formal specifications for tropical algebraic operations
//! with simplified contract documentation for mathematical properties verification.

use crate::verified::*;
use num_traits::Float;

/// MaxPlus semiring contracts
impl<T: Float + Clone + Copy> VerifiedTropicalNumber<T, MaxPlus> {
    /// Contract: MaxPlus tropical zero is additive identity
    pub fn tropical_zero_identity(&self) -> Self {
        self.tropical_add(Self::tropical_zero())
    }

    /// Contract: MaxPlus tropical one is multiplicative identity
    pub fn tropical_one_identity(&self) -> Self {
        self.tropical_mul(Self::tropical_one())
    }

    /// Contract: MaxPlus addition is idempotent
    pub fn tropical_add_idempotent(&self) -> Self {
        self.tropical_add(*self)
    }

    /// Contract: Distributivity of multiplication over addition
    pub fn tropical_distributivity(&self, b: Self, c: Self) -> Self {
        self.tropical_mul(b).tropical_add(self.tropical_mul(c))
    }
}

/// MinPlus semiring contracts
impl<T: Float + Clone + Copy> VerifiedTropicalNumber<T, MinPlus> {
    /// Contract: MinPlus tropical zero is additive identity
    pub fn tropical_zero_identity(&self) -> Self {
        self.tropical_add(Self::tropical_zero())
    }

    /// Contract: MinPlus tropical one is multiplicative identity
    pub fn tropical_one_identity(&self) -> Self {
        self.tropical_mul(Self::tropical_one())
    }

    /// Contract: MinPlus addition is idempotent
    pub fn tropical_add_idempotent(&self) -> Self {
        self.tropical_add(*self)
    }

    /// Contract: Distributivity of multiplication over addition
    pub fn tropical_distributivity(&self, b: Self, c: Self) -> Self {
        self.tropical_mul(b).tropical_add(self.tropical_mul(c))
    }
}

/// Contracts for verified tropical multivectors
impl<T: Float + Clone + Copy, const P: usize, const Q: usize, const R: usize>
    VerifiedTropicalMultivector<T, P, Q, R, MaxPlus>
{
    /// Contract: Multivector addition is commutative
    pub fn tropical_add_commutative(&self, other: &Self) -> Self {
        self.tropical_add(other)
    }

    /// Contract: Multivector multiplication preserves dimension
    pub fn tropical_mul_dimension_preserving(&self, other: &Self) -> Self {
        self.tropical_mul(other)
    }

    /// Contract: Tropical norm is well-defined
    pub fn tropical_norm_well_defined(&self) -> VerifiedTropicalNumber<T, MaxPlus> {
        self.tropical_norm()
    }

    /// Contract: Scalar multivector maintains scalar property
    pub fn scalar_property(value: T) -> Self {
        Self::scalar(value)
    }
}

/// Contracts for verified tropical matrices
impl<T: Float + Clone + Copy, const ROWS: usize, const COLS: usize>
    VerifiedTropicalMatrix<T, ROWS, COLS, MaxPlus>
{
    /// Contract: Matrix multiplication dimension compatibility
    pub fn tropical_mul_dimensions<const K: usize>(
        &self,
        other: &VerifiedTropicalMatrix<T, COLS, K, MaxPlus>,
    ) -> VerifiedTropicalMatrix<T, ROWS, K, MaxPlus> {
        self.tropical_mul(other)
    }

    /// Contract: Matrix element access is safe
    pub fn safe_get(&self, row: usize, col: usize) -> Option<VerifiedTropicalNumber<T, MaxPlus>> {
        self.get(row, col)
    }

    /// Contract: Matrix element setting is safe
    pub fn safe_set(
        &mut self,
        row: usize,
        col: usize,
        value: VerifiedTropicalNumber<T, MaxPlus>,
    ) -> Result<(), &'static str> {
        self.set(row, col, value)
    }
}

/// Semiring axiom verification contracts
pub mod semiring_axioms {
    use super::*;

    /// Verify tropical semiring axioms for MaxPlus
    pub fn verify_maxplus_semiring_axioms<T: Float + Clone + Copy>(
        a: VerifiedTropicalNumber<T, MaxPlus>,
        b: VerifiedTropicalNumber<T, MaxPlus>,
        c: VerifiedTropicalNumber<T, MaxPlus>,
    ) -> bool {
        // Associativity of addition
        let assoc_add = (a.tropical_add(b)).tropical_add(c).value()
            == a.tropical_add(b.tropical_add(c)).value();

        // Commutativity of addition
        let comm_add = a.tropical_add(b).value() == b.tropical_add(a).value();

        // Associativity of multiplication
        let assoc_mul = (a.tropical_mul(b)).tropical_mul(c).value()
            == a.tropical_mul(b.tropical_mul(c)).value();

        // Commutativity of multiplication
        let comm_mul = a.tropical_mul(b).value() == b.tropical_mul(a).value();

        // Additive identity
        let zero = VerifiedTropicalNumber::<T, MaxPlus>::tropical_zero();
        let add_identity =
            a.tropical_add(zero).value() == a.value() && zero.tropical_add(a).value() == a.value();

        // Multiplicative identity
        let one = VerifiedTropicalNumber::<T, MaxPlus>::tropical_one();
        let mul_identity =
            a.tropical_mul(one).value() == a.value() && one.tropical_mul(a).value() == a.value();

        // Distributivity
        let distrib = a.tropical_mul(b.tropical_add(c)).value()
            == a.tropical_mul(b).tropical_add(a.tropical_mul(c)).value();

        // Idempotency of addition
        let idempotent = a.tropical_add(a).value() == a.value();

        assoc_add
            && comm_add
            && assoc_mul
            && comm_mul
            && add_identity
            && mul_identity
            && distrib
            && idempotent
    }

    /// Verify tropical semiring axioms for MinPlus
    pub fn verify_minplus_semiring_axioms<T: Float + Clone + Copy>(
        a: VerifiedTropicalNumber<T, MinPlus>,
        b: VerifiedTropicalNumber<T, MinPlus>,
        c: VerifiedTropicalNumber<T, MinPlus>,
    ) -> bool {
        // Similar structure to MaxPlus but with MinPlus operations
        let assoc_add = (a.tropical_add(b)).tropical_add(c).value()
            == a.tropical_add(b.tropical_add(c)).value();

        let comm_add = a.tropical_add(b).value() == b.tropical_add(a).value();

        let assoc_mul = (a.tropical_mul(b)).tropical_mul(c).value()
            == a.tropical_mul(b.tropical_mul(c)).value();

        let comm_mul = a.tropical_mul(b).value() == b.tropical_mul(a).value();

        let zero = VerifiedTropicalNumber::<T, MinPlus>::tropical_zero();
        let add_identity =
            a.tropical_add(zero).value() == a.value() && zero.tropical_add(a).value() == a.value();

        let one = VerifiedTropicalNumber::<T, MinPlus>::tropical_one();
        let mul_identity =
            a.tropical_mul(one).value() == a.value() && one.tropical_mul(a).value() == a.value();

        let distrib = a.tropical_mul(b.tropical_add(c)).value()
            == a.tropical_mul(b).tropical_add(a.tropical_mul(c)).value();

        let idempotent = a.tropical_add(a).value() == a.value();

        assoc_add
            && comm_add
            && assoc_mul
            && comm_mul
            && add_identity
            && mul_identity
            && distrib
            && idempotent
    }
}

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

    #[test]
    fn test_maxplus_semiring_contracts() {
        let a = VerifiedTropicalNumber::<f64, MaxPlus>::new(2.0);
        let b = VerifiedTropicalNumber::<f64, MaxPlus>::new(3.0);
        let c = VerifiedTropicalNumber::<f64, MaxPlus>::new(1.0);

        assert!(semiring_axioms::verify_maxplus_semiring_axioms(a, b, c));
    }

    #[test]
    fn test_minplus_semiring_contracts() {
        let a = VerifiedTropicalNumber::<f64, MinPlus>::new(2.0);
        let b = VerifiedTropicalNumber::<f64, MinPlus>::new(3.0);
        let c = VerifiedTropicalNumber::<f64, MinPlus>::new(1.0);

        assert!(semiring_axioms::verify_minplus_semiring_axioms(a, b, c));
    }

    #[test]
    fn test_tropical_identities() {
        let a = VerifiedTropicalNumber::<f64, MaxPlus>::new(5.0);

        // Test additive identity
        let zero_result = a.tropical_zero_identity();
        assert_eq!(zero_result.value(), a.value());

        // Test multiplicative identity
        let one_result = a.tropical_one_identity();
        assert_eq!(one_result.value(), a.value());

        // Test idempotency
        let idempotent_result = a.tropical_add_idempotent();
        assert_eq!(idempotent_result.value(), a.value());
    }

    #[test]
    fn test_multivector_contracts() {
        type TropMV = VerifiedTropicalMultivector<f64, 2, 0, 0, MaxPlus>;

        let mv1 = TropMV::scalar(3.0);
        let mv2 = TropMV::scalar(4.0);

        // Test commutativity
        let result = mv1.tropical_add_commutative(&mv2);
        assert_eq!(result.dimension(), 2);

        // Test dimension preservation
        let mul_result = mv1.tropical_mul_dimension_preserving(&mv2);
        assert_eq!(mul_result.dimension(), mv1.dimension());
        assert_eq!(mul_result.signature(), mv1.signature());

        // Test norm
        let norm = mv1.tropical_norm_well_defined();
        assert!(!norm.value().is_nan());
    }

    #[test]
    fn test_matrix_contracts() {
        let mut matrix = VerifiedTropicalMatrix::<f64, 2, 2, MaxPlus>::new();
        let val = VerifiedTropicalNumber::new(1.5);

        // Test safe operations
        let get_result = matrix.safe_get(0, 1);
        assert!(get_result.is_some());

        let set_result = matrix.safe_set(0, 1, val);
        assert!(set_result.is_ok());
    }
}
