andrevidela

struct Vector<A> {
    let fst: A
    let snd: A
}

extension Vector: CustomStringConvertible where A: CustomStringConvertible {
    var description: String {
        return "Vector<\(String(describing: A.self))>(\(fst.description), \(snd.description))"
    }
}

andrevidela

infix operator ◊: MultiplicationPrecedence

/// Protocol for scalar multiplication operation
protocol Scalar {
    associatedtype ScalarVal
    static func ◊ (_ lhs: ScalarVal, _ rhs: Self) -> Self
}

andrevidela

extension Additive where Self: TwoDimensions, Self.ComponentVal: Additive {
    static var addId: Self {
        return Self.make2D(Self.ComponentVal.addId, Self.ComponentVal.addId)
    }
    static func + (lhs: Self, rhs: Self) -> Self {
        return make2D(lhs.fst + rhs.fst, lhs.snd + rhs.snd)
    }
}

andrevidela

/// A protocol for getting the magnitude of an object
protocol Magnitude {
    associatedtype MagVal: Comparable
    var magSquare: MagVal { get }
}

andrevidela

extension Magnitude where
    Self: TwoDimensions,
    Self.ComponentVal: Multiplicative,
    Self.ComponentVal: Additive,
    Self.ComponentVal == Self.MagVal {
    var magSquare: Self.MagVal {
        return self.fst * self.fst + self.snd * self.snd
    }
}

andrevidela

/// Protocol for multiplication with identity
protocol Multiplicative {
    static var multId: Self { get }
    static func * (_ lhs: Self, _ rhs: Self) -> Self
}

andrevidela

/// Protocol for 2D coordinate systems
protocol TwoDimensions {
    associatedtype ComponentVal
    static func make2D(_ fst: ComponentVal, _ snd: ComponentVal) -> Self
    var fst: ComponentVal { get } // The first component
    var snd: ComponentVal { get } // The second component
}

andrevidela

// Ints are Additive, the identity is 0
extension Int: Additive {
    static var addId: Int { return 0 }
}

andrevidela

// Ints are Multiplicative, the identity is 1
extension Int: Multiplicative {
    static var multId: Int {
        return 1
    }
}

andrevidela

/// Protocol for addition with identity
protocol Additive {
    static var addId: Self { get }
    static func + (_ lhs: Self, _ rhs: Self) -> Self
}