A stab at implementing AnyEquatable with implicit conversions, leveraging AnyHashable. Unfortunately it’s not possible to get the full magic of AnyHashable, in particular with type-erased types.

AnyEquatable.swift

import Foundation

public struct AnyEquatable: Equatable {
    private struct EquatableBox<T: Equatable>: Hashable {
        let value: T

        func hash(into hasher: inout Hasher) {
            preconditionFailure("EquatableBox must never be hashed")
        }
    }

    public let base: Any
    private let hashable: AnyHashable

    public init<T: Equatable>(_ value: T) {
        base = value
        hashable = AnyHashable(EquatableBox(value: value))
    }

    // This overload is required for cases like NSString - String equality to work as intended. Unfortunately, this
    // means that type-erased NSStrings (("Foo" as NSString) as Any) won’t be handled correctly.
    //
    // AnyHashable works around this with a combination of underscored protocols and special runtime functions.
    public init<T: Hashable>(_ value: T) {
        base = value
        hashable = AnyHashable(value)
    }

    public init(_ value: AnyHashable) {
        base = value
        hashable = value
    }

    public init(_ value: AnyEquatable) {
        self = value
    }

    public static func == (lhs: Self, rhs: Self) -> Bool {
        return lhs.hashable == rhs.hashable
    }
}


struct S: Equatable {
    let value: String
}

struct I: Equatable {
    let value: Int
}

struct I8: Equatable {
    let value: Int8
}

let string1 = AnyEquatable(S(value: "Hello"))
let string2 = AnyEquatable(S(value: "Hello"))
let string3 = AnyEquatable(S(value: "30"))
let int1 = AnyEquatable(I(value: 10))
let int2 = AnyEquatable(I(value: 10))
let int3 = AnyEquatable(I(value: 30))
let i8 = AnyEquatable(I(value: 10))

string1 == string2 // true
string1 == string3 // false
int1 == int2 // true
int1 == int3 // false
string3 == int3 // false
i8 == int1 // true
i8 == int3 // false


let string = AnyEquatable("Hello" as String)
let nsString = AnyEquatable("Hello" as NSString)

nsString == string // true