[singleton] How to define Singleton in TypeScript

You can use class expressions for this (as of 1.6 I believe).

var x = new (class {
    /* ... lots of singleton logic ... */
    public someMethod() { ... }
})();

or with the name if your class needs to access its type internally

var x = new (class Singleton {
    /* ... lots of singleton logic ... */
    public someMethod(): Singleton { ... }
})();

Another option is to use a local class inside of your singleton using some static members

class Singleton {

    private static _instance;
    public static get instance() {

        class InternalSingleton {
            someMethod() { }

            //more singleton logic
        }

        if(!Singleton._instance) {
            Singleton._instance = new InternalSingleton();
        }

        return <InternalSingleton>Singleton._instance;
    }
}

var x = Singleton.instance;
x.someMethod();