Reusing function type with different parameters amount (overloading)

Bug Report

Is there any reason it's not possible to re-use a function type that is overloaded aka has different possible amount of arguments?

In the playground I put some code that shows this issue, but I will put a quick snippet here:

declare function foo(c: {a: number; b: string}): void
declare function foo(a: number, b: string): void


foo({ a: 1, b: "2" })

foo(1, "2")

// This doesn't work but is relatively understandable
const bar1: typeof foo = (a_c, b) => {
    a_c
    b
}

// This should work, why it doesn't?
const bar2: typeof foo = (...args) => {
    args
}

// it works fine, but you can't access the second parameter
const bar3: typeof foo = (a_c) => {  
    a_c
}

// it works fine, but you can't access the parameters
const bar4: typeof foo = () => {
}

bar2 in this example doesn't work, and the error that is given is Type '(args_0: number | { a: number; b: string; }, args_1: unknown) => void' is not assignable to type '{ (c: { a: number; b: string; }): void; (a: number, b: string): void; }'.

🔎 Search Terms

arguments overload parameter function

🕗 Version & Regression Information

In 4.4.0-beta & 4.3.5:

In 4.2.3 and before:

⏯ Playground Link

https://www.typescriptlang.org/play?target=99&jsx=0&ts=4.3.5#code/CYUwxgNghgTiAEAzArgOzAFwJYHtVJxwAowAueAbynNWQFsAjEGAbngfIGcMYtUBzAL4BKcgDccWYAFgAUKEiwEKdNjwFi1eLUbMANOy48+-UfAlS5V2YkJEK8LQEYDHeACIATO-gjrt4hcPb2FrAHow+AAVAAssTnhgHBBOVAByDHgAdxwYAGt2ZEz4+DhobDEQCABPeDRQGG4oVGAoBggQOTA8bnZYJ3IMaoAHEBxEDXgAXngiKAB9MFdhaYA+Sjl4LcdFze2GOUFwyNiSzhicZAhgbNy8gyyY2qxMpJT0jAB+Lp7MhlhPIMRmMJgFprMAHRQ2D8TgrKbrCh7LYwziHY7wF63fIJRB8ECuIrwaqXeBgZoZRxgMApBIYGIITjgPA3YawKB0EAYZg-VC9f4wADMQNG40mMzmi3hiK2yJ2YHRsjkEUxmRyOKQ+MJmRJyDJFMyUGptPg9IQbJgHK5zDRsm6fL+sAALCKQeLZtKNrIjrIgA

🙁 Actual behavior

It just errors out when trying to use "...args" to get all the possible arguments of the function

🙂 Expected behavior

To be able to use "...args" or similar to get the arguments and typescript to not complain just for trying to use it

Comienza reproduciendo el comportamiento de asignación de sobrecargas en el TypeScript Playground enlazado usando las versiones indicadas 4.3.5 y 4.4.0-beta. Compara los ejemplos aceptados y rechazados y, a continuación, determina el comportamiento previsto para las implementaciones con parámetros rest de funciones sobrecargadas; el trabajo estará terminado cuando el comportamiento y el tipado esperado estén establecidos y cubiertos por una prueba adecuada del compilador.