Is there a Haskell equivalent of OOP's abstract classes, using algebraic data types or polymorphism?

In Haskell, is it possible to write a function with a signature that can accept two different (although similar) data types, and operate differently depending on what type is passed in?

An example might make my question clearer. If I have a function named myFunction, and two types named MyTypeA and MyTypeB, can I define myFunction so that it can only accept data of type MyTypeA or MyTypeB as its first parameter?

type MyTypeA = (Int, Int, Char, Char)
type MyTypeB = ([Int], [Char])

myFunction :: MyTypeA_or_MyTypeB -> Char
myFunction constrainedToTypeA = something
myFunction constrainedToTypeB = somethingElse

In an OOP language, you could write what I'm trying to achieve like so:

public abstract class ConstrainedType {
}

public class MyTypeA extends ConstrainedType {
    ...various members...
}

public class MyTypeB extends ConstrainedType {
    ...various members...
}

...

public Char myFunction(ConstrainedType a) {
    if (a TypeOf MyTypeA) {
        return doStuffA();
    }
    else if (a TypeOf MyTypeB) {
        return doStuffB();
    }
}

I've been reading about algebraic data types and I think I need to define a Haskell type, but I'm not sure how to go about defining it so that it can store one type or another, and also how I use it in my own functions.