How to override the slice functionality of list in its derived class

You need to provide custom __getitem__(), __setitem__ and __delitem__ hooks.

These are passed a slice object when slicing the list; these have start, stop and step attributes. However, these values could be None, to indicate defaults. Take into account that the defaults actually change when you use a negative stride!

However, they also have a slice.indices() method, which when given a length produces a tuple of (start, stop, step) values suitable for a range() object. This method takes care of such pesky details as slicing with a negative strides and no start or stop indices:

def __getitem__(self, key):
    if isinstance(key, slice):
        indices = range(*key.indices(len(self.list)))
        return [self.list[i] for i in indices]
    return self.list[key]

or, for your case:

def __getitem__(self, key):
    return self.list[key]

because a list can take the slice object directly.

In Python 2, list.__getslice__ is called for slices without a stride (so only start and stop indices) if implemented, and the built-in list type implements it so you'd have to override that too; a simple delegation to your __getitem__ method should do fine:

def __getslice__(self, i, j):
    return self.__getitem__(slice(i, j))

class MyList(list):
    def __init__(self, lst):
        self.list = lst

doesn't make much sense... self is the list object itself, and it has already been created at this point, maybe you want to override __new__, however you probably don't need to touch that. Anyway you want to override __getitem__ like so:

def __getitem__(self, val):
    if isinstance( val, slice):
        # do stuff here