'Halloween' in relation to the 4 narrative theories

Tzvetan Todorov
Todorov's theory explain how a story will begin with a state of equilibrium between two opposing forces.  This equilibrium is then disrupted by some event that then sparks a series of events to restore the problems and restore order to the world of fiction.  This theory is the base of the classic Hollywood structure.

In relation to Halloween it doesn't explain the narrative structure of the story too well as it does not really explain how this equilibrium has been disrupted.  It mainly just says how the story has a beginning where everyone is alive and happy.  The equilibrium being disrupted by the bogey man escaping sparking a chain of events eventually resulting in the ending where the equilibrium wasn't fully restored as the bogey man was still alive.

Vladimir Propp
Propp's theory was based off the 100's of folk tales he read resulting in him identifying 8 character roles and 31 narrative functions.  The 8 character roles he identified were the villain, the hero, the donor, the helper, the princess, the princesses father, the dispatcher and the false hero.

Being based of folk tales, it is hard to define these roles to Halloween or any more obscure genre like horror.  This is genrally because horror doesn't like to stick to the general codes and conventions that a more conventional genre like action does.  Obviously the hero is the girl that lives at the end and the villan is the bogey man.  The doctor is a helper as he is trying to find and stop the villan throughout the movie, the also saves the girl at the end.  Even with this information though it still only tells us that there are these roles that the characters play.  It is not in depth still.

Claude Levi-Strauss
Levi-Strauss looks a bit more deep into the narrative structure by looking at a narrative in terms of binary oppositions.  Instead of 1's and 0's we look at oppsites such as good and evil or light and dark.  These binary oppositions can genrally be associated to particular genres or multiple where good and evil can be applied to many genres but more obscure ones like natural and supernatural genrally stick to sci-fi and horror.

This theory better explains the story of haloween and can easily be tied to its horror genre through the binary oppositions that occur.  A couple of examples for this would be natural vs supernatural as we see at the end, the boogie man was not human.  Light vs dark because we only saw the murders happen at night where evil is genrally at it's strongest.  Looking at all these binary oppositions we can easily piece together a good idea of what the story is about.

Bordwell and Thompson
This technically isn't a narrative theory but does put together some interesting ideas.  In their book "Film Art: An Introduction" they defined narrative as "a chain of events in a cause-effect relationship, occuring in time and space".  In a way, this is similar to Todorov's theory but on a much more open and deeper level.  The theory defines where the event took place, when the event took place and what span of time the event took place over.  It explains how narrative will manipulate our awareness of time and place though techniques such as flashbacks or jumps between place and time.

This theory also can explain the narrative of halloween on a much deeper level and breaks down the plot of the story.  Right from the start of the story when we see the vision of the boy walking up the stairs, we see he is holding a knife, we immediatly know he is going to murder the occupents of the house and come to a shock when the mask is taken off and we see the kind standing there with the knife.  We know that something is wrong.  The movie then makes it clear that time has passed and that the man who escaped the asylum was the same boy who murdered his family.

Conclusion
Halloween being a horror movie means that a deeper analysis is required when looking into the narrative for the story.  This is why explaining the story's equilabrium or assigning character roles is not enough to analyse a more obscure genre like horror.  A deeper look is required which is why the last 2 theories are better suited to explain halloween.