I. Less is more - the three unities
Keeping within self-imposed limits often helps to keep a story structured and interesting, and restrictions may be an efficient way of creating suspense. "Die Hard" has received considerable praise for its claustrophobic atmosphere; it can in fact bear comparing to one of the most restrictive styles in Western theatre, the French Classicism.
The Classical style was prevalent in French theatre for most of the 17th century, with Corneille, Racine and Molière as its best-known representatives. Its ambition was to produce dramatic works in the fashion of Classical Greece, hence its name. Molière's comedies have made its way to the international stage, while the dramas of Corneille and Racine are little known outside a limited circle of theatre historians and traditionally educated French speakers.
The French Classical movement revived a number of rules that a dramatic author was expected to follow - originally the Aristotelian rules of the classical drama. The most important of those are the three unities: the unity of time, space and action.
The Unity of Time rule says that plot and story time should be equal. If a drama takes three hours to perform, the actions depicted in it should be limited to three hours: no major jumps in time (as in "Act Two: a year later"), no flashbacks etc are permitted.
The Unity of Space rule says that the space of a play's action should equal the space on stage. If a drama is set in the king's palace, it won't contain scenes taking place in a nearby forest or in the Arabian desert.
The Unity of Action rule limits the action of a play to one storyline. There are few secondary conflicts, and the rule forbids the introduction of another set of protagonists in a different setting to be connected up with the original storyline in its conclusion.

Unity of Action
The use of Unity of Action is almost native to the narrative cinema of Hollywood. In a Hollywood movie, the protagonists and their motives are introduced in the exposition, then a collision occurs and creates a conflict; this leads to a crisis, a turning point, and the final resolution of the conflict. The structure is very much like that of a French Classical drama or, for that matter, an antique tragedy. In other words, this is in no way specific for "Die Hard", but rather a trait that Hollywood narratives share with Classical drama.

Unity of Time
The application of Unity of Time on "Die Hard" is more interesting.
Just as in a Classical drama, we find out about people's background from their actions and from dialogue, rather than from the story taking us back and forth in time - indicating an intention to keep the story contained within a restricted timeframe.
True, the duration of the plot and the story are not identical, but the only difference is generated by glossing over time where nothing of dramatic importance happens. 10-12 hours concentrated into a two-hour movie are still within the same time "continuum" that would be disrupted by, say, skipping over a week or a month. We can easily follow the way the events depicted change the protagonists, while letting the plot cover a longer time period would imply that the people in question develop also because of events that we don't get to see.
The story isn't running against an obvious, externally imposed deadline - i.e. we are spared the formulaic ploys of ticking countdowns. We are not told about the factual deadline, Gruber's intention to blow up the building when leaving it, until very late into the story - it's just one of the many tools used to escalate the suspense. But throughout the film its pacing indicates that the conflict has to be resolved before the night is over. This impression is strengthened by the fact that the story starts at sunset, creating an expectation of a resolution at sunrise.

Unity of Space
Much of what makes "Die Hard" an enjoyable, suspenseful film is connected to its adherence to the Unity of Space. True, in a film there is no "stage space" to relate to, but the action in "Die Hard" focuses very strictly on Nakatomi Plaza, contrasting "inside" and "outside", turning the building into one of the film's protagonists and generating the claustrophobic atmosphere that is the film's chief suspense-creating instrument.

The scenes that take place in other locations all point towards Nakatomi Plaza.
There is a number of sequences bringing various participants to the location. Initially, we follow the arrival of John McClane and Argyle the chauffeur. Then, Hans Gruber and his following arrive and trigger the action. Al Powell is called in, his arrival eventually leads to more police with their vehicles and equipment, and the FBI with helicopters, getting to the scene. The TV journalist, Dick Thornburg, causes yet another vehicle and crew to move towards the building.
All of them _arrive_ and either enter the building or focus all their attention on it. None _leave_ until after the basic conflict is resolved.

The distinction between _inside_ Nakatomi Plaza and _outside_ it is steadily reinforced in many ways, creating an increasing sense of tension and suspense.
When Hans Gruber and his following arrive, they take over the entrance and cut off all means of communication, sealing off the building. Later, Al Powell is permitted to enter the lobby while he is a lone harmless cop, but the building's defences are brought fully into play when the police arrives in a force and tries to storm it, and the inside-outside tension escalates even more with the arrival of the FBI and their helicopters, when we clearly understand what is in store for them on the roof.
The filmmakers take good care to connect anything that happens in other location to the inside of Nakatomi Plaza. Even the comments on television, as external as can be, are brought inside the building by Gruber's gang switching on a TV set. Thus even the action at Holly Gennero's house, with Thornburg bullying the help and interviewing the children, is made relevant to the main action inside the Nakatomi, when Gruber watches the interview and makes the connection to the photos in Holly's office.

The function of music
A special mention must go to "Die Hard"s music score. It is almost a schoolbook example of music supporting and reinforcing the definition of plot elements and action space.
The main driving force of the story, Hans Gruber's gang and their criminal intent, have not only their own easily identifiable musical theme, but the theme also helps characterize them as "Eurotrash", with the accent on "Euro-": the theme comes from the final movement of Beethoven's Ninth symphony, recognized as the "national" anthem of the European Union. And what more, the composer sticks quite strictly to Beethoven's musical idiom, either borrowing from the Ninth symphony or composing within the style, whenever the music relates to the gang's action inside Nakatomi Plaza.
A noteworthy detail is the string quartet at the initial Christmas party, before anything untoward happens, playing a pretty, innocuous version of the same Beethoven theme.
On the opposing side, we meet the easygoing good guy Al Powell and his theme, "Let It Snow". It provides a musical contrast to the sophisticated, powerful, threatening style that accompanies Gruber's actions inside the building. "Let It Snow" is fun, Christmas spirit, a connection to the world not affected by the drama inside Nakatomi. Above all, "Let It Snow" signifies _outside_, a relief from the claustrophobia, and the promise of a happy ending.

II. Hamlet McClane???
Many "Die Hard" fans would be surprised to learn that the director, John McTiernan, mentions Shakespeare as one of his sources of inspiration. He points out similarities between "Die Hard" and "A Midsummer's Night's Dream": the story takes place at night during a holiday, is propeled by forces out of the ordinary, and leaves its protagonists re-united in the morning but permanently changed.

Other, more general properties that "Die Hard"shares with Shakespearean theatre have to do with techniques of entertainment, of spinning a captivating tale.

The making of a good yarn
We tend to think of Shakespeare - with bored veneration - as The Bard, but a dramatic author around the year 1600 was very much a commercial entertainer. He had to keep the attention of a mixed audience (rich and poor, men and women, young and old) in an open-air theatre and with little recourse to "special effects". This meant mastering the techniques of storytelling and character development, and many of those techniques work just as well 400 years later.

A basically tragic, highly dramatic plot is sometimes interspersed with comedy to provide a much-needed variation. McClane's wisecracks, such as "Those are very bad for you" of the dead bandit's cigarettes, or "Beeep - wrong answer, Hans!" over the radio to Gruber, echo Hamlet's "Words, words, words" to Polonius - the Danish prince being in his own way a "fly in the ointment" of the rotten State of Denmark.
An often noted trick of Shakespeare's trade is the presence of comical figures who contribute to the development of the drama: some of the best-known examples are the gravediggers in "Hamlet" and the amateur actors in "A Midsummer's Night's Dream". Their most obvious"Die Hard" equivalent is, of course, Argyle the limo driver.
Like many Shakespearean villains, Hans Gruber is both intelligent and charismatic, driven by realistic human motives that the viewer can identify with. Compare this to the standard-issue movie bad guy, who is either mad, or "evil" in some vague, abstract, formulaic way, and generally present only to provide the story with the necessary element of threat and the protagonist with someone to eliminate in the course of the happy ending.
Shakespeare's women are characters in their own right, rather than just serving as decorative elements or motivation/reward for the hero's heroics. In "Die Hard", Holly Gennero is a competent professional, able to assume responsibility, stand up to the villain and contribute her share in keeping him off balance.
And lastly, a good tale sketches even background characters as individuals with perceptible human motivations: "Hamlet" starts out with a soldier on guard duty complaining about the cold, and his relief telling him to go off to bed - it's past midnight. Similarly, an anonymous "Die Hard" bandit, waiting for the police to storm the building, gets hungry and helps himself to some candy bars.

III. Man at work
In plain formulaic heroic fantasy, the hero only needs to flex his muscles, look imperturbable, and get on with the business of rooting out Evil and claiming his reward in the guise of the busty blonde. He is a hero to stare at in awe and bafflement, cast in bronze at best, but in most cases simply painted on cardboard. Not so in a piece of "classical" entertainment in our sense.

The protagonist of "Die Hard" functions, first and foremost, as a plausible object of identification. He reacts and adapts to the restrictions imposed by the plot, he experiences stress, fear, hope, anger, serving as a conduit for the viewer's perceptions and reactions. Still, this is an escapist movie, and the hero has to be a bit larger than life to satisfy an audience in search of thrill and entertainment - not a realistic depiction of ordinary life.

Willis fits the bill admirably. In this first of his action movies, he does one of his very best representations of the blue-collar hero. And since, according to the director McTiernan, a lot of the dialogue and action is improvised, it isn't just a case of capable handling of a good script.

In the "Making of" DVD feature, Willis explains how he found inspiration for McClane's humor from talking to actual working policemen about their reactions and strategies when there is a job to be done under extreme stress.
Other parts of dialogue that help identification, and that make the film interesting for people other than males in the 15-25 age bracket, are those relating to McClane's marital situation. He may be a male chauvinist by force of habit, but his commitment to Holly is strong enough to get him to question his own attitudes. In an extreme situation, when he tries to put it all in one - as he believes - final message, he even borrows a piece of psychological jargon that Holly must have spouted at him in a fight: "I should have been more supportive".

Physically, Willis has just the right prerequisites. His John McClane is a working cop in good physical shape, not some oiled muscle mountain from the cover of a fantasy book. You can actually see McClane-class muscle most days of the week in any serious fitness studio. Similarly, his face is a normal human one, not a piece of Greek statuary or something hewn in granite around 1930.
And Willis makes intelligent use of his equipment. Both his body language and his mimics clearly display McClane's thoroughly human reactions to the strain that he labors under. He bounces about with excitement when he thinks that the fire brigade is coming to rescue; his face has just the right slighly ridiculous strained expression when he sneaks about the stairwell trying to find out if there are enemies about; when he looks up from the bandit killed in the struggle on the stairs, we can read in his face that McClane may never have killed anyone before, and certainly not in a hand-to-hand fight. There is actually very little square-jawed, steely-eyed looks in the original John McClane.

In all, "Die Hard" is a piece of entertainment that shares important traits with some of the best of the theatrical tradition. In Bruce Willis' concept of John McClane it finds just the right balance of hero and identification object that the style requires.