By Martín Abadi, Luca Cardelli
Procedural languages are ordinarily good understood and their formal foundations forged within the different types of quite a few lambda-calculi. For object-oriented languages but the scenario isn't as uncomplicated. during this ebook the authors suggest and strengthen a distinct process by means of constructing item calculi during which items are handled as primitives. utilizing item calculi, the authors may be able to clarify either the semantics of items and their typing principles and reveal the way to advance the entire most vital suggestions of object-oriented programming languages: self, dynamic dispatch, sessions, inheritance, secure and personal equipment, prototyping, subtyping, covariance and contravariance, and procedure specialization. Many researchers and graduate scholars will locate this a massive improvement of the underpinnings of object-oriented programming.
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Additional info for A theory of Objects
The operations fst(c) and snd(c) extract the left and right components, respectively, of an element c of type AxB. We say that x is a covariant operator (in both arguments), because AxB varies in the same sense as A or B: AxB <: A'xB' provided that A <: A' and B <: B' We can justify this property as follows. 1f A <: A' and B <: B', then by subsumption we have a: A' and b: B', so that (a,b) has also type A'xB'. Therefore any pair of type AxB has also type A'xB' whenever A <: A ' and B <: B'. In other words, the inclusion AxB <: A 'xB' between product types is valid whenever A <: A' and B <: B'.
So the initial value of the contents field and the code of the get method are inherited by reCell from cell. The set method could be inherited implicitly like the get method, but is instead overridden in reCell. It is common to say, informally, that c' inherits from c, to mean that c' is a subclass of c. Note, though, that a subclass of a class with no fields may override all the methods of the superclass and therefore inherit nothing. Conversely, there are mechanisms for sharing method code that do not rely on the subclass relation (for example, straightforward procedural abstraction).