By Martín Abadi, Luca Cardelli
Procedural languages are as a rule good understood and their formal foundations forged within the types of numerous lambda-calculi. For object-oriented languages but the state of affairs isn't really as simple. during this booklet the authors suggest and boost a special method by way of constructing item calculi during which gadgets are taken care of as primitives. utilizing item calculi, the authors may be able to clarify either the semantics of items and their typing ideas and display tips on how to enhance the entire most crucial suggestions of object-oriented programming languages: self, dynamic dispatch, periods, inheritance, safe and personal equipment, prototyping, subtyping, covariance and contravariance, and procedure specialization. Many researchers and graduate scholars will locate this a huge improvement of the underpinnings of object-oriented programming.
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Additional info for A theory of Objects
This condition can be relaxed to allow method specialization, that is, to allow an overriding method to adopt different argument and result types, specialized for the subclass. I
Structural subtyping (subtyping determined by type structure) has desirable properties, such as supporting type matching in distributed and persistent systems (15, 95) . A disadvantage is the possibility of accidental matching of unrelated types. However, one can avoid such accidents by imposing distinctions on top of structural subtyping (95). In contrast, subtyping based on type names is hard to define precisely, and does not support structural subtyping. For our present purposes we use a particularly simple form of structural subtyping.
Therefore every function of type A~B has also type A'~B'whenever A' <: A and B <: B'. In other words, the inclusion A~B <: A' ~B' between function types is valid whenever A' <: A and B <: B'. In the case of functions of multiple arguments, for example of type (AIxA2)~B, we have contravariance in both Al and A2. This is because product, which is covariant in both of its arguments, is found in a contravariant context.
A theory of Objects by Martín Abadi, Luca Cardelli