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I'm a newbie in both formal mathematics and theoretical computer science, so please bear with me if you find my question is not properly framed. Object Oriented Modeling seems very useful in defining complex interactions when simulating real world. But it's mostly used in programming. I was wondering if we have a similar concept in mathematics. When we're doing programming, we can understand the concept of "Objects" and "Object Oriented Programming" and just implement it. But do we have formal definition of "Objects" in terms of Set Theory? Or for that matter, any other formal mathematical theory?

Can we implement/ formally define three primary object orient modeling concepts- 1. Encapsulation 2. Inheritance 3. Polymorphism

I know question is too broad, but would really appreciate if you can provide some pointers as well so that I can understand these concepts better.

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    X-Posted [here](http://cstheory.stackexchange.com/questions/11345), voting to close. [Due to lack of reasonable closing reasons, I have chosen Off Topic, even though it is not completely off topic.]2012-05-05

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There is rich literature on mathematical modeling of programming languages, and object-oriented ones are no exception. I would recommend Benjamin Pierce's book "Types and programming languages" as a general introduction to the subject. Robert Harper's "Practical Foundations for Programming Languages" is also very good and available online.

You specifically ask about mathematical models for object-oriented languages. You could look at Abadi's and Cardelli's Theory of Objects and go on from there.

Lastly, you should have asked this question on the cstheory StackExchange.

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    Oops, I meant cstheory. Fixed.2012-05-05