On understanding types, data abstraction, and polymorphism

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On understanding types, data abstraction, and polymorphism

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Rambling on Software: Understanding Types
Dr. Terry J Coatta (07/13/2008)

Source

ACM Computing Surveys (CSUR) archive
Volume 17 , Issue 4 (December 1985) table of contents
The MIT Press scientific computation series

Pages: 471 - 523

Year of Publication: 1985

ISSN:0360-0300

Authors

Luca Cardelli	AT&T Bell Laboratories, Murray Hill, NJ
Peter Wegner	Brown Univ., Providence, RI

Publisher

ACM New York, NY, USA

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Downloads (6 Weeks): 78, Downloads (12 Months): 480, Citation Count: 270

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ABSTRACT

Our objective is to understand the notion of type in programming languages, present a model of typed, polymorphic programming languages that reflects recent research in type theory, and examine the relevance of recent research to the design of practical programming languages. Object-oriented languages provide both a framework and a motivation for exploring the interaction among the concepts of type, data abstraction, and polymorphism, since they extend the notion of type to data abstraction and since type inheritance is an important form of polymorphism. We develop a &lgr;-calculus-based model for type systems that allows us to explore these interactions in a simple setting, unencumbered by complexities of production programming languages. The evolution of languages from untyped universes to monomorphic and then polymorphic type systems is reviewed. Mechanisms for polymorphism such as overloading, coercion, subtyping, and parameterization are examined. A unifying framework for polymorphic type systems is developed in terms of the typed &lgr;-calculus augmented to include binding of types by quantification as well as binding of values by abstraction. The typed &lgr;-calculus is augmented by universal quantification to model generic functions with type parameters, existential quantification and packaging (information hiding) to model abstract data types, and bounded quantification to model subtypes and type inheritance. In this way we obtain a simple and precise characterization of a powerful type system that includes abstract data types, parametric polymorphism, and multiple inheritance in a single consistent framework. The mechanisms for type checking for the augmented &lgr;-calculus are discussed. The augmented typed &lgr;-calculus is used as a programming language for a variety of illustrative examples. We christen this language Fun because fun instead of &lgr; is the functional abstraction keyword and because it is pleasant to deal with. Fun is mathematically simple and can serve as a basis for the design and implementation of real programming languages with type facilities that are more powerful and expressive than those of existing programming languages. In particular, it provides a basis for the design of strongly typed object-oriented languages.

REFERENCES

Note: OCR errors may be found in this Reference List extracted from the full text article. ACM has opted to expose the complete List rather than only correct and linked references.

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INDEX TERMS

Classification:
D. Software
D.3 PROGRAMMING LANGUAGES
D.3.3 Language Constructs and Features
Subjects: Abstract data types; Data types and structures

F. Theory of Computation
F.3 LOGICS AND MEANINGS OF PROGRAMS
F.3.3 Studies of Program Constructs
Subjects: Type structure
F.4 MATHEMATICAL LOGIC AND FORMAL LANGUAGES
F.4.1 Mathematical Logic
Subjects: Lambda calculus and related systems

General Terms:
Languages, Theory

REVIEW

"Edward A. Schneider : Reviewer"

With the large amount of work done in the last few years on types, this paper is long overdue. The second-order typed &lgr;-calculus is used as a model for typed programs. The model is shown to be very flexible, permitting both parametric and in more...

Collaborative Colleagues:

Luca Cardelli: colleagues

Peter Wegner: colleagues

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