Abstract types have existential type

@article{Mitchell1988AbstractTH,
  title={Abstract types have existential type},
  author={John C. Mitchell and Gordon D. Plotkin},
  journal={ACM Trans. Program. Lang. Syst.},
  year={1988},
  volume={10},
  pages={470-502}
}
Abstract data type declarations appear in typed programming languages like Ada, Alphard, CLU and ML. This form of declaration binds a list of identifiers to a type with associated operations, a composite “value” we call a data algebra. We use a second-order typed lambda calculus SOL to show how data algebras may be given types, passed as parameters, and returned as results of function calls. In the process, we discuss the semantics of abstract data type declarations and review a connection… 
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References

SHOWING 1-10 OF 86 REFERENCES

Abstract types have existential types

This work uses a second-order typed lambda calculus SOL to show how data algebras may be given types, passed as parameters, and returned as results of function calls.

A Kernel Language for Abstract Data Types and Modules

This work uses typed lambda calculus with bindings, declarations, and types as first-class values to build modules, interfaces and implementations, abstract data types, generic types, recursive types, and unions in a concise operational semantics given by inference rules.

Polymorphic Type Inference and Containment

Data types, parameters and type checking

A treatment of type-checking that makes it possible to do completely static checking with a general parameterization mechanism allowing parameterized types, types as parameters, and even a disciplined form of self-application.

On the Semantics of "Data Type"

This paper describes a new approach to defining the meaning of data types and gives its application to the definition of a typed lambda calculus extension and proves that the language is "strongly typed".

Semantic Models for Second-Order Lambda Calculus

This work aims to releive the model theorist of syntactic considerations for the second-order lambda calculus, a typed expression language with polymorphic functions and abstract data types.

The Semantics of Second-Order Lambda Calculus

Data types as values: polymorphism, type-checking, encapsulation

This paper describes a novel approach to the treatment of data types in programming languages, which allows a simple interpretation of "polymorphic" or "generic" procedures, makes a simple set of…

Number theoretic functions computable by polymorphic programs

  • R. Statman
  • Computer Science
    22nd Annual Symposium on Foundations of Computer Science (sfcs 1981)
  • 1981
The polymorphic typed A-calculus is a model for such higher level programming languages as ALPHARD, MODEL, and RUSSELL and allows functions to be taken on as both arguments and values.

A Theory of Data Type Representation Independence

Two characterizations of representation independence are defined and shown to hold in TypeL given appropriate restrictions on the environments, and may be applied to high level language expressions if the semantics of these expressions can be defined by transformations into TypeL expressions.
...