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Compiling polymorphism using intensional type analysis
 In Symposium on Principles of Programming Languages
, 1995
"... The views and conclusions contained in this document are those of the authors and should not be interpreted as ..."
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Cited by 260 (18 self)
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The views and conclusions contained in this document are those of the authors and should not be interpreted as
Using dependent types to express modular structure
 In Thirteenth ACM Symposium on Principles of Programming Languages
, 1986
"... Several related typed languages for modular programming and data abstraction have been proposed recently, including Pebble, SOL, and ML modules. We review and compare the basic typetheoretic ideas behind these languages and evaluate how they ..."
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Cited by 125 (5 self)
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Several related typed languages for modular programming and data abstraction have been proposed recently, including Pebble, SOL, and ML modules. We review and compare the basic typetheoretic ideas behind these languages and evaluate how they
Type Theories and ObjectOriented Programming
 ACM Computing Surveys
, 1988
"... Objectoriented programming is becoming a popular approach to the construction of complex software systems. Benefits of object orientation include support for modular design, code sharing, and extensibility. In order to make the most of these advantages, a type theory for objects and their interacti ..."
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Cited by 49 (0 self)
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Objectoriented programming is becoming a popular approach to the construction of complex software systems. Benefits of object orientation include support for modular design, code sharing, and extensibility. In order to make the most of these advantages, a type theory for objects and their interactions should be developed to aid checking and
Type Checking with Universes
, 1991
"... Various formulations of constructive type theories have been proposed to serve as the basis for machineassisted proof and as a theoretical basis for studying programming languages. Many of these calculi include a cumulative hierarchy of "universes," each a type of types closed under a collectio ..."
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Cited by 24 (6 self)
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Various formulations of constructive type theories have been proposed to serve as the basis for machineassisted proof and as a theoretical basis for studying programming languages. Many of these calculi include a cumulative hierarchy of "universes," each a type of types closed under a collection of typeforming operations. Universes are of interest for a variety of reasons, some philosophical (predicative vs. impredicative type theories), some theoretical (limitations on the closure properties of type theories), and some practical (to achieve some of the advantages of a type of all types without sacrificing consistency.) The Generalized Calculus of Constructions (CC ! ) is a formal theory of types that includes such a hierarchy of universes. Although essential to the formalization of constructive mathematics, universes are tedious to use in practice, for one is required to make specific choices of universe levels and to ensure that all choices are consistent. In this pa...
TypeTheoretic Methodology For Practical Programming Languages
 DEPARTMENT OF COMPUTER SCIENCE, CORNELL UNIVERSITY
, 1998
"... The significance of type theory to the theory of programming languages has long been recognized. Advances in programming languages have often derived from understanding that stems from type theory. However, these applications of type theory to practical programming languages have been indirect; the ..."
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Cited by 22 (3 self)
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The significance of type theory to the theory of programming languages has long been recognized. Advances in programming languages have often derived from understanding that stems from type theory. However, these applications of type theory to practical programming languages have been indirect; the differences between practical languages and type theory have prevented direct connections between the two. This dissertation presents systematic techniques directly relating practical programming languages to type theory. These techniques allow programming languages to be interpreted in the rich mathematical domain of type theory. Such interpretations lead to semantics that are at once denotational and operational, combining the advantages of each, and they also lay the foundation for formal verification of computer programs in type theory. Previous type theories either have not provided adequate expressiveness to interpret practical languages, or have provided such expressiveness at the expense of essential features of the type theory. In particular, no previous type theory has supported a notion of partial functions (needed to interpret recursion in practical languages), and a notion of total functions and objects (needed to reason about data values), and an intrinsic notion of equality (needed for most interesting results). This dissertation presents the first type theory incorporating all three, and discusses issues arising in the design of that type theory. This type theory is used as the target of a typetheoretic semantics for a expressive programming calculus. This calculus may serve as an internal language for a variety of functional programming languages. The semantics is stated as a syntaxdirected embedding of the programming calculus into type theory. A critical point arising in both the type theory and the typetheoretic semantics is the issue of admissibility. Admissibility governs what types it is legal to form recursive functions over. To build a useful type theory for partial functions it is necessary to have a wide class of admissible types. In particular, it is necessary for all the types arising in the typetheoretic semantics to be admissible. In this dissertation I present a class of admissible types that is considerably wider than any previously known class.
NuPRL’s class theory and its applications
 Foundations of Secure Computation, NATO ASI Series, Series F: Computer & System Sciences
, 2000
"... This article presents a theory of classes and inheritance built on top of constructive type theory. Classes are defined using dependent and very dependent function types that are found in the Nuprl constructive type theory. Inheritance is defined in terms of a general subtyping relation over the und ..."
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Cited by 15 (7 self)
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This article presents a theory of classes and inheritance built on top of constructive type theory. Classes are defined using dependent and very dependent function types that are found in the Nuprl constructive type theory. Inheritance is defined in terms of a general subtyping relation over the underlying types. Among the basic types is the intersection type which plays a critical role in the applications because it provides a method of composing program components. The class theory is applied to defining algebraic structures such as monoids, groups, rings, etc. and relating them. It is also used to define communications protocols as infinite state automata. The article illustrates the role of these formal automata in defining the services of a distributed group communications system. In both applications the inheritance mechanisms allow reuse of proofs and the statement of general properties of system composition. 1
Generative Type Abstraction and Typelevel Computation (Extended Version)
"... Modular languages support generative type abstraction, ensuring that an abstract type is distinct from its representation, except inside the implementation where the two are synonymous. We show that this wellestablished feature is in tension with the nonparametric features of newer type systems, s ..."
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Cited by 15 (9 self)
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Modular languages support generative type abstraction, ensuring that an abstract type is distinct from its representation, except inside the implementation where the two are synonymous. We show that this wellestablished feature is in tension with the nonparametric features of newer type systems, such as indexed type families and GADTs. In this paper we solve the problem by using kinds to distinguish between parametric and nonparametric contexts. The result is directly applicable to Haskell, which is rapidly developing support for typelevel computation, but the same issues should arise whenever generativity and nonparametric features are combined.
Embedding Type Structure in Semantics
, 1985
"... We show how a programming language designer may embed the type structure of of a programming language in the more robust type structure of the typed lambda calculus. This is done by translating programs of the language into terms of the typed lambda calculus. Our translation, however, does not alway ..."
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Cited by 13 (1 self)
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We show how a programming language designer may embed the type structure of of a programming language in the more robust type structure of the typed lambda calculus. This is done by translating programs of the language into terms of the typed lambda calculus. Our translation, however, does not always yield a welltyped lambda term. Programs whose translations are not welltyped are considered meaningless, that is, illtyped. We give a conditionally typecorrect semantics for a simple language with continuation semantics. We provide a set of static typechecking rules for our source language, and prove that they are sound and complete: that is, a program passes the typing rules if and only if its translation is welltyped. This proves the correctness of our static semantics relative to the wellestablished typing rules of the typed lambdacalculus. 1. Introduction Denotational semantics has proved to be a powerful language for expressing the language designer's decisions about the beh...
Programming With Types
 CORNELL UNIVERSITY
, 2002
"... Runtime type analysis is an increasingly important linguistic mechanism in modern programming languages. Language runtime systems use it to implement services such as accurate garbage collection, serialization, cloning and structural equality. Component frameworks rely on it to provide reflection m ..."
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Cited by 11 (1 self)
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Runtime type analysis is an increasingly important linguistic mechanism in modern programming languages. Language runtime systems use it to implement services such as accurate garbage collection, serialization, cloning and structural equality. Component frameworks rely on it to provide reflection mechanisms so they may discover and interact with program interfaces dynamically. Runtime type analysis is also crucial for large, distributed systems that must be dynamically extended, because it allows those systems to check program invariants when new code and new forms of data are added. Finally, many generic userlevel algorithms for iteration, pattern matching, and unification can be defined through type analysis mechanisms. However, existing frameworks for runtime type analysis were designed for simple type systems. They do not scale well to the sophisticated type systems of modern and nextgeneration programming languages that include complex constructs such as firstclass abstract types, recursive types, objects, and type parameterization. In addition, facilities to support type analysis often require complicated