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Reflections on Standard ML
 FUNCTIONAL PROGRAMMING, CONCURRENCY, SIMULATION AND AUTOMATED REASONING, VOLUME 693 OF LNCS
, 1992
"... Standard ML is one of a number of new programming languages developed in the 1980s that are seen as suitable vehicles for serious systems and applications programming. It offers an excellent ratio of expressiveness to language complexity, and provides competitive efficiency. Because of its type an ..."
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Cited by 198 (4 self)
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Standard ML is one of a number of new programming languages developed in the 1980s that are seen as suitable vehicles for serious systems and applications programming. It offers an excellent ratio of expressiveness to language complexity, and provides competitive efficiency. Because of its type and module system, Standard ML manages to combine safety, security, and robustness with much of the flexibility of dynamically typed languages like Lisp. It is also has the most welldeveloped scientific foundation of any major language. Here I review the strengths and weaknesses of Standard ML and describe some of what we have learned through the design, implementation, and use of the language.
An Interpretation of Typed OOP in a Language with State
 Lisp and Symbolic Computation
, 1995
"... . In this paper we give semantics to Loop, an expressive typed objectoriented programming language with updatable instance variables. Loop has a rich type system that allows for the typing of methods operating over an openended "self " type. We prove the type system given is sound; i.e., welltype ..."
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Cited by 19 (7 self)
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. In this paper we give semantics to Loop, an expressive typed objectoriented programming language with updatable instance variables. Loop has a rich type system that allows for the typing of methods operating over an openended "self " type. We prove the type system given is sound; i.e., welltyped programs do not experience "message not understood" errors. The semantics of Loop is given by a translation into a statebased language, Soop, that contains reference cells, records, and a form of Fbounded polymorphic type. Keywords: Objectoriented programming, type systems, state in programming 1. Introduction Developing full and faithful type systems for objectoriented programming languages is a wellknown and difficult research problem. To frame the problem we desire a static type system that preserves all of the classic features of (untyped) classbased OOP, including treatment of two particularly difficult issues: binary methods and object subsumption. Significant steps have rece...
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
Subtyping Recursive Types in Kernel Fun
 In IEEE Symposium on Logic in Computer Science (LICS
, 1999
"... The problem of defining and checking a subtype relation between recursive types was studied in [3] for a first order type system, but for second order systems, which combine subtyping and parametric polymorphism, only negative results are known [17]. ..."
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Cited by 6 (1 self)
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The problem of defining and checking a subtype relation between recursive types was studied in [3] for a first order type system, but for second order systems, which combine subtyping and parametric polymorphism, only negative results are known [17].
Subject reduction and minimal types for higher order subtyping
 In Proceedings of the Second Chinese Language Processing Workshop
, 1997
"... We define the typed lambda calculus F ω ∧ , a natural generalization of Girard’s system F ω with intersection types and bounded polymorphism. A novel aspect of our presentation is the use of term rewriting techniques to present intersection types, which clearly splits the computational semantics (re ..."
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Cited by 6 (3 self)
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We define the typed lambda calculus F ω ∧ , a natural generalization of Girard’s system F ω with intersection types and bounded polymorphism. A novel aspect of our presentation is the use of term rewriting techniques to present intersection types, which clearly splits the computational semantics (reduction rules) from the syntax (inference rules) of the system. We establish properties such as ChurchRosser for the reduction relation on types and terms, and Strong Normalization for the reduction on types. We prove that types are preserved by computation (Subject Reduction property), and that the system satisfies the Minimal Types property. On the way to establishing these results, we define algorithms for type inference and subtype checking. 1
Type Theoretical Foundations for Data Structures, Classes, and Objects
, 2004
"... In this thesis we explore the question of how to represent programming data structures in a constructive type theory. The basic data structures in programing languages are records and objects. Most known papers treat such data structure as primitive. That is, they add new primitive type constructors ..."
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Cited by 5 (0 self)
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In this thesis we explore the question of how to represent programming data structures in a constructive type theory. The basic data structures in programing languages are records and objects. Most known papers treat such data structure as primitive. That is, they add new primitive type constructors and supporting axioms for records and objects. This approach is not satisfactory. First of all it complicates a type theory a lot. Second, the validity of the new axioms is not easily established. As we will see the naive choice of axioms can lead to contradiction even in the simplest cases. We will show that records and objects can be defined in a powerful enough type theory. We will also show how to use these type constructors to define abstract data structure. BIOGRAPHICAL SKETCH Alexei Kopylov was born in Moscow State University on April 2, 1974. His parents were students in the Department of Mathematics and Mechanics there. First year of his life Alexei lived in a student dormitory in the main building of the Moscow State University. Then his parents moved to Chernogolovka, a cozy scientific town near Moscow. Alexei returned to Moscow State University as a student in 1991. Five years later he graduated from the Department of Mathematics and Mechanics and entered the graduate school of the same Department.
Naïve computational type theory
 Proof and SystemReliability, Proceedings of International Summer School Marktoberdorf, July 24 to August 5, 2001, volume 62 of NATO Science Series III
, 2002
"... The basic concepts of type theory are fundamental to computer science, logic and mathematics. Indeed, the language of type theory connects these regions of science. It plays a role in computing and information science akin to that of set theory in pure mathematics. There are many excellent accounts ..."
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Cited by 5 (1 self)
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The basic concepts of type theory are fundamental to computer science, logic and mathematics. Indeed, the language of type theory connects these regions of science. It plays a role in computing and information science akin to that of set theory in pure mathematics. There are many excellent accounts of the basic ideas of type theory, especially at the interface of computer science and logic — specifically, in the literature of programming languages, semantics, formal methods and automated reasoning. Most of these are very technical, dense with formulas, inference rules, and computation rules. Here we follow the example of the mathematician Paul Halmos, who in 1960 wrote a 104page book called Naïve Set Theory intended to make the subject accessible to practicing mathematicians. His book served many generations well. This article follows the spirit of Halmos ’ book and introduces type theory without recourse to precise axioms and inference rules, and with a minimum of formalism. I start by paraphrasing the preface to Halmos ’ book. The sections of this article follow his chapters closely. Every computer scientist agrees that every computer scientist must know some type theory; the disagreement begins in trying to decide how much is some. This article contains my partial answer to that question. The purpose of the article is to tell the beginning student of advanced computer science the basic type theoretic facts of life, and to do so with a minimum of philosophical discourse and logical formalism. The point throughout is that of a prospective computer scientist eager to study programming languages, or database systems, or computational complexity theory, or distributed systems or information discovery. In type theory, “naïve ” and “formal ” are contrasting words. The present treatment might best be described as informal type theory from a naïve point of view. The concepts are very general and very abstract; therefore they may
Inheritance of Proofs
, 1996
"... The CurryHoward isomorphism, a fundamental property shared by many type theories, establishes a direct correspondence between programs and proofs. This suggests that the same structuring principles that ease programming be used to simplify proving as well. To exploit objectoriented structuring me ..."
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Cited by 4 (0 self)
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The CurryHoward isomorphism, a fundamental property shared by many type theories, establishes a direct correspondence between programs and proofs. This suggests that the same structuring principles that ease programming be used to simplify proving as well. To exploit objectoriented structuring mechanisms for verification, we extend the objectmodel of Pierce and Turner, based on the higher order typed calculus F ! , with a proof component. By enriching the (functional) signature of objects with a specification, the methods and their correctness proofs are packed together in the objects. The uniform treatment of methods and proofs gives rise in a natural way to objectoriented proving principles  including inheritance of proofs, late binding of proofs, and encapsulation of proofs  as analogues to objectoriented programming principles. We have used Lego, a typetheoretic proof checker, to explore the feasibility of this approach. In particular, we have verified a small hier...
AntiSymmetry of HigherOrder Subtyping
 In Proceedings of the 8th Annual Conference on Computer Science Logic (CSL’99), J. Flum and M. RodríguezArtalejo, Eds. SpringerVerlag LNCS 1683
, 1999
"... . This paper shows that the subtyping relation of a higherorder lambda calculus, F ! , is antisymmetric. It exhibits the rst such proof, establishing in the process that the subtyping relation is a partial orderreexive, transitive, and antisymmetric up to equality. While a subtyping relat ..."
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Cited by 4 (1 self)
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. This paper shows that the subtyping relation of a higherorder lambda calculus, F ! , is antisymmetric. It exhibits the rst such proof, establishing in the process that the subtyping relation is a partial orderreexive, transitive, and antisymmetric up to equality. While a subtyping relation is reexive and transitive by denition, antisymmetry is a derived property. The result, which may seem obvious to the nonexpert, is technically challenging, and had been an open problem for almost a decade. In this context, typed operational semantics for subtyping oers a powerful new technology to solve the problem: of particular importance is our extended rule for the wellformedness of types with head variables. The paper also gives a presentation of F ! without a relation for equality, apparently the rst such, and shows its equivalence with the traditional presentation. 1 Introduction Objectoriented programming languages such as Smalltalk, C++, Modula 3, and ...
Notes on Discrete Mathematics for Computer Scientists
, 2003
"... 1.2 Formal Languages.......................... 2 ..."