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27
Dependent Intersection: A New Way of Defining Records in Type Theory
"... Record types are an important tool for programming and are essential in objectoriented calculi. Dependent record types are proven to be very useful for program specification and verification. Unfortunately, all known embedding of the dependent record type in the type theory had some imperfections. I ..."
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Cited by 19 (2 self)
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Record types are an important tool for programming and are essential in objectoriented calculi. Dependent record types are proven to be very useful for program specification and verification. Unfortunately, all known embedding of the dependent record type in the type theory had some imperfections. In this paper we present a new type constructor, dependent intersection, i.e., the intersection of two types, where the second type may depend on elements of the first one (do not confuse it with the intersection of a family of types). This new type constructor allows us to define dependent records in a very simple way.
Building Reliable, HighPerformance Networks with the Nuprl Proof Development System
 UNDER CONSIDERATION FOR PUBLICATION IN J. FUNCTIONAL PROGRAMMING
"... Proof systems for expressive type theories provide a foundation for the verification and synthesis of programs. But despite their successful application to numerous programming problems there remains an issue with scalability. Are proof environments capable of reasoning about large software systems? ..."
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Cited by 17 (4 self)
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Proof systems for expressive type theories provide a foundation for the verification and synthesis of programs. But despite their successful application to numerous programming problems there remains an issue with scalability. Are proof environments capable of reasoning about large software systems? Can the support they offer be useful in practice? In this article we answer this question by showing how the Nuprl proof development system and its rich type theory have contributed to the design of reliable, highperformance networks by synthesizing optimized code for application configurations of the Ensemble group communication toolkit. We present a typetheoretical semantics of OCaml, the implementation language of Ensemble, and tools for automatically importing system code into the Nuprl system. We describe reasoning strategies for generating verifiably correct fastpath optimizations of application configurations that substantially reduce endtoend latency in Ensemble. We also discuss briefly how to use Nuprl for checking configurations against specifications and for the design of reliable adaptive network protocols.
Phobos: A frontend approach to extensible compilers
, 2003
"... This paper describes a practical approach for implementing domainspecific languages with extensible compilers. Given a compiler with one or more frontend languages, we introduce the idea of a "generic" frontend that allows the syntactic and semantic specification of domainspecific languages. Phob ..."
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Cited by 14 (9 self)
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This paper describes a practical approach for implementing domainspecific languages with extensible compilers. Given a compiler with one or more frontend languages, we introduce the idea of a "generic" frontend that allows the syntactic and semantic specification of domainspecific languages. Phobos, our generic frontend, offers modular language specification, allowing the programmer to define new syntax and semantics incrementally.
A Computational Approach to Reflective MetaReasoning about Languages with Bindings
 In MERLIN ’05: Proceedings of the 3rd ACM SIGPLAN workshop on Mechanized
, 2005
"... We present a foundation for a computational metatheory of languages with bindings implemented in a computeraided formal reasoning environment. Our theory provides the ability to reason abstractly about operators, languages, openended languages, classes of languages, etc. The theory is based on th ..."
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Cited by 12 (2 self)
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We present a foundation for a computational metatheory of languages with bindings implemented in a computeraided formal reasoning environment. Our theory provides the ability to reason abstractly about operators, languages, openended languages, classes of languages, etc. The theory is based on the ideas of higherorder abstract syntax, with an appropriate induction principle parameterized over the language (i.e. a set of operators) being used. In our approach, both the bound and free variables are treated uniformly and this uniform treatment extends naturally to variablelength bindings. The implementation is reflective, namely there is a natural mapping between the metalanguage of the theoremprover and the object language of our theory. The object language substitution operation is mapped to the metalanguage substitution and does not need to be defined recursively. Our approach does not require designing a custom type theory; in this paper we describe the implementation of this foundational theory within a generalpurpose type theory. This work is fully implemented in the MetaPRL theorem prover, using the preexisting NuPRLlike MartinL ofstyle computational type theory. Based on this implementation, we lay out an outline for a framework for programming language experimentation and exploration as well as a general reflective reasoning framework. This paper also includes a short survey of the existing approaches to syntactic reflection. 1
MetaPRL  A Modular Logical Environment
, 2003
"... MetaPRL is the latest system to come out of over twenty five years of research by the Cornell PRL group. While initially created at Cornell, MetaPRL is currently a collaborative project involving several universities in several countries. The MetaPRL system combines the properties of an interactive ..."
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Cited by 8 (2 self)
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MetaPRL is the latest system to come out of over twenty five years of research by the Cornell PRL group. While initially created at Cornell, MetaPRL is currently a collaborative project involving several universities in several countries. The MetaPRL system combines the properties of an interactive LCFstyle tacticbased proof assistant, a logical framework, a logical programming environment, and a formal methods programming toolkit. MetaPRL is distributed under an opensource license and can be downloaded from http://metaprl.org/. This paper provides an overview of the system focusing on the features that did not exist in the previous generations of PRL systems.
Markov’s principle for propositional type theory
 Computer Science Logic, Proceedings of the 10 th Annual Conference of the EACSL
, 2001
"... Abstract. In this paper we show how to extend a constructive type theory with a principle that captures the spirit of Markov’s principle from constructive recursive mathematics. Markov’s principle is especially useful for proving termination of specific computations. Allowing a limited form of class ..."
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Cited by 7 (5 self)
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Abstract. In this paper we show how to extend a constructive type theory with a principle that captures the spirit of Markov’s principle from constructive recursive mathematics. Markov’s principle is especially useful for proving termination of specific computations. Allowing a limited form of classical reasoning we get more powerful resulting system which remains constructive and valid in the standard constructive semantics of a type theory. We also show that this principle can be formulated and used in a propositional fragment of a type theory.
Formalizing Abstract Algebra in Type Theory with Dependent Records
 Universitat Freiburg
, 2003
"... algebra suitable for a general reasoning. One of the most common ways to formalize abstract algebra is to make use of a module system to specify an algebra as a theory. However, this approach suffers from the fact that modules are usually not firstclass objects in the formal system. In this paper, ..."
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Cited by 6 (2 self)
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algebra suitable for a general reasoning. One of the most common ways to formalize abstract algebra is to make use of a module system to specify an algebra as a theory. However, this approach suffers from the fact that modules are usually not firstclass objects in the formal system. In this paper, we develop a new approach based on the use of dependent record types. In our account, all algebraic structures are firstclass objects, with the natural subtyping properties due to record extension (for example, a group is a subtype of a monoid). Our formalization cleanly separates the axiomatization of the algebra from its typing properties, corresponding more closely to a textbook presentation. 1
Quotient Types: A Modular Approach
 ITUT Recommendation H.324
, 2002
"... In this paper we introduce a new approach to axiomatizing quotient types in type theory. We suggest replacing the existing monolithic rule set by a modular set of rules for a specially chosen set of primitive operations. This modular formalization of quotient types turns out to be much easier to use ..."
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Cited by 6 (3 self)
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In this paper we introduce a new approach to axiomatizing quotient types in type theory. We suggest replacing the existing monolithic rule set by a modular set of rules for a specially chosen set of primitive operations. This modular formalization of quotient types turns out to be much easier to use and free of many limitations of the traditional monolithic formalization. To illustrate the advantages of the new approach, we show how the type of collections (that is known to be very hard to formalize using traditional quotient types) can be naturally formalized using the new primitives. We also show how modularity allows us to reuse one of the new primitives to simplify and enhance the rules for the set types.
Fault Tolerance using WholeProcess Migration and Speculative Execution
, 2003
"... This thesis examines programming language concepts that facilitate faulttolerant distributed programming. New language primitives are introduced for wholeprocess migration, which allows an active process to be transferred from one machine to another, and speculative execution, which enables optimi ..."
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Cited by 6 (1 self)
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This thesis examines programming language concepts that facilitate faulttolerant distributed programming. New language primitives are introduced for wholeprocess migration, which allows an active process to be transferred from one machine to another, and speculative execution, which enables optimistic computing based on an unverified assumption. These primitives are developed in the context of the Mojave Compiler Collection, a multilanguage multiarchitecture compiler with ties to the MetaPRL theorem prover. The new primitives
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.