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27
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
Compiler Implementation in a Formal Logical Framework
 In Proceedings of the 2003 workshop on Mechanized
, 2003
"... The task of designing and implementing a compiler can be a dicult and errorprone process. In this paper, we present a new approach based on the use of higherorder abstract syntax and term rewriting in a logical framework. All program transformations, from parsing to code generation, are cleanly is ..."
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Cited by 4 (2 self)
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The task of designing and implementing a compiler can be a dicult and errorprone process. In this paper, we present a new approach based on the use of higherorder abstract syntax and term rewriting in a logical framework. All program transformations, from parsing to code generation, are cleanly isolated and specified as term rewrites. This has several advantages. The correctness of the compiler depends solely on a small set of rewrite rules that are written in the language of formal mathematics. In addition, the logical framework guarantees the preservation of scoping, and it automates many frequentlyoccurring tasks including substitution and rewriting strategies. As we show, compiler development in a logical framework can be easier than in a generalpurpose language like ML, in part because of automation, and also because the framework provides extensive support for examination, validation, and debugging of the compiler transformations. The paper is organized around a case study, using the MetaPRL logical framework to compile an MLlike language to Intel x86 assembly. We also present a scoped formalization of x86 assembly in which all registers are immutable.
Robustness and the Internet: Theoretical Foundations
, 2002
"... This article uses the Internet as a starting point to illustrate universal aspects of complex systems throughout technology and biology. Complexity in most systems is driven by the need for robustness to uncertainty in their environments and component parts far more than by basic functionality. Prot ..."
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Cited by 3 (1 self)
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This article uses the Internet as a starting point to illustrate universal aspects of complex systems throughout technology and biology. Complexity in most systems is driven by the need for robustness to uncertainty in their environments and component parts far more than by basic functionality. Protocols organize highly structured and complex modular hierarchies to achieve robustness, but also create fragilities to rare or neglected perturbations. We claim these are also the most important and universal features of complex systems. All of this complexity is largely hidden, deliberately creating the illusion of superficially simple systems, which encourages development of specious theories. We also discuss an emerging theoretical foundation for the Internet. The aim is to provide a framework for understanding both the successes and shortcomings of existing Internet technology, offer alternative protocols for identified problems, guide rational design for future evolution of ubiquitous networking, and suggest what new mathematics and technology will be needed for a useful, general theory of complex systems.
Formal Design Environments
 International Conference on Theorem Proving in Higher Order Logics (TPHOLs), 2002. Appears in NASA technical report NASA
, 2002
"... We present the design of a formal integrated design environment. The longterm goal of this effort is to allow seamless interaction between software production tools and formal design and analysis tools, especially between compilers and higherorder theorem provers. The work in this report is the in ..."
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We present the design of a formal integrated design environment. The longterm goal of this effort is to allow seamless interaction between software production tools and formal design and analysis tools, especially between compilers and higherorder theorem provers. The work in this report is the initial design and architecture for integration of 1) the MetaPRL logical framework, 2) a multilanguage compiler we call Mojave, and 3) a generic extensible parser we call Phobos. The integration is currently performed at the level of the Mojave functional intermediate representation, allowing the use of the theorem prover for program analysis, transformation, and optimization.
Formalizing type operations using the “Image” type constructor
 Workshop on Logic, Language, Information and Computation (WoLLIC
, 2006
"... In this paper we introduce a new approach to formalizing certain type operations in type theory. Traditionally, many type constructors in type theory are independently axiomatized and the correctness of these axioms is argued semantically. In this paper we introduce a notion of an “image ” of a give ..."
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In this paper we introduce a new approach to formalizing certain type operations in type theory. Traditionally, many type constructors in type theory are independently axiomatized and the correctness of these axioms is argued semantically. In this paper we introduce a notion of an “image ” of a given type under a mapping that captures the spirit of many of such semantical arguments. This allows us to use the new “image ” type to formalize within the type theory a large range of type constructors that were traditionally formalized via postulated axioms. We demonstrate the ability of the “image ” constructor to express “forgetful ” types by using it to formalize the “squash ” and “set ” type constructors. We also demonstrate its ability to handle types with nontrivial equality relations by using it to formalize the union type operator. We demonstrate the ability of the “image ” constructor to express certain inductive types by showing how the type of lists and a higherorder abstract syntax type can be naturally formalized using the new type constructor. The work presented in this paper have been implemented in the MetaPRL proof assistant and all the derivations checked by MetaPRL.
Formalizing abstract algebra in constructive set theory
, 2002
"... Abstract. We present a machinechecked formalization of elementary abstract algebra in constructive set theory. Our formalization uses an approach where we start by specifying the group axioms as a collection of inference rules, defining a logic for groups. Then we can tell whether a given set with ..."
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Cited by 2 (1 self)
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Abstract. We present a machinechecked formalization of elementary abstract algebra in constructive set theory. Our formalization uses an approach where we start by specifying the group axioms as a collection of inference rules, defining a logic for groups. Then we can tell whether a given set with a binary operation is a group or not, and derive all properties of groups constructively from these inference rules as well as the axioms of the set theory. The formalization of all other concepts in abstract algebra is based on that of the group. We give an example of a formalization of a concrete group, the Klein 4group. 1
Some Mathematical Case Studies in ProofPowerHOL
, 2004
"... TPHOLs conference covers all aspects of theorem proving in higher order logics as well as related topics in theorem proving and verification. There were 42 papers submitted to TPHOLs 2004 in the full research category, each of which was refereed by at least 3 reviewers selected by the program commit ..."
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Cited by 2 (0 self)
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TPHOLs conference covers all aspects of theorem proving in higher order logics as well as related topics in theorem proving and verification. There were 42 papers submitted to TPHOLs 2004 in the full research category, each of which was refereed by at least 3 reviewers selected by the program committee. Of these submissions, 21 were accepted for presentation at the conference and publication in volume 3223 of Springer’s Lecture Notes in Computer Science series. In keeping with longstanding tradition, TPHOLs 2004 also offered a venue for the presentation of work in progress, where researchers invite discussion by means of a brief introductory talk and then discuss their work at a poster
Formal Compiler Implementation in a Logical Framework
 In MERλIN, Second ACM SIGPLAN Workshop on
, 2003
"... The task of designing and implementing a compiler can be a difficult and errorprone process. In this paper, we present a new approach based on the use of higherorder abstract syntax and term rewriting in a logical framework. All program transformations, from parsing to code generation, are cleanly ..."
Abstract

Cited by 1 (1 self)
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The task of designing and implementing a compiler can be a difficult and errorprone process. In this paper, we present a new approach based on the use of higherorder abstract syntax and term rewriting in a logical framework. All program transformations, from parsing to code generation, are cleanly isolated and specified as term rewrites. This has several advantages. The correctness of the compiler depends solely on a small set of rewrite rules that are written in the language of formal mathematics. In addition, the logical framework guarantees the preservation of scoping, and it automates many frequentlyoccurring tasks including substitution and rewriting strategies. As we show, compiler development in a logical framework can be easier than in a generalpurpose language like ML, in part because of automation, and also because the framework provides extensive support for examination, validation, and debugging of the compiler transformations. The paper is organized around a case study, using the MetaPRL logical framework to compile an MLlike language to Intel x86 assembly. We also present a scoped formalization of x86 assembly in which all registers are immutable.
A theory of nested speculative execution
 In 9th International Conference on Coordination Models and Languages (Coordination
, 2007
"... Abstract. Implementing distributed applications is a challenging task. Developers of such systems are confronted with issues like faulttolerance, efficient synchronization mechanisms, and the correctness of the distributed code. This paper introduces a new programming model based on speculative exe ..."
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Abstract. Implementing distributed applications is a challenging task. Developers of such systems are confronted with issues like faulttolerance, efficient synchronization mechanisms, and the correctness of the distributed code. This paper introduces a new programming model based on speculative execution that addresses these issues. Speculations provide distributed atomic rollback and enable optimistic execution of synchronization points. We present an operational semantics for nested speculative execution and synthetic benchmarks to illustrate the low overhead of speculations. 1
Naïve Type Theory
, 2002
"... 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 ..."
Abstract
 Add to MetaCart
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