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A Linearly Typed Assembly Language
 In Workshop on Types in Compilation
"... Today's typesafe lowlevel languages rely on garbage collection to recycle heapallocated objects safely. We present LTAL, a safe, lowlevel, yet simple language that "stands on its own": it guarantees safe execution within a fixed memory space, without relying on external runtime support. We demo ..."
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Cited by 146 (35 self)
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Today's typesafe lowlevel languages rely on garbage collection to recycle heapallocated objects safely. We present LTAL, a safe, lowlevel, yet simple language that "stands on its own": it guarantees safe execution within a fixed memory space, without relying on external runtime support. We demonstrate the expressiveness of LTAL by giving a typepreserving compiler for the functional core of ML. But this independence comes at a steep price: LTAL's type system imposes a draconian discipline of linearity that ensures that memory can be reused safely, but prohibits any useful kind of sharing. We present the results of experiments with a prototype LTAL system that show just how high the price of linearity can be.
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
From System F to Typed Assembly Language (Extended Version)
, 1998
"... We motivate the design of a statically typed assembly language (TAL) and present a typepreserving translation from System F to TAL. The TAL we present is based on a conventional RISC assembly language, but its static type system provides support for enforcing highlevel language abstractions, such a ..."
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Cited by 8 (4 self)
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We motivate the design of a statically typed assembly language (TAL) and present a typepreserving translation from System F to TAL. The TAL we present is based on a conventional RISC assembly language, but its static type system provides support for enforcing highlevel language abstractions, such as closures, tuples, and objects, as well as userdefined abstract data types. The type system ensures that welltyped programs cannot violate these abstractions. In addition, the typing constructs place almost no restrictions on lowlevel optimizations such as register allocation, instruction selection, or instruction scheduling. Our translation to TAL is specified as a sequence of typepreserving transformations, including CPS and closure conversion phases; typecorrect source programs are mapped to typecorrect assembly language. A key contribution is an approach to polymorphic closure conversion that is considerably simpler than previous work. The compiler and typed assembly language prov...
Simple, Efficient Object Encoding using Intersection Types
 In International Conference on Functional Programming
, 1999
"... I present a typetheoretic encoding of objects that interprets method dispatch by selfapplication (i.e., method functions are applied to the objects containing them) but still validates the expected subtyping relationships. The naive typing of selfapplication fails to validate the expected subtypi ..."
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Cited by 6 (0 self)
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I present a typetheoretic encoding of objects that interprets method dispatch by selfapplication (i.e., method functions are applied to the objects containing them) but still validates the expected subtyping relationships. The naive typing of selfapplication fails to validate the expected subtyping relationships because it is too permissive and allows application to similarly typed objects that are not self. This new encoding solves this problem by constraining methods to be applied only to self using existential and intersection types. Using this typing, I give a full account of objects including self types and method update. The typing constructs used in this encoding appear to be quite rich, but they may be axiomatized in a novel, restricted fashion that is metatheoretically simple. 1 Introduction Objectoriented programming languages usually provide builtin primitives for objectrelated computing. However, there is also considerable interest in explaining such object primitives...
Programming Language Semantics in Foundational Type Theory
 In Proc. the IFIP TC2/WG2.2,2.3 International Conference on Programming Concepts and Methods (PROCOMET’98
, 1996
"... There are compelling benefits to using foundational type theory as a framework for programming language semantics. I give a semantics of an expressive programming calculus in the foundational type theory of Nuprl. Previous typetheoretic semantics have used less expressive type theories, or have sacr ..."
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Cited by 5 (1 self)
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There are compelling benefits to using foundational type theory as a framework for programming language semantics. I give a semantics of an expressive programming calculus in the foundational type theory of Nuprl. Previous typetheoretic semantics have used less expressive type theories, or have sacrificed important programming constructs such as recursion and modules. The primary mechanisms of this semantics are partial types, for typing recursion, set types, for encoding power and singleton kinds, which are used for subtyping and module programming, and very dependent function types, for encoding signatures. Keywords Semantics, program verification, type theory, functional programming 1 INTRODUCTION Type theory has become a popular framework for formal reasoning in computer science and has formed the basis for a number of automated deduction systems, including Automath, Nuprl, HOL and Coq, among others. In addition to formalizing mathematics, these systems are widely used for the a...
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
E cient Object Encoding using Intersection Types
"... I present atypetheoretic encoding of objects that interprets method dispatch by selfapplication (i.e., method functions are applied to the objects containing them) but still validates the expected subtyping relationships. The naive typing of selfapplication fails to validate the expected subtypin ..."
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Cited by 1 (0 self)
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I present atypetheoretic encoding of objects that interprets method dispatch by selfapplication (i.e., method functions are applied to the objects containing them) but still validates the expected subtyping relationships. The naive typing of selfapplication fails to validate the expected subtyping relationships because it is too permissive and allows application to similarly typed objects that are not self. This new encoding solves this problem by constraining methods to be applied only to self using existential and intersection types. Using this typing, I give a full account of objects including self types and method update. The typing constructs used in this encoding appear to be quite rich, but they may be axiomatized in a novel, restricted fashion that is metatheoretically simple.
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
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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
Typed Intermediate Languages
"... Programs written in a typed language are guaranteed to satisfy the safety properties of the type system without runtime checks. A type system for an intermediate language allows static verification of safety properties independent of source languages, and opens up opportunities for advanced compiler ..."
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Programs written in a typed language are guaranteed to satisfy the safety properties of the type system without runtime checks. A type system for an intermediate language allows static verification of safety properties independent of source languages, and opens up opportunities for advanced compiler optimizations. This paper surveys three major intermediate languages: Java bytecode, typed assembly language and proofcarrying code. Java bytecode requires minimal type annotation but sophisticated verification algorithms. Typed assembly language permits lowlevel constructs such as registers and instruction blocks, yet still enforces controlflow safety and memory safety. Proofcarrying code provides a general framework for any safety properties definable in a metalogical framework. We motivate the use of typed intermediate languages, illustrate the type systems of the three languages mentioned above with examples, and compare their tradeoffs of expressiveness versus complexity. Additionally, we assess the impact of the three languages and identify research directions for future work. 1