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117
A Syntactic Approach to Type Soundness
 Information and Computation
, 1992
"... We present a new approach to proving type soundness for Hindley/Milnerstyle polymorphic type systems. The keys to our approach are (1) an adaptation of subject reduction theorems from combinatory logic to programming languages, and (2) the use of rewriting techniques for the specification of the la ..."
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Cited by 538 (21 self)
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We present a new approach to proving type soundness for Hindley/Milnerstyle polymorphic type systems. The keys to our approach are (1) an adaptation of subject reduction theorems from combinatory logic to programming languages, and (2) the use of rewriting techniques for the specification of the language semantics. The approach easily extends from polymorphic functional languages to imperative languages that provide references, exceptions, continuations, and similar features. We illustrate the technique with a type soundness theorem for the core of Standard ML, which includes the first type soundness proof for polymorphic exceptions and continuations. 1 Type Soundness Static type systems for programming languages attempt to prevent the occurrence of type errors during execution. A definition of type error depends on a specific language and type system, but always includes the use of a function on arguments for which it is not defined, and the attempted application of a nonfunction. ...
The Revised Report on the Syntactic Theories of Sequential Control and State
 Theoretical Computer Science
, 1992
"... The syntactic theories of control and state are conservative extensions of the v calculus for equational reasoning about imperative programming facilities in higherorder languages. Unlike the simple v calculus, the extended theories are mixtures of equivalence relations and compatible congruen ..."
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Cited by 255 (36 self)
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The syntactic theories of control and state are conservative extensions of the v calculus for equational reasoning about imperative programming facilities in higherorder languages. Unlike the simple v calculus, the extended theories are mixtures of equivalence relations and compatible congruence relations on the term language, which significantly complicates the reasoning process. In this paper we develop fully compatible equational theories of the same imperative higherorder programming languages. The new theories subsume the original calculi of control and state and satisfy the usual ChurchRosser and Standardization Theorems. With the new calculi, equational reasoning about imperative programs becomes as simple as reasoning about functional programs. 1 The syntactic theories of control and state Most calculusbased programming languages provide imperative programming facilities such as assignment statements, exceptions, and continuations. Typical examples are ML [16], Schem...
The slam calculus: programming with secrecy and integrity
 In POPL ’98: Proceedings of the 25th ACM SIGPLANSIGACT Symposium on Principles of Programming Languages
, 1998
"... The SLam calculus is a typed λcalculus that maintains security information as well as type information. The type system propagates security information for each object in four forms: the object’s creators and readers, and the object’s indirect creators and readers (i.e., those agents who, through f ..."
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Cited by 235 (1 self)
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The SLam calculus is a typed λcalculus that maintains security information as well as type information. The type system propagates security information for each object in four forms: the object’s creators and readers, and the object’s indirect creators and readers (i.e., those agents who, through flowofcontrol or the actions of other agents, can influence or be influenced by the content of the object). We prove that the type system prevents security violations and give some examples of its power. 1
A Core Calculus of Dependency
 IN PROC. 26TH ACM SYMP. ON PRINCIPLES OF PROGRAMMING LANGUAGES (POPL
, 1999
"... Notions of program dependency arise in many settings: security, partial evaluation, program slicing, and calltracking. We argue that there is a central notion of dependency common to these settings that can be captured within a single calculus, the Dependency Core Calculus (DCC), a small extension ..."
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Cited by 228 (25 self)
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Notions of program dependency arise in many settings: security, partial evaluation, program slicing, and calltracking. We argue that there is a central notion of dependency common to these settings that can be captured within a single calculus, the Dependency Core Calculus (DCC), a small extension of Moggi's computational lambda calculus. To establish this thesis, we translate typed calculi for secure information flow, bindingtime analysis, slicing, and calltracking into DCC. The translations help clarify aspects of the source calculi. We also define a semantic model for DCC and use it to give simple proofs of noninterference results for each case.
Reasoning about Programs in ContinuationPassing Style
 Lisp and Symbolic Computation
"... Plotkin's v calculus for callbyvalue programs is weaker than the fij calculus for the same programs in continuationpassing style (CPS). To identify the callby value axioms that correspond to fij on CPS terms, we define a new CPS transformation and an inverse mapping, both of which are interes ..."
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Cited by 161 (13 self)
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Plotkin's v calculus for callbyvalue programs is weaker than the fij calculus for the same programs in continuationpassing style (CPS). To identify the callby value axioms that correspond to fij on CPS terms, we define a new CPS transformation and an inverse mapping, both of which are interesting in their own right. Using the new CPS transformation, we determine the precise language of CPS terms closed under fijtransformations, as well as the callbyvalue axioms that correspond to the socalled administrative fijreductions on CPS terms. Using the inverse mapping, we map the remaining fi and j equalities on CPS terms to axioms on callbyvalue terms. On the pure (constant free) set ofterms, the resulting set of axioms is equivalent to Moggi's computational calculus. If the callbyvalue language includes the control operators abort and callwithcurrentcontinuation, the axioms are equivalent to an extension of Felleisen et al.'s vCcalculus and to the equational subtheory of Talcott's logic IOCC. Contents 1 Compiling with and without Continuations 4 2 : Calculi and Semantics 7 3 The Origins and Practice of CPS 10 3.1 The Original Encoding : : : : : : : : : : : : : : : : : : : : : 10 3.2 The Universe of CPS Terms : : : : : : : : : : : : : : : : : : 11 4 A Compacting CPS Transformation 13
On the Expressive Power of Programming Languages
 Science of Computer Programming
, 1990
"... The literature on programming languages contains an abundance of informal claims on the relative expressive power of programming languages, but there is no framework for formalizing such statements nor for deriving interesting consequences. As a first step in this direction, we develop a formal noti ..."
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Cited by 132 (4 self)
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The literature on programming languages contains an abundance of informal claims on the relative expressive power of programming languages, but there is no framework for formalizing such statements nor for deriving interesting consequences. As a first step in this direction, we develop a formal notion of expressiveness and investigate its properties. To validate the theory, we analyze some widely held beliefs about the expressive power of several extensions of functional languages. Based on these results, we believe that our system correctly captures many of the informal ideas on expressiveness, and that it constitutes a foundation for further research in this direction. 1 Comparing Programming Languages The literature on programming languages contains an abundance of informal claims on the expressive power of programming languages. Arguments in these contexts typically assert the expressibility or nonexpressibility of programming constructs relative to a language. Unfortunately, pro...
Typing FirstClass Continuations in ML
, 1992
"... An extension of ML with continuation primitives similar to those found in Scheme is considered. A number of alternative type systems are discussed, and several programming examples are given. A continuationbased operational semantics is defined for a small, purely functional, language, and the soun ..."
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Cited by 93 (14 self)
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An extension of ML with continuation primitives similar to those found in Scheme is considered. A number of alternative type systems are discussed, and several programming examples are given. A continuationbased operational semantics is defined for a small, purely functional, language, and the soundness of the DamasMilner polymorphic type assignment system with respect to this semantics is proved. The full DamasMilner type system is shown to be unsound in the presence of firstclass continuations. Restrictions on polymorphism similar to those introduced in connection with reference types are shown to suffice for soundness. 1 Introduction Firstclass continuations are a simple and natural way to provide access to the flow of evaluation in functional languages. The ability to seize the "current continuation" (control state of the evaluator) provides a simple and natural basis for defining numerous higherlevel constructs such as coroutines [22], exceptions [41], and logic variables [...
Representing control: a study of the CPS transformation
, 1992
"... This paper investigates the transformation of v terms into continuationpassing style (CPS). We show that by appropriate jexpansion of Fischer and Plotkin's twopass equational specification of the CPS transform, we can obtain a static and contextfree separation of the result terms into "esse ..."
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Cited by 81 (7 self)
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This paper investigates the transformation of v terms into continuationpassing style (CPS). We show that by appropriate jexpansion of Fischer and Plotkin's twopass equational specification of the CPS transform, we can obtain a static and contextfree separation of the result terms into "essential" and "administrative" constructs. Interpreting the former as syntax builders and the latter as directly executable code, we obtain a simple and efficient onepass transformation algorithm, easily extended to conditional expressions, recursive definitions, and similar constructs. This new transformation algorithm leads to a simpler proof of Plotkin's simulation and indifference results. Further we show how CPSbased control operators similar to but more general than Scheme's call/cc can be naturally accommodated by the new transformation algorithm. To demonstrate the expressive power of these operators, we use them to present an equivalent but even more concise formulation of t...
A CurryHoward foundation for functional computation with control
 In Proceedings of ACM SIGPLANSIGACT Symposium on Principle of Programming Languages
, 1997
"... We introduce the type theory ¯ v , a callbyvalue variant of Parigot's ¯calculus, as a CurryHoward representation theory of classical propositional proofs. The associated rewrite system is ChurchRosser and strongly normalizing, and definitional equality of the type theory is consistent, compatib ..."
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Cited by 77 (3 self)
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We introduce the type theory ¯ v , a callbyvalue variant of Parigot's ¯calculus, as a CurryHoward representation theory of classical propositional proofs. The associated rewrite system is ChurchRosser and strongly normalizing, and definitional equality of the type theory is consistent, compatible with cut, congruent and decidable. The attendant callbyvalue programming language ¯pcf v is obtained from ¯ v by augmenting it by basic arithmetic, conditionals and fixpoints. We study the behavioural properties of ¯pcf v and show that, though simple, it is a very general language for functional computation with control: it can express all the main control constructs such as exceptions and firstclass continuations. Prooftheoretically the dual ¯ v constructs of naming and ¯abstraction witness the introduction and elimination rules of absurdity respectively. Computationally they give succinct expression to a kind of generic (forward) "jump" operator, which may be regarded as a unif...
A Generalization of Exceptions and Control in MLlike Languages
 IN PROC. FPCA
, 1995
"... We add functional continuations and prompts to a language with an MLstyle type system. The operators significantly extend and simplify the control operators in SML/NJ, and can be themselves used to implement (simple) exceptions. We prove that welltyped terms never produce runtime type errors and ..."
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Cited by 61 (0 self)
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We add functional continuations and prompts to a language with an MLstyle type system. The operators significantly extend and simplify the control operators in SML/NJ, and can be themselves used to implement (simple) exceptions. We prove that welltyped terms never produce runtime type errors and give a module for implementing them in the latest version of SML/NJ.