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Dynamic typing in a statically typed language
 ACM Trans. Program. Lang. Syst
, 1991
"... Abstract. Dynamic typing can be useful in statically typed languages. We extend the simply typed λcalculus with dynamic typing and elaborate additional features like polymorphism and subtyping. 1 ..."
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Cited by 154 (4 self)
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Abstract. Dynamic typing can be useful in statically typed languages. We extend the simply typed λcalculus with dynamic typing and elaborate additional features like polymorphism and subtyping. 1
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 [...
Semantics of memory management for polymorphic languages
 In 1st Workshop on Higher Order Operational Techniques in Semantics, A. Gordon and A. Pitts, Eds. Publications of the Newton Institute
, 1997
"... The views and conclusions contained in this document arethose of the authors and should not be interpreted as representing o cial policies, either expressed or implied, of the Advanced We present a static and dynamic semantics for an abstract machine that evaluates expressions of a polymorphic progr ..."
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Cited by 42 (8 self)
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The views and conclusions contained in this document arethose of the authors and should not be interpreted as representing o cial policies, either expressed or implied, of the Advanced We present a static and dynamic semantics for an abstract machine that evaluates expressions of a polymorphic programming language. Unlike traditional semantics, our abstract machine exposes many important issues of memory management, such as value sharing and control representation. We prove the soundness of the static semantics with respect to the dynamic semantics using traditional techniques. We then show how these same techniques may be used to establish the soundness of various memory management strategies, including typebased, tagfree garbage collection� tailcall elimination � and environment strengthening. Keywords: management Type theory and operational semantics are remarkably e ective tools for programming
The Rewriting Logic Semantics Project
 SOS 2005 PRELIMINARY VERSION
, 2005
"... Rewriting logic is a flexible and expressive logical framework that unifies denotational semantics and SOS in a novel way, avoiding their respective limitations and allowing very succinct semantic definitions. The fact that a rewrite theory’s axioms include both equations and rewrite rules provides ..."
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Cited by 39 (11 self)
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Rewriting logic is a flexible and expressive logical framework that unifies denotational semantics and SOS in a novel way, avoiding their respective limitations and allowing very succinct semantic definitions. The fact that a rewrite theory’s axioms include both equations and rewrite rules provides a very useful “abstraction knob” to find the right balance between abstraction and observability in semantic definitions. Such semantic definitions are directly executable as interpreters in a rewriting logic language such as Maude, whose generic formal tools can be used to endow those interpreters with powerful program analysis capabilities.
Rewriting Logic Semantics: From Language Specifications to Formal Analysis Tools
 In Proceedings of the IJCAR 2004. LNCS
, 2004
"... Abstract. Formal semantic definitions of concurrent languages, when specified in a wellsuited semantic framework and supported by generic and efficient formal tools, can be the basis of powerful software analysis tools. Such tools can be obtained for free from the semantic definitions; in our exper ..."
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Cited by 38 (9 self)
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Abstract. Formal semantic definitions of concurrent languages, when specified in a wellsuited semantic framework and supported by generic and efficient formal tools, can be the basis of powerful software analysis tools. Such tools can be obtained for free from the semantic definitions; in our experience in just the few weeks required to define a language’s semantics even for large languages like Java. By combining, yet distinguishing, both equations and rules, rewriting logic semantic definitions unify both the semantic equations of equational semantics (in their higherorder denotational version or their firstorder algebraic counterpart) and the semantic rules of SOS. Several limitations of both SOS and equational semantics are thus overcome within this unified framework. By using a highperformance implementation of rewriting logic such as Maude, a language’s formal specification can be automatically transformed into an efficient interpreter. Furthermore, by using Maude’s breadth first search command, we also obtain for free a semidecision procedure for finding failures of safety properties; and by using Maude’s LTL model checker, we obtain, also for free, a decision procedure for LTL properties of finitestate programs. These possibilities, and the competitive performance of the analysis tools thus obtained, are illustrated by means of a concurrent Camllike language; similar experience with Java (source and JVM) programs is also summarized. 1
Research Directions in Rewriting Logic
, 1998
"... Rewriting logic expresses an essential equivalence between logic and computation. System states are in bijective correspondence with formulas, and concurrent computations are in bijective correspondence with proofs. Given this equivalence between computation and logic, a rewriting logic axiom of the ..."
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Cited by 31 (12 self)
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Rewriting logic expresses an essential equivalence between logic and computation. System states are in bijective correspondence with formulas, and concurrent computations are in bijective correspondence with proofs. Given this equivalence between computation and logic, a rewriting logic axiom of the form t \Gamma! t 0 has two readings. Computationally, it means that a fragment of a system 's state that is an instance of the pattern t can change to the corresponding instance of t 0 concurrently with any other state changes; logically, it just means that we can derive the formula t 0 from the formula t. Rewriting logic is entirely neutral about the structure and properties of the formulas/states t. They are entirely userdefinable as an algebraic data type satisfying certain equational axioms. Because of this ecumenical neutrality, rewriting logic has, from a logical viewpoint, good properties as a logical framework, in which many other logics can be naturally represented. And, computationally, it has also good properties as a semantic framework, in which many different system styles and models of concurrent computation and many different languages can be naturally expressed without any distorting encodings. The goal of this paper is to provide a relatively gentle introduction to rewriting logic, and to paint in broad strokes the main research directions that, since its introduction in 1990, have been pursued by a growing number of researchers in Europe, the US, and Japan. Key theoretical developments, as well as the main current applications of rewriting logic as a logical and semantic framework, and the work on formal reasoning to prove properties of specifications are surveyed.
Type Checking with Universes
, 1991
"... Various formulations of constructive type theories have been proposed to serve as the basis for machineassisted proof and as a theoretical basis for studying programming languages. Many of these calculi include a cumulative hierarchy of "universes," each a type of types closed under a collectio ..."
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Cited by 24 (6 self)
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Various formulations of constructive type theories have been proposed to serve as the basis for machineassisted proof and as a theoretical basis for studying programming languages. Many of these calculi include a cumulative hierarchy of "universes," each a type of types closed under a collection of typeforming operations. Universes are of interest for a variety of reasons, some philosophical (predicative vs. impredicative type theories), some theoretical (limitations on the closure properties of type theories), and some practical (to achieve some of the advantages of a type of all types without sacrificing consistency.) The Generalized Calculus of Constructions (CC ! ) is a formal theory of types that includes such a hierarchy of universes. Although essential to the formalization of constructive mathematics, universes are tedious to use in practice, for one is required to make specific choices of universe levels and to ensure that all choices are consistent. In this pa...
Observers for Linear Types
 ESOP ’92: 4th European Symposium on Programming, Rennes, France, Proceedings
, 1992
"... Linear types provide the framework for a safe embedding of mutable state in functional languages by enforcing the principle that variables of linear type must be used exactly once. A potential disadvantage of this approach is that it places read accesses to suchvariables under the same restrictio ..."
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Cited by 23 (4 self)
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Linear types provide the framework for a safe embedding of mutable state in functional languages by enforcing the principle that variables of linear type must be used exactly once. A potential disadvantage of this approach is that it places read accesses to suchvariables under the same restriction as write accesses, and thus prevents reads to proceed in parallel. We present here an extension of linear types which augments the usual distinction between linear and nonlinear bya third state, observers of linear variables. Since, unlike linear variables, observers can be duplicated, multiple concurrent reads are made possible. On the other hand, observers must be shortlived enough to never overlap with mutations. The resulting type system is in many aspects similar to the one of ML: It is polymorphic, has principal types, and admits a type reconstruction algorithm. 1 Introduction We are investigating a type system that addresses the update problem in functional languages: How...
Substructural Logical Specifications
, 2012
"... Any opinions, findings, conclusions or recommendations expressed in this publication are those of the author and A logical framework and its implementation should serve as a flexible tool for specifying, simulating, and reasoning about formal systems. When the formal systems we are interested in exh ..."
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Cited by 3 (2 self)
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Any opinions, findings, conclusions or recommendations expressed in this publication are those of the author and A logical framework and its implementation should serve as a flexible tool for specifying, simulating, and reasoning about formal systems. When the formal systems we are interested in exhibit state and concurrency, however, existing logical frameworks fall short of this goal. Logical frameworks based on a rewriting interpretation of substructural logics, ordered and linear logic in particular, can help. To this end, this dissertation introduces and demonstrates four methodologies for developing and using substructural logical frameworks for specifying and reasoning about stateful and concurrent systems. Structural focalization is a synthesis of ideas from Andreoli’s focused sequent calculi and Watkins’s hereditary substitution. We can use structural focalization to take a logic and define a restricted form of derivations, the focused derivations, that form the basis of a logical framework. We apply this methodology to define SLS, a logical framework for substructural logical specifications, as a fragment of ordered
Nominal Verification of Algorithm W
, 2008
"... The MilnerDamas typing algorithm W is one of the classic algorithms in Computer Science. In this paper we describe a formalised soundness and completeness proof for this algorithm. Our formalisation is based on names for both term and type variables, and is carried out in Isabelle/HOL using the Nom ..."
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Cited by 2 (1 self)
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The MilnerDamas typing algorithm W is one of the classic algorithms in Computer Science. In this paper we describe a formalised soundness and completeness proof for this algorithm. Our formalisation is based on names for both term and type variables, and is carried out in Isabelle/HOL using the Nominal Datatype Package. It turns out that in our formalisation we have to deal with a number of issues that are often overlooked in informal presentations of W. 1