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111
An observationally complete program logic for imperative higherorder functions
 In Proc. LICS’05
, 2005
"... Abstract. We propose a simple compositional program logic for an imperative extension of callbyvalue PCF, built on Hoare logic and our preceding work on program logics for pure higherorder functions. A systematic use of names and operations on them allows precise and general description of comple ..."
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Cited by 39 (11 self)
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Abstract. We propose a simple compositional program logic for an imperative extension of callbyvalue PCF, built on Hoare logic and our preceding work on program logics for pure higherorder functions. A systematic use of names and operations on them allows precise and general description of complex higherorder imperative behaviour. The proof rules of the logic exactly follow the syntax of the language and can cleanly embed, justify and extend the standard proof rules for total correctness of Hoare logic. The logic offers a foundation for general treatment of aliasing and local state on its basis, with minimal extensions. After establishing soundness, we prove that valid assertions for programs completely characterise their behaviour up to observational congruence, which is proved using a variant of finite canonical forms. The use of the logic is illustrated through reasoning examples which are hard to assert and infer using existing program logics.
Categorical Models for Local Names
 LISP AND SYMBOLIC COMPUTATION
, 1996
"... This paper describes the construction of categorical models for the nucalculus, a language that combines higherorder functions with dynamically created names. Names are created with local scope, they can be compared with each other and passed around through function application, but that is all. T ..."
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Cited by 39 (2 self)
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This paper describes the construction of categorical models for the nucalculus, a language that combines higherorder functions with dynamically created names. Names are created with local scope, they can be compared with each other and passed around through function application, but that is all. The intent behind this language is to examine one aspect of the imperative character of Standard ML: the use of local state by dynamic creation of references. The nucalculus is equivalent to a certain fragment of ML, omitting side effects, exceptions, datatypes and recursion. Even without all these features, the interaction of name creation with higherorder functions can be complex and subtle; it is particularly difficult to characterise the observable behaviour of expressions. Categorical monads, in the style of Moggi, are used to build denotational models for the nucalculus. An intermediate stage is the use of a computational metalanguage, which distinguishes in the type system between values and computations. The general requirements for a categorical model are presented, and two specific examples described in detail. These provide a sound denotational semantics for the nucalculus, and can be used to reason about observable equivalence in the language. In particular a model using logical relations is fully abstract for firstorder expressions.
A Naïve Time Analysis and its Theory of Cost Equivalence
 Journal of Logic and Computation
, 1995
"... Techniques for reasoning about extensional properties of functional programs are well understood, but methods for analysing the underlying intensional or operational properties have been much neglected. This paper begins with the development of a simple but useful calculus for time analysis of nons ..."
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Cited by 39 (7 self)
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Techniques for reasoning about extensional properties of functional programs are well understood, but methods for analysing the underlying intensional or operational properties have been much neglected. This paper begins with the development of a simple but useful calculus for time analysis of nonstrict functional programs with lazy lists. One limitation of this basic calculus is that the ordinary equational reasoning on functional programs is not valid. In order to buy back some of these equational properties we develop a nonstandard operational equivalence relation called cost equivalence, by considering the number of computation steps as an `observable' component of the evaluation process. We define this relation by analogy with Park's definition of bisimulation in CCS. This formulation allows us to show that cost equivalence is a contextual congruence (and thus is substitutive with respect to the basic calculus) and provides useful proof techniques for establishing costequivalen...
Imperative Objects and Mobile Processes
 MATH. STRUCT. COMPUT. SCI
, 1998
"... An interpretation of Abadi and Cardelli's firstorder Imperative Object Calculus into a typed picalculus is presented. The interpretation validates the subtyping relation and the typing judgements of the Object Calculus, and is computationally adequate. The proof of computational adequacy make ..."
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Cited by 39 (11 self)
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An interpretation of Abadi and Cardelli's firstorder Imperative Object Calculus into a typed picalculus is presented. The interpretation validates the subtyping relation and the typing judgements of the Object Calculus, and is computationally adequate. The proof of computational adequacy makes use of (a picalculus version) of ready simulation, and of a factorisation of the interpretation into a functional part and a very simple imperative part. The interpretation can be used to compare and contrast the Imperative and the Functional Object Calculi, and to prove properties about them, within a unified framework.
Operational Properties of Lily, a Polymorphic Linear Lambda Calculus with Recursion
"... Plotkin has advocated the combination of linear lambda calculus, polymorphism and fixed point recursion as an expressive semantic metalanguage. We study its expressive power from an operational point of view. We show that the naturally callbyvalue operators of linear lambda calculus can be given a ..."
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Cited by 36 (1 self)
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Plotkin has advocated the combination of linear lambda calculus, polymorphism and fixed point recursion as an expressive semantic metalanguage. We study its expressive power from an operational point of view. We show that the naturally callbyvalue operators of linear lambda calculus can be given a callbyname semantics without affecting termination at exponential types and hence without affecting ground contextual equivalence. This result is used to prove properties of a logical relation that provides a new extensional characterisation of ground contextual equivalence and relational parametricity properties of polymorphic types.
Operational Semantics for MultiLanguage Programs
, 2007
"... Interlanguage interoperability is big business, as the success of Microsoft’s.NET and COM and Sun’s JVM show. Programming language designers are designing programming languages that reflect that fact — SML#, Mondrian, and Scala, to name just a few examples, all treat interoperability with other lan ..."
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Cited by 34 (5 self)
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Interlanguage interoperability is big business, as the success of Microsoft’s.NET and COM and Sun’s JVM show. Programming language designers are designing programming languages that reflect that fact — SML#, Mondrian, and Scala, to name just a few examples, all treat interoperability with other languages as a central design feature. Still, current multilanguage research tends not to focus on the semantics of interoperation features, but only on how to implement them efficiently. In this paper, we take first steps toward higherlevel models of interoperating systems. Our technique abstracts away the lowlevel details of interoperability like garbage collection and representation coherence, and lets us focus on semantic properties like typesafety and observable equivalence. Beyond giving simple expressive models that are natural compositions of singlelanguage models, our studies have uncovered several interesting facts about interoperability. For example, higherorder contracts naturally emerge as the glue to ensure that interoperating languages respect each other’s type systems. While we present our results in an abstract setting, they shed light on real multilanguage systems and tools such as the JNI, SWIG, and Haskell’s stable pointers.
Compilation and Equivalence of Imperative Objects
, 1998
"... We adopt the untyped imperative object calculus of Abadi and Cardelli as a minimal setting in which to study problems of compilation and program equivalence that arise when compiling objectoriented languages. We present both a bigstep and a smallstep substitutionbased operational semantics fo ..."
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Cited by 32 (4 self)
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We adopt the untyped imperative object calculus of Abadi and Cardelli as a minimal setting in which to study problems of compilation and program equivalence that arise when compiling objectoriented languages. We present both a bigstep and a smallstep substitutionbased operational semantics for the calculus. Our rst two results are theorems asserting the equivalence of our substitutionbased semantics with a closurebased semantics like that given by Abadi and Cardelli. Our third result is a direct proof of the correctness of compilation to a stackbased abstract machine via a smallstep decompilation algorithm. Our fourth result is that contextual equivalence of objects coincides with a form of Mason and Talcott's CIU equivalence; the latter provides a tractable means of establishing operational equivalences. Finally, we prove correct an algorithm, used in our prototype compiler, for statically resolving method osets. This is the rst study of correctness of an objectoriented abstract machine, and of operational equivalence for the imperative object calculus.
Modular Specification Of Interaction Policies In Distributed Computing
, 1996
"... Software executing on distributed systems consists of many asynchronous, autonomous components which interact in order to coordinate local activity. The need for such coordination, as well as requirements such as heterogeneity, scalability, security and availability, considerably increase the comple ..."
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Cited by 32 (0 self)
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Software executing on distributed systems consists of many asynchronous, autonomous components which interact in order to coordinate local activity. The need for such coordination, as well as requirements such as heterogeneity, scalability, security and availability, considerably increase the complexity of code in distributed applications. Moreover, changing requirements, as well as changes in hardware platforms, lead to software that is constantly evolving and complicates reuse. To support development and evolution of distributed applications requires techniques which allow coordination code to be specified, customized, and maintained independently of application components; goals which cannot be realized solely through objectoriented techniques. This thesis demonstrates that metalevel specification of interaction policies enables modular description of component interaction policies, as well as customization of policy implementations. We present the highlevel language Dil for spec...
The impact of higherorder state and control effects on local relational reasoning
, 2010
"... Reasoning about program equivalence is one of the oldest problems in semantics. In recent years, useful techniques have been developed, based on bisimulations and logical relations, for reasoning about equivalence in the setting of increasingly realistic languages—languages nearly as complex as ML o ..."
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Cited by 31 (13 self)
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Reasoning about program equivalence is one of the oldest problems in semantics. In recent years, useful techniques have been developed, based on bisimulations and logical relations, for reasoning about equivalence in the setting of increasingly realistic languages—languages nearly as complex as ML or Haskell. Much of the recent work in this direction has considered the interesting representation independence principles enabled by the use of local state, but it is also important to understand the principles that powerful features like higherorder state and control effects disable. This latter topic has been broached extensively within the framework of game semantics, resulting in what Abramsky dubbed the “semantic cube”: fully abstract gamesemantic characterizations of various axes in the design space of MLlike languages. But when it comes to reasoning about many actual examples, game semantics does not yet supply a useful technique for proving equivalences. In this paper, we marry the aspirations of the semantic cube to the powerful proof method of stepindexed Kripke logical relations. Building on recent work of Ahmed, Dreyer, and Rossberg, we define the first fully abstract logical relation for an MLlike language with recursive types, abstract types, general references and call/cc. We then show how, under orthogonal restrictions to the expressive power of our language—namely, the restriction to firstorder state and/or the removal of call/cc—we can enhance the proving power of our possibleworlds model in correspondingly orthogonal ways, and we demonstrate this proving power on a range of interesting examples. Central to our story is the use of state transition systems to model the way in which properties of local state evolve over time.
References, Local Variables and Operational Reasoning
 In Seventh Annual Symposium on Logic in Computer Science
, 1992
"... this paper we regard the following as synonyms: references, program variables, pointers, locations, and unary cells) to a programming language complicates life. Adding them to the simply typed lambda calculus causes the failure of most of the nice mathematical properties and some of the more basic r ..."
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Cited by 30 (4 self)
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this paper we regard the following as synonyms: references, program variables, pointers, locations, and unary cells) to a programming language complicates life. Adding them to the simply typed lambda calculus causes the failure of most of the nice mathematical properties and some of the more basic rules (such as j). For example strong normalization fails since it is possible, for each provably nonempty function type, to construct a Y combinator for that type. References also interact unpleasantly with polymorphism [34, 35]. They are also troublesome from a denotational point of view as illustrated by the lack of fully abstract models. For example, in [22] Meyer and Sieber give a series of examples of programs that are operationally equivalent (according to the intended semantics of blockstructured Algollike programs) but which are not given equivalent denotations in traditional denotational semantics. They propose various modifications to the denotational semantics which solve some of these discrepancies, but not all. In [27, 26] a denotational semantics that overcomes some of these problems is presented. However variations on the seventh example remain problematic. Since numerous proof systems for Algol are sound for the denotational models in question, [8, 7, 32, 28, 16, 27, 26], these equivalences, if expressible, must be independent of these systems. The problem which motivated Meyer and Sieber's paper, [22], was to provide mathematical justification for the informal but convincing proofs of the operational equivalence of their examples. In this paper we approach the same problem, but from an operational rather than denotational perspective. This paper accomplishes two goals. Firstly, we present the firstorder part of a new logic for reasoning about programs....