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55
Reasoning about local variables with operationallybased logical relations
 In LICS
, 1996
"... A parametric logical relation between the phrases of an Algollike language is presented. Its definition involves the structural operational semantics of the language, but was inspired by recent denotationallybased work of O’Hearn and Reynolds on translating Algol into a predicatively polymorphic l ..."
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Cited by 32 (3 self)
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A parametric logical relation between the phrases of an Algollike language is presented. Its definition involves the structural operational semantics of the language, but was inspired by recent denotationallybased work of O’Hearn and Reynolds on translating Algol into a predicatively polymorphic linear lambda calculus. The logical relation yields an applicative characterisation of contextual equivalence for the language and provides a useful (and complete) method for proving equivalences. Its utility is illustrated by giving simple and direct proofs of some contextual equivalences, including an interesting equivalence due to O’Hearn which hinges upon the undefinability of ‘snapback ’ operations (and which goes beyond the standard suite of ‘MeyerSieber ’ examples). Whilst some of the mathematical intricacies of denotational semantics are avoided, the hard work in this operational approach lies in establishing the ‘fundamental property’ for the logical relation—the proof of which makes use of a compactness property of fixpoint recursion with respect to evaluation of phrases. But once this property has been established, the logical relation provides a verification method with an attractively low mathematical overhead. 1.
A Stratified Semantics of General References Embeddable in HigherOrder Logic (Extended Abstract)
, 2002
"... Amal J. Ahmed Andrew W. Appel # Roberto Virga Princeton University {amal,appel,rvirga}@cs.princeton.edu Abstract We demonstrate a semantic model of general references  that is, mutable memory cells that may contain values of any (staticallychecked) closed type, including other references. Our mo ..."
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Cited by 30 (8 self)
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Amal J. Ahmed Andrew W. Appel # Roberto Virga Princeton University {amal,appel,rvirga}@cs.princeton.edu Abstract We demonstrate a semantic model of general references  that is, mutable memory cells that may contain values of any (staticallychecked) closed type, including other references. Our model is in terms of execution sequences on a von Neumann machine
Imperative selfadjusting computation
 In POPL ’08: Proceedings of the 35th annual ACM SIGPLANSIGACT symposium on Principles of programming languages
, 2008
"... Recent work on selfadjusting computation showed how to systematically write programs that respond efficiently to incremental changes in their inputs. The idea is to represent changeable data using modifiable references, i.e., a special data structure that keeps track of dependencies between read an ..."
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Cited by 28 (16 self)
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Recent work on selfadjusting computation showed how to systematically write programs that respond efficiently to incremental changes in their inputs. The idea is to represent changeable data using modifiable references, i.e., a special data structure that keeps track of dependencies between read and writeoperations, and to let computations construct traces that later, after changes have occurred, can drive a change propagation algorithm. The approach has been shown to be effective for a variety of algorithmic problems, including some for which adhoc solutions had previously remained elusive. All previous work on selfadjusting computation, however, relied on a purely functional programming model. In this paper, we show that it is possible to remove this limitation and support modifiable references that can be written multiple times. We formalize this using a language AIL for which we define evaluation and changepropagation semantics. AIL closely resembles a traditional higherorder imperative programming language. For AIL we state and prove consistency, i.e., the property that although the semantics is inherently nondeterministic, different evaluation paths will still give observationally equivalent results. In the imperative setting where pointer graphs in the store can form cycles, our previous proof techniques do not apply. Instead, we make use of a novel form of a stepindexed logical relation that handles modifiable references. We show that AIL can be realized efficiently by describing implementation strategies whose overhead is provably constanttime per primitive. When the number of reads and writes per modifiable is bounded by a constant, we can show that change propagation becomes as efficient as it was in the pure case. The general case incurs a slowdown that is logarithmic in the maximum number of such operations. We use DFS and related algorithms on graphs as our running examples and prove that they respond to insertions and deletions of edges efficiently. 1.
Correctness of Data Representations involving Heap Data Structures
 Science of Computer Programming
, 2003
"... While the semantics of local variables in programming languages is by now wellunderstood, the semantics of pointeraddressed heap variables is still an outstanding issue. In particular, the commonly assumed relational reasoning principles for data representations have not been validated in a se ..."
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Cited by 22 (7 self)
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While the semantics of local variables in programming languages is by now wellunderstood, the semantics of pointeraddressed heap variables is still an outstanding issue. In particular, the commonly assumed relational reasoning principles for data representations have not been validated in a semantic model of heap variables. In this paper, we de ne a parametricity semantics for a Pascallike language with pointers and heap variables which gives such reasoning principles. It is found that the correspondences between data representations are not simply relations between states, but more intricate correspondences that also need to keep track of visible locations whose pointers can be stored and leaked.
Elementary Structures in Process Theory (1) Sets with Renaming
, 1997
"... We study a general algebraic framework which underlies a wide range of computational formalisms... ..."
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Cited by 19 (6 self)
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We study a general algebraic framework which underlies a wide range of computational formalisms...
A game semantics of local names and good variables
 of Lecture Notes in Computer Science
, 2004
"... Abstract. We describe a game semantics for local names in a functional setting. It is based on a category of dialogue games acted upon by the automorphism group of the natural numbers; this allows properties of names such as freshness and locality to be characterized semantically. We describe a mode ..."
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Cited by 17 (4 self)
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Abstract. We describe a game semantics for local names in a functional setting. It is based on a category of dialogue games acted upon by the automorphism group of the natural numbers; this allows properties of names such as freshness and locality to be characterized semantically. We describe a model of the nucalculus in this category, and extend it with named references (without bad variables) using names as pointers to a store. After refining the semantics via a notion of garbage collection, we prove that the compact elements are definable as terms, and hence obtain a full abstraction result. 1 Introduction Local names are a pervasive and subtle feature of programming languages and other calculi. Not only are they used for manipulating important constructs such as locally bound references and exceptions, namepassing is itself a very expressive computational paradigm, as demonstrated by the sscalculus, for example. Local names can also represent items of secret information which are dynamically generated, passed between agents and used to access further information or activity. They therefore have a key r^ole in specifying properties of secure systems [1, 24].
Logical reasoning for higherorder functions with local state
 In Foundations of Software Science and Computation Structure
"... ABSTRACT. We introduce an extension of Hoare logic for callbyvalue higherorder functions with MLlike local reference generation. Local references may be generated dynamically and exported outside their scope, may store higherorder functions and may be used to construct complex mutable data stru ..."
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Cited by 13 (4 self)
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ABSTRACT. We introduce an extension of Hoare logic for callbyvalue higherorder functions with MLlike local reference generation. Local references may be generated dynamically and exported outside their scope, may store higherorder functions and may be used to construct complex mutable data structures. This primitive is captured logically using a predicate asserting reachability of a reference name from a possibly higherorder datum and quantifiers over hidden references. We explore the logic’s descriptive and reasoning power with nontrivial programming examples combining higherorder procedures and dynamically generated local state. Axioms for reachability and local invariant play a central role for reasoning about the examples.
Full abstraction for nominal general references
 In LICS ’07: Proceedings of the 22nd Annual IEEE Symposium on Logic in Computer Science (Wroclaw, 2007), IEEE Computer
"... Vol. 5 (3:8) 2009, pp. 1–69 www.lmcsonline.org ..."
About permutation algebras, (pre)sheaves and named sets
 In Higher Order and Symbolic Computation
, 2006
"... Abstract. In this paper, we survey some wellknown approaches proposed as general models for calculi dealing with names (like e.g. process calculi with namepassing). We focus on (pre)sheaf categories, nominal sets, permutation algebras and named sets. We study the relationships among these models, w ..."
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Cited by 10 (2 self)
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Abstract. In this paper, we survey some wellknown approaches proposed as general models for calculi dealing with names (like e.g. process calculi with namepassing). We focus on (pre)sheaf categories, nominal sets, permutation algebras and named sets. We study the relationships among these models, which allow for transferring techniques and constructions from one model to the other.
Mathematical models of computational and combinatorial structures. Invited address for Foundations
 of Software Science and Computation Structures (FOSSACS 2005
, 2005
"... Abstract. The general aim of this talk is to advocate a combinatorial perspective, together with its methods, in the investigation and study of models of computation structures. This, of course, should be taken in conjunction with the wellestablished views and methods stemming from algebra, category ..."
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Cited by 9 (3 self)
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Abstract. The general aim of this talk is to advocate a combinatorial perspective, together with its methods, in the investigation and study of models of computation structures. This, of course, should be taken in conjunction with the wellestablished views and methods stemming from algebra, category theory, domain theory, logic, type theory, etc. In support of this proposal I will show how such an approach leads to interesting connections between various areas of computer science and mathematics; concentrating on one such example in some detail. Specifically, I will consider the line of my research involving denotational models of the pi calculus and algebraic theories with variablebinding operators, indicating how the abstract mathematical structure underlying these models fits with that of Joyal’s combinatorial species of structures. This analysis suggests both the unification and generalisation of models, and in the latter vein I will introduce generalised species of structures and their calculus. These generalised species encompass and generalise various of the notions of species used in combinatorics. Furthermore, they have a rich mathematical structure (akin to models of Girard’s linear logic) that can be described purely within Lawvere’s generalised logic. Indeed, I will present and treat the cartesian closed structure, the linear structure, the differential structure, etc. of generalised species axiomatically in this mathematical framework. As an upshot, I will observe that the setting allows for interpretations of computational calculi (like the lambda calculus, both typed and untyped; the recently introduced differential lambda calculus of Ehrhard and Regnier; etc.) that can be directly seen as translations into a more basic elementary calculus of interacting agents that compute by communicating and operating upon structured data.