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Statedependent representation independence
 In Proceedings of the 36th ACM SIGPLANSIGACT Symposium on Principles of Programming Languages
, 2009
"... Mitchell’s notion of representation independence is a particularly useful application of Reynolds ’ relational parametricity — two different implementations of an abstract data type can be shown contextually equivalent so long as there exists a relation between their type representations that is pre ..."
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Cited by 88 (24 self)
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Mitchell’s notion of representation independence is a particularly useful application of Reynolds ’ relational parametricity — two different implementations of an abstract data type can be shown contextually equivalent so long as there exists a relation between their type representations that is preserved by their operations. There have been a number of methods proposed for proving representation independence in various pure extensions of System F (where data abstraction is achieved through existential typing), as well as in Algol or Javalike languages (where data abstraction is achieved through the use of local mutable state). However, none of these approaches addresses the interaction of existential type abstraction and local state. In particular, none allows one to prove representation independence results for generative ADTs — i.e., ADTs that both maintain some local state and define abstract types whose internal
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 56 (16 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.
A Kripke Logical Relation Between ML and Assembly
"... There has recently been great progress in proving the correctness of compilers for increasingly realistic languages with increasingly realistic runtime systems. Most work on this problem has focused on proving the correctness of a particular compiler, leaving open the question of how to verify the c ..."
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There has recently been great progress in proving the correctness of compilers for increasingly realistic languages with increasingly realistic runtime systems. Most work on this problem has focused on proving the correctness of a particular compiler, leaving open the question of how to verify the correctness of assembly code that is handoptimized or linked together from the output of multiple compilers. This has led Benton and other researchers to propose more abstract, compositional notions of when a lowlevel program correctly realizes a highlevel one. However, the state of the art in socalled “compositional compiler correctness ” has only considered relatively simple highlevel and lowlevel languages. In this paper, we propose a novel, extensional, compilerindependent notion of equivalence between highlevel programs in an expressive, impure MLlike λcalculus and lowlevel programs in an (only slightly) idealized assembly language. We define this equivalence by means of a biorthogonal, stepindexed, Kripke logical relation, which enables us to reason quite flexibly about assembly code that uses local state in a different manner than the highlevel code it implements (e.g., selfmodifying code). In contrast to prior work, we factor our relation in a symmetric, languagegeneric fashion, which helps to simplify and clarify the formal presentation, and we also show how to account for the presence of a garbage collector. Our approach relies on recent developments in Kripke logical relations for MLlike languages, in particular the idea of possible worlds as state transition systems. 1.
A Stepindexed Semantics of Imperative Objects
"... Stepindexed semantic models of types were proposed as an alternative to purely syntactic proofs of type safety using subject reduction. Building on work by Ahmed, Appel and others, we introduce a stepindexed model for the imperative object calculus of Abadi and Cardelli. Providing a semantic accou ..."
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Cited by 7 (0 self)
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Stepindexed semantic models of types were proposed as an alternative to purely syntactic proofs of type safety using subject reduction. Building on work by Ahmed, Appel and others, we introduce a stepindexed model for the imperative object calculus of Abadi and Cardelli. Providing a semantic account of this calculus using more ‘traditional’, domaintheoretic approaches has proved challenging due to the combination of dynamically allocated objects, higherorder store, and an expressive type system. Here we show that the stepindexed model can interpret a rich type discipline with object types, subtyping, recursive and bounded quantified types in the presence of state.
A STEPINDEXED SEMANTICS OF IMPERATIVE OBJECTS ∗
, 2009
"... Vol. 5 (4:2) 2009, pp. 1–48 ..."
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