Limitations of Applicative Bisimulation (Preliminary Report)

We present a series of examples that illuminate an important aspect of the semantics of higher-order functions with local state. Namely that certain behaviour of such functions can only be observed by pro- viding them with arguments that contain the functions themselves. This provides evidence for the necessity of complex conditions for functions in modern semantics for state, such as logical relations and Kripke-like bisimulations, where related functions are applied to related arguments (that may contain the functions). It also suggests that simpler semantics, such as those based on applicative bisimulations where functions are ap- plied to identical arguments, would not scale to higher-order languages with local state

Environmental Bisimulations for Delimited-Control Operators with Dynamic Prompt Generation

International audienceWe present sound and complete environmental bisimilarities for a variant of Dybvig et al.'s calculus of multi-prompted delimited-control operators with dynamic prompt generation. The reasoning principles that we obtain generalize and advance the existing techniques for establishing program equivalence in calculi with single-prompted delimited control. The basic theory that we develop is presented using Madiot et al.'s framework that allows for smooth integration and composition of up-to techniques facilitating bisimulation proofs. We also generalize the framework in order to express environmental bisimulations that support equivalence proofs of evaluation contexts representing continuations. This change leads to a novel and powerful up-to technique enhancing bisimulation proofs in the presence of control operators

Environmental Bisimulations for Probabilistic Higher-Order Languages

International audienceEnvironmental bisimulations for probabilistic higher-order languages are studied. In contrast with applicative bisimulations, environmental bisimulations are known to be more robust and do not require sophisticated techniques such as Howe's in the proofs of congruence. As representative calculi, call-by-name and call-by-value λ-calculus, and a (call-by-value) λ-calculus extended with references (i.e., a store) are considered. In each case full abstraction results are derived for probabilistic environmental similarity and bisimilarity with respect to contextual preorder and contextual equivalence, respectively. Some possible enhancements of the (bi)simulations, as 'up-to techniques', are also presented. Probabilities force a number of modifications to the definition of environmental bisimulations in non-probabilistic languages. Some of these modifications are specific to probabilities, others may be seen as general refinements of environmental bisimulations, applicable also to non-probabilistic languages. Several examples are presented, to illustrate the modifications and the differences

Environmental bisimulations for probabilistic higher-order languages

Environmental bisimulations for probabilistic higher-order languages are studied. In contrastwith applicative bisimulations, environmental bisimulations are known to be more robust and do not require sophisticated techniques such as Howe's in the proofs of congruence. As representative calculi, call-by-name and call-by-value λ-calculus, and a (call-by-value) λ-calculus extended with references (i.e., a store) are considered. In each case, full abstraction results are derived for probabilistic environmental similarity and bisimilarity with respect to contextual preorder and contextual equivalence, respectively. Some possible enhancements of the (bi)simulations, as "up-to techniques," are also presented. Probabilities force a number of modifications to the definition of environmental bisimulations in nonprobabilistic languages. Some of thesemodifications are specific to probabilities, others may be seen as general refinements of environmental bisimulations, applicable also to non-probabilistic languages. Several examples are presented, to illustrate the modifications and the differences

Bisimulations for Delimited-Control Operators

We present a comprehensive study of the behavioral theory of an untyped $\lambda$-calculus extended with the delimited-control operators shift and reset. To that end, we define a contextual equivalence for this calculus, that we then aim to characterize with coinductively defined relations, called bisimilarities. We consider different styles of bisimilarities (namely applicative, normal-form, and environmental) within a unifying framework, and we give several examples to illustrate their respective strengths and weaknesses. We also discuss how to extend this work to other delimited-control operators

Refactoring and representation independence for class hierarchies

AbstractRefactoring transformations are important for productivity and quality in software evolution. Modular reasoning about semantics preserving transformations is difficult even in typed class-based languages because transformations can change the internal representations for multiple interdependent classes and because encapsulation can be violated by pointers to mutable objects. In this paper, an existing theory of representation independence for a single class, based on a simple notion of ownership confinement, is generalized to a hierarchy of classes and used to prove refactoring rules that embody transformations of complete class trees. This allows us to formalize refactorings that inherently involve class inheritance, such as Pull Up or Push Down Field; moreover, this makes it possible to generalize refactorings previously restricted to change of data representation of private attributes (like Extract Class and Encapsulate Field) to address data refinement of protected attributes, dealing with the impact that the corresponding transformations may cause in the subclasses. The utility of the proposed rules is shown in a relatively extensive case study. Shortcomings of the theory are described as a challenge to other approaches to heap encapsulation and relational reasoning for classes