Resource Transition Systems and Full Abstraction for Linear Higher-Order Effectful Programs

International audienceWe investigate program equivalence for linear higher-order (sequential) languages endowed with primitives for computational effects. More specifically, we study operationally-based notions of program equivalence for a linear λ-calculus with explicit copying and algebraic effects à la Plotkin and Power. Such a calculus makes explicit the interaction between copying and linearity, which are intensional aspects of computation, with effects, which are, instead, extensional. We review some of the notions of equivalences for linear calculi proposed in the literature and show their limitations when applied to effectful calculi where copying is a first-class citizen. We then introduce resource transition systems, namely transition systems whose states are built over tuples of programs representing the available resources, as an operational semantics accounting for both intensional and extensional interactive behaviours of programs. Our main result is a sound and complete characterization of contextual equivalence as trace equivalence defined on top of resource transition systems

Resource transition systems and full abstraction for linear higher-order effectful programs

We investigate program equivalence for linear higher-order (sequential) languages endowed with primitives for computational effects. More specifically, we study operationally-based notions of program equivalence for a linear \u3b3-calculus with explicit copying and algebraic effects \ue0 la Plotkin and Power. Such a calculus makes explicit the interaction between copying and linearity, which are intensional aspects of computation, with effects, which are, instead, extensional. We review some of the notions of equivalences for linear calculi proposed in the literature and show their limitations when applied to effectful calculi where copying is a first-class citizen. We then introduce resource transition systems, namely transition systems whose states are built over tuples of programs representing the available resources, as an operational semantics accounting for both intensional and extensional interactive behaviours of programs. Our main result is a sound and complete characterization of contextual equivalence as trace equivalence defined on top of resource transition systems

Resource Transition Systems and Full Abstraction for Linear Higher-Order Effectful Programs

International audienceWe investigate program equivalence for linear higher-order (sequential) languages endowed with primitives for computational effects. More specifically, we study operationally-based notions of program equivalence for a linear λ-calculus with explicit copying and algebraic effects à la Plotkin and Power. Such a calculus makes explicit the interaction between copying and linearity, which are intensional aspects of computation, with effects, which are, instead, extensional. We review some of the notions of equivalences for linear calculi proposed in the literature and show their limitations when applied to effectful calculi where copying is a first-class citizen. We then introduce resource transition systems, namely transition systems whose states are built over tuples of programs representing the available resources, as an operational semantics accounting for both intensional and extensional interactive behaviours of programs. Our main result is a sound and complete characterization of contextual equivalence as trace equivalence defined on top of resource transition systems

Abstract Semantics by Observable Contexts

The operational behavior of interactive systems is usually given in terms of transition systems labeled with actions, which, when visible, represent both observations and interactions with the external world. The abstract semantics is given in terms of behavioral equivalences, which depend on the action labels and on the amount of branching structure considered. Behavioural equivalences are often congruences with respect to the operations of the language, and this property expresses the compositionality of the abstract semantics. A simpler approach, inspired by classical formalisms like pi-calculus, Petri nets, term and graph rewriting, and pioneered by the Chemical Abstract Machine [13], defines operational semantics by means of structural axioms and reaction rules. Process calculi representing complex systems, in particular those able to generate and communicate names, are often defined in this way, since structural axioms give a clear idea of the intended structure of the states while reaction rules, which are often non-conditional, give a direct account of the possible steps. Transitions caused by reaction rules, however, are not labeled, since they represent evolutions of the system without interactions with the external world. Thus reduction semantics in itself is neither abstract nor compositional. One standard solution, pioneered in [89], is that of defining a saturated transition system as follows: a process p can do a move with label C[-] and become q, iff C[p]--> q. Saturated semantics, i.e., the abstract semantics defined over the saturated transition system, are always congruences, but they are usually untractable since they have to tackle all possible contexts of which there are usually an infinite number. Moreover, in several paradigmatic cases, saturated semantics are too coarse. For example, in Milner's Calculus of Communicating Systems (CCS), saturated bisimilarity cannot distinguish "always divergent processes" and for this reason Milner and Sangiorgi introduced barbs. These are observations on the states representing the ability to interact over some channels. Sewell introduced a different approach that consists in deriving a transition system where labels are not all contexts but just the minimal ones allowing a system to reach a rule. In such a way, one obtains two advantages: firstly one avoids considering all contexts, and secondly, labels precisely represent interactions, i.e., the portion of environment that is really needed to react. This idea was then refined by Leifer and Milner in the theory of reactive systems, where the categorical notion of idem relative pushout precisely captures this idea of minimal context. In this thesis, we show that in some cases this approach works well (e.g., CCS) but often, the resulting abstract semantics are too strict. In our opinion, they are not really observational since the observer can know exactly how much structure a process needs to reach a specific rule, and thus the observation depends on the rules. One result of the thesis is that of providing evidence of this through several interesting formalisms modeled as reactive systems: Logic Programming, a fragment of open pi-calculus, and an interactive version of Petri nets. Moreover, we introduce two alternative definitions of bisimilarity that efficiently characterize saturated bisimilarity, namely semi-saturated bisimilarity and symbolic bisimilarity. These allow us to reason about saturated semantics without considering all contexts, but saturated semantics are in several cases too coarse. In order to have a framework that is suitable for many formalisms, we add to the above approach observations. Indeed, in our opinion, labels cannot represent both interactions and observations, because these two concepts are in general different, like for example, in the asynchronous calculi where receiving is not observable. Thus, we believe that some notion of observation, either on transitions or on states (e.g. barbs), is necessary. A further result of the thesis is that of providing a generalization of the above theory starting not just from purely reaction rules, but from transition systems labeled with observations. Here we can easily reuse saturated transition systems by defining them as follows: a process p can do a move with context C[-] and observation o and become q iff C[p] --o--> q. Again, saturated semantics, i.e. abstract semantics defined over the above transition systems, are congruences. Analogously to the case of reactive systems, we can define semi-saturated bisimilarity and symbolic bisimilarity as efficient characterizations of saturated semantics. The definition of symbolic bisimilarity which arises from this generalization is similar to the abstract semantics of several works. Here we consider open and asynchronous pi-calculus, by showing that their abstract semantics are instances of our general concepts of saturated and symbolic semantics. We also apply our approach to open Petri nets (that are an interactive version of P/T Petri nets) obtaining a new symbolic semantics for them, that efficiently characterizes their abstract semantics. We round up the thesis with a coalgebraic characterization for saturated, semi-saturated and symbolic bisimilarity. Universal Coalgebra provides a categorical framework where abstract semantics of interactive systems are described as morphisms to their minimal representatives. More precisely, if the category of coalgebras has final object 1, then the unique morphisms from a certain coalgebra to 1 equates all the bisimilar states. In other words, the final object can be seen as a universe of abstract behaviors and the unique morphism as a function assigning to each system its abstract behavior. This characterization of abstract semantics is not only theoretically interesting, but also pragmat- ically useful, since it suggests an algorithm which can check the equivalence: one computes the image of some coalgebras through the unique morphism (that for the finite lts corresponds to the list partitioning algorithm by Kanellakis and Smolka), and these coalgebras are behaviorally equivalent if their images are the same. Ordinary labeled transition systems can be represented as coalgebras, and the resulting abstract semantics exactly coincides with canonical bisimilarity. Then, providing a coalgebraic characterization of saturated bisimilarity is almost straightforward. The case of semi-saturated and symbolic bisimilarities are more complicated because their definitions are asymmetric. In order to properly characterizes semi-saturated and symbolic cases, we first introduce a new notion of redundancy on transitions and then normalized coalgebras: a special kind of coalgebras without redundant transitions. We prove that the category of normalized coalgebras is isomorphic to the category of saturated coalgebras (the coalgebras containing all the redundant transitions), where the large saturated transition system can be directly modelled. In doing this, we use the notions of normalization that throws away all the redundant transitions, and of saturation that adds all the redundant transitions. Both are natural transformations between the endofunctors (defining the two categories of coalgebras) and one is the inverse of the other. As a corollary of the isomorphism theorem, saturated bisimilarity can be characterized as bisimilarity in the category of normalized coalgebras, i.e., abstracting away from redundant transitions. This is interesting because, on the one hand, it provides us with a canonical representatives for ~S without redundant transitions (and then much smaller with respect to the saturated ones), on the other hand, it suggests a minimization algorithm for "efficiently" computing ~S

Accounting for 'disclosure': Lesbian parents' identity management in home and school contexts.

This qualitative research explores working-class (educated) lesbian parents' identity management strategies within home and school contexts. Following an evaluation of epistemological debates and social science approaches to theorizing 'self, I highlight the utility of a feminist social constructionist approach to research, and the centrality of language and discourse in the constitution of lesbian parents' subjectivities. This work is informed by poststructuralist, feminist and psychological theories of identity and subjectivity and I take a 'relational approach' to explore ways in which historically and culturally specific ideologies and discourses of sexuality, family and parenting shape lesbian parents' discursive practices and subjectivities. Seven working-class (educated) lesbian parents from the north-east of England took part in interviews about their lesbian parent families and their interactions with their children, friends, family and school staff to explore how lesbian parents talk about their lesbian parent identity and disclosure/concealment of their sexuality. Specifically, a discursive analytic approach was utilized to explore lesbian parents' accounts for disclosure/concealment of their sexual identity and of their lesbian parenting/families, within home-school contexts. From this investigation I identified a key interpretative repertoire: 'sexuality as a form of knowledge' that the women used to construct homosexuality as normal, dangerous, private and progressive. A key finding from this investigation is the discursive strategy of 'positioning others' within constructions of sexuality. Interactive positioning functioned to rationalize accounts for disclosure or concealment of the women's sexuality at different discursive moments and contexts. I problematize existing essentialist models of 'coming out' and highlight how disclosure/concealment of sexual identity can be theorized as an 'accountable' activity which acknowledges the synthesis of culture and subjectivity at the point of discourse. This work also acknowledges ways in which class subjectivity can shape lesbian parents' discursive practices in their negotiation of 'difference'