Step-Indexed Relational Reasoning for Countable Nondeterminism

Programming languages with countable nondeterministic choice are computationally interesting since countable nondeterminism arises when modeling fairness for concurrent systems. Because countable choice introduces non-continuous behaviour, it is well-known that developing semantic models for programming languages with countable nondeterminism is challenging. We present a step-indexed logical relations model of a higher-order functional programming language with countable nondeterminism and demonstrate how it can be used to reason about contextually defined may- and must-equivalence. In earlier step-indexed models, the indices have been drawn from {\omega}. Here the step-indexed relations for must-equivalence are indexed over an ordinal greater than {\omega}

First steps in synthetic guarded domain theory: step-indexing in the topos of trees

We present the topos S of trees as a model of guarded recursion. We study the internal dependently-typed higher-order logic of S and show that S models two modal operators, on predicates and types, which serve as guards in recursive definitions of terms, predicates, and types. In particular, we show how to solve recursive type equations involving dependent types. We propose that the internal logic of S provides the right setting for the synthetic construction of abstract versions of step-indexed models of programming languages and program logics. As an example, we show how to construct a model of a programming language with higher-order store and recursive types entirely inside the internal logic of S. Moreover, we give an axiomatic categorical treatment of models of synthetic guarded domain theory and prove that, for any complete Heyting algebra A with a well-founded basis, the topos of sheaves over A forms a model of synthetic guarded domain theory, generalizing the results for S

Relational Parametricity for Computational Effects

According to Strachey, a polymorphic program is parametric if it applies a uniform algorithm independently of the type instantiations at which it is applied. The notion of relational parametricity, introduced by Reynolds, is one possible mathematical formulation of this idea. Relational parametricity provides a powerful tool for establishing data abstraction properties, proving equivalences of datatypes, and establishing equalities of programs. Such properties have been well studied in a pure functional setting. Many programs, however, exhibit computational effects, and are not accounted for by the standard theory of relational parametricity. In this paper, we develop a foundational framework for extending the notion of relational parametricity to programming languages with effects.Comment: 31 pages, appears in Logical Methods in Computer Scienc

Fifty years of Hoare's Logic

We present a history of Hoare's logic.Comment: 79 pages. To appear in Formal Aspects of Computin

Non uniform (hyper/multi)coherence spaces

In (hyper)coherence semantics, proofs/terms are cliques in (hyper)graphs. Intuitively, vertices represent results of computations and the edge relation witnesses the ability of being assembled into a same piece of data or a same (strongly) stable function, at arrow types. In (hyper)coherence semantics, the argument of a (strongly) stable functional is always a (strongly) stable function. As a consequence, comparatively to the relational semantics, where there is no edge relation, some vertices are missing. Recovering these vertices is essential for the purpose of reconstructing proofs/terms from their interpretations. It shall also be useful for the comparison with other semantics, like game semantics. In [BE01], Bucciarelli and Ehrhard introduced a so called non uniform coherence space semantics where no vertex is missing. By constructing the co-free exponential we set a new version of this last semantics, together with non uniform versions of hypercoherences and multicoherences, a new semantics where an edge is a finite multiset. Thanks to the co-free construction, these non uniform semantics are deterministic in the sense that the intersection of a clique and of an anti-clique contains at most one vertex, a result of interaction, and extensionally collapse onto the corresponding uniform semantics.Comment: 32 page

Identity ambiguity and the promises and practices of hybrid e-HRM project teams

The role of IS project team identity work in the enactment of day-to-day relationships with their internal clients is under-researched. We address this gap by examining the identity work undertaken by an electronic human resource management (e-HRM) 'hybrid' project team engaged in an enterprise-wide IS implementation for their multi-national organisation. Utilising social identity theory, we identify three distinctive, interrelated dimensions of project team identity work (project team management, team 'value propositions' (promises) and the team's 'knowledge practice'). We reveal how dissonance between two perspectives of e-HRM project identity work (clients' expected norms of project team's service and project team's expected norms of themselves) results in identity ambiguity. Our research contributions are to identity studies in the IS project management, HR and hybrid literatures and to managerial practice by challenging the assumption that hybrid experts are the panacea for problems associated with IS projects

Typed feature structures, definite equivalences, greatest model semantics, and nonmonotonicity

Typed feature logics have been employed as description languages in modern type-oriented grammar theories like HPSG and have laid the theoretical foundations for many implemented systems. However, recursivity pose severe problems and have been addressed through specialized powerdomain constructions which depend on the particular view of the logician. In this paper, we argue that definite equivalences introduced by Smolka can serve as the formal basis for arbitrarily formalized typed feature structures and typed feature-based grammars/lexicons, as employed in, e.g., TFS or TDL. The idea here is that type definitions in such systems can be transformed into an equivalent definite program, whereas the meaning of the definite program then is identified with the denotation of the type system. Now, models of a definite program P can be characterized by the set of ground atoms which are logical consequences of the definite program. These models are ordered by subset inclusion and, for reasons that will become clear, we propose the greatest model as the intended interpretation of P, or equivalent, as the denotation of the associated type system. Our transformational approach has also a great impact on nonmonotonically defined types, since under this interpretation, we can view the type hierarchy as a pure transport medium, allowing us to get rid of the transitivity of type information (inheritance), and yielding a perfectly monotonic definite program

Fruits of Gregory Bateson’s epistemological crisis: embodied mind-making and interactive experience in research and professional praxis

Background: The espoused rationale for this special issue, situated “at the margins of cybernetics,” was to revisit and extend the common genealogy of cybernetics and communication studies. Two possible topics garnered our attention: 1) the history of intellectual adventurers whose work has appropriated cybernetic concepts; and 2) the remediation of cybernetic metaphors. Analysis: A heuristic for engaging in first- and second-order R&D praxis, the design of which was informed by co-research with pastoralists (1989–1993) and the authors’ engagements with the scholarship of Bateson and Maturana, was employed and adapted as a reflexive in-quiry framework.Conclusion and implications: This inquiry challenges the mainstream desire for change and the belief in getting the communication right in order to achieve change. The authors argue this view is based on an epistemological error that continues to produce the very problems it intends to diminish, and thus we live a fundamental error in epistemology, false ontology, and misplaced practice. The authors offer instead conceptual and praxis possibilities for triggering new co-evolutionary trajectories