2,274 research outputs found
A dependent nominal type theory
Nominal abstract syntax is an approach to representing names and binding
pioneered by Gabbay and Pitts. So far nominal techniques have mostly been
studied using classical logic or model theory, not type theory. Nominal
extensions to simple, dependent and ML-like polymorphic languages have been
studied, but decidability and normalization results have only been established
for simple nominal type theories. We present a LF-style dependent type theory
extended with name-abstraction types, prove soundness and decidability of
beta-eta-equivalence checking, discuss adequacy and canonical forms via an
example, and discuss extensions such as dependently-typed recursion and
induction principles
Descriptive complexity for pictures languages (extended abstract)
This paper deals with descriptive complexity of picture languages of any
dimension by syntactical fragments of existential second-order logic.
- We uniformly generalize to any dimension the characterization by
Giammarresi et al. \cite{GRST96} of the class of \emph{recognizable} picture
languages in existential monadic second-order logic. - We state several logical
characterizations of the class of picture languages recognized in linear time
on nondeterministic cellular automata of any dimension. They are the first
machine-independent characterizations of complexity classes of cellular
automata.
Our characterizations are essentially deduced from normalization results we
prove for first-order and existential second-order logics over pictures. They
are obtained in a general and uniform framework that allows to extend them to
other "regular" structures. Finally, we describe some hierarchy results that
show the optimality of our logical characterizations and delineate their
limits.Comment: 33 pages - Submited to Lics 201
The Session Abstract Machine (Extended Version)
We build on a fine-grained analysis of session-based interaction as provided
by the linear logic typing disciplines to introduce the SAM, an abstract
machine for mechanically executing session-typed processes. A remarkable
feature of the SAM's design is its ability to naturally segregate and
coordinate sequential with concurrent session behaviours. In particular,
implicitly sequential parts of session programs may be efficiently executed by
deterministic sequential application of SAM transitions, amenable to
compilation, and without concurrent synchronisation mechanisms. We provide an
intuitive discussion of the SAM structure and its underlying design, and state
and prove its correctness for executing programs in a session calculus
corresponding to full classical linear logic CLL. We also discuss extensions
and applications of the SAM to the execution of linear and session-based
programming languages.Comment: Extended Version of ESOP pape
Musings on Encodings and Expressiveness
This paper proposes a definition of what it means for one system description
language to encode another one, thereby enabling an ordering of system
description languages with respect to expressive power. I compare the proposed
definition with other definitions of encoding and expressiveness found in the
literature, and illustrate it on a case study: comparing the expressive power
of CCS and CSP.Comment: In Proceedings EXPRESS/SOS 2012, arXiv:1208.244
Core higher-order session processes: tractable equivalences and relative expressiveness
This work proposes tractable bisimulations for the higher-order - calculus with session primitives (HO ) and o ers a complete study of the expressivity of its most significant subcalculi. First we develop three typed bisimulations, which are shown to coincide with contextual equivalence. These characterisations demonstrate that observing as inputs only a specific finite set of higher-order values (which inhabit session types) su ces to reason about HO processes. Next, we identify HO, a minimal, second-order subcalculus of HO in which higher-order applications/abstractions, name-passing, and recursion are absent. We show that HO can encode HO extended with higher-order applications and abstractions and that a first-order session -calculus can encode HO . Both encodings are fully abstract. We also prove that the session -calculus with passing of shared names cannot be encoded into HO without shared names. We show that HO , HO, and are equally expressive; the expressivity of HO enables e ective reasoning about typed equivalences for higher-order processes
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