44,805 research outputs found
Using Session Types for Reasoning About Boundedness in the Pi-Calculus
The classes of depth-bounded and name-bounded processes are fragments of the
pi-calculus for which some of the decision problems that are undecidable for
the full calculus become decidable. P is depth-bounded at level k if every
reduction sequence for P contains successor processes with at most k active
nested restrictions. P is name-bounded at level k if every reduction sequence
for P contains successor processes with at most k active bound names.
Membership of these classes of processes is undecidable. In this paper we use
binary session types to decise two type systems that give a sound
characterization of the properties: If a process is well-typed in our first
system, it is depth-bounded. If a process is well-typed in our second, more
restrictive type system, it will also be name-bounded.Comment: In Proceedings EXPRESS/SOS 2017, arXiv:1709.0004
Strong normalization of lambda-Sym-Prop- and lambda-bar-mu-mu-tilde-star- calculi
In this paper we give an arithmetical proof of the strong normalization of
lambda-Sym-Prop of Berardi and Barbanera [1], which can be considered as a
formulae-as-types translation of classical propositional logic in natural
deduction style. Then we give a translation between the
lambda-Sym-Prop-calculus and the lambda-bar-mu-mu-tilde-star-calculus, which is
the implicational part of the lambda-bar-mu-mu-tilde-calculus invented by
Curien and Herbelin [3] extended with negation. In this paper we adapt the
method of David and Nour [4] for proving strong normalization. The novelty in
our proof is the notion of zoom-in sequences of redexes, which leads us
directly to the proof of the main theorem
Wave-Style Token Machines and Quantum Lambda Calculi
Particle-style token machines are a way to interpret proofs and programs,
when the latter are written following the principles of linear logic. In this
paper, we show that token machines also make sense when the programs at hand
are those of a simple quantum lambda-calculus with implicit qubits. This,
however, requires generalising the concept of a token machine to one in which
more than one particle travel around the term at the same time. The presence of
multiple tokens is intimately related to entanglement and allows us to give a
simple operational semantics to the calculus, coherently with the principles of
quantum computation.Comment: In Proceedings LINEARITY 2014, arXiv:1502.0441
A Type System for a Stochastic CLS
The Stochastic Calculus of Looping Sequences is suitable to describe the
evolution of microbiological systems, taking into account the speed of the
described activities. We propose a type system for this calculus that models
how the presence of positive and negative catalysers can modify these speeds.
We claim that types are the right abstraction in order to represent the
interaction between elements without specifying exactly the element positions.
Our claim is supported through an example modelling the lactose operon
Session Types as Generic Process Types
Behavioural type systems ensure more than the usual safety guarantees of
static analysis. They are based on the idea of "types-as-processes", providing
dedicated type algebras for particular properties, ranging from protocol
compatibility to race-freedom, lock-freedom, or even responsiveness. Two
successful, although rather different, approaches, are session types and
process types. The former allows to specify and verify (distributed)
communication protocols using specific type (proof) systems; the latter allows
to infer from a system specification a process abstraction on which it is
simpler to verify properties, using a generic type (proof) system. What is the
relationship between these approaches? Can the generic one subsume the specific
one? At what price? And can the former be used as a compiler for the latter?
The work presented herein is a step towards answers to such questions.
Concretely, we define a stepwise encoding of a pi-calculus with sessions and
session types (the system of Gay and Hole) into a pi-calculus with process
types (the Generic Type System of Igarashi and Kobayashi). We encode session
type environments, polarities (which distinguish session channels end-points),
and labelled sums. We show forward and reverse operational correspondences for
the encodings, as well as typing correspondences. To faithfully encode session
subtyping in process types subtyping, one needs to add to the target language
record constructors and new subtyping rules. In conclusion, the programming
convenience of session types as protocol abstractions can be combined with the
simplicity and power of the pi-calculus, taking advantage in particular of the
framework provided by the Generic Type System.Comment: In Proceedings EXPRESS/SOS 2014, arXiv:1408.127
Reversible Multiparty Sessions with Checkpoints
Reversible interactions model different scenarios, like biochemical systems
and human as well as automatic negotiations. We abstract interactions via
multiparty sessions enriched with named checkpoints. Computations can either go
forward or roll back to some checkpoints, where possibly different choices may
be taken. In this way communications can be undone and different conversations
may be tried. Interactions are typed with global types, which control also
rollbacks. Typeability of session participants in agreement with global types
ensures session fidelity and progress of reversible communications.Comment: In Proceedings EXPRESS/SOS 2016, arXiv:1608.0269
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