500 research outputs found
Process Realizability
We develop a notion of realizability for Classical Linear Logic based on a
concurrent process calculus.Comment: Appeared in Foundations of Secure Computation: Proceedings of the
1999 Marktoberdorf Summer School, F. L. Bauer and R. Steinbruggen, eds. (IOS
Press) 2000, 167-18
Explicit connection actions in multiparty session types
This work extends asynchronous multiparty session types (MPST) with explicit connection actions to support protocols with op- tional and dynamic participants. The actions by which endpoints are connected and disconnected are a key element of real-world protocols that is not treated in existing MPST works. In addition, the use cases motivating explicit connections often require a more relaxed form of mul- tiparty choice: these extensions do not satisfy the conservative restric- tions used to ensure safety in standard syntactic MPST. Instead, we de- velop a modelling-based approach to validate MPST safety and progress for these enriched protocols. We present a toolchain implementation, for distributed programming based on our extended MPST in Java, and a core formalism, demonstrating the soundness of our approach. We discuss key implementation issues related to the proposed extensions: a practi- cal treatment of choice subtyping for MPST progress, and multiparty correlation of dynamic binary connections
Realizability Toposes from Specifications
We investigate a framework of Krivine realizability with I/O effects, and
present a method of associating realizability models to specifications on the
I/O behavior of processes, by using adequate interpretations of the central
concepts of `pole' and `proof-like term'. This method does in particular allow
to associate realizability models to computable functions.
Following recent work of Streicher and others we show how these models give
rise to triposes and toposes
Lewis meets Brouwer: constructive strict implication
C. I. Lewis invented modern modal logic as a theory of "strict implication".
Over the classical propositional calculus one can as well work with the unary
box connective. Intuitionistically, however, the strict implication has greater
expressive power than the box and allows to make distinctions invisible in the
ordinary syntax. In particular, the logic determined by the most popular
semantics of intuitionistic K becomes a proper extension of the minimal normal
logic of the binary connective. Even an extension of this minimal logic with
the "strength" axiom, classically near-trivial, preserves the distinction
between the binary and the unary setting. In fact, this distinction and the
strong constructive strict implication itself has been also discovered by the
functional programming community in their study of "arrows" as contrasted with
"idioms". Our particular focus is on arithmetical interpretations of the
intuitionistic strict implication in terms of preservativity in extensions of
Heyting's Arithmetic.Comment: Our invited contribution to the collection "L.E.J. Brouwer, 50 years
later
Recommended from our members
Mathematical Logic: Proof Theory, Constructive Mathematics
The workshop “Mathematical Logic: Proof Theory, Constructive Mathematics” was centered around proof-theoretic aspects of core mathematics and theoretical computer science as well as homotopy type theory and logical aspects of computational complexity
Parameterized Concurrent Multi-Party Session Types
Session types have been proposed as a means of statically verifying
implementations of communication protocols. Although prior work has been
successful in verifying some classes of protocols, it does not cope well with
parameterized, multi-actor scenarios with inherent asynchrony. For example, the
sliding window protocol is inexpressible in previously proposed session type
systems. This paper describes System-A, a new typing language which overcomes
many of the expressiveness limitations of prior work. System-A explicitly
supports asynchrony and parallelism, as well as multiple forms of
parameterization. We define System-A and show how it can be used for the static
verification of a large class of asynchronous communication protocols.Comment: In Proceedings FOCLASA 2012, arXiv:1208.432
Extracting total Amb programs from proofs
We present a logical system CFP (Concurrent Fixed Point Logic) supporting the
extraction of nondeterministic and concurrent programs that are provably total
and correct. CFP is an intuitionistic first-order logic with inductive and
coinductive definitions extended by two propositional operators: Rrestriction,
a strengthening of implication, and an operator for total concurrency. The
source of the extraction are formal CFP proofs, the target is a lambda calculus
with constructors and recursion extended by a constructor Amb (for McCarthy's
amb) which is interpreted operationally as globally angelic choice and is used
to implement nondeterminism and concurrency. The correctness of extracted
programs is proven via an intermediate domain-theoretic denotational semantics.
We demonstrate the usefulness of our system by extracting a nondeterministic
program that translates infinite Gray code into the signed digit
representation. A noteworthy feature of CFP is the fact that the proof rules
for restriction and concurrency involve variants of the classical law of
excluded middle that would not be interpretable computationally without Amb.Comment: 39 pages + 4 pages appendix. arXiv admin note: text overlap with
arXiv:2104.1466
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