143 research outputs found
The heart of intersection type assignment: Normalisation proofs revisited
AbstractThis paper gives a new proof for the approximation theorem and the characterisation of normalisability using intersection types for a system with ‘w and a ≤-relation that is contra-variant over arrow types. The technique applied is to define reduction on derivations and to show a strong normalisation result for this reduction. From this result, the characterisation of strong normalisation and the approximation result will follow easily; the latter, in its turn, will lead to the characterisation of (head) normalisability
The Heart of Intersection Type Assignment
This paper gives a new proof for the approximation theorem and the characterisation of normalisability using intersection types. The technique applied is to define reduction on derivations and to show a strong normalisation result for this reduction. From this result, the characterisation of strong normalisation and the approximation result will follow easily; the latter, in its turn, will lead to the characterisation of (head-)normalisability
The Heart of Intersection Type Assignment
This paper gives a new proof for the approximation theorem and the characterisation of normalisability using intersection types. The technique applied is to define reduction on derivations and to show a strong normalisation result for this reduction. From this result, the characterisation of strong normalisation and the approximation result will follow easily; the latter, in its turn, will lead to the characterisation of (head-)normalisability
Adding Negation to Lambda Mu
We present , an extension of Parigot's -calculus by
adding negation as a type constructor, together with syntactic constructs that
represent negation introduction and elimination. We will define a notion of
reduction that extends 's reduction system with two new reduction
rules, and show that the system satisfies subject reduction. Using Aczel's
generalisation of Tait and Martin-L\"of's notion of parallel reduction, we show
that this extended reduction is confluent. Although the notion of type
assignment has its limitations with respect to representation of proofs in
natural deduction with implication and negation, we will show that all
propositions that can be shown in there have a witness in . Using
Girard's approach of reducibility candidates, we show that all typeable terms
are strongly normalisable, and conclude the paper by showing that type
assignment for enjoys the principal typing property.Comment: 37 page
Characterisation of Strongly Normalising lambda-mu-Terms
We provide a characterisation of strongly normalising terms of the
lambda-mu-calculus by means of a type system that uses intersection and product
types. The presence of the latter and a restricted use of the type omega enable
us to represent the particular notion of continuation used in the literature
for the definition of semantics for the lambda-mu-calculus. This makes it
possible to lift the well-known characterisation property for
strongly-normalising lambda-terms - that uses intersection types - to the
lambda-mu-calculus. From this result an alternative proof of strong
normalisation for terms typeable in Parigot's propositional logical system
follows, by means of an interpretation of that system into ours.Comment: In Proceedings ITRS 2012, arXiv:1307.784
Orchestrated Session Compliance
We investigate the notion of orchestrated compliance for client/server
interactions in the context of session contracts. Devising the notion of
orchestrator in such a context makes it possible to have orchestrators with
unbounded buffering capabilities and at the same time to guarantee any message
from the client to be eventually delivered by the orchestrator to the server,
while preventing the server from sending messages which are kept indefinitely
inside the orchestrator. The compliance relation is shown to be decidable by
means of 1) a procedure synthesising the orchestrators, if any, making a client
compliant with a server, and 2) a procedure for deciding whether an
orchestrator behaves in a proper way as mentioned before.Comment: In Proceedings ICE 2015, arXiv:1508.0459
Logical equivalence for subtyping object and recursive types
Subtyping in first order object calculi is studied with respect to the logical semantics obtained by identifying terms that satisfy the same set of predicates, as formalised through an assignment system. It is shown that equality in the full first order -calculus is modelled by this notion, which in turn is included in a Morris-style contextual equivalence
A fully-abstract semantics of lambda-mu in the pi-calculus
We study the lambda-mu-calculus, extended with explicit substitution, and
define a compositional output-based interpretation into a variant of the
pi-calculus with pairing that preserves single-step explicit head reduction
with respect to weak bisimilarity. We define four notions of weak equivalence
for lambda-mu -- one based on weak reduction, two modelling weak head-reduction
and weak explicit head reduction (all considering terms without weak
head-normal form equivalent as well), and one based on weak approximation --
and show they all coincide. We will then show full abstraction results for our
interpretation for the weak equivalences with respect to weak bisimilarity on
processes.Comment: In Proceedings CL&C 2014, arXiv:1409.259
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