1,779 research outputs found
Inhabitation for Non-idempotent Intersection Types
The inhabitation problem for intersection types in the lambda-calculus is
known to be undecidable. We study the problem in the case of non-idempotent
intersection, considering several type assignment systems, which characterize
the solvable or the strongly normalizing lambda-terms. We prove the
decidability of the inhabitation problem for all the systems considered, by
providing sound and complete inhabitation algorithms for them
Bounding normalization time through intersection types
Non-idempotent intersection types are used in order to give a bound of the
length of the normalization beta-reduction sequence of a lambda term: namely,
the bound is expressed as a function of the size of the term.Comment: In Proceedings ITRS 2012, arXiv:1307.784
Introduction to linear logic and ludics, part II
This paper is the second part of an introduction to linear logic and ludics,
both due to Girard. It is devoted to proof nets, in the limited, yet central,
framework of multiplicative linear logic and to ludics, which has been recently
developped in an aim of further unveiling the fundamental interactive nature of
computation and logic. We hope to offer a few computer science insights into
this new theory
A proof of strong normalisation using domain theory
Ulrich Berger presented a powerful proof of strong normalisation using
domains, in particular it simplifies significantly Tait's proof of strong
normalisation of Spector's bar recursion. The main contribution of this paper
is to show that, using ideas from intersection types and Martin-Lof's domain
interpretation of type theory one can in turn simplify further U. Berger's
argument. We build a domain model for an untyped programming language where U.
Berger has an interpretation only for typed terms or alternatively has an
interpretation for untyped terms but need an extra condition to deduce strong
normalisation. As a main application, we show that Martin-L\"{o}f dependent
type theory extended with a program for Spector double negation shift.Comment: 16 page
Types as Resources for Classical Natural Deduction
We define two resource aware typing systems for the lambda-mu-calculus based on non-idempotent intersection and union types. The
non-idempotent approach provides very simple combinatorial arguments - based on decreasing measures of type derivations - to characterize head and strongly normalizing terms. Moreover, typability provides upper bounds for the length of head-reduction sequences and maximal reduction sequences
Characterization of strong normalizability for a sequent lambda calculus with co-control
We study strong normalization in a lambda calculus of proof-terms
with co-control for the intuitionistic sequent calculus. In this sequent
lambda calculus, the management of formulas on the left hand
side of typing judgements is “dual" to the management of formulas
on the right hand side of the typing judgements in Parigot’s lambdamu
calculus - that is why our system has first-class “co-control".
The characterization of strong normalization is by means of intersection
types, and is obtained by analyzing the relationship with
another sequent lambda calculus, without co-control, for which a
characterization of strong normalizability has been obtained before.
The comparison of the two formulations of the sequent calculus,
with or without co-control, is of independent interest. Finally, since
it is known how to obtain bidirectional natural deduction systems
isomorphic to these sequent calculi, characterizations are obtained
of the strongly normalizing proof-terms of such natural deduction
systems.The authors would like to thank the anonymous
referees for their valuable comments and helpful suggestions.
This work was partly supported by FCT—Fundação para a Ciência
e a Tecnologia, within the project UID-MAT-00013/2013; by
COST Action CA15123 - The European research network on types
for programming and verification (EUTypes) via STSM; and by the
Ministry of Education, Science and Technological Development,
Serbia, under the projects ON174026 and III44006.info:eu-repo/semantics/publishedVersio
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