3,803 research outputs found
On the Values of Reducibility Candidates
The straightforward elimination of union types is known to break subject reduction, and for some extensions of the lambda-calculus, to break strong normalization as well. Similarly, the straightforward elim- ination of implicit existential types breaks subject reduction. We propose elimination rules for union types and implicit existential quantification which use a form call-by-value issued from Girard's re- ducibility candidates. We show that these rules remedy the above men- tioned difficulties, for strong normalization and, for the existential quan- tification, for subject reduction as well. Moreover, for extensions of the lambda-calculus based on intuitionistic logic, we show that the obtained existential quantification is equivalent to its usual impredicative encoding w.r.t. provability in realizability models built from reducibility candidates and biorthogonals
Proving termination of evaluation for System F with control operators
We present new proofs of termination of evaluation in reduction semantics
(i.e., a small-step operational semantics with explicit representation of
evaluation contexts) for System F with control operators. We introduce a
modified version of Girard's proof method based on reducibility candidates,
where the reducibility predicates are defined on values and on evaluation
contexts as prescribed by the reduction semantics format. We address both
abortive control operators (callcc) and delimited-control operators (shift and
reset) for which we introduce novel polymorphic type systems, and we consider
both the call-by-value and call-by-name evaluation strategies.Comment: In Proceedings COS 2013, arXiv:1309.092
Linearity in the non-deterministic call-by-value setting
We consider the non-deterministic extension of the call-by-value lambda
calculus, which corresponds to the additive fragment of the linear-algebraic
lambda-calculus. We define a fine-grained type system, capturing the right
linearity present in such formalisms. After proving the subject reduction and
the strong normalisation properties, we propose a translation of this calculus
into the System F with pairs, which corresponds to a non linear fragment of
linear logic. The translation provides a deeper understanding of the linearity
in our setting.Comment: 15 pages. To appear in WoLLIC 201
Confluence via strong normalisation in an algebraic \lambda-calculus with rewriting
The linear-algebraic lambda-calculus and the algebraic lambda-calculus are
untyped lambda-calculi extended with arbitrary linear combinations of terms.
The former presents the axioms of linear algebra in the form of a rewrite
system, while the latter uses equalities. When given by rewrites, algebraic
lambda-calculi are not confluent unless further restrictions are added. We
provide a type system for the linear-algebraic lambda-calculus enforcing strong
normalisation, which gives back confluence. The type system allows an abstract
interpretation in System F.Comment: In Proceedings LSFA 2011, arXiv:1203.542
Period doubling and reducibility in the quasi-periodically forced logistic map
We study the dynamics of the Forced Logistic Map in the cylinder. We compute
a bifurcation diagram in terms of the dynamics of the attracting set. Different
properties of the attracting set are considered, as the Lyapunov exponent and,
in the case of having a periodic invariant curve, its period and its
reducibility. This reveals that the parameter values for which the invariant
curve doubles its period are contained in regions of the parameter space where
the invariant curve is reducible. Then we present two additional studies to
explain this fact. In first place we consider the images and the preimages of
the critical set (the set where the derivative of the map w.r.t the
non-periodic coordinate is equal to zero). Studying these sets we construct
constrains in the parameter space for the reducibility of the invariant curve.
In second place we consider the reducibility loss of the invariant curve as
codimension one bifurcation and we study its interaction with the period
doubling bifurcation. This reveals that, if the reducibility loss and the
period doubling bifurcation curves meet, they do it in a tangent way
Deduction modulo theory
This paper is a survey on Deduction modulo theor
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