1,128 research outputs found
Unifying Functional Interpretations: Past and Future
This article surveys work done in the last six years on the unification of
various functional interpretations including G\"odel's dialectica
interpretation, its Diller-Nahm variant, Kreisel modified realizability,
Stein's family of functional interpretations, functional interpretations "with
truth", and bounded functional interpretations. Our goal in the present paper
is twofold: (1) to look back and single out the main lessons learnt so far, and
(2) to look forward and list several open questions and possible directions for
further research.Comment: 18 page
Optimal transient growth in an incompressible flow past a backward-slanted step
With the aim of providing a first step in the quest for a reduction of the
aerodynamic drag on the rear-end of a car, we study the phenomena of separation
and reattachment of an incompressible flow focusing on a specific aerodynamic
geometry, namely a backward-slanted step at 25 degrees of inclination. The
ensuing recirculation bubble provides the basis for an analytical and numerical
investigation of streamwise-streak generation, lift-up effect, and
turbulent-wake and Kelvin-Helmholtz instabilities. A linear stability analysis
is performed, and an optimal control problem with a steady volumic forcing is
tackled by means of variational formulation, adjoint method, penalization
scheme and orthogonalization algorithm. Dealing with the transient growth of
spanwise-periodic perturbations and inspired by the need of
physically-realizable disturbances, we finally provide a procedure attaining a
kinetic-energy maximal gain of the order of one million with respect to the
power introduced by the external forcing.Comment: 17 figure
A Type System For Call-By-Name Exceptions
We present an extension of System F with call-by-name exceptions. The type
system is enriched with two syntactic constructs: a union type for programs
whose execution may raise an exception at top level, and a corruption type for
programs that may raise an exception in any evaluation context (not necessarily
at top level). We present the syntax and reduction rules of the system, as well
as its typing and subtyping rules. We then study its properties, such as
confluence. Finally, we construct a realizability model using orthogonality
techniques, from which we deduce that well-typed programs are weakly
normalizing and that the ones who have the type of natural numbers really
compute a natural number, without raising exceptions.Comment: 25 page
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