It is shown by a purely syntactic argument how the completeness of resolution in type theory implies the consistency of type theory with axioms of extensionality, descriptions, and infinity. In this system the natural numbers are defined, and Peanos Postulates proved; indeed, classical analysis and much more can be formalized here. Nevertheless, Godels results show that the completeness of reso...

We present an experiment where Ramsey-type spectroscopy is applied to autoionizing states of krypton by using the ninth harmonic (88 nm) of a femtosecond Ti:sapphire laser. The ionization process, detected by an electron-energy spectrometer, shows the characteristic quantum interference pattern. The behavior of the fringe contrast compares favorably with a simple essential-state model, whose pa...

The language MLF is an extension of System F that permits robust first-order partial type inference with second-order polymorphism. We propose an extension of MLF’s graphical presentation with higherorder types and reduction at the type level as in System Fω. As inference of higher-order types won’t be possible in general, the extension introduces System F-style explicit type abstraction and ty...

We present a new predicative and decidable type system , called ML , suitable for languages that integrate functional programming and parametric polymorphism in the tradition of ML 21, 28], and class-based object-oriented programming and higher-order multi-methods in the tradition of CLOS 12]. Instead of using ex-tensible records as a foundation for object-oriented extensions of functional lang...

The order type of a point set in Rd maps a (d+1)-tuple of points to its orientation (e.g., clockwise or counterclockwise in R2). Two point sets X and Y have the same order type if there exists a mapping f from X to Y for which every (d+1)-tuple (a1, a2, . . . , ad+1) of X and the corresponding tuple (f(a1), f(a2), . . . , f(ad+1)) in Y have the same orientation. In this paper we investigate the...

Let A be a function with derivatives of order m and DγA∈ Λ̇β (0 < β < 1, |γ| =m). The authors in the paper proved that ifΩ∈ Ls(Sn−1) (s≥ n/(n−β)) is homogeneous of degree zero and satisfies a vanishing condition, then both the higher-order Marcinkiewicz-type integral μΩ and its variation μ̃ A Ω are bounded from L p(Rn) to Lq(Rn) and from L1(Rn) to Ln/(n−β),∞(Rn), where 1 < p < n/β and 1/q = 1/p− ...

We propose a framework of consistent finite-order priors to facilitate the incorporation of higher-order uncertainties into Bayesian game analysis, without invoking the concept of a universal type space. Several recent models, which give rise to stunning results with higher-order uncertainties, turn out to operate with certain consistent order-2 priors. We introduce canonical representations of...

We develop a general tool to formalize and reason about languages expressed using higher-order abstract syntax in a proof-tool based on type theory (Coq). A language is specified by its signature, which consists of sets of sort and operation names and typing rules. These rules prescribe the sorts and bindings of each operation. An algebra of terms is associated to a signature, using de Bruijn n...