On sets of terms with a given intersection type

We are interested in how much of the structure of a strongly normalizable lambda term is captured by its intersection types and how much all the terms of a given type have in common. In this note we consider the theory BCD (Barendregt, Coppo, and Dezani) of intersection types without the top element. We show: for each strongly normalizable lambda term M, with beta-eta normal form N, there exists an intersection type A such that, in BCD, N is the unique beta-eta normal term of type A. A similar result holds for finite sets of strongly normalizable terms for each intersection type A if the set of all closed terms M such that, in BCD, M has type A, is infinite then, when closed under beta-eta conversion, this set forms an adaquate numeral system for untyped lambda calculus. A number of related results are also proved

Genus distributions for two classes of graphs

The set of orientable imbeddings of a graph can be partitioned according to the genus of the imbedding surfaces. A genus-respecting breakdown of the number of orientable imbeddings is obtained for every graph in each of two infinite classes. It is proved that the genus distribution of any member of either class is strongly unimodal. These are the first two infinite classes of graphs for which such calculations have been achieved, except for a few classes, such as trees and cycles, whose members have all their cellular orientable imbeddings in the sphere

Genus Distributions for Two Classes of Graphs

The set of orientable imbeddings of a graph can be partitioned according to the genus of the imbedding surfaces. A genus-respecting breakdown of the number of orientable imbeddings is obtained for every graph in each of two infinite classes. These are the first two infinite classes of graphs for which such calculations have been achieved, except for a few classes, such as trees and cycles, whose members have all their polygonal orientable imbeddings in the sphere

Solution of a Problem of Barendregt on Sensible lambda-Theories

H is the theory extending β-conversion by identifying all closed unsolvables. Hω is the closure of this theory under the ω-rule (and β-conversion). A long-standing conjecture of H. Barendregt states that the provable equations of Hω form Π11-complete set. Here we prove that conjecture.Comment: 17 page

Soft Session Types

We show how systems of session types can enforce interactions to be bounded for all typable processes. The type system we propose is based on Lafont's soft linear logic and is strongly inspired by recent works about session types as intuitionistic linear logic formulas. Our main result is the existence, for every typable process, of a polynomial bound on the length of any reduction sequence starting from it and on the size of any of its reducts.Comment: In Proceedings EXPRESS 2011, arXiv:1108.407

Analytic Tableaux for Simple Type Theory and its First-Order Fragment

We study simple type theory with primitive equality (STT) and its first-order fragment EFO, which restricts equality and quantification to base types but retains lambda abstraction and higher-order variables. As deductive system we employ a cut-free tableau calculus. We consider completeness, compactness, and existence of countable models. We prove these properties for STT with respect to Henkin models and for EFO with respect to standard models. We also show that the tableau system yields a decision procedure for three EFO fragments

Overconfident Investors, Predictable Returns, and Excessive Trading

The last several decades have witnessed a shift away from a fully rational paradigm of financial markets toward one in which investor behavior is influenced by psychological biases. Two principal factors have contributed to this evolution: a body of evidence showing how psychological bias affects the behavior of economic actors; and an accumulation of evidence that is hard to reconcile with fully rational models of security market trading volumes and returns. In particular, asset markets exhibit trading volumes that are high, with individuals and asset managers trading aggressively, even when such trading results in high risk and low net returns. Moreover, asset prices display patterns of predictability that are difficult to reconcile with rational-expectations–based theories of price formation. In this paper, we discuss the role of overconfidence as an explanation for these patterns

Initial Public Offerings and the Firm Location

The firm geographic location matters in IPOs because investors have a strong preference for newly issued local stocks and provide abnormal demand in local offerings. Using equity holdings data for more than 53,000 households, we show the probability to participate to the stock market and the proportion of the equity wealth is abnormally increasing with the volume of the IPOs inside the investor region. Upon nearly the universe of the 167,515 going public and private domestic manufacturing firms, we provide consistent evidence that the isolated private firms have higher probability to go public, larger IPO underpricing cross-sectional average and volatility, and less pronounced long-run under-performance. Similar but opposite evidence holds for the local concentration of the investor wealth. These effects are economically relevant and robust to local delistings, IPO market timing, agglomeration economies, firm location endogeneity, self-selection bias, and information asymmetries, among others. Findings suggest IPO waves have a strong geographic component, highlight that underwriters significantly under-estimate the local demand component thus leaving unexpected money on the table, and support state-contingent but constant investor propensity for risk