Intersection types were originally introduced as idempotent, i.e., modulo the equivalence σ ∧σ = σ . In fact, they have been used essentially for semantic purposes, for building filter models for λ -calculus, where the interpretation of types as properties of terms induces naturally the idempotence property. Recently it has been observed that, when dropping idempotency, intersection types can b...

We present quantitative analysis of various (syntactic and behavioral) properties of random λ-terms. Our main results are that asymptotically all the terms are strongly normalizing and that any fixed closed term almost never appears in a random term. Surprisingly, in combinatory logic (the translation of the λ-calculus into combinators) the result is exactly opposite. We show that almost all te...

The effect of heat treatment at 850 o Con the microstructure and mechanical properties of SAE 1025 carbon steel has been studied. Annealing, normalizing and age-hardening heat-treatments at 850 o C were used for the experimental work. Hardness tests, tensile tests and metallography were carried out on the heat-treated and control samples. The results were further analyzed using the one-way ANOV...

This study focuses on the development of new methodological approaches to dust-preparation and burning separated particles, including through use polyfractional ensembles. Coal dust screening by means sieve analysis is described in standard methods. However, order further results obtained during mathematical modeling particle motion fuel-air mixture exothermal reactions oxidation while a torch,...

Description Logics [1] are nowadays widely accepted as formalisms for implementing rigorous domain ontologies, and have been used in biomedicine in projects such as GONG [2] and SNOMED-CT [3]. A key feature of such ontologies is that the associated reasoning facilities allow us to discover inconsistencies and other problems in an automatic fashion. This is important since ontologies of complex ...

We present quantitative analysis of various (syntactic and behavioral) properties of random λ-terms. Our main results are that asymptotically all the terms are strongly normalizing and that any fixed closed term almost never appears in a random term. Surprisingly, in combinatory logic (the translation of the λ-calculus into combinators) the result is exactly opposite. We show that almost all te...

We characterize β-strongly normalizing λ-terms by means of a non-idempotent intersection type system. More precisely, we first define a memory calculus K together with a non-idempotent intersection type system K, and we show that a K-term t is typable in K if and only if t is K-strongly normalizing. We then show that β-strong normalization is equivalent to K-strong normalization. We conclude si...

Maximum likelihood parameter estimation is frequently replaced by various techniques because of its intractable normalizing constant. In the same way, the literature displays various alternatives for distributions involving such unreachable constants. In this paper, we consider a Gibbs distribution π and present a recurrence formula allowing a recursive calculus of the marginals of π and in the...

An Adaptive Exchange Algorithm for Sampling from Distributions with Intractable Normalizing Constants Faming Liang, Ick Hoon Jin, Qifan Song & Jun S. Liu To cite this article: Faming Liang, Ick Hoon Jin, Qifan Song & Jun S. Liu (2015): An Adaptive Exchange Algorithm for Sampling from Distributions with Intractable Normalizing Constants, Journal of the American Statistical Association, DOI: 10.1...

We show various (syntactic and behavioral) properties of random λ-terms. Our main results are that at least 3/4 of the terms are strongly normalizing and that any fixed closed term almost never appears in a random term. Surprisingly, in combinatory logic (the translation of the λ-calculus into combinators) the result is different. We show that almost all terms are not strongly normalizing, beca...