We develop an efficient representation and a pre-unification algorithm in the style of Huet for the This extended abstract has been submitted to the Twelfth Annual Symposium on Logic in Computer Science LICS’97, Warsaw, Poland, June 29th – July 2nd 1997. linear λ-calculus λ→−◦&> which includes intuitionistic functions (→), linear functions (−◦), additive pairing (&), and additive unit (>). Appl...

We present a new class of second-order uniication problems, which we have called linear. We deal with completely general second-order typed uniication problems, but we restrict the set of uniiers under consideration: they instantiate free variables by linear terms, i.e. terms where any-abstractions bind one and only one occurrence of a bound variable. Linear second-order uniication properly ext...

where the A{ are rational integers, is called an integral linear recurrence of order k. Given such a linear recurrence and an integer c, one would like to know for what n does f(n) — c? In a very few particular instances (e.g. see [2], [6]) this question has been answered, but in general the question is very difficult. A less exacting problem is the determination of upper and lower bounds on th...

Higher-Order Linear Ramified Recurrence (HOLRR) is a PTIME sound and complete typed lambda caluclus. Its terms are those of a linear (affine) λ-calculus – every variable occurs at most once – extended with a limited recursive scheme on a word algebra. Completeness for PTIME holds by embedding Leivant’s ramified recurrence on words into HOLRR. Soundness is established at all types – and not only...

We consider the di?erential equation f<sup>''</sup> +A(z)f<sup>'</sup> +B(z)f = 0, where A(z) and B(z) are entire complex functions. improve various restrictions on coe?cients prove that all non-trivial solutions of in?nite order.

A linear ordering is said to be representable if it can be order-embedded into the reals. Representable linear orderings have been characterized as those which are separable in the order topology and have at most countably many jumps. We use this characterization to study the representability of a lexicographic product of linear orderings. First we count the jumps in a lexicographic product in ...

This paper provides characterization theorems for preferences that can be represented by U(x1, ..., xn)=min{xk}, U(x1, ..., xn)=max{xk}, U(x1, ..., xn)=; u(xk), or combinations of these functionals. The main assumption is partial separability, where changing a common component of two vectors does not reverse strict preferences, but may turn strict preferences into indifference. We discuss appli...