Contrary to all expectations, the-calculus, the canonical simply-typed lambda-calculus with explicit substitutions, is not strongly normalising. This result has led to a proliferation of calculi with explicit substitutions. This paper shows that the reducibility method provides a general criterion when a calculus of explicit substitution is strongly normalising for all untyped lambda-terms that...

Extending the-calculus with either explicit substitution or generalised reduction has been the subject of extensive research recently which still has many open problems. Due to this reason, the properties of a calculus combining both generalised reduction and explicit substitutions have never been studied. This paper presents such a calculus sg and shows that it is a desirable extension of the-...

Substitution of a metallic diaphragm for the power piston of a Stirling engine is shown to be a promising approach to transmitting power for a heat-actuated heat pump through a hermetic seal. Hydraulic fluid under high pressure transfers the power from the diaphragu to the compressor plunger, which is balanced by a counterweight. The discussion is divided into three parts which deal with the in...

Based on the increasing property of ratio of average reversed hazard rates of two non-negative random variables a new stochastic order for the sake of comparison of two lifetime distributions is proposed. This stochastic order admits some distinguishing properties. In order to illustrate the obtained results, a semi-parametric model which is called reverse hazard power and a mixture model of pr...

Extending the-calculus with either explicit substitution or generalised reduction has been the subject of extensive research recently and still has many open problems. This paper is the rst investigation into the properties of a calculus combining both generalised reduction and explicit substitutions. We present a calculus, gs, that combines a calculus of explicit substitution, s, and a calculu...

We present the ! and !e calculi, the two-sorted (term and substitution) versions of the s (cf. KR95a]) and se (cf. KR96a]) cal-culi, respectively. We establish an isomorphism between the s-calculus and the term restriction of the !-calculus, which extends to an isomor-phism between se and the term restriction of !e. Since the ! and !e calculi are given in the style of the-calculus (cf. ACCL91])...

A ring R is called a left APP-ring if the left annihilator lR(Ra) is right s-unital as an ideal of R for any element a ∈ R. We consider left APP-property of the skew formal power series ring R[[x;α]] where α is a ring automorphism of R. It is shown that if R is a ring satisfying descending chain condition on right annihilators then R[[x;α]] is left APP if and only if for any sequence (b0, b1, ....