We introduce a type theoretical framework in which canon ical term rewriting systems can be represented faithfully both from the logical and the computational points of view The framework is based on congruence types a new syntax which combines inductive algebraic and quotient types Congruence types improve on existing work to combine type theories with algebraic rewriting by making explicit th...

OBJECTIVE The ability of alliance to predict outcome has been widely demonstrated, but less is known about the effect of the level of congruence between patient and therapist alliance ratings on outcome. In the current study we examined whether the degree of congruence between patient and therapist alliance ratings can predict symptomatic levels 1 month later in treatment. METHOD The sample c...

We show that noncongruence subgroups of SL2(Z) projectively equivalent to congruence subgroups are ubiquitous. More precisely, they always exist if the congruence subgroup in question is a principal congruence subgroup Γ(N) of level N > 2, and they exist in many cases also for Γ0(N). The motivation for asking this question is related to modular forms: projectively equivalent groups have the sam...

The testing equivalence te that is used as a reference in verification and testing theory in LOTOS is not a congruence, and no explicit definition of the least congruence stronger than te has been found. The critical LOTOS context in which congruence is lost is the hiding context that creates divergence. In this paper we first survey this problem and present three known variants of te that are ...

During the last decade, CCS has been extended in diierent directions, among them priority and real time. One of the most satisfactory results for CCS is Milner's complete proof system for observational congruence 31]. Observational congruence is fair in the sense that it is possible to escape divergence, reeected by the axiom recX:(:X + P) = recX:::P. In this paper we discuss observational cong...

For any k ≥ 0, all primes n satisfy the congruence nσk(n) ≡ 2 mod φ(n). We show that this congruence in fact characterizes the primes, in the sense that it is satisfied by only finitely many composite n. This characterization generalizes the results of Lescot and Subbarao for the cases k = 0 and k = 1. For 0 ≤ k ≤ 14, we enumerate the composite n satisfying the congruence. We also prove that an...

Let S be a smooth affine algebraic curve, and let S̊ be the Riemann surface obtained by removing a point from S. We provide evidence for the congruence subgroup property of mapping class groups by showing that the congruence kernel ker ( M̂od(S̊)→ Out ( π̂1(S̊) )) lies in the centralizer of every braid in Mod(S̊). As a corollary, we obtain a new proof of Asada’s theorem that the congruence subgroup p...

Previous research on cross-cultural leadership has examined the effects of leadership-society congruence without explaining how positive outcomes might result when there is a fit between leadership and societal culture, and via which mechanisms the effects of such congruence are transmitted. We fill this gap by developing a culturally contingency model of leader-society value congruence effects...

A completeness theorem is established for logics with congruence endowed with general semantics (in the style of general frames). As a corollary, completeness is shown to be preserved by fibring logics with congruence provided that congruence is retained in the resulting logic. The class of logics with equivalence is shown to be closed under fibring and to be included in the class of logics wit...