See Gurevich and Vovk (2017) for an in-depth study of p-values. One of the findings of this paper is that test statistics that take values in arbitrary linearly ordered sets (with measurable initial segments $(-\infty,r]$) do not always produce valid p-values; imposing the restriction that the linear order is short resolves this difficulty (practical statisticians usually consider test statistics that take values in the real line, which is short, and therefore, they are on safe ground). However, this does not mean that we cannot generalize the notions of conformal predictor and conformal transducer to conformity measures taking values in an arbitrary linearly ordered set rather than $\mathbb{R}$; in fact, it is easy to see that the standard properties of validity remain intact without the shortness requirement.