论文标题
关于寄生和完整的部分应用结构
On posetal and complete partial applicative structures
论文作者
论文摘要
每个部分应用结构都会产生索引的二进制关系，这是从集合类别到具有二进制关系的集合类别的违反函数，并映射了它们。在本文中，我们表征了这些部分应用结构，从而产生了索引关系，从而满足了代数或计算特性方面的某些基本特性。然后，我们将提供有关这些部分应用结构的特征，从而产生索引的预订和索引posets，我们将将后者与某些特定类别的单位部分内部函数相关联。我们将分析Posetal情况下一系列计算和代数性质之间的关系。最后，我们将通过为部分应用结构提供一些必要的条件来完成部分应用结构，以使部分申请的结构完整地置于索引前期。
Every partial applicative structure gives rise to an indexed binary relation, that is a contravariant functor from the category of sets to the category of sets endowed with binary relations and maps preserving them. In this paper we characterize those partial applicative structures giving rise to indexed relations satisfying certain elementary properties in terms of algebraic or computational properties. We will then provide a characterization of those partial applicative structures giving rise to indexed preorders and indexed posets, and we will relate the latter ones to some particular classes of unary partial endofunctions. We will analyze the relation between a series of computational and algebraic properties in the posetal case. Finally, we will study the problem of existence of suprema in the case of partial applicative structures giving rise to indexed preorders, by providing some necessary conditions for a partial applicative structure to be complete.
