This paper brings mathematical tools to bear on the study of package dependencies in software systems. We introduce structures known as Dependency Structures with Choice (DSC) that provide a mathematical account of such dependencies, inspired by the definition of general event structures in the study of concurrency. We equip DSCs with a particular notion of morphism and show that the category of DSCs is isomorphic to the category of antimatroids. We study the exactness properties of these equivalent categories, and show that they are finitely complete, have finite coproducts but not all coequalizers. Further, we show construct a functor from a category of DSCs equipped with a certain subclass of morphisms to the opposite of the category of finite distributive lattices, making use of a simple finite characterization of the Bruns-Lakser completion, and finally, we introduce a formal account of versions of packages and introduce a mathematical account of package version-bound policies.

翻译：本文为软件系统包件依赖性的研究带来了数学工具。 我们引入了被称为 " 选择依赖性结构 " (DSC)的结构,这种结构根据货币研究中一般事件结构定义的启发,为这种依赖性提供了数学说明。 我们为DSC配备了一种特殊的形态概念,并表明DSC的类别与抗甲状腺类别不相形色。 我们研究了这些等同类别的精确性,并表明它们有限地完整,具有有限的共同产品,但并非全部的平衡性。 此外,我们展示了从一个配备某种亚类变式的DSC类中构建一个配有某种亚类的变式的配料,与有限分配性拉特克相对,利用对布伦斯-Lakser完成的简单限定的定性,最后,我们引入了对各种软件版本的正式描述,并引入了组合组合组合组合政策的数学账户。