This paper rigorously and concisely defines, in the context of our (Elementary) Mathematical Data Model ((E)MDM), the mathematical concepts of self-map, compound mapping, totality, one-to-oneness, non-primeness, ontoness, bijectivity, default value, (null-)reflexivity, irreflexivity, (null-)symmetry, asymmetry, (null-)idempotency, anti-idempotency, (null-)equivalence, acyclicity, (null-)representative system mapping, the properties that relate them, and the corresponding corollaries on the coherence and minimality of sets made of such mapping properties viewed as database constraints. Its main contribution is the pseudocode algorithm used by MatBase, our intelligent database management system prototype based on both (E)MDM, the relational, and the entity-relationship data models, for enforcing self-map, atomic, and compound mapping constraint sets. We prove that this algorithm guarantees the satisfiability, coherence, and minimality of such sets, while being very fast, solid, complete, and minimal. In the sequel, we also presented the relevant MatBase user interface as well as the tables of its metacatalog used by this algorithm.

翻译：本文在我们的（初等）数学数据模型（(E)MDM）框架下，严谨而简明地定义了自映射、复合映射、全射性、单射性、非素性、满射性、双射性、默认值、（空）自反性、非自反性、（空）对称性、非对称性、（空）幂等性、反幂等性、（空）等价性、无环性、（空）代表系统映射等数学概念，以及它们之间的关联性质，并将这些映射性质视为数据库约束时，关于约束集合一致性与极小性的相应推论。本文的核心贡献在于提出了MatBase所使用的伪代码算法——MatBase是我们基于(E)MDM、关系数据模型及实体-联系数据模型开发的智能数据库管理系统原型，该算法用于强制实施自映射、原子及复合映射约束集合。我们证明该算法在保证此类集合可满足性、一致性与极小性的同时，具有高效性、稳健性、完备性与极小性。此外，我们还介绍了MatBase中与此算法相关的用户界面及其元目录所使用的数据表。