This paper rigorously and concisely defines, in the context of our (Elementary) Mathematical Data Model ((E)MDM), the mathematical concepts of self-map, composite 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 composite mapping constraint sets. We prove that this algorithm guarantees the satisfiability, coherence, and minimality of such sets, while being very fast, sound, 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）背景下，严谨而简明地定义了自映射、复合映射、全映射性、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，关于此类约束集的一致性与极小性所对应的推论。本文的主要贡献在于提出了MatBase所使用的伪代码算法——MatBase是我们基于(E)MDM、关系数据模型和实体-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。我们证明该算法能保证此类约束集的可满足性、一致性与极小性，同时具有高效性、可靠性、完备性与极小性。此外，本文还介绍了MatBase的相关用户界面以及该算法所使用的元目录表。