Gremlin is a graph traversal machine and language designed, developed, and
distributed by the Apache TinkerPop project. Gremlin, as a graph traversal
machine, is composed of three interacting components: a graph $G$, a traversal
$\Psi$, and a set of traversers $T$. The traversers move about the graph
according to the instructions specified in the traversal, where the result of
the computation is the ultimate locations of all halted traversers. A Gremlin
machine can be executed over any supporting graph computing system such as an
OLTP graph database and/or an OLAP graph processor. Gremlin, as a graph
traversal language, is a functional language implemented in the user's native
programming language and is used to define the $\Psi$ of a Gremlin machine.
This article provides a mathematical description of Gremlin and details its
automaton and functional properties. These properties enable Gremlin to
naturally support imperative and declarative querying, host language
agnosticism, user-defined domain specific languages, an extensible
compiler/optimizer, single- and multi-machine execution models, hybrid depth-
and breadth-first evaluation, as well as the existence of a Universal Gremlin
Machine and its respective entailments.

本文介绍了 Gremlin 的数学描述和功能属性，它支持命令式和声明式查询，用户定义的特定领域语言，可扩展的编译器 / 优化器，单机和多机执行模型，混合深度和广度优先评估以及存在通用的 Gremlin 机器和相应的蕴含关系。