## 2 Related Research  
[PERSON] et al. [25] first proposed the concept of data provenance and applied it to heterogeneous databases. Earlier research mainly focused on fine-grained (tuple, value). Annotation propagation [26; 27] or inverse operation were the typical methods used to track data provenance. [PERSON] et al. [28] obtained provenance data by inverting the original query to solve the problems of data volume expansion and computational complexity. Later, [PERSON] et al. [19; 20] proposed the lineage approach, which utilized reverse queries to compute tuple-level provenance data and gave the first standardized definition of tuple-level data provenance in the relational database. Based on lineage, [PERSON] et al. [21] presented the tuple-, field-, and value-level provenance representations, called why-provenance and where-provenance, respectively, to track data provenance from different perspectives. [PERSON] et al. [22] introduced a \"provenance semiring\" structure of provenance representation, called how-provenance. How-provenance canonically explains the generation of tuples and plays a vital role in uncertain databases and computing data credibility. [PERSON] [23; 24] proposed perm-provenance on the basis of lineage, which could adapt to complex SQL queries. In the meantime, perm-transformation was proposed with a re lational expression tree structure to describe and compare provenance transformation. The utilization of the rewrite mechanism in provenance queries makes it possible that the query engine simultaneously computes provenance data and query results, along with the optimal utilization of the computation engine and the optimization for calculation efficiency. Lineage, why-, where-, and how-provenance, and extensions and optimizations of previous research [17,29] form the theoretical foundation for subsequent provenance models and applications. The typical applications of data provenance are: (1) Orchestra [30] is a collaborative data-sharing system based on how-provenance in a P2P environment, which takes advantage of the characteristics of provenance transformation to synchronize data on different ends. (2) DBNotes [14], a system based on where-provenance, tracked provenance information by attaching zero or more notes to every value in a relation and propagating the attached notes to the result of queries. (3) Based on how-provenance, the Trio system [15] quantitatively calculates the credibility of data in the uncertainty database by combining and distilling data provenance and uncertainty theory. (4) SPIDER [31] proposes a method of \"Route\" as a description of the relationship between source and target data with schema mapping, tracking the transformation process of the target data, which is very useful for understanding and exploring schema mappings. In recent years, most research built on previous studies and applied them to business contexts. Specifically, research directions include data provenance of distributed systems [32, 33, 34, 35, 36], compaction of data provenance information with full-featured query languages [37, 38, 39, 40, 41, 42], etc. Studies on full-featured query language are intimately related to our study, and we highlight them below: ProvenanceCurious [43] is a tool for inferring data provenance in scripting languages. It demonstrates a provenance graph to represent a view of data dependencies, which helps to debug. This tool is implemented only with Python as the scripting language, without more details or a formal definition of the transformation process. Inspired by the ideas of program slicing and abstract interpretation, [PERSON] et al. [44] proposed an approach to translate the query language into an abstract Turing complete language (similar to Python), which can compute and track fine-grained (tuple, value) provenance data based on why- and where-provenance. This method embraces any SQL constructs, such as (correlated) sub-queries, recursive common table expressions, and built-in and user-defined functions, which are valuable in real-world database scenarios.