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It is used, directly or indirectly, on an everyday basis by people who design databases, and it is used in commercial systems to reason about the consistency and correctness of a data design.{{cn|date=November 2012}} New applications of the chase in meta-data management and data exchange are still being discovered.
The Chase has its origins in two seminal papers, one by [[Alfred V. Aho]], [[Catriel Beeri]], and [[Jeffrey D. Ullman]].<ref>[[Alfred V. Aho]], [[Catriel Beeri]], and [[Jeffrey D. Ullman]]: "The Theory of Joins in Relational Databases", ACM Trans. Datab. Syst. 4(3):297-314, 1979 .</ref> and the other by [[David Maier]], [[Alberto O. Mendelzon]], and [[Yehoshua Sagiv]]<ref>
[[David Maier]], [[Alberto O. Mendelzon]], and [[Yehoshua Sagiv]]: "Testing Implications of Data Dependencies". ACM Trans. Datab. Syst. 4(4):455-469, 1979.</ref>
In its simplest application the chase is used for testing whether the [[projection (relational algebra)|projection]] of a [[relation schema]] constrained by some [[functional dependency|functional dependencies]] onto a given decomposition can be [[join dependency|recovered by rejoining the projections]]. Let ''t'' be a tuple in <math>\pi_{S_1}(R) \bowtie \pi_{S_2}(R) \bowtie ... \bowtie \pi_{S_k}(R)</math> where ''R'' is a [[relation (database)|relation]] and ''F'' is a set of functional dependencies (FD). If tuples in ''R'' are represented as ''t<sub>1</sub>, ..., t<sub>k</sub>'', the join of the projections of each ''t<sub>i</sub>'' should agree with ''t'' on <math>\pi_{S_i}(R)</math> where ''i'' = 1, 2, ..., ''k''. If ''t<sub>i</sub>'' is not on <math>\pi_{S_i}(R)</math>, the value is unknown.
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