Speeding up symbolic reasoning for relational queries

Abstract

The ability to reason about relational queries plays an important role across many types of database applications, such as test data generation, query equivalence checking, and computer-assisted query authoring. Unfortunately, symbolic reasoning about relational queries can be challenging because relational tables are multisets (bags) of tuples, and the underlying languages, such as SQL, can introduce complex computation among tuples. We propose a space refinement algorithm that soundly reduces the space of tables such applications need to consider. The refinement procedure, independent of the specific dataset application, uses the abstract semantics of the query language to exploit the provenance of tuples in the query output to prune the search space. We implemented the refinement algorithm and evaluated it on SQL using three reasoning tasks: bounded query equivalence checking, test generation for applications that manipulate relational data, and concolic testing of database applications. Using real world benchmarks, we show that our refinement algorithm significantly speeds up (up to 100×) the SQL solver when reasoning about a large class of challenging SQL queries, such as those with aggregations. CCS Concepts: • Theory of computation → Logic and verification; Database query languages (principles);

Synthesizing database programs for schema refactoring

“…Since our goal is to synthesize a new version of the program that is equivalent to a previous version, this paper is particularly related to verification techniques for checking Synthesizing Database Programs for Schema Refactoring PL, 2019, USA equivalence [11-13, 52, 54]. Most of these papers focus on equivalence between individual SQL queries [11][12][13]52]. The only work that addresses the problem of verifying equivalence between entire database programs is Mediator, which automatically infers a bisimulation invariant between the two programs [54].…”

Using active learning to synthesize models of applications that access databases

“…Like many database test data generation approaches [23,41,68,70,71,74], Solve uses a row-based approach to translate path constraints into SMT formulas. For each query Q i in W that is required to retrieve at least one or at least two rows, Solve generates variables that model the required number of rows of the relevant tables.…”

Visualization by example

“…Similar to these efforts, we also use program analysis to prove infeasibility of partial programs but with two key differences: First, our analysis is tailored to table transformation programs and infers inclusion constraints between tables. Second, since neither forward nor backward reasoning is sufficient to meaningfully prune the search space on their own, we use bi-directional analysis to improve pruning power without having to resort to heavy-weight semantics motivated by prior work in program analysis [Chandra et al 2009;Dhurjati et al 2006;Reps et al 1995] and verification [Wang et al 2018a]. In this respect, our synthesis method is similar to Synqid [Polikarpova et al 2016] which uses a form of bidirectional refinement type checking to prune its search space.…”

“…For example, in the reasoning rule for summarize in Figure 12, we over-approximate all aggregation functions as uninterpreted functions; thus the inferred pre-condition only requires that input table t include content from non-aggregated columns (T ′ ) in the output table t ′ . While a more precise analysis rule could consider the underlying semantics of different aggregation operators, this kind of reasoning would be prohibitively expensive [Wang et al 2018a] and outweigh the benefits obtained from better pruning.…”