Provenance for database queries or scientific workflows is often motivated as providing explanation, increasing understanding of the underlying data sources and processes used to compute the query, and reproducibility, the capability to recompute the results on different inputs, possibly specialized to a part of the output. Many provenance systems claim to provide such capabilities; however, most lack formal definitions or guarantees of these properties, while others provide formal guarantees only for relatively limited classes of changes. Building on recent work on provenance traces and slicing for functional programming languages, we introduce a detailed tracing model of provenance for multiset-valued Nested Relational Calculus, define trace slicing algorithms that extract subtraces needed to explain or recompute specific parts of the output, and define query slicing and differencing techniques that support explanation. We state and prove correctness properties for these techniques and present a proof-of-concept implementation in Haskell.
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