We propose a new multidimensional array query model giving array bounds and other shape-related metadata a central role. Arrays are treated as shaped maps from indices to values. Schemas are augmented by shape constraints. Queries also have shape preconditions. Within this framework, we introduce the index-based array queries expressing index reorganizations and value summarizations. We define them via adeclarative, rule-based language with shape-membership constraints inits rule bodies and subscripting and aggregation in its rule heads. We explore safety (including bounds analysis) and query equivalence for various subclasses divided according to the aggregator type, whether we allow disjunctions, and whether we allow (limited) Presburger arithmetic in index and shape terms. We show safety istractable in the nonarithmetic cases, while state safety remains in P in the arithmetic ones. We show that, for a class of monoid-based setand bag aggregators, equivalence reduces to equivalence of index-cores- core queries collecting array indices rather than values. Forset-aggregator queries, we give complete characterizations of equivalence in terms of containment maps and show the equivalenceproblems are in P in the nonarithmetic, conjunctive case and in coNP in all others.

While much recent research has focussed on extending databases beyond the traditional relational model, relatively little has been done to develop database tools for querying data organized in (multidimensional) arrays. The scientific computing community has made little use of available database technology. Instead, multidimensional scientific data is typically stored in local files conforming to various data exchange formats and queried via specialized access libraries tied in to general purpose programming languages.To allow such data to be queried using known database techniques, we design and implement a query language for multidimensional arrays. Our main design decision is to treat arrays as functions from index sets to values rather than as collection types. This leads to clean syntax and semantics as well as simple but powerful optimization rules.We present a calculus for arrays that extends standard calculi for complex objects. We derive a higher-level comprehension style query language based on this calculus and describe its implementation, including a data driver for the NetCDF data exchange format. Next, we explore some optimization rules obtained from the equational laws of our core calculus. Finally, we study the expressiveness of our calculus and prove that it essentially corresponds to adding ranking to a query language for complex objects.