We present a calculus for processing semistructured data that spans differences of application area among several novel query languages, broadly categorized as "NoSQL". This calculus lets users define their own operators, capturing a wider range of data processing capabilities, whilst providing a typing precision so far typical only of primitive hard-coded operators. The type inference algorithm is based on semantic type checking, resulting in type information that is both precise, and flexible

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... enough to handle structured and semistructured data. We illustrate the use of this calculus by encoding a large fragment of Jaql, including operations and iterators over JSON, embedded SQL expressions, and co-grouping, and show how the encoding directly yields a typing discipline for Jaql as it is, namely without the addition of any type definition or type annotation in the code.