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...each with different tradeoffs. For example, previous work encoding relational algebra in Agda suggests that schemas should be represented as functions from a finite set of column names to basic types =-=[9]-=-, but in practice, we found that a concrete encoding using a list of type names yields a more workable representation. • Another choice was how to represent finite sets. Finite sets are a common abstr...

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...ilies (Dybjer, 1994), especially the identity type ( ≡ ), is central to the Agda system and to our derivations. A recent development of relations in dependent type theory was carried out by Gonzalía (=-=Gonzalía, 2006-=-), Ch. 5. The advances in Agda’s notation and support for hidden arguments between that derivation and our work is striking. There has been a trend in recent years to bridge the gap between dependent ...

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...[7] sense) Set, explicitly breaking Set into subtypes where the functional dependencies hold. The general idea of capturing data invariants such as functional dependency with types has a long history =-=[9]-=- [19] [3]. 2.3.2 Terms for checking dependencies In the above section we added types of the form Rel row Σ that intuitively correspond to relations over row where Σ holds. In this section we add a con...

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...or indexes). We thus chose to formalize this version. ? This work is partially supported by ANR project Typex no 11BS0200702. 1.1 Related Work The first attempt in that direction is found in Gonzalia =-=[5, 6]-=-. This work investigates different formalizations of the unnamed version of the model and only addresses data definition and relational algebra aspects. A more recent formalization is found in Malecha...