The Monad Comprehension Calculus (MCC) is a highly expressive query language equal in expressive power to a subset of the Haskell programming language. This expressivity allows the MCC to subsume a variety of user-facing query languages, from nested relational algebra to OQL. The MCC possess a number of highlydesirable properties, including a normal form for queries that eliminates treatment of collection types. Within the last decade sophisticated SQL/OQL optimization techniques based on semantic optimization have been applied to the MCC’s SQL/OQL fragment. In this paper we begin to apply relational optimizations to the entirety of the MCC. We do not approach the level of sophistication possible in the SQL/OQL fragment, and our optimizations are simple rewrites based on intra-relation functional dependencies. Still, by exploiting the so-called algebra of programming, the fledgling point-free functional dependency theory, and a translation from a subset of the MCC to nested relational algebra, we are able to reason about relational optimizations in the broader context of the MCC in an equational, compositional, and easily mechanizable way. We demonstrate how to optimize functional programs by exploiting knowledge about their functional dependencies, and how to optimize relational queries translated into MCC based on the underlying, rich algebraic structure of the MCC. 1.

We examine schema mappings from a type-theoretic perspective and aim to facilitate and formalize the reuse of mappings. Starting with the mapping language of Clio, we present a type-checking algorithm such that typeable mappings are necessarily satisfiable. We add type variables to the schema language and present a theory of polymorphism, including a sound and complete type inference algorithm and a semantic notion of a principal type of a mapping. Principal types, which intuitively correspond to the minimum amount of schema structure required by the mappings, have an important application for mapping reuse. Concretely, we show that mappings can be reused, with the same semantics, on any schemas as long as these schemas are expansions (i.e., subtypes) of the principal types.