## Paper: Database query languages embedded in the typed lambda calculus (at LICS 1993)

**Gerd G. Hillebrand Paris C. Kanellakis Harry G. Mairson**

### Abstract

It is shown how to naturally embed, in the typed λ-calculus with equality, many database query languages, including the relational calculus/algebra, inflationary Datalog, and the complex object calculus/algebra. The embeddings considered are such that a database is a λ-term coding list of tuples and a query is a λ-term which when applied to the input database normalizes to the output database. In addition, if the query expressed is a PTIME query, then the normal form can be computed in a number of reduction steps polynomial in the size of the input database. It is also shown that, for all PTIME queries, there is such an embedding in the order-three typed λ-calculus with equality

### BibTeX

@InProceedings{HillebrandKanellaki-Databasequerylangua, author = {Gerd G. Hillebrand and Paris C. Kanellakis and Harry G. Mairson}, title = {Database query languages embedded in the typed lambda calculus}, booktitle = {Proceedings of the Eighth Annual IEEE Symposium on Logic in Computer Science (LICS 1993)}, year = {1993}, month = {June}, pages = {332--343}, location = {Montreal, Canada}, publisher = {IEEE Computer Society Press} }