• Corpus ID: 5115249

Kleisli Database Instances

@article{Spivak2012KleisliDI,
  title={Kleisli Database Instances},
  author={David I. Spivak},
  journal={ArXiv},
  year={2012},
  volume={abs/1209.1011}
}
We use monads to relax the atomicity requirement for data in a database. Depending on the choice of monad, the database fields may contain generalized values such as lists or sets of values, or they may contain exceptions such as various types of nulls. The return operation for monads ensures that any ordinary database instance will count as one of these generalized instances, and the bind operation ensures that generalized values behave well under joins of foreign key sequences. Different… 
Query Combinators
TLDR
Rabbit semantics enables pipeline notation, encouraging its users to construct database queries as a series of distinct steps, each individually crafted and tested, and it is believed that Rabbit can serve as a practical tool for data analytics.
Functional query languages with categorical types
TLDR
It is proved that every hereditarily domain-independent higher-order logic program can be translated into the nested relational algebra, thereby allowing higher- order logic to be used as a query language and giving a higher-orders generalization of Codd's theorem.
Relational foundations for functorial data migration
TLDR
This work studies the data transformation capabilities associated with schemas that are presented by directed multi-graphs and path equations, and presents an algebraic query language FQL based on these functors, proves that FQL is closed under composition, and proves that SPCU can be implemented with FQL.
Categories at Work 5.1 Adjoint Functors 5.1.1 Discussion and Definition
  • Mathematics
We have now set up an understanding of the basic notions of category theory: categories, functors, natural transformations, and universal properties. We have discussed many sources of examples:
David I. Spivak: Curriculum Vitae
Employment University of Oregon, Mathematics: Paul Olum Visiting Assistant Professor. 2007-present. University of Oregon, Computer Science: guest instructor. Spring 2008, Fall 2008. University of

References

SHOWING 1-10 OF 36 REFERENCES
Data Base Mappings and Monads: (Co)Induction
  • Z. Majkic
  • Computer Science, Mathematics
    ArXiv
  • 2011
TLDR
The semantics of database mappings in the relational DB category based on the power-view monad T and monadic algebras is presented and some Universal algebra considerations based on monads and relationships between this DB category and the standard Set category are stressed.
Database queries and constraints via lifting problems
  • David I. Spivak
  • Computer Science
    Mathematical Structures in Computer Science
  • 2013
TLDR
This paper shows that certain queries and constraints correspond to lifting problems, as found in modern approaches to algebraic topology, and explains how giving users access to certain parts of Qry(π), rather than direct access to π, improves the ability to manage the impact of schema evolution.
Functorial data migration
A Relational Model of Data Large Shared Data Banks
  • F. E.
  • Computer Science
  • 2000
TLDR
A model based on n-ary relations, a normal form for data base relations, and the concept of a universal data sublanguage are introduced and certain operations on relations are discussed and applied to the problems of redundancy and consistency in the user's model.
A relational model of data for large shared data banks
TLDR
A model based on n-ary relations, a normal form for data base relations, and the concept of a universal data sublanguage are introduced and certain operations on relations are discussed and applied to the problems of redundancy and consistency in the user's model.
A Calculus for Collections and Aggregates
TLDR
A calculus that should play for database query languages the same role that the lambda calculus plays for functional programming, and a new concept: monads enriched with algebraic structure is introduced.
Notions of Computation and Monads
  • E. Moggi
  • Computer Science
    Inf. Comput.
  • 1991
Monad comprehensions : a versatile representation for queries
This chapter is an exploration of the possibilities that open up if we consistently adopt a style of database query and collection processing which allows us to look inside collections and thus
Higher Operads, Higher Categories
Part I. Background: 1. Classical categorical structures 2. Classical operads and multicategories 3. Notions of monoidal category Part II. Operads. 4. Generalized operads and multicategories: basics
...
...