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Functorial Data Migration: From Theory to Practice [article]

Ryan Wisnesky, David I. Spivak, Patrick Schultz, Eswaran Subrahmanian
2015 arXiv   pre-print
In this paper we describe a functorial data migration scenario about the manufacturing service capability of a distributed supply chain.  ...  Introduction to Functorial Data Migration In the functorial data model, which originated with Rosebrugh and others in the late 1990s [3] , a database schema is a finitely presented category [1] (essentially  ...  The reason is that many techniques from relational database theory, such as join re-ordering, can be applied directly to select/from/where syntax.  ... 
arXiv:1502.05947v2 fatcat:uesztqv5jnavfmssoysvldh4xa

Functorial data migration

David I. Spivak
2012 Information and Computation  
We show that morphisms of schemas induce three "data migration functors", which translate instances from one schema to the other in canonical ways.  ...  We also show how to connect a database and a functional programming language by introducing a functorial connection between the schema and the category of types for that language.  ...  One may perform a sequence of data migration functors, e.g. moving data from one schema to another, then changing the data types, and finally filtering the result.  ... 
doi:10.1016/j.ic.2012.05.001 fatcat:sumnhl6bznc6bcwh4x35jgpcaq

Functorial Data Migration [article]

David I. Spivak
2013 arXiv   pre-print
We show that morphisms of schemas induce three "data migration functors", which translate instances from one schema to the other in canonical ways.  ...  We also show how to connect a database and a functional programming language by introducing a functorial connection between the schema and the category of types for that language.  ...  One may perform a sequence of data migration functors, e.g. moving data from one schema to another, then changing the data types, and finally filtering the result.  ... 
arXiv:1009.1166v4 fatcat:gvtiswjbknbyhb7tmeaebjblmy

Relational foundations for functorial data migration

David I. Spivak, Ryan Wisnesky
2015 Proceedings of the 15th Symposium on Database Programming Languages - DBPL 2015  
A morphism M between schemas S and T , which can be generated from a visual mapping between graphs, induces three adjoint data migration functors, ΣM : S → T , ΠM : S → T , and ∆M : T → S.  ...  . * Spivak acknowledges support from ONR grants N000141010841 and N000141310260.  ...  The authors would like to thank Lucian Popa for answering our many questions about database theory.  ... 
doi:10.1145/2815072.2815075 dblp:conf/dbpl/SpivakW15 fatcat:tp7sbjr63vajfj7iusirjfoxnm

Informal Data Transformation Considered Harmful [article]

Eric Daimler, Ryan Wisnesky
2020 arXiv   pre-print
to data scientists spending 80% of their time cleaning data), but rather to formally and automatically guarantee that data integrity is preserved as it transformed (migrated, integrated, composed, queried  ...  that the solution to achieving better data integrity in the enterprise is not to clean and validate data ex-post-facto whenever needed (the so-called data lake approach to data management, which can lead  ...  In short, there is little to be lost in moving to a categorytheoretic ("functorial") approach to data migration from the traditional, relational approach.  ... 
arXiv:2001.00338v1 fatcat:cuyyeg2kv5horb6brekjt7eqmy

Categorical Data Integration for Computational Science [article]

Kristopher Brown, David I. Spivak, Ryan Wisnesky
2019 arXiv   pre-print
Likewise, this feature of CQL migrations allows those who draw from public data sources to be sure only data which meets their specification will actually be transferred.  ...  We argue some open problems in the field of data sharing in computational science are addressable by working within this paradigm of functorial data migration.  ...  Data Availability Data and code required to reproduce these findings are available to download from https://github.com/krisbrown/cql_data_integration.  ... 
arXiv:1903.10579v1 fatcat:idsg7exy7jazjbtudjskezigxq

Algebraic data integration

PATRICK SCHULTZ, RYAN WISNESKY
2017 Journal of functional programming  
In this paper, we develop an algebraic approach to data integration by combining techniques from functional programming, category theory, and database theory.  ...  We present a query language based on for/where/return syntax where each query denotes a sequence of data migration functors; a pushout-based design pattern for performing data integration using our formalism  ...  Acknowledgements The authors would like to thank David Spivak and Peter Gates. Patrick Schultz was supported by AFOSR grant FA9550-14-1-0031, ONR grant N000141310260, and NASA grant NNH13ZEA001N.  ... 
doi:10.1017/s0956796817000168 fatcat:4wptmbkq45fjlmdppnu33lg4w4

Algebraic Data Integration [article]

Patrick Schultz, Ryan Wisnesky
2017 arXiv   pre-print
In this paper we develop an algebraic approach to data integration by combining techniques from functional programming, category theory, and database theory.  ...  We present a query language based on for/where/return syntax where each query denotes a sequence of data migration functors; a pushout-based design pattern for performing data integration using our formalism  ...  An Equational Formalism for Functorial Data Migration In this section we describe how to use multi-sorted equational theories to define schemas and instances, and how to migrate data from one schema to  ... 
arXiv:1503.03571v7 fatcat:i7m3v6hbb5e2vkzvvuzg5kdxtm

Category Theory Based Solution for the Building Block Replacement Problem in Materials Design

Tristan Giesa, David I. Spivak, Markus J. Buehler
2012 Advanced Engineering Materials  
Abbreviated Title: Category theory and materials design  ...  The mathematical field of category theory provides a formal specification language, which lies at the heart of such a methodology.  ...  Acknowledgements: Support from AFOSR and ONR is acknowledged.  ... 
doi:10.1002/adem.201200109 fatcat:jeztkqcukjgi3ij4nkguoyn4gy

Categories for Planning and Scheduling

Spencer Breiner, Peter Denno, Eswaran Subrahmanian
2020 Notices of the American Mathematical Society  
) • Schema mappings (functors) • Meta-theory (schema diagrams, constructors) • Data migration (change of base) • Data integration (colimits/pushouts) The payoff from all this abstraction is flexibility  ...  Together with functorial semantics, induces canonical change-of-base transformations (Δ , Σ ) that can be used to move data from one context to another.  ... 
doi:10.1090/noti2186 fatcat:gkbldvabjvfvnjadn7rqx6d43i

Functorial aggregation [article]

David I. Spivak
2022 arXiv   pre-print
The operation lives alongside querying – or more generally data migration – in typical database usage: one wants to know how much Canadians spent on cell phones in 2021, for example, and such requests  ...  be completely absent from the literature.  ...  We sometimes refer to prafunctors as data migration functors, because a prafunctor as in (5) migrates data from C to D by assigning to each object ∈ D a duc-query on C-Set.  ... 
arXiv:2111.10968v4 fatcat:kzk2x2dvynffrkhvs5rsqewoze

A Memory Evolutive System-Model of Immunocompetence with Applications to SARS-CoV-2 Immunity

Javier Burgos- Salcedo
2022 Scholars Academic Journal of Biosciences  
Finally, a practical method to measure the immunocompetence status was established, using elements of the theory of small random graphs and considering the characteristics of the immune networks, established  ...  pathogenic microorganisms to which we are exposed.  ...  In mathematics, the term functor is used in the theory of categories to designate that function from one category to another that takes objects to objects and maps to maps, so that the composition of maps  ... 
doi:10.36347/sajb.2022.v10i04.002 fatcat:r7kiqt7lmvbxnakbxrvqm7quta

A qualitative mathematical model of immunocompetence with applications to SARS-CoV-2 immunity [article]

Javier Burgos-Salcedo
2021 bioRxiv   pre-print
Finally, a practical method to measure the immunocompetence status is established, using elements of the theory of small random graphs and taking into account the characteristics of the immune networks  ...  In addition, a possible mechanism of functorial nature is proposed, which may explain how immunocompetence is achieved in an organism endowed with innate and adaptive components of its immune system.  ...  In mathematics, the term functor is used in the theory of categories to designate that function from one category to another that takes objects to objects and maps to maps, so that the composition of maps  ... 
doi:10.1101/2021.12.08.471857 fatcat:3vzgre55vnbevj3log4ef4tcwy

Categorical Data Structures for Technical Computing [article]

Evan Patterson, Owen Lynch, James Fairbanks
2022 arXiv   pre-print
Many mathematical objects can be represented as functors from finitely-presented categories 𝖢 to 𝖲𝖾𝗍. For instance, graphs are functors to 𝖢 from the category with two parallel arrows.  ...  Derived from previous work on algebraic databases, acsets are a joint generalization of graphs and data frames.  ...  Government is authorized to reproduce and distribute reprints for Government purposes notwithstanding any copyright notation herein.  ... 
arXiv:2106.04703v2 fatcat:k6zhsoexwraf5ots452mljytpi

Knowledge Representation in Bicategories of Relations [article]

Evan Patterson
2017 arXiv   pre-print
In a more theoretical vein, we draw on categorical logic to show how relational ologs can be translated to and from logical theories in a fragment of first-order logic.  ...  On a practical level, we show by example that relational ologs have a friendly and intuitive--yet fully precise--graphical syntax, derived from the string diagrams of monoidal categories.  ...  I am grateful to Thomas Icard for his encouragement of this project.  ... 
arXiv:1706.00526v2 fatcat:iyr2xxdteveqzlzjy6l6gq73oe
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