Algebraic Databases
summary
Claim: schemas are categories and schema mappings are functors, which give three concrete data migrations Delta/Pi/Sigma that implement projection product and outer-union including labeled nulls. The project ships an open source tool AQL (jar and binaries) that executes these migrations, checks integrity constraints, produces joins via schema design, and exposes provenance as monadic units. The software originates from MIT work, is in active use for data integration experiments, and demonstrably runs on example instances.
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chapters (17)
- 0:00Start
- 2:37Review of Category Theory
- 2:59Category Theory
- 5:07Functors
- 5:39Example of Functors
- 7:30Introduction
- 8:31Data Integrity Constraints
- 11:26Nullable Fields
- 16:12Morphism of Databases
- 16:53Network Transformation
- 17:45Are Data Mappings Mutations of the Database
- 22:02Composition of Functions
- 35:10Outer Disjoint Union
- 39:12Joins
- 43:05Monads
- 49:17Sigma-Delta Data Migration
- 52:01Benefits
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