CatDB Research
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Categorical database research

Typed schemas and mappings as executable database objects

CatDB moves integration meaning from bespoke pipelines into typed, composable, versioned schema mappings while treating federation and materialization as execution strategies.

Nineteen papers develop the model from categorical schema semantics through physical planning, migration, integration, provenance, formalization, and distributed workspaces.

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Source-to-domain integration

Four source schemas, one canonical commerce schema

A retailer keeps customer records, orders, fulfillment links, and product search data in different systems. Four typed mappings connect those physical schemas to one domain.

Physical source schemasEach system keeps its native shape
Typed mappingsSource fields acquire domain meaning
Canonical schemaOne model for queries and integration
01

PostgreSQL

Customer records

crm_customers(
  customer_uuid, full_name, email
)
  • customer_uuid → Customer.id
  • full_name → Customer.name
maps to Customer
02

MongoDB

Online orders

orders { orderNo, custRef,
  lines: [{ sku, qty }] }
  • orderNo → Order.number
  • lines[] → LineItem
maps to Order + LineItem
03

Neo4j

Fulfillment graph

(Order {order_no})
-[:CONTAINS {qty}]->(Product {sku})
  • order_no → Order.number
  • CONTAINS → LineItem.product
maps to Order + Product
04

Vector index

Catalog search

{ product_id, embedding,
  metadata: { sku, title } }
  • product_id → Product.id
  • metadata.sku → Product.sku
maps to Product
Commerce v1

Shared typed domain

CustomerOrderLineItemProduct
Customer.id
UUID
Order.number
Text
LineItem.qty
Integer
Product.sku
Text
Canonical query pathCustomer.orders.items.product
The mappings meet at the canonical schema. They do not require the source databases to adopt the same tables, documents, graph edges, or indexes.

Research archive

A connected program with executable checks

19reviewed manuscripts
706pages across the paper series
Slice 5shared semantic fixture set
43matching Rust and Haskell outcomes

Paper sequence

Five connected research arcs

The sequence starts with schema semantics, then moves through migration, integration, execution, distribution, implementation, formalization, and the MDReader design.

  1. P1–P4
    Schemas, migration, and integration

    Define meaning, then compose it across systems.

  2. P5–P8
    Federation, materialization, identity, and updates

    Plan reads and writes without hiding ambiguity or loss.

  3. P9–P14
    Workspaces, distribution, provenance, and cost

    Carry semantic structure into distributed execution.

  4. P15–P17
    Rust, Haskell, and Lean

    Separate production representation, reference semantics, and proof.

  5. P18 + S
    MDReader and the synthesis

    Apply the model and state the full systems thesis.

Browse all nineteen papers

Reference application

One Markdown corpus, many typed views

Paper P18 applies the CatDB model to documents, research claims, architecture decisions, requirements, tasks, evidence, and agent context.

Explore the MDReader design

Evaluation protocol

Can semantic compilation preserve native performance?

Eight benchmark groups define the baselines, measurements, and falsification conditions for compilation, execution, integration, migration, and distributed behavior.

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Research boundary

A narrow thesis, stated precisely

CatDB moves integration meaning into typed, composable, versioned schema mappings. It treats federation and materialization as execution strategies, without claiming to remove data movement, coordination, or physical planning.

Read the claim boundaries