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* Relational Algebra Engine
:PROPERTIES:
:CATEGORY: relational-algebra
:END:
A pure Erlang implementation of E. F. Codd’s relational algebra.
Relations are treated as mathematical sets of tuples; operations are defined exactly
as in relational theory, with optional aleph₀ (infinite) relations.
** Core Specification
The theoretical backbone of the system.
*** TODO Define relation as a strict mathematical set
- [ ] Each tuple is a set of attributes (no duplicates, no ordering)
- [ ] Each attribute = (name, value) pair
- [ ] Attribute domains are strongly typed
*** TODO Enforce "Codd's axioms" in implementation
- [ ] No duplicate tuples in any relation
- [ ] No implicit ordering of tuples or attributes
- [ ] All operations closed over the relation type
- [ ] Proper domain checking in all operations
** Data Model Layer (`relation.erl`)
Fundamental constructs of the relational model.
*** TODO Implement attributes, tuples, relations, and schemas
*** TODO Add schema validation for domain and arity
*** TODO Add conversion helpers:
- [ ] tuple <-> map
- [ ] schema validation checks
** Algebraic Operations (`operations.erl`)
The complete set of classical relational algebra operators.
*** TODO Selection (σ)
*** TODO Projection (π)
*** TODO Cartesian Product (×)
*** TODO Natural Join (⋈)
*** TODO Theta Join (⋈θ)
*** TODO Union (∪)
*** TODO Intersection (∩)
*** TODO Difference (−)
*** TODO Rename (ρ)
*** TODO Set semantics enforcement (remove duplicates after each op)
** Infinite Relations (`aleph0.erl`)
Representation of aleph₀-relations (countably infinite generators).
*** TODO Implement integer() generator
*** TODO Implement plus(), minus(), multiply(), neg() relations
*** TODO Add constraints and modes for partially bound arguments
*** TODO Implement lazy generation using streams or coroutines
*** TODO Support user-defined infinite relations
** Unified Relation Abstraction (`unified_relation.erl`)
A bridge between finite and infinite relations.
*** TODO Implement unified type for finite and aleph₀
*** TODO Implement unified select, project, join, union, etc.
*** TODO Support type checking between finite and infinite relations
*** TODO Add automatic materialization with configurable limits
*** TODO Implement caching/memoization for aleph₀ evaluations
** Backend Integration (Mnesia)
Persistent storage and retrieval of finite relations.
*** TODO Map finite relations to Mnesia tables
*** TODO Support schema registration and domain enforcement
*** TODO Add persistence for partially materialized aleph₀ relations
*** TODO Add atomic transactional updates
*** TODO Add indexing support for joins
** Correctness and Validation
Ensuring theoretical fidelity.
*** TODO Implement relational algebra test suite
*** TODO Verify closure and idempotence of all operations
*** TODO Add property-based tests with PropEr or QuickCheck
*** TODO Compare semantics with formal definitions (e.g., Date & Darwen)
** Developer Tools
Optional but desirable tools for exploration and testing.
*** TODO Add REPL-like console for interactive relational queries
*** TODO Add pretty-printer for relations and schemas
*** TODO Add visualization of join graphs and operation pipelines
*** TODO Add Org Babel integration for relational queries
** Documentation
Literate and theoretical exposition.
*** TODO Write README with theoretical introduction
*** TODO Add module-level comments summarizing relational definitions
*** TODO Include examples of finite and aleph₀ joins
*** TODO Provide link to E. F. Codd’s original papers
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