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diff --git a/docs/features.org b/docs/features.org new file mode 100644 index 0000000..a6e592e --- /dev/null +++ b/docs/features.org @@ -0,0 +1,96 @@ +* 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 + |