%%% Core Records
-record(database_state, {hash, name, tree, relations, timestamp}).
-record(relation, {
hash, % Content hash (finite) or generator hash (infinite)
name, % Relation name (atom)
tree, % Merkle tree (mutable only), undefined for immutable/generator-based
schema, % #{attribute_name => relation_name}
constraints, % #relation_constraints{} - all constraint types (1OP, 2OP, 3OP)
cardinality, % {finite, N} | aleph_zero | continuum
generator, % Generator function (immutable only), undefined for tree-based
membership_criteria, % #{attribute_name => constraint:relational_constraint()} - domain membership test
provenance, % attribute_provenance() - maps attribute to source relation
lineage % lineage_op() - operation tree showing derivation
}).
-record(tuple, {hash, relation, attribute_map}).
-record(attribute, {hash, value}).
%% Specification record for creating immutable relations
-record(domain, {
name, % Atom - relation name
schema, % #{attribute_name => relation_name}
generator, % {module, function} - tuple generator
membership_criteria, % #{attribute_name => constraint:relational_constraint()} - domain membership
cardinality % {finite, N} | aleph_zero | continuum
}).
%% Attribute constraint (1OP - 1st Order Property)
%% Constrains values of a specific attribute in a relation
-record(attribute_constraint, {
attribute :: atom(), % Attribute name (e.g., salary)
domain :: atom() | #relation{}, % Domain or relation this attribute draws from
constraints :: [term()] % Additional relational constraints beyond domain membership
}).
%% Relation constraints - holds all types of constraints for a relation
-record(relation_constraints, {
attribute_constraints :: #{atom() => #attribute_constraint{}}, % 1OPs - attribute constraints
tuple_constraints :: [term()], % 2OPs - inter-attribute constraints (future)
multi_tuple_constraints :: [term()] % 3OPs - multi-tuple constraints (future)
}).
%%% Cardinality Types
-type cardinality() :: {finite, non_neg_integer()} % Finite set with N elements
| aleph_zero % Countably infinite (ℵ₀)
| continuum. % Uncountably infinite (2^ℵ₀)
-type constraints() :: #{atom() => constraint:relational_constraint()}.
-type boundedness_constraints() :: #{atom() => constraints()}.
%%% Generator Types
-type generator_fun() :: fun((constraints()) -> generator_result()).
-type generator_result() ::
done % No more tuples
| {value, map(), generator_fun()} % Tuple and continuation
| {error, term()}. % Error
-type generator_spec() ::
{primitive, atom()} % Built-in: naturals, integers, rationals
| {custom, generator_fun()} % User-defined generator
| {take, atom(), pos_integer()} % Take N from relation
| {derived, relational_op()}. % Derived from relational operation
-type relational_op() ::
{select, atom(), constraints()}
| {project, atom(), [atom()]}
| {join, atom(), atom(), join_spec()}.
-type join_spec() ::
{equijoin, atom()} % Natural join on attribute
| {theta, atom(), atom(), atom()}. % Theta join: op(attr1, attr2)
%%% Provenance Types (for updatable views)
%% Relation-level provenance (tracks operation lineage)
-type provenance() :: undefined
| {base, atom()} % Base relation
| {join, provenance(), provenance()}
| {select, provenance(), constraints()}
| {project, provenance(), [atom()]}
| {take, provenance(), pos_integer()}.
%% Attribute-level provenance (tracks data lineage for each attribute)
%% Maps attribute name to its source (relation, original_attribute_name)
-type attribute_provenance() :: #{atom() => {atom(), atom()}}.
%% Tuple-level lineage (tracks complete operational history)
%% Operation tree showing how the tuple was derived
-type lineage_op() ::
{base, atom()} % Base relation
| {select, fun(), lineage_op()} % Filter operation
| {project, [atom()], lineage_op()} % Projection
| {join, atom(), lineage_op(), lineage_op()} % Join on attribute
| {theta_join, fun(), lineage_op(), lineage_op()} % Join with predicate
| {sort, fun(), lineage_op()} % Sort operation
| {take, pos_integer(), lineage_op()} % Limit operation
| {aggregate, atom(), atom(), lineage_op()}. % Aggregation (future)
