%%% 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, % #{attribute_name => constraint_spec()} - integrity constraints
cardinality, % {finite, N} | aleph_zero | continuum
generator, % Generator function (immutable only), undefined for tree-based
membership_criteria, % #{attribute_name => constraint_spec()} - domain membership test
mutability, % mutable | immutable
provenance % Provenance tracking for updatable views (future)
}).
-record(tuple, {hash, relation, attribute_map}).
-record(attribute, {hash, value}).
%% Specification record for creating immutable relations
-record(immutable_relation_spec, {
name, % Atom - relation name
schema, % #{attribute_name => relation_name}
generator, % {module, function} - tuple generator
membership_criteria, % #{attribute_name => constraint_spec()} - domain membership
cardinality % {finite, N} | aleph_zero | continuum
}).
%%% Cardinality Types
-type cardinality() :: {finite, non_neg_integer()} % Finite set with N elements
| aleph_zero % Countably infinite (ℵ₀)
| continuum. % Uncountably infinite (2^ℵ₀)
%%% Mutability Types
-type mutability() :: mutable % Supports insert/delete (tree-based)
| immutable. % Read-only (generator-based or protected)
%%% Constraint Types
-type constraint_spec() ::
{eq, term()} % Equality: attr = value
| {neq, term()} % Inequality: attr ≠ value
| {lt, number()} % Less than: attr < value
| {lte, number()} % Less than or equal: attr ≤ value
| {gt, number()} % Greater than: attr > value
| {gte, number()} % Greater than or equal: attr ≥ value
| {in, [term()]} % Membership: attr ∈ list
| {range, number(), number()} % Range: attr ∈ [min, max]
| {member_of, atom()} % Type constraint: attr ∈ Relation
| {'and', [term()]}
| is_integer
| is_float.
-type constraints() :: #{atom() => constraint_spec()}.
-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)
%% Tuple metadata (contains provenance, lineage, and other system-managed fields)
-type tuple_metadata() :: #{
provenance => attribute_provenance(),
lineage => lineage_op()
% Future: timestamp, version, etc.
}.
%% Tuples with metadata use a nested 'meta' field:
%% #{id => 1, name => "Alice",
%% meta => #{
%% provenance => #{id => {employees, id}, name => {employees, name}},
%% lineage => {select, fun(T) -> maps:get(age, T) > 30 end, {base, employees}}
%% }}
