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%%% 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 (finite only), undefined for infinite
schema, % #{attribute_name => type}
constraints, % #{attribute_name => constraint_spec()} - integrity constraints
cardinality, % {finite, N} | aleph_zero | continuum
generator, % Generator function (infinite only), undefined for finite
provenance % Provenance tracking for updatable views (future)
}).
-record(tuple, {hash, relation, attribute_map}).
-record(attribute, {hash, value}).
%%% Cardinality Types
-type cardinality() :: {finite, non_neg_integer()} % Finite set with N elements
| aleph_zero % Countably infinite (ℵ₀)
| continuum. % Uncountably infinite (2^ℵ₀)
%%% 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
-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)
-type provenance() :: undefined
| {base, atom()} % Base relation
| {join, provenance(), provenance()}
| {select, provenance(), constraints()}
| {project, provenance(), [atom()]}
| {take, provenance(), pos_integer()}.
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