ExpressSets

ExpressSets is a conceptual framework for representing and manipulating sets of items through expressive set expressions. It models sets as trees of operations and operands, enabling complex constructions to be described succinctly and evaluated in a controlled, often lazy, fashion.

An ExpressSet can be built from a finite list of elements, a predicate over a domain, or a combination of both. The central idea is a SetExpr, a tree whose internal nodes represent operations such as union, intersection, difference, and complement, and whose leaves are base sets or predicates.

Key features include lazy evaluation, caching of subexpressions, and algebraic simplification. Predicates can be treated as first-class operands, allowing symbolic or infinite domains to be represented, while evaluation is driven by data sources through push-down filters when possible.

Use cases span database query planning, data analytics pipelines, streaming filters, and constraint solving, where the solution space is naturally described as a composition of set operations.

Limitations include potential performance costs for deep expression trees and predicates that are expensive to evaluate, particularly without effective caching and sharing of subexpressions.

See also: set theory, relational algebra, predicate logic, symbolic computation.