○{∠}

Compose

Compose Universal Language expressions from the five geometric primitives and eleven operations. Each composition is a blueprint — a foundational expression pattern built from pure geometric logic.

Expression Builder

Select primitives and operations to compose expressions. Click Validate to check well-formedness against the UL syntax engine.

Primitives

Operations

Composition

Select primitives and operations above to compose

Build UL expressions by chaining atoms and transformations

Sort Reference

eEntity

Things that exist — points, embedded assertions, results of modification

rRelation

Connections between entities — lines, curves, directed or undirected

mModifier

Transformations that alter — angles, extracted properties

aAssertion

Complete statements — predications, conjoined/disjoined frames

Blueprints

Discovered UL expression patterns — recipes for constructing meaning from geometric primitives. Each blueprint names a foundational pattern of expression.

How Composition Works

1. Choose Primitives

Start with the five geometric atoms: Point (entity), Line (relation), Angle (modifier), Curve (process), Enclosure (assertion).

2. Apply Operations

Transform and combine using the eleven operations: predicate, negate, conjoin, embed, and more. Each has a typed signature.

3. Validate & Discover

Every well-formed expression has a unique sort, level, and semantic reading. The validation engine checks well-formedness against the six UL syntax rules.

Related Sections