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
Things that exist — points, embedded assertions, results of modification
Connections between entities — lines, curves, directed or undirected
Transformations that alter — angles, extracted properties
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.