Linearized syntactic objects as constituency trees

A linearized syntactic object is a rose tree over vertices, so relabelling its vertices gives a constituency tree with the same shape: a lexical leaf becomes a terminal, the bare label of an internal node a projection, and a trace a trace. The positions, and so the branching nodes, are the object's, so the tree pronounces the object's tokens in order and its c-command is the object's, which is c-command between the terms at those positions when the commander's term occurs once (its terms). Whatever reads a constituency tree, the type-driven composition engine, binding configurations and the spans of prosodic constituency, then reads a Minimalist object.

Implementation notes

• Categories are Unit. The engine, c-command and the yield ignore categories; the categories a head function assigns (Minimalist.lexicalHeadAt) depend on the position, not on the vertex, and are not a relabelling.
• A constituency tree has traces and binders only, so a copy is not represented. The trace of a token has the index ι gives the token, plus one, and the index-free trace has index 0, so that no token's trace shares the index-free trace's. No binder is introduced: a trace is free in the tree, interpreted by the assignment.

References

• Heim & Kratzer 1998, Semantics in Generative Grammar formalized
• Marcolli et al. 2025, Mathematical Structure of Syntactic Merge: An Algebraic Model for Generative Linguistics formalized
• Collins & Stabler 2016, A Formalization of Minimalist Syntax