Merge and the formal recognition of the workspace

Chomsky reconceives Merge as an operation on the workspace (10): it targets two accessible terms P and Q and adds {P, Q}. What else the output holds follows from two third-factor principles, Preservation of Terms (11) and Minimal Yield (12), under which accessibility, the members of the workspace and their terms, grows by exactly one. Keeping the Merge-ees as members would raise it by more (18), so they leave the workspace (20); External and Internal Merge then satisfy Minimal Yield (21)–(22), and Parallel and Sideward Merge, Late Merge and Countercyclic Merge do not (23)–(25).

Marcolli, Chomsky and Berwick state Minimal Yield over a count of accessible terms, and its condition on size is this one at the count of distinct terms (minimalYield_of_minimalist). Their Sideward Merge of type 2(b) is MERGE leaving the extracted term's trace, an inaccessible leaf, and satisfies their Minimal Yield; MERGE of the same targets leaving the term's copy keeps it accessible where it was and violates Minimal Yield (sideward2b).

Implementation notes

• MERGE is Workspace.merge, MERGE leaving copies, and Preservation of Terms Workspace.terms_subset_terms_merge; MERGE leaving traces is Workspace.mergeWith.
• The terms of an object are counted once each, so the lower copy of an internally merged term is not counted again, minimal search finding the higher copy first; copies in different members of the workspace are counted apart.
• The leaves a to d stand for the chapter's schematic lexical items.

References

• Kitahara & Seely 2026, Merge and the formal recognition of the workspace
• Marcolli et al. 2025, Mathematical Structure of Syntactic Merge: An Algebraic Model for Generative Linguistics formalized