The Minimalist Program seeks the most parsimonious principles explaining universal grammar. It reduces core operations to Merge (binary combination) and Move (displacement), arguing that much linguistic complexity emerges from simple mechanisms interacting with interface systems. This program fundamentally reframes generative syntax toward parsimony and explanatory adequacy.
From your work with X-bar theory and syntactic movement, you have a rich toolkit for describing sentence structure: specifiers, heads, complements, movement to checking positions, traces and copies. The Minimalist Program does not discard this descriptive machinery; it asks a more fundamental question: why does grammar have the specific properties it does? What forces are responsible? The answer it proposes is radical in its simplicity — most of what we observe follows from a single recursive operation interacting with requirements imposed by the systems that use linguistic output.
That operation is Merge. Merge takes two syntactic objects — at the start of a derivation, these are lexical items drawn from the numeration — and combines them into a new set. This is binary and recursive: every syntactic structure, however complex, is built by iterating this one operation. What you analyzed as phrasal projections in X-bar theory — the NP dominating a head noun, the VP dominating verb and complement — are the output of repeated Merge operations. The hierarchical structure of sentences, which grammarians have described with tree diagrams since generative grammar began, falls out from a mechanism no more complex than set formation.
Movement, which in earlier frameworks was a separate operation triggered by specific phrase-structure rules, gets a new analysis in minimalism. The key insight is that displacement — the fact that elements appear in positions different from where they are semantically interpreted — can be treated as Internal Merge: Merge applied to an object already present in the derivation. When a wh-phrase moves to the front of a question, it is not obeying a separate "move alpha" rule; it is being Merged again, from an already-internal position. This unification is a theoretical achievement because it reduces the primitive operations of the grammar from two to one.
What drives movement in this framework is feature-checking. Lexical items carry uninterpretable formal features (like a wh-feature or a Case feature) that must be eliminated before the derivation can interface with phonology and semantics. Internal Merge positions an element where its features can be valued and deleted. This means syntactic computation is, in a sense, driven by the requirements of the two interfaces — the Phonological Form (PF) that sends structure to the articulatory-perceptual system, and the Logical Form (LF) that sends it to the conceptual-intentional system. The grammar is, on this view, a solution to the problem of connecting sound and meaning.
The philosophical ambition behind all of this is the Strong Minimalist Thesis: that the language faculty is an optimal — or near-optimal — solution to the interface conditions, given the requirement that it use only the most elementary computationally available operations. If correct, this would explain why language has the specific formal properties it does (binary branching, displacement, recursive embedding) without stipulating those properties as primitive facts about the human genome. Whether the thesis is fully defensible is actively debated, but it has driven two decades of productive formal work on what can and cannot be derived from minimal assumptions.