Post-Syntactic Operations (Distributed Morphology)

@cite{embick-noyer-2001} @cite{halle-marantz-1993}

Post-syntactic operations modify the output of the Syntax before Vocabulary Insertion. Linglib already has Impoverishment (feature deletion) and Fission (terminal splitting). This module adds the remaining operations from the DM inventory:

• Lowering: a head adjoins downward to its complement head at PF
• Local Dislocation: linear adjacency is traded for affixation
• Fusion: two adjacent terminals merge into one
• Dissociated Node Insertion: a morphosyntactic node is inserted that has no source in the syntactic derivation

These operations apply after syntax and before Vocabulary Insertion, in the morphological structure (MS) — a representation derived from syntax that serves as input to VI.

@cite{kalin-bjorkman-etal-2026} §3.3.3, §4.2, §4.4, §4.5.2.

structure Morphology.DM.PostSyntactic.LoweringRule (Head : Type) : Type

Lowering (@cite{embick-noyer-2001}): a head X adjoins downward to the head Y of its complement, at PF.

Precondition: X c-commands Y (X selects YP as complement). Effect: X affixes to Y, forming [Y X+Y] (or [Y Y+X]).

Canonical example: English tense lowering — T lowers to V at PF, yielding V+T (walk-ed). When lowering is blocked (by an intervening element), do-support repairs the structure.

Lowering is the PF counterpart of head raising: both produce complex heads, but lowering goes down (counter to the Head Movement Constraint). It is post-syntactic because the Syntax generates X above Y; the downward adjunction happens at PF.

• source : Head

  The head that lowers (e.g., T).

• target : Head

  The head it lowers to (e.g., V).

• leftAdjoin : Bool

  Is the source head left-adjoined (prefix) or right-adjoined (suffix) to the target?

def Morphology.DM.PostSyntactic.LoweringRule.apply {Head : Type} (r : LoweringRule Head) : Head × Head

Apply lowering: merge source into target, producing a complex head. Returns the ordered pair of heads (left, right).

Equations

• r.apply = if r.leftAdjoin = true then (r.source, r.target) else (r.target, r.source)

structure Morphology.DM.PostSyntactic.LocalDislocationRule (Elem : Type) : Type

Local Dislocation (@cite{embick-noyer-2001}): takes two linearly adjacent elements X and Y (where X precedes Y), and adjoins X to Y (or vice versa), potentially reordering them.

Unlike Lowering, Local Dislocation is sensitive to linear adjacency, not hierarchical structure. It cannot skip over intervening material.

Notation from Embick & Noyer (2001):

• Input: [X * [Y * Z]] (* = linear adjacency)
• Output: [[ Y+X ] * Z] (+ = morphological attachment)

Canonical use: p-bound clitics that "tuck in" to a phrase they are linearly adjacent to, appearing to disrupt constituency.

• triggers : Elem → Bool

  Does this element undergo dislocation?

• leftAdjoin : Bool

  Does the dislocated element left-adjoin or right-adjoin to its host?

structure Morphology.DM.PostSyntactic.FusionRule (Terminal : Type) : Type

Fusion (@cite{halle-marantz-1993}): merges two adjacent terminal nodes into a single terminal before Vocabulary Insertion.

The fused node bears the union of both terminals' features. A single Vocabulary Item then spells out the fused bundle, yielding a portmanteau.

Canonical example: French du = Fusion of P[de] and D[le.MASC.SG]. The fused node [P, D, MASC, SG] is spelled out by the VI du.

Fusion is the DM mechanism for deriving portmanteaux from syntactically distinct heads. It applies between structurally adjacent terminals (typically head and complement head).

@cite{kalin-bjorkman-etal-2026} §4.4.

• terminal1 : Terminal

  First terminal (structurally higher).

• terminal2 : Terminal

  Second terminal (structurally lower / complement head).

def Morphology.DM.PostSyntactic.FusionRule.apply {Terminal Features : Type} (r : FusionRule Terminal) (getFeatures : Terminal → Features) (union : Features → Features → Features) : Features

The result of Fusion: a single terminal bearing features from both inputs. Parameterized over a feature-union operation.

Equations

• r.apply getFeatures union = union (getFeatures r.terminal1) (getFeatures r.terminal2)

structure Morphology.DM.PostSyntactic.DissociatedNode (Feature : Type) : Type

Dissociated Node Insertion (@cite{halle-marantz-1993}; @cite{embick-noyer-2001} call this "node-sprouting"): insertion of a morphosyntactic terminal node that has no source in the narrow syntactic derivation.

Dissociated nodes are introduced post-syntactically to provide positions for morphemes that are "ornamental" — present in the morphological structure but not required by the syntax.

Canonical examples:

• Theme vowels in Romance: the vowel between verb root and inflectional suffix (cant-a-nt 'singing') has no syntactic source but is required for well-formedness.
• Linkers in compounds: Dutch -s- in wetgeving-s-advies 'legislative advice'.
• Agreement nodes: in some analyses, agreement morphemes are dissociated nodes inserted at PF, not present in syntax.

@cite{kalin-bjorkman-etal-2026} §4.5.2.

• features : List Feature

  Features borne by the inserted node (may be empty for purely phonotactic elements like theme vowels).

• insertAfter : Bool

  Structural context: where is the node inserted? true = after the host terminal; false = before.