Paradigms: forms over ordered cells

The morphologist's primary observable: a paradigm assigns a surface form to each of n linearly ordered cells. One type serves both research lines that consume it — realization-pattern typology (*ABA and contiguity, Morphology/Paradigm/Contiguity.lean) and paradigm-cell information theory (implicative structure and complexity, Morphology/Paradigm/Complexity.lean). [AM13a]'s inflection classes are paradigms with frequency weights (ParadigmSystem); [Bob12]-style realization patterns are paradigms over graded cells.

Main declarations

• Paradigm n F — assignment of a form to each of the n cells
• ParadigmSystem n Form — paradigms with frequency weights, organized by inflection class
• cellDistribution, jointCellDistribution — empirical form distributions at cells
• eComplexity — count of inflection classes (Ackerman-Malouf E-complexity)

@[reducible, inline]

abbrev Morphology.Paradigm (n : ℕ) (F : Type u_1) : Type u_1

A paradigm over n linearly ordered cells: the form occupying each cell. The single carrier for realization patterns ([Bob12]'s AAA/ABB/ABC shapes; see Morphology/Paradigm/Contiguity.lean) and for inflection-class rows ([AM13a]; a weighted system of paradigms is a ParadigmSystem).

Equations

• Morphology.Paradigm n F = (Fin n → F)

structure Morphology.ParadigmSystem (numCells : ℕ) (Form : Type u_1) : Type u_1

A paradigm system: paradigms (inflection classes) paired with frequency weights.

• entries : List (Paradigm numCells Form × ℚ)

def Morphology.groupBySum {α : Type u_1} [DecidableEq α] (tagged : List (α × ℚ)) : List (α × ℚ)

Group a tagged list by key, summing associated ℚ values.

Equations

• One or more equations did not get rendered due to their size.

def Morphology.ParadigmSystem.cellDistribution {n : ℕ} {Form : Type u_1} [DecidableEq Form] (ps : ParadigmSystem n Form) (c : Fin n) : List (Form × ℚ)

Empirical distribution of forms at cell c: pairs each surface form with the total frequency of inflection classes realizing it at c.

Equations

• ps.cellDistribution c = Morphology.groupBySum (List.map (fun (x : Morphology.Paradigm n Form × ℚ) => match x with | (ic, f) => (ic c, f)) ps.entries)

def Morphology.ParadigmSystem.jointCellDistribution {n : ℕ} {Form : Type u_1} [DecidableEq Form] (ps : ParadigmSystem n Form) (ci cj : Fin n) : List ((Form × Form) × ℚ)

Joint empirical distribution of forms at cell pair (ci, cj).

Equations

• One or more equations did not get rendered due to their size.

def Morphology.ParadigmSystem.eComplexity {n : ℕ} {Form : Type u_1} (ps : ParadigmSystem n Form) : ℕ

E-complexity ([AM13a]): the number of inflection classes in the paradigm system.

Equations

• ps.eComplexity = ps.entries.length