Haspelmath (2021): Bound forms, welded forms, and affixes: Basic concepts for morphological comparison

Haspelmath defines an affix as a bound morph that is not a root, that must occur on a root, and that cannot occur on roots of different root classes, where a bound form occurs on a root when it is next to the root or next to an affix that occurs on the root. Roots are the morphs denoting a thing, an action or a property. The definition is Morphology.Comparative.IsAffixIn with the contentful morphs as roots. This file checks it against the paper's examples and shows what its recursion needs: the inductive reading misses affixes that occur only next to other affixes, and when markers separate roots the definition can have two incompatible solutions.

Main results

• latin_affixes: Latin -bi, -v, -s and -isti are affixes, -s and -isti only through -bi and -v.
• turkish_affixes: Turkish mu is not an affix, so neither is -sun, written as a suffix, while -iyor is.
• polish_scie_not_affix, english_article_not_affix, russian_li_not_affix: bound forms on roots of two classes are not affixes.
• italian_object_affixes: the Italian object person forms are affixes on either side of the verb, though the Italian fragment records mi as a clitic.
• variableOrder_affixes: with two suffixes in either order, the least solution has no affix and the greatest has both.
• separated_affixes: when two markers separate two roots, each marker is an affix in some solution but no solution has both.
• suffixBeforeRoot_not_affix: occurrence on a root is adjacency on either side, so a suffix followed by a root of another class is not an affix.

Implementation notes

Each example is an inventory of the paper's free forms, each a list of morphs with textbook attachment labels, together with the classes of its roots. The paper's segmentations are kept, so Polish domu and zrobili are single morphs. The welded forms of §5 are not formalized.

References

• [Has21a]

Latin (16)

def Haspelmath2021c.lauda : Morphology.Morph

The Latin action root lauda- 'praise'.

Equations

• Haspelmath2021c.lauda = Morphology.Morph.root "lauda"

def Haspelmath2021c.s : Morphology.Morph

The Latin second singular suffix -s.

Equations

• Haspelmath2021c.s = Morphology.Morph.suff "s"

def Haspelmath2021c.bi : Morphology.Morph

The Latin future suffix -bi.

Equations

• Haspelmath2021c.bi = Morphology.Morph.suff "bi"

def Haspelmath2021c.v : Morphology.Morph

The Latin perfect suffix -v.

Equations

• Haspelmath2021c.v = Morphology.Morph.suff "v"

def Haspelmath2021c.isti : Morphology.Morph

The Latin second singular perfect suffix -isti.

Equations

• Haspelmath2021c.isti = Morphology.Morph.suff "isti"

def Haspelmath2021c.latin : List (List Morphology.Morph)

The Latin free forms of (16), lauda-s, lauda-bi-s and lauda-v-isti.

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def Haspelmath2021c.latinClass (m : Morphology.Morph) : Option Morphology.Comparative.RootClass

The class of the Latin root.

Equations

• Haspelmath2021c.latinClass m = if m = Haspelmath2021c.lauda then some Morphology.Comparative.RootClass.action else none

theorem Haspelmath2021c.latin_affixes : (∀ m ∈ [bi, v, s, isti], Morphology.Comparative.IsAffixIn latin latinClass (Morphology.Comparative.IsContentful latinClass) m) ∧ Morphology.Comparative.AffixStep latin latinClass (Morphology.Comparative.IsContentful latinClass) ∅ bi ∧ ¬Morphology.Comparative.AffixStep latin latinClass (Morphology.Comparative.IsContentful latinClass) ∅ s ∧ ¬Morphology.Comparative.AffixStep latin latinClass (Morphology.Comparative.IsContentful latinClass) ∅ isti

The four suffixes of (16) are affixes, -s and -isti because they occur next to -bi and -v. With no affixes given, only -bi and -v pass.

Turkish (18)

def Haspelmath2021c.gel : Morphology.Morph

The Turkish action root gel 'come'.

Equations

• Haspelmath2021c.gel = Morphology.Morph.root "gel"

def Haspelmath2021c.iyor : Morphology.Morph

The Turkish progressive suffix -iyor.

Equations

• Haspelmath2021c.iyor = Morphology.Morph.suff "iyor"

def Haspelmath2021c.sun : Morphology.Morph

The Turkish second singular -sun, written as a suffix.

Equations

• Haspelmath2021c.sun = Morphology.Morph.suff "sun"

def Haspelmath2021c.mu : Morphology.Morph

The Turkish question particle mu, written apart.

Equations

• Haspelmath2021c.mu = Morphology.Morph.encl "mu"

def Haspelmath2021c.su : Morphology.Morph

The Turkish object root su 'water'.

Equations

• Haspelmath2021c.su = Morphology.Morph.root "su"

def Haspelmath2021c.turkish : List (List Morphology.Morph)

The Turkish free forms of (18), gel-iyor-sun, gel-iyor mu-sun and su mu.

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def Haspelmath2021c.turkishClass (m : Morphology.Morph) : Option Morphology.Comparative.RootClass

The classes of the Turkish roots.

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theorem Haspelmath2021c.turkish_affixes : Morphology.Comparative.IsAffixIn turkish turkishClass (Morphology.Comparative.IsContentful turkishClass) iyor ∧ ¬Morphology.Comparative.IsAffixIn turkish turkishClass (Morphology.Comparative.IsContentful turkishClass) mu ∧ sun.kind = Morphology.Morph.Kind.bound Morphology.Morph.Position.after Morphology.Morph.Attachment.affix ∧ ¬Morphology.Comparative.IsAffixIn turkish turkishClass (Morphology.Comparative.IsContentful turkishClass) sun

In (18), mu occurs on a verb and on a noun, so it is not an affix, and -sun follows it in (18b), so -sun is not an affix either, although it is written as a suffix; -iyor is one.

Bound forms on roots of two classes (15)

def Haspelmath2021c.w : Morphology.Morph

The Polish preposition w 'in'.

Equations

• Haspelmath2021c.w = Morphology.Morph.free "w"

def Haspelmath2021c.domu : Morphology.Morph

The Polish object form domu 'house'.

Equations

• Haspelmath2021c.domu = Morphology.Morph.root "domu"

def Haspelmath2021c.to : Morphology.Morph

The Polish demonstrative to 'that'.

Equations

• Haspelmath2021c.to = Morphology.Morph.free "to"

def Haspelmath2021c.zrobili : Morphology.Morph

The Polish action form zrobili 'did'.

Equations

• Haspelmath2021c.zrobili = Morphology.Morph.root "zrobili"

def Haspelmath2021c.scie : Morphology.Morph

The Polish second plural =ście.

Equations

• Haspelmath2021c.scie = Morphology.Morph.encl "ście"

def Haspelmath2021c.polish : List (List Morphology.Morph)

The Polish free forms of (15), W domu to zrobili=ście? and W domu=ście to zrobili?.

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def Haspelmath2021c.polishClass (m : Morphology.Morph) : Option Morphology.Comparative.RootClass

The classes of the Polish roots.

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theorem Haspelmath2021c.polish_scie_not_affix : ¬Morphology.Comparative.IsAffixIn polish polishClass (Morphology.Comparative.IsContentful polishClass) scie

In (15), =ście occurs on a verb and on a noun, so it is not an affix.

def Haspelmath2021c.a : Morphology.Morph

The English indefinite article a.

Equations

• Haspelmath2021c.a = Morphology.Morph.free "a"

def Haspelmath2021c.an : Morphology.Morph

The English indefinite article an.

Equations

• Haspelmath2021c.an = Morphology.Morph.free "an"

def Haspelmath2021c.house : Morphology.Morph

The English object root house.

Equations

• Haspelmath2021c.house = Morphology.Morph.root "house"

def Haspelmath2021c.apple : Morphology.Morph

The English object root apple.

Equations

• Haspelmath2021c.apple = Morphology.Morph.root "apple"

def Haspelmath2021c.big : Morphology.Morph

The English property root big.

Equations

• Haspelmath2021c.big = Morphology.Morph.root "big"

def Haspelmath2021c.open : Morphology.Morph

The English property root open.

Equations

• Haspelmath2021c.open = Morphology.Morph.root "open"

def Haspelmath2021c.english : List (List Morphology.Morph)

The English free forms a house, an apple, a big house and an open house.

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def Haspelmath2021c.englishClass (m : Morphology.Morph) : Option Morphology.Comparative.RootClass

The classes of the English roots.

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theorem Haspelmath2021c.english_article_not_affix : ¬Morphology.Comparative.IsAffixIn english englishClass (Morphology.Comparative.IsContentful englishClass) a ∧ ¬Morphology.Comparative.IsAffixIn english englishClass (Morphology.Comparative.IsContentful englishClass) an

The English indefinite article occurs on nouns and on prenominal adjectives, so neither of its shapes is a prefix.

def Haspelmath2021c.znaesh : Morphology.Morph

The Russian action form znaeš' 'you know'.

Equations

• Haspelmath2021c.znaesh = Morphology.Morph.root "znaeš'"

def Haspelmath2021c.zdorov : Morphology.Morph

The Russian property form zdorov 'well'.

Equations

• Haspelmath2021c.zdorov = Morphology.Morph.root "zdorov"

def Haspelmath2021c.zdes : Morphology.Morph

The Russian adverb zdes' 'here'.

Equations

• Haspelmath2021c.zdes = Morphology.Morph.free "zdes'"

def Haspelmath2021c.li : Morphology.Morph

The Russian interrogative enclitic li.

Equations

• Haspelmath2021c.li = Morphology.Morph.encl "li"

def Haspelmath2021c.russian : List (List Morphology.Morph)

The Russian free forms znaeš' li?, zdorov li? and zdes' li?.

Equations

• Haspelmath2021c.russian = [[Haspelmath2021c.znaesh, Haspelmath2021c.li], [Haspelmath2021c.zdorov, Haspelmath2021c.li], [Haspelmath2021c.zdes, Haspelmath2021c.li]]

def Haspelmath2021c.russianClass (m : Morphology.Morph) : Option Morphology.Comparative.RootClass

The classes of the Russian roots.

Equations

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theorem Haspelmath2021c.russian_li_not_affix : ¬Morphology.Comparative.IsAffixIn russian russianClass (Morphology.Comparative.IsContentful russianClass) li

li occurs on verbs and adjectives, so it is not an affix.

Italian (19)

def Haspelmath2021c.mi : Morphology.Morph

The Italian first singular dative mi, before the verb.

Equations

• Haspelmath2021c.mi = Morphology.Morph.procl Italian.Pronouns.mi_dat.form

def Haspelmath2021c.mmi : Morphology.Morph

The Italian first singular dative -mmi, after an imperative.

Equations

• Haspelmath2021c.mmi = Morphology.Morph.encl "mmi"

def Haspelmath2021c.da : Morphology.Morph

The Italian action root da 'give'.

Equations

• Haspelmath2021c.da = Morphology.Morph.root "da"

def Haspelmath2021c.italian : List (List Morphology.Morph)

The Italian free forms of (19), mi da and da-mmi.

Equations

• Haspelmath2021c.italian = [[Haspelmath2021c.mi, Haspelmath2021c.da], [Haspelmath2021c.da, Haspelmath2021c.mmi]]

def Haspelmath2021c.italianClass (m : Morphology.Morph) : Option Morphology.Comparative.RootClass

The class of the Italian root.

Equations

• Haspelmath2021c.italianClass m = if m = Haspelmath2021c.da then some Morphology.Comparative.RootClass.action else none

theorem Haspelmath2021c.italian_object_affixes : Italian.Pronouns.mi_dat.strength = some Pronoun.Strength.clitic ∧ Morphology.Comparative.IsAffixIn italian italianClass (Morphology.Comparative.IsContentful italianClass) mi ∧ Morphology.Comparative.IsAffixIn italian italianClass (Morphology.Comparative.IsContentful italianClass) mmi

In (19), the object person forms always occur on verb roots, on either side, so they are affixes, although the Italian fragment records mi as a clitic.

Solutions of the definition

inductive Haspelmath2021c.Schematic : Type

The schematic inventories have three roots and two bound morphs.

• y : Schematic
• y₁ : Schematic
• y₂ : Schematic
• x : Schematic
• z : Schematic

@[instance_reducible]

instance Haspelmath2021c.instDecidableEqSchematic : DecidableEq Schematic

Equations

• Haspelmath2021c.instDecidableEqSchematic x✝ y✝ = if h : x✝.ctorIdx = y✝.ctorIdx then isTrue ⋯ else isFalse ⋯

@[instance_reducible]

instance Haspelmath2021c.instFintypeSchematic : Fintype Schematic

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@[instance_reducible]

instance Haspelmath2021c.instReprSchematic : Repr Schematic

Equations

• Haspelmath2021c.instReprSchematic = { reprPrec := Haspelmath2021c.instReprSchematic.repr }

def Haspelmath2021c.instReprSchematic.repr : Schematic → ℕ → Std.Format

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def Haspelmath2021c.schematicClass : Schematic → Option Morphology.Comparative.RootClass

The classes of the schematic roots.

Equations

• Haspelmath2021c.schematicClass Haspelmath2021c.Schematic.y = some Morphology.Comparative.RootClass.action
• Haspelmath2021c.schematicClass Haspelmath2021c.Schematic.y₂ = some Morphology.Comparative.RootClass.action
• Haspelmath2021c.schematicClass Haspelmath2021c.Schematic.y₁ = some Morphology.Comparative.RootClass.object
• Haspelmath2021c.schematicClass Haspelmath2021c.Schematic.x = none
• Haspelmath2021c.schematicClass Haspelmath2021c.Schematic.z = none

def Haspelmath2021c.variableOrder : List (List Schematic)

One root with two suffixes in either order.

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theorem Haspelmath2021c.variableOrder_affixes : (∀ (m : Schematic), ¬Morphology.Comparative.AffixStep variableOrder schematicClass (Morphology.Comparative.IsContentful schematicClass) ∅ m) ∧ {m : Schematic | Morphology.Comparative.IsAffixIn variableOrder schematicClass (Morphology.Comparative.IsContentful schematicClass) m} = {Schematic.x, Schematic.z} ∧ ∀ f ∈ variableOrder, Morphology.Comparative.RootsContiguous (Morphology.Comparative.IsContentful schematicClass) f

With two suffixes in either order, the empty set solves the definition, so its least solution has no affix, while both suffixes are affixes, its greatest solution.

def Haspelmath2021c.separated : List (List Schematic)

Two roots of different classes separated by two bound morphs, each also next to one root.

Equations

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theorem Haspelmath2021c.separated_affixes : Morphology.Comparative.IsAffixIn separated schematicClass (Morphology.Comparative.IsContentful schematicClass) Schematic.x ∧ Morphology.Comparative.IsAffixIn separated schematicClass (Morphology.Comparative.IsContentful schematicClass) Schematic.z ∧ ¬Morphology.Comparative.AffixStep separated schematicClass (Morphology.Comparative.IsContentful schematicClass) {m : Schematic | m = Schematic.x ∨ m = Schematic.z} Schematic.x ∧ ¬Morphology.Comparative.AffixStep separated schematicClass (Morphology.Comparative.IsContentful schematicClass) {m : Schematic | m = Schematic.x ∨ m = Schematic.z} Schematic.z

When two markers separate two roots, each marker is an affix in some solution of the definition, but given that both are affixes, neither passes.

def Haspelmath2021c.suffixBeforeRoot : List (List Schematic)

A suffix that always follows an object root, followed in a longer free form by an action root.

Equations

• Haspelmath2021c.suffixBeforeRoot = [[Haspelmath2021c.Schematic.y₁, Haspelmath2021c.Schematic.x], [Haspelmath2021c.Schematic.y₁, Haspelmath2021c.Schematic.x, Haspelmath2021c.Schematic.y₂]]

theorem Haspelmath2021c.suffixBeforeRoot_not_affix : ¬Morphology.Comparative.IsAffixIn suffixBeforeRoot schematicClass (Morphology.Comparative.IsContentful schematicClass) Schematic.x

Occurrence on a root is adjacency on either side, so a suffix that always follows an object root but precedes an action root in a longer free form occurs on roots of two classes, and is not an affix.