Stump (2006): Heteroclisis and paradigm linkage #
This file formalizes Stump's account of heteroclisis, the property of a lexeme whose paradigm contains forms built on stems of two or more inflection classes. A rule of paradigm linkage gives a content cell of a lexeme a form correspondent built on one of the lexeme's stems: the universal default assigns the root, and narrower language-specific rules override it by Pāṇini's principle, assigning a coradical, a stem that differs from the root in form or in inflection class. The paper's rules (5), (14), (15), (17) and (18), with the endings of the Czech declension fragment, after Short's tables and the rules of Mluvnice češtiny, realize every form of the Czech nouns in its Tables 1, 6 and 8, read from the forms data, once the masculine a-stems' nominative plural in -ové is read from their own class and FILOSOF's, which neither grammar gives, is supplied. The heteroclisis of Czech PRAMEN is morphosyntactically conditioned, its inflection class fixed by the property sets its cells express, whereas that of Sanskrit AHAN is morphologically conditioned, following a pattern of alternation among Strong, Middle and Weakest stems. Stump's Sanskrit rules of paradigm linkage (20a,b) "are independently motivated by the need to account for the pattern of stem alternation in nonheteroclite paradigms such as the masculine and neuter paradigms of PRATYAÑC" (p. 295): one list of rules gives the grades of PRATYAÑC's stems, which share a declension, and the stems of AHAN, which do not. The paper measures how closely a heteroclite paradigm's class boundary follows an inflectional category, and claims that the categories serving as absolute correlates are privileged: every rule of paradigm linkage sensitive to some category is sensitive to a privileged one.
Main definitions #
attested: the forms of a Czech cell, every matching row of the forms data.Decl.toClass,CzNoun.noun: the paper's declensions as classes of Short's tables, and the nouns as entries of the Czech noun fragment.Stem,Entry,inferSoftMasc: stems individuated by lexeme and declension, lexical entries read off the nouns, and the rule of stem inference (18).CellRule,rulesFor,stemFor: the rules of paradigm linkage (14), (15) and (17) as domain rules, resolved by the Elsewhere engine with the root of rule (5) as the fallback.classNomPl,nomPlOverride,suppliedNomPl: the masculine a-stems' nominative plural read from their class, FILOSOF's, which neither grammar gives, and the two together.czRealize,czLinkage: the realization of form cells and the Czech paradigm linkage.degreeNum,degree: the degree of correlation of a category with a class split.IsAbsoluteCorrelate,IsMaximalCorrelate,IsCloven,IsFractured,IsIntersectiveCorrelate: the paper's classification of heteroclite paradigms, over any cells pairing a case with a number.SensitiveTo,Privileged,SatisfiesPCR: the privileged category restriction.SktForm,f₁: Sanskrit form property sets and the property mapping (10).strength,rule20a,rule20b,sktLinkage: the strong and weak property sets of (19), the rules (20a,b), and the linkage of PRATYAÑC and AHAN.hrdLinkage,matLinkage: Sanskrit HṚD(AYA) and Russian MAT'.
Main results #
realize_matches_tables: the rules realize every attested form of the nine Czech nouns.czRealizeTable_stemFor_iff: the fragment's endings alone miss exactly the six nominative and vocative plurals of PŘEDSEDA, SLUHA and FILOSOF.predseda_eq_hrdina,sluha_eq_hrdina_iff: rules (14) and (15) rebuild Short's paradigm of the masculine a-stems, from which SLUHA's departs only in the locative plural.sluha_locPl,filolog_locPl,filologu_voc: the grammars' velar forms, derived, the locative plurals alike through the soft-masculine coradical and the hard-masculine stem.pramen_eq_koren_pattern: rule (14) gives PRAMEN the classes the grammars give kořen.heteroclite_iff,segments_invariant,pramen_suppletive: PRAMEN, PŘEDSEDA, SLUHA and FILOLOG are heteroclite on form-identical stems, and heteroclisis is suppletion.degreeNum_eq_card_iff: a category is an absolute correlate exactly when the class split factors through it.pramen_degrees,predseda_degrees,sluha_degrees,filolog_degrees: the paper's figures.isAbsoluteCorrelate_of_rules: rules seeing only a category make it an absolute correlate.pcr,not_satisfiesPCR_hypothetical: the Czech rules satisfy (40), and a case-only rule would violate it.fractured_minimal_intersective_privileged: claim (39) for the Czech nouns.rules_match_table9,rules_match_table10: (19) and (20a,b) give PRATYAÑC's grades and AHAN's stems at every cell of Tables 9 and 10.pratyanc_not_heteroclite,ahan_heteroclite,ahan_grade_eq_pratyancN: one list of rules makes AHAN heteroclite and PRATYAÑC not, with the same grades.ahan_degrees,ahan_fractured: AHAN's paradigm is fractured, its case correlation .71.hrd_cloven,privileged_case,pcr_skt: case, the absolute correlate of HṚD(AYA)'s cloven paradigm, is privileged, and (20a,b) satisfy (40).hrd_form_suppletive,mat_suppletive_not_heteroclite: suppletion with and without heteroclisis.
Implementation notes #
A Czech noun's segments are the stem of its entry in the Czech noun fragment, the citation form less
the nominative singular ending of its class, so PŘEDSEDA's root and coradical share the segments
předsed. A stem's endings are the fragment's endings of its noun in the class that the stem's
declension is for the noun's animacy, with the velar vocative singular -u and locative plural -ích
and the noun's lexical nominative plural, MUŽ's -i or -ové and FILOLOG's -ové, and the stem is
inflected as the fragment inflects it, palatalized before the masculine locative plural -ích and the
animate nominative plural -i. Where the paper and the grammars differ the paper's forms stand and
the difference is stated: the nominative and vocative plurals in -ové of PŘEDSEDA and SLUHA,
realized on the hard-masculine coradical, whose class gives -i, are read from their own class, and
FILOSOF's, which neither grammar gives, is an override; Stump's hard-feminine roots for the
masculine a-stems rebuild Short's separate hrdina declension; and his soft-masculine coradical of
velar stems gives the locative plurals in -ích that Mluvnice češtiny's rule gives the
hard-masculine stem.
Sanskrit endings are read off exemplars, chosen by declension among PRATYAÑC, NĀMAN and MANAS. Rules
compete by domain inclusion, the rendering of Pāṇini's principle, and selection falls back on the
root, by (5) and (12). Gender is taken as lexical: PRATYAÑC's masculine and neuter are two lexemes,
clause (ii) of f₁ is vacuous, and the feminine, whose ī-stem pratīcī (n. 18) would make PRATYAÑC
heteroclite, is left out, as are n. 21's stem indexing and n. 22's alternants. Sanskrit sandhi
(aho-bhis, pratyag-) is unstated, so no forms are built. Rows are filtered by language.
References #
Cells and the attested forms #
A content cell of a Czech noun is a cell of Short's declension tables, pairing a case of the Czech inventory with a number, gender being constant within a paradigm.
Equations
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caseOf c reads a case of the forms data as a case.
Equations
- Stump2006.caseOf UD.Case.Nom = some Case.nom
- Stump2006.caseOf UD.Case.Gen = some Case.gen
- Stump2006.caseOf UD.Case.Dat = some Case.dat
- Stump2006.caseOf UD.Case.Acc = some Case.acc
- Stump2006.caseOf UD.Case.Voc = some Case.voc
- Stump2006.caseOf UD.Case.Loc = some Case.loc
- Stump2006.caseOf UD.Case.Ins = some Case.inst
- Stump2006.caseOf UD.Case.Abl = some Case.abl
- Stump2006.caseOf x✝ = none
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The case of a form's cell.
Equations
- Stump2006.caseOfForm f = Option.bind f.cell.case_ Stump2006.caseOf
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The number of a form's cell.
Equations
- Stump2006.numberOfForm f = Option.bind f.cell.number Stump2006.numberOf
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czForms are the Czech rows of the forms data, those of Tables 1, 6 and 8.
Equations
- Stump2006.czForms = List.filter (fun (x : Data.Forms.Form Stump2006.Forms.Cell) => x.languageId == "czec1258") Stump2006.Forms.all
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The Czech nouns of Tables 1, 6 and 8 are POKOJ 'room', PRAMEN 'spring', MOST 'bridge', ŽENA 'woman', PŘEDSEDA 'president', FILOSOF 'philosopher', SLUHA 'servant', FILOLOG 'philologist' and MUŽ 'man'.
- pokoj : CzNoun
- pramen : CzNoun
- most : CzNoun
- zena : CzNoun
- predseda : CzNoun
- filosof : CzNoun
- sluha : CzNoun
- filolog : CzNoun
- muz : CzNoun
Instances For
Equations
- Stump2006.instDecidableEqCzNoun x✝ y✝ = if h : x✝.ctorIdx = y✝.ctorIdx then isTrue ⋯ else isFalse ⋯
Equations
- Stump2006.instFintypeCzNoun = { elems := { val := ↑Stump2006.CzNoun.enumList, nodup := Stump2006.CzNoun.enumList_nodup }, complete := Stump2006.instFintypeCzNoun._proof_1 }
Equations
- Stump2006.instReprCzNoun.repr Stump2006.CzNoun.pokoj prec✝ = Repr.addAppParen (Std.Format.nest (if prec✝ ≥ 1024 then 1 else 2) (Std.Format.text "Stump2006.CzNoun.pokoj")).group prec✝
- Stump2006.instReprCzNoun.repr Stump2006.CzNoun.pramen prec✝ = Repr.addAppParen (Std.Format.nest (if prec✝ ≥ 1024 then 1 else 2) (Std.Format.text "Stump2006.CzNoun.pramen")).group prec✝
- Stump2006.instReprCzNoun.repr Stump2006.CzNoun.most prec✝ = Repr.addAppParen (Std.Format.nest (if prec✝ ≥ 1024 then 1 else 2) (Std.Format.text "Stump2006.CzNoun.most")).group prec✝
- Stump2006.instReprCzNoun.repr Stump2006.CzNoun.zena prec✝ = Repr.addAppParen (Std.Format.nest (if prec✝ ≥ 1024 then 1 else 2) (Std.Format.text "Stump2006.CzNoun.zena")).group prec✝
- Stump2006.instReprCzNoun.repr Stump2006.CzNoun.predseda prec✝ = Repr.addAppParen (Std.Format.nest (if prec✝ ≥ 1024 then 1 else 2) (Std.Format.text "Stump2006.CzNoun.predseda")).group prec✝
- Stump2006.instReprCzNoun.repr Stump2006.CzNoun.filosof prec✝ = Repr.addAppParen (Std.Format.nest (if prec✝ ≥ 1024 then 1 else 2) (Std.Format.text "Stump2006.CzNoun.filosof")).group prec✝
- Stump2006.instReprCzNoun.repr Stump2006.CzNoun.sluha prec✝ = Repr.addAppParen (Std.Format.nest (if prec✝ ≥ 1024 then 1 else 2) (Std.Format.text "Stump2006.CzNoun.sluha")).group prec✝
- Stump2006.instReprCzNoun.repr Stump2006.CzNoun.filolog prec✝ = Repr.addAppParen (Std.Format.nest (if prec✝ ≥ 1024 then 1 else 2) (Std.Format.text "Stump2006.CzNoun.filolog")).group prec✝
- Stump2006.instReprCzNoun.repr Stump2006.CzNoun.muz prec✝ = Repr.addAppParen (Std.Format.nest (if prec✝ ≥ 1024 then 1 else 2) (Std.Format.text "Stump2006.CzNoun.muz")).group prec✝
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Equations
- Stump2006.instReprCzNoun = { reprPrec := Stump2006.instReprCzNoun.repr }
l.paramId is the concept that the forms of l express in the forms data.
Equations
- Stump2006.CzNoun.pokoj.paramId = "room"
- Stump2006.CzNoun.pramen.paramId = "spring"
- Stump2006.CzNoun.most.paramId = "bridge"
- Stump2006.CzNoun.zena.paramId = "woman"
- Stump2006.CzNoun.predseda.paramId = "president"
- Stump2006.CzNoun.filosof.paramId = "philosopher"
- Stump2006.CzNoun.sluha.paramId = "servant"
- Stump2006.CzNoun.filolog.paramId = "philologist"
- Stump2006.CzNoun.muz.paramId = "man"
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The attested forms of a cell are the segments of every row of the forms data for the noun whose case code decodes to the comparative value of the cell's case and whose number code to its number, so a cell with two alternants has two.
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- One or more equations did not get rendered due to their size.
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Every cell has an attested form, so no statement about the attested forms holds for want of a row.
FILOSOF's dative singular has two alternants, filosofovi and filosofu.
Stems and lexical entries #
Equations
- Stump2006.instDecidableEqDecl x✝ y✝ = if h : x✝.ctorIdx = y✝.ctorIdx then isTrue ⋯ else isFalse ⋯
Equations
- Stump2006.instFintypeDecl = { elems := { val := ↑Stump2006.Decl.enumList, nodup := Stump2006.Decl.enumList_nodup }, complete := Stump2006.instFintypeDecl._proof_1 }
Equations
- Stump2006.instReprDecl = { reprPrec := Stump2006.instReprDecl.repr }
Equations
- Stump2006.instReprDecl.repr Stump2006.Decl.softMasc prec✝ = Repr.addAppParen (Std.Format.nest (if prec✝ ≥ 1024 then 1 else 2) (Std.Format.text "Stump2006.Decl.softMasc")).group prec✝
- Stump2006.instReprDecl.repr Stump2006.Decl.hardMasc prec✝ = Repr.addAppParen (Std.Format.nest (if prec✝ ≥ 1024 then 1 else 2) (Std.Format.text "Stump2006.Decl.hardMasc")).group prec✝
- Stump2006.instReprDecl.repr Stump2006.Decl.hardFem prec✝ = Repr.addAppParen (Std.Format.nest (if prec✝ ≥ 1024 then 1 else 2) (Std.Format.text "Stump2006.Decl.hardFem")).group prec✝
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A declension is, for animate and for inanimate stems, a declension of Short's tables, the soft masculine being that of muž or stroj, the hard masculine that of chlap or hrad, and the hard feminine that of žena.
Equations
- Stump2006.Decl.softMasc.toClass true = Czech.Declension.Class.muz
- Stump2006.Decl.softMasc.toClass false = Czech.Declension.Class.stroj
- Stump2006.Decl.hardMasc.toClass true = Czech.Declension.Class.chlap
- Stump2006.Decl.hardMasc.toClass false = Czech.Declension.Class.hrad
- Stump2006.Decl.hardFem.toClass x✝ = Czech.Declension.Class.zena
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For either animacy, distinct declensions are distinct classes of Short's.
Decl.ofClass k is the declension of the root of a noun of Short's class k, where the
nouns of the tables include one: the soft masculine for muž and stroj, the hard masculine
for chlap and hrad, and the hard feminine for žena and for the masculine a-stems of
hrdina, whose roots the paper takes to be hard-feminine.
Equations
- Stump2006.Decl.ofClass Czech.Declension.Class.muz = some Stump2006.Decl.softMasc
- Stump2006.Decl.ofClass Czech.Declension.Class.stroj = some Stump2006.Decl.softMasc
- Stump2006.Decl.ofClass Czech.Declension.Class.chlap = some Stump2006.Decl.hardMasc
- Stump2006.Decl.ofClass Czech.Declension.Class.hrad = some Stump2006.Decl.hardMasc
- Stump2006.Decl.ofClass Czech.Declension.Class.zena = some Stump2006.Decl.hardFem
- Stump2006.Decl.ofClass Czech.Declension.Class.hrdina = some Stump2006.Decl.hardFem
- Stump2006.Decl.ofClass x✝ = none
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The root declension of the class a declension is, for either animacy, is that declension.
l.noun is the entry of l in the Czech noun fragment.
Equations
- Stump2006.CzNoun.pokoj.noun = Czech.pokoj
- Stump2006.CzNoun.pramen.noun = Czech.pramen
- Stump2006.CzNoun.most.noun = Czech.most
- Stump2006.CzNoun.zena.noun = Czech.zena
- Stump2006.CzNoun.predseda.noun = Czech.predseda
- Stump2006.CzNoun.filosof.noun = Czech.filosof
- Stump2006.CzNoun.sluha.noun = Czech.sluha
- Stump2006.CzNoun.filolog.noun = Czech.filolog
- Stump2006.CzNoun.muz.noun = Czech.muz
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Equations
- Stump2006.instDecidableEqStem.decEq { lexeme := a, decl := a_1 } { lexeme := b, decl := b_1 } = if h : a = b then h ▸ if h : a_1 = b_1 then h ▸ isTrue ⋯ else isFalse ⋯ else isFalse ⋯
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Equations
- One or more equations did not get rendered due to their size.
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Equations
- Stump2006.instReprStem = { reprPrec := Stump2006.instReprStem.repr }
A lexical entry records a noun's stem segments, the declension of its root, whether it inflects as animate, and whether it belongs to the PRAMEN class of rule (14).
- lexeme : CzNoun
lexemeis the noun the entry describes. - segments : List String
segmentsare the segments of the noun's stems. - rootDecl : Decl
rootDeclis the declension of the noun's root. - animate : Bool
animaterecords whether the noun inflects as animate. - pramenClass : Bool
pramenClassrecords membership in the PRAMEN class, a lexical stipulation.
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Equations
- One or more equations did not get rendered due to their size.
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Equations
- Stump2006.instReprEntry = { reprPrec := Stump2006.instReprEntry.repr }
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- One or more equations did not get rendered due to their size.
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entry l is the lexical entry of l, read off its noun. The segments are the noun's stem,
the root declension is that of the noun's singular class, so that PRAMEN's root is
soft-masculine (p. 289) and PŘEDSEDA's and SLUHA's are hard-feminine, and the noun inflects as
animate when its gender is the masculine animate. Membership in the PRAMEN class, which PRAMEN,
PŘEDSEDA and SLUHA have, is the lexical stipulation of rule (14).
Equations
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The segments of a stem are those of its lexeme's entry.
Equations
- z.segments = (Stump2006.entry z.lexeme).segments
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A stem is a root when it inflects in its lexeme's root declension.
Equations
- z.IsRoot = (z.decl = (Stump2006.entry z.lexeme).rootDecl)
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The hard-masculine coradical of a noun of the PRAMEN class is its stem in the hard-masculine declension.
Equations
- e.hardMascCoradical = if e.pramenClass = true then some { lexeme := e.lexeme, decl := Stump2006.Decl.hardMasc } else none
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A noun belongs to the PŘEDSEDA subclass, "a subclass of masculine animate members of the PRAMEN class" (p. 290), when it is an animate member of the PRAMEN class.
Equations
- e.InPredsedaSubclass = (e.pramenClass = true ∧ e.animate = true)
Instances For
Equations
- Stump2006.instDecidablePredEntryInPredsedaSubclass x✝ = { decide := decide (x✝.pramenClass = true) && decide (x✝.animate = true), reflects_decide := ⋯ }
inferSoftMasc is the Czech rule of stem inference (18) (p. 292), which reads "If lexeme L
has a stem s belonging to the hard-masculine declension and s ends in a back obstruent, then L
has s′ as its soft-masculine coradical, where s′ is like s except that it belongs to the
soft-masculine declension." The back obstruents are Short's velars.
Equations
- Stump2006.inferSoftMasc z = if z.decl = Stump2006.Decl.hardMasc ∧ Czech.Declension.IsVelar z.segments then some { lexeme := z.lexeme, decl := Stump2006.Decl.softMasc } else none
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The hard-masculine stem of a noun is its root if that is hard-masculine, and otherwise its hard-masculine coradical.
Equations
- e.hardMascStem = if e.rootDecl = Stump2006.Decl.hardMasc then some e.root else e.hardMascCoradical
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The soft-masculine coradical of a noun is the stem that rule (18) infers from its hard-masculine stem.
Equations
- e.softMascCoradical = e.hardMascStem.bind Stump2006.inferSoftMasc
Instances For
Rule (18) supplies a soft-masculine coradical to SLUHA, whose hard-masculine stem is a coradical, and to FILOLOG, whose hard-masculine stem is its root, and to no other noun.
A hard-masculine coradical is a stem of its own noun.
A soft-masculine coradical is a stem of its own noun.
Rules of paradigm linkage #
A rule of paradigm linkage, instantiated for one noun, gives the cells of its domain form correspondents built on its exponent, a stem. Rules are ordered by Pāṇini's principle, by which "competition between two or more morphological markings is resolved in favor of the marking having the narrowest 'meaning'" (n. 5): a rule whose domain is included in another's is the more specific.
Instances For
datLocSg is the set of dative and locative singular cells.
Equations
- One or more equations did not get rendered due to their size.
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Rule (14) (p. 289) reads "Where L is a nominal lexeme that belongs to the PRAMEN class and has s as its hard-masculine coradical, if σ = {plural X}, then the content-cell ⟨L, σ⟩ has ⟨s, σ⟩ as its form-correspondent."
Equations
- Stump2006.rule14 e = Option.map (fun (x : Stump2006.Stem) => { dom := Stump2006.plural, exponent := x }) e.hardMascCoradical
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Rule (15) (p. 290) reads "Where L is a nominal lexeme that belongs to the PŘEDSEDA subclass and has s as its hard-masculine coradical, if σ = {α singular X} and α = dative or locative, then the content-cell ⟨L, σ⟩ has ⟨s, σ⟩ as its form-correspondent."
Equations
- Stump2006.rule15 e = if e.InPredsedaSubclass then Option.map (fun (x : Stump2006.Stem) => { dom := Stump2006.datLocSg, exponent := x }) e.hardMascCoradical else none
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Rule (17) (p. 292) reads "Where L is a nominal lexeme having s as its soft-masculine coradical, if σ = {locative plural X}, then the content-cell ⟨L, σ⟩ has ⟨s, σ⟩ as its form-correspondent."
Equations
- Stump2006.rule17 e = Option.map (fun (x : Stump2006.Stem) => { dom := Stump2006.locPl, exponent := x }) e.softMascCoradical
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The language-specific rules of paradigm linkage applying to a noun are those of (14), (15)
and (17) whose coradicals and classes the noun has. The universal default (5) is not among
them: it is the root that Linkage.ofRules falls back on.
Equations
- Stump2006.rulesFor e = (Stump2006.rule14 e).toList ++ (Stump2006.rule15 e).toList ++ (Stump2006.rule17 e).toList
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czRoot l is the root of l, the stem that rule (5), the universal default rule of
paradigm linkage (p. 286), gives every cell that none of the rules of l reaches.
Equations
- Stump2006.czRoot l = (Stump2006.entry l).root
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The stem of a cell's form correspondent is the one Pāṇini's principle selects, that of an applicable rule no applicable rule is narrower than, or the root where no rule applies.
Equations
- Stump2006.stemFor l σ = Morphology.Exponence.RuleSet.realizeMinimalD (Stump2006.czRules l) (fun (x : Stump2006.CzCell) => Stump2006.czRoot l) σ
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Every noun's entry describes that noun.
Realization #
The endings of a stem at a cell are the fragment's endings of its noun in the class its declension is for the noun's animacy: the class's endings on the noun's stem, a velar stem of the hard masculines taking the vocative singular -u (Short, p. 465; Mluvnice češtiny, p. 292) and a velar stem of the hard masculines or the masculine a-stems the locative plural -ích (Mluvnice češtiny, p. 292), with the noun's lexical nominative plural.
Equations
- z.classEndings σ = z.lexeme.noun.endingsIn (z.decl.toClass (Stump2006.entry z.lexeme).animate) σ
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The endings of a stem at a cell in the fragment are its class endings, less the -u alternating with -ovi, which is "restricted to roots belonging to the hard-masculine declension" (n. 14). The restriction is Stump's, and the fact it derives is Mluvnice češtiny's: "-u mají pouze jména podtypu I.A s tzv. skloňováním tvrdým" '-u is had only by the nouns of subtype I.A, with the so-called hard declension', and "V III. typu má D a L sg podobu jedinou, nevariantní, a to -ovi: předsedovi, husitovi, sluhovi, rikšovi" 'in type III the dative and locative singular have a single, non-variant form, -ovi' (p. 292).
Equations
- z.tableEndings σ = if ¬z.IsRoot ∧ ["o", "v", "i"] ∈ (z.classEndings σ).toFinset then (z.classEndings σ).toFinset.erase ["u"] else (z.classEndings σ).toFinset
Instances For
nomVocPl is the set of nominative and vocative plural cells.
Equations
- One or more equations did not get rendered due to their size.
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The nominative and vocative plural endings of a noun of the masculine a-declension, read from its own class. PŘEDSEDA and SLUHA take their plural on the hard-masculine coradical, whose class gives chlapi's -i (Short, Table 9.2), but their class gives hrdinové (Short, Table 9.5), and Mluvnice češtiny names the nouns in -a among those with one form, předsed-ové (p. 293).
Equations
- One or more equations did not get rendered due to their size.
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The nominative and vocative plural endings of Tables 6 and 8 that neither grammar gives: FILOSOF's -ové. Short's tables leave out the "many formally and semantically distinctive groups with nominative plural in -é or -ové" without placing filosof in one (Short, p. 466), and Mluvnice češtiny gives no plural of filozof, its borrowed compounds in -ové being those in -graf, -fil, -fob and -nom (p. 296).
Equations
- Stump2006.nomPlOverride Stump2006.CzNoun.filosof = some [["o", "v", "é"]]
- Stump2006.nomPlOverride x✝ = none
Instances For
The nominative and vocative plural endings the study supplies beyond the fragment's endings of the stem: those of the noun's own class, and otherwise the override.
Equations
- Stump2006.suppliedNomPl l = (Stump2006.classNomPl l).or (Stump2006.nomPlOverride l)
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The endings of a stem at a cell are those of the fragment, save at the nominative and vocative plural of a noun whose endings there the study supplies, the vocative plural being the nominative (Short, p. 465).
Equations
- z.endings σ = if σ ∈ Stump2006.nomVocPl then (Option.map List.toFinset (Stump2006.suppliedNomPl z.lexeme)).getD (z.tableEndings σ) else z.tableEndings σ
Instances For
A stem is inflected with an ending as the fragment inflects the noun's stem in the stem's class, palatalized before the masculine locative plural -ích and the animate nominative plural -i (Mluvnice češtiny, p. 279). So the soft-masculine coradical of a velar stem palatalizes before -ích, as Short's geolozích (Short, p. 462) and sluzích (Short, p. 467) show.
Instances For
The form cell ⟨z, σ⟩ is realized as z inflected with each of its endings.
Equations
- Stump2006.czRealize z σ = Finset.image (z.inflect σ) (z.endings σ)
Instances For
The realization by the fragment's endings alone, without the endings the study supplies.
Equations
- Stump2006.czRealizeTable z σ = Finset.image (z.inflect σ) (z.tableEndings σ)
Instances For
The Czech paradigm linkage gives each content cell the stem its rules select, and preserves its property set.
Instances For
Off the nominative and vocative plural, and for a noun whose endings there the study does not supply, a stem is realized by the fragment's endings alone.
The study supplies the nominative plural of PŘEDSEDA, SLUHA and FILOSOF alone.
The fragment's endings alone realize the attested forms at every cell but the nominative and vocative plural of PŘEDSEDA, SLUHA and FILOSOF, where Tables 6 and 8 give -ové: MUŽ's and FILOLOG's nominative plurals are the fragment's.
The hard-masculine coradical of a noun of the PŘEDSEDA subclass realizes the dative and locative singular with -ovi alone, the prediction of n. 14 that předsed and sluh lack the -u alternant. It agrees with Short's hrdinovi (Table 9.5) and his remark that "-ovi is specifically associated with animates" (Short, p. 467), and with Mluvnice češtiny's single form předsedovi, sluhovi (p. 292).
PŘEDSEDA's paradigm, derived by rules (14) and (15) from a hard-feminine root and a hard-masculine coradical, is Short's paradigm of the masculine a-stems, hrdina (Table 9.5), on its stem.
Without its own class's nominative plural, PŘEDSEDA's paradigm agrees with hrdina's in twelve of its fourteen cells, the nominative and vocative plural of the hard-masculine coradical being chlapi's -i (Short, Table 9.2).
SLUHA's paradigm is hrdina's on its stem but in the locative plural, where rules (17) and (18) give the palatalized sluzích for the table's -ech.
Rules (17) and (18), with the second palatalization, give SLUHA's locative plural sluzích, the form both grammars give (Short, p. 467; Mluvnice češtiny, pp. 292, 300). The fragment's rule that a velar stem of the hard masculines takes -ích on the palatalized stem gives SLUHA's hard-masculine coradical the same form, so the form alone does not decide between Stump's route through the soft-masculine coradical and the grammar's rule, which differ in the class the cell inflects in and so in the degrees of correlation.
Rules (17) and (18), with the second palatalization, give FILOLOG's locative plural filolozích, as Short gives geolozích for geolog 'geologist' (Short, p. 462) and Mluvnice češtiny filolozích itself (p. 295). The fragment's velar rule gives FILOLOG's hard-masculine root the same form.
FILOLOG's vocative singular is filologu, the -u of a velar hard-masculine stem (Short, p. 465; Mluvnice češtiny, p. 292), where the table's ending is chlape's -e.
Heteroclisis #
cellClass l σ is the declension that the cell σ of l inflects in.
Equations
- Stump2006.cellClass l σ = (Stump2006.stemFor l σ).decl
Instances For
PRAMEN is heteroclite, its paradigm drawing on stems of two declensions.
Exactly PRAMEN, PŘEDSEDA, SLUHA and FILOLOG are heteroclite.
Every noun's stems share their segments, so the heteroclite nouns alternate between stems that differ in declension alone.
PRAMEN's paradigm "exhibits a kind of stem suppletion" (pp. 282–283), since its two stems, though phonologically identical, are two stems.
PRAMEN's class in each cell, as rule (14) assigns it, is the class the fragment gives kořen in that cell's number, stroj in the singular and hrady in the plural (Short, p. 469), Mluvnice češtiny listing kořen and pramen together among the masculines in -en- that decline soft in the singular and hard in the plural (p. 310).
The degree of correlation #
degreeNum A cls is the numerator of the degree of A-correlation (p. 309), the sum over
the values v of A of "the largest number of cells in P that carry the specification v and
inflect as members of the same inflection class".
Equations
- Stump2006.degreeNum A cls = ∑ v : V, Finset.univ.sup fun (k : K) => {σ : C | A σ = v ∧ cls σ = k}.card
Instances For
The count is the number of cells exactly when the class split factors through the category.
The degree of A-correlation (p. 309) is the count over the number of cells.
Equations
- Stump2006.degree A cls = ↑(Stump2006.degreeNum A cls) / ↑(Fintype.card C)
Instances For
The degree is one exactly when the class split factors through the category.
Correlates of heteroclisis #
The paper's classification of heteroclite paradigms applies to any cells pairing a case in A
with a number in B, and to any class map cls giving the inflection class of each cell.
The inflectional categories of a noun are number and case.
Instances For
Equations
- Stump2006.instDecidableEqCategory x✝ y✝ = if h : x✝.ctorIdx = y✝.ctorIdx then isTrue ⋯ else isFalse ⋯
Equations
- Stump2006.instFintypeCategory = { elems := { val := ↑Stump2006.Category.enumList, nodup := Stump2006.Category.enumList_nodup }, complete := Stump2006.instFintypeCategory._proof_1 }
Equations
- Stump2006.instReprCategory.repr Stump2006.Category.number prec✝ = Repr.addAppParen (Std.Format.nest (if prec✝ ≥ 1024 then 1 else 2) (Std.Format.text "Stump2006.Category.number")).group prec✝
- Stump2006.instReprCategory.repr Stump2006.Category.case prec✝ = Repr.addAppParen (Std.Format.nest (if prec✝ ≥ 1024 then 1 else 2) (Std.Format.text "Stump2006.Category.case")).group prec✝
Instances For
Equations
- Stump2006.instReprCategory = { reprPrec := Stump2006.instReprCategory.repr }
c.proj σ is the value of the category c at the cell σ.
Equations
- Stump2006.Category.number.proj x✝ = Sum.inr x✝.2
- Stump2006.Category.case.proj x✝ = Sum.inl x✝.1
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A category is an absolute correlate of a paradigm's heteroclisis "if and only if the degree of A-correlation in that paradigm is 1.0" (p. 309), that is, when the paradigm's class split factors through the category.
Equations
- Stump2006.IsAbsoluteCorrelate c cls = Function.FactorsThrough cls c.proj
Instances For
A paradigm is cloven when it is heteroclite, two of its cells inflecting in distinct classes, and has an absolute correlate (p. 309).
Equations
- Stump2006.IsCloven cls = ((∃ (σ : A × B) (τ : A × B), cls σ ≠ cls τ) ∧ ∃ (c : Stump2006.Category), Stump2006.IsAbsoluteCorrelate c cls)
Instances For
A paradigm is fractured when it is heteroclite, two of its cells inflecting in distinct classes, and lacks any absolute correlate (p. 309).
Equations
- Stump2006.IsFractured cls = ((∃ (σ : A × B) (τ : A × B), cls σ ≠ cls τ) ∧ ∀ (c : Stump2006.Category), ¬Stump2006.IsAbsoluteCorrelate c cls)
Instances For
A class split factoring through both categories is constant.
projOn S σ records the values at σ of the categories in S.
Equations
- Stump2006.projOn S σ = (if Stump2006.Category.case ∈ S then some σ.1 else none, if Stump2006.Category.number ∈ S then some σ.2 else none)
Instances For
Categories are intersective correlates of a paradigm's heteroclisis when "for each well-formed property set τ specified for exactly the categories A₁, . . . , A_n there is a single inflection class C such that every cell in P realizing τ inflects as a member of C" (p. 313).
Equations
- Stump2006.IsIntersectiveCorrelate cls S = Function.FactorsThrough cls (Stump2006.projOn S)
Instances For
Adding categories to intersective correlates keeps them intersective correlates.
A single category is an intersective correlate exactly when it is an absolute one.
Both categories together are an intersective correlate of every paradigm.
The minimal intersective correlate of a fractured paradigm is the pair of both categories.
A rule is sensitive to the value of a category when its applicability does not factor through the other category.
Equations
- Stump2006.SensitiveTo r c = ¬Function.FactorsThrough (Morphology.Exponence.Applies r) c.other.proj
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A category is privileged for a family cls of class maps, one for each lexeme, when it
serves as an absolute correlate of a cloven paradigm: "the inflectional categories serving as
absolute correlates of heteroclisis in a given language are PRIVILEGED" (p. 315).
Equations
- Stump2006.Privileged cls c = ∃ (l : L), Stump2006.IsCloven (cls l) ∧ Stump2006.IsAbsoluteCorrelate c (cls l)
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A system of rules satisfies the privileged category restriction (40) (p. 316), which reads
"If a rule of paradigm linkage applies to lexemes belonging to a privileged syntactic category C
and this rule is sensitive to the value of any inflectional category, then it is sensitive to
the value of a privileged inflectional category for members of C." The lexemes L are taken to
form one privileged syntactic category, so the antecedent on the syntactic category is left
implicit.
Equations
- One or more equations did not get rendered due to their size.
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A category is a maximal correlate when its degree "is higher than any other inflectional category's degree of correlation in that paradigm" (p. 309).
Equations
- Stump2006.IsMaximalCorrelate c cls = ∀ (c' : Stump2006.Category), c' ≠ c → Stump2006.degreeNum c'.proj cls < Stump2006.degreeNum c.proj cls
Instances For
A category is an absolute correlate exactly when its degree of correlation is one.
An absolute correlate of a heteroclite paradigm is its maximal correlate.
Equations
- Stump2006.instDecidableIsAbsoluteCorrelate c cls = { decide := decide (∀ a ∈ Finset.univ, (fun (σ : A × B) => ∀ (τ : A × B), c.proj σ = c.proj τ → cls σ = cls τ) a), reflects_decide := ⋯ }
Equations
- One or more equations did not get rendered due to their size.
Equations
- One or more equations did not get rendered due to their size.
Equations
- Stump2006.instDecidableSensitiveTo r c = { decide := !decide (Function.FactorsThrough (Morphology.Exponence.Applies r) c.other.proj), reflects_decide := ⋯ }
Equations
- One or more equations did not get rendered due to their size.
Equations
- One or more equations did not get rendered due to their size.
Correlates of Czech heteroclisis #
PRAMEN's degree of number correlation is 14/14 and its degree of case correlation .50.
PŘEDSEDA's degree of number correlation is .86 (= 12/14) and its degree of case correlation .64.
SLUHA's degree of number correlation is .79 (= 11/14) and its degree of case correlation .57.
FILOLOG's degrees of number and of case correlation are both .93 (= 13/14) (p. 313).
PRAMEN's paradigm is cloven.
PŘEDSEDA's paradigm is fractured.
SLUHA's paradigm is fractured.
FILOLOG's paradigm is fractured.
Number is a maximal correlate of heteroclisis in the fractured paradigms of PŘEDSEDA and SLUHA, as (38) (p. 312) has it: "just as number is the absolute correlate of heteroclisis in the cloven paradigm of Czech PRAMEN, it is likewise the maximal correlate of heteroclisis in the fractured paradigms of PŘEDSEDA and SLUHA."
FILOLOG's fractured paradigm has no maximal correlate (p. 313), so (38), by which maximal correlates of fractured paradigms "tend to be" the absolute correlates of cloven ones, states a tendency.
Rules sensitive to a category #
Rules whose applicability sees only A make a noun's class split factor through A. So
by (41a), number "would be an absolute correlate of heteroclisis in the cloven paradigms of
type-I verbal lexemes" (p. 317).
A category is an absolute correlate of a noun's paradigm when none of its rules is sensitive to the other category.
Number is an absolute correlate of PRAMEN's heteroclisis because (14), its one language-specific rule, is insensitive to case, as is the default (5).
Number is a maximal correlate of heteroclisis in PRAMEN's paradigm, as of any paradigm it is an absolute correlate of.
The privileged category restriction #
Number is privileged for Czech nouns.
Case is not privileged, for "in Czech, for example, number is the only privileged inflectional category among the categories relevant for nominal inflection" (p. 316).
The Czech rules satisfy (40), since (14) is sensitive to number and (15) and (17), though sensitive to case, are "also sensitive to the value of the privileged inflectional category for nouns" (p. 316).
A hypothetical system adds to the Czech rules one giving the genitive cells of the PŘEDSEDA subclass the hard-masculine coradical, a rule sensitive to case alone. It is modelled on the paper's hypothetical (41) and Table 26, whose type-II rule is sensitive to tense and person but not number; it leaves PRAMEN, and so the privilege of number, untouched.
Equations
- One or more equations did not get rendered due to their size.
Instances For
The hypothetical system violates (40), so the restriction is not vacuous.
Claim (39) (p. 313) holds for Czech nouns, every fractured paradigm having a privileged category among its minimal intersective correlates. The claim "is trivially true of fractured paradigms in which only two inflectional categories are distinguished" (p. 313), as here.
Sanskrit cells, stems and form property sets #
The Sanskrit cases are the nominative, vocative, accusative, instrumental, dative, ablative, genitive and locative.
Equations
Instances For
The Sanskrit numbers are the singular, the dual and the plural.
Equations
Instances For
A Sanskrit content cell pairs a case with a number, gender being constant within a paradigm.
Equations
Instances For
SktCell.of c n is the cell of case c and number n.
Equations
- Stump2006.SktCell.of c n hc hn = (⟨c, hc⟩, ⟨n, hn⟩)
Instances For
The genders of the Sanskrit paradigms considered are the masculine and the neuter.
Instances For
Equations
- Stump2006.instDecidableEqSktGender x✝ y✝ = if h : x✝.ctorIdx = y✝.ctorIdx then isTrue ⋯ else isFalse ⋯
Equations
- Stump2006.instFintypeSktGender = { elems := { val := ↑Stump2006.SktGender.enumList, nodup := Stump2006.SktGender.enumList_nodup }, complete := Stump2006.instFintypeSktGender._proof_1 }
Equations
- Stump2006.instReprSktGender = { reprPrec := Stump2006.instReprSktGender.repr }
Equations
- Stump2006.instReprSktGender.repr Stump2006.SktGender.masc prec✝ = Repr.addAppParen (Std.Format.nest (if prec✝ ≥ 1024 then 1 else 2) (Std.Format.text "Stump2006.SktGender.masc")).group prec✝
- Stump2006.instReprSktGender.repr Stump2006.SktGender.neut prec✝ = Repr.addAppParen (Std.Format.nest (if prec✝ ≥ 1024 then 1 else 2) (Std.Format.text "Stump2006.SktGender.neut")).group prec✝
Instances For
g.ud is the gender g in the forms data.
Instances For
The Sanskrit declensions considered are the neuter a-stem declension of HṚD(AYA)'s hṛdaya (Table 4), the general consonant-stem declension, followed by HṚD(AYA)'s hṛd and by every stem of PRATYAÑC (Table 9), and the neuter an-stem and neuter as-stem declensions (Table 10).
Instances For
Equations
- Stump2006.instDecidableEqSktDecl x✝ y✝ = if h : x✝.ctorIdx = y✝.ctorIdx then isTrue ⋯ else isFalse ⋯
Equations
- Stump2006.instFintypeSktDecl = { elems := { val := ↑Stump2006.SktDecl.enumList, nodup := Stump2006.SktDecl.enumList_nodup }, complete := Stump2006.instFintypeSktDecl._proof_1 }
Equations
- Stump2006.instReprSktDecl.repr Stump2006.SktDecl.aStem prec✝ = Repr.addAppParen (Std.Format.nest (if prec✝ ≥ 1024 then 1 else 2) (Std.Format.text "Stump2006.SktDecl.aStem")).group prec✝
- Stump2006.instReprSktDecl.repr Stump2006.SktDecl.consStem prec✝ = Repr.addAppParen (Std.Format.nest (if prec✝ ≥ 1024 then 1 else 2) (Std.Format.text "Stump2006.SktDecl.consStem")).group prec✝
- Stump2006.instReprSktDecl.repr Stump2006.SktDecl.anStem prec✝ = Repr.addAppParen (Std.Format.nest (if prec✝ ≥ 1024 then 1 else 2) (Std.Format.text "Stump2006.SktDecl.anStem")).group prec✝
- Stump2006.instReprSktDecl.repr Stump2006.SktDecl.asStem prec✝ = Repr.addAppParen (Std.Format.nest (if prec✝ ≥ 1024 then 1 else 2) (Std.Format.text "Stump2006.SktDecl.asStem")).group prec✝
Instances For
Equations
- Stump2006.instReprSktDecl = { reprPrec := Stump2006.instReprSktDecl.repr }
Equations
- Stump2006.instDecidableEqSktStem.decEq { form := a, decl := a_1 } { form := b, decl := b_1 } = if h : a = b then h ▸ if h : a_1 = b_1 then h ▸ isTrue ⋯ else isFalse ⋯ else isFalse ⋯
Instances For
Equations
- One or more equations did not get rendered due to their size.
Instances For
Equations
- Stump2006.instReprSktStem = { reprPrec := Stump2006.instReprSktStem.repr }
A form case is a case or the property [nominative ∨ accusative] that the operator ∨ joins, "such that any rule realizing p or p′ also realizes [p ∨ p′]" (p. 286).
- plain (c : ↥SktCase) : SktFormCase
- nomAcc : SktFormCase
Instances For
Equations
- Stump2006.instDecidableEqSktFormCase.decEq (Stump2006.SktFormCase.plain a) (Stump2006.SktFormCase.plain b) = if h : a = b then h ▸ isTrue ⋯ else isFalse ⋯
- Stump2006.instDecidableEqSktFormCase.decEq (Stump2006.SktFormCase.plain c) Stump2006.SktFormCase.nomAcc = isFalse ⋯
- Stump2006.instDecidableEqSktFormCase.decEq Stump2006.SktFormCase.nomAcc (Stump2006.SktFormCase.plain c) = isFalse ⋯
- Stump2006.instDecidableEqSktFormCase.decEq Stump2006.SktFormCase.nomAcc Stump2006.SktFormCase.nomAcc = isTrue ⋯
Instances For
A form property set pairs a form case with a number. It omits gender, which is lexical for the lexemes considered.
Equations
Instances For
ι σ is the form property set specified exactly as the content property set σ.
Equations
- Stump2006.ι σ = (Stump2006.SktFormCase.plain σ.1, σ.2)
Instances For
Distinct content property sets have distinct identically specified form property sets.
The property mapping f₁ g of a lexeme of gender g is (10) (p. 288), which reads "Where α
is any gender and β is any oblique case: (i) if σ = {neut nom X} or {neut acc X}, then
f₁(σ) = {neut [nom ∨ acc] X}; (ii) if σ = {α β X}, then f₁(σ) = {β X}; (iii) otherwise
f₁(σ) = σ." Gender being lexical here and absent from form property sets, clause (ii) is
vacuous.
Equations
- Stump2006.f₁ Stump2006.SktGender.masc x✝ = Stump2006.ι x✝
- Stump2006.f₁ Stump2006.SktGender.neut x✝ = if ↑x✝.1 = Case.nom ∨ ↑x✝.1 = Case.acc then (Stump2006.SktFormCase.nomAcc, x✝.2) else Stump2006.ι x✝
Instances For
Sanskrit HṚD(AYA) (Table 4) #
Equations
- Stump2006.instDecidableEqSktNoun x✝ y✝ = if h : x✝.ctorIdx = y✝.ctorIdx then isTrue ⋯ else isFalse ⋯
Equations
- Stump2006.instFintypeSktNoun = { elems := { val := ↑Stump2006.SktNoun.enumList, nodup := Stump2006.SktNoun.enumList_nodup }, complete := Stump2006.instFintypeSktNoun._proof_1 }
Equations
- Stump2006.instReprSktNoun = { reprPrec := Stump2006.instReprSktNoun.repr }
Equations
- Stump2006.instReprSktNoun.repr Stump2006.SktNoun.hrdaya prec✝ = Repr.addAppParen (Std.Format.nest (if prec✝ ≥ 1024 then 1 else 2) (Std.Format.text "Stump2006.SktNoun.hrdaya")).group prec✝
Instances For
The direct cases are the nominative, vocative and accusative.
Equations
Instances For
hrdStem σ is the stem of the cell σ, since "the direct ... case forms of HṚD(AYA) are
built on the stem hṛdaya, while its remaining, oblique case forms are built on the stem hṛd"
(p. 282). Its stems' declensions follow their final segments, for "because hṛdaya is a neuter
stem ending in a, it follows the neuter a-stem declension ..., but because hṛd is a neuter stem
ending in a consonant, it instead follows the neuter consonant-stem declension" (p. 282).
Equations
- Stump2006.hrdStem σ = if ↑σ.1 ∈ Stump2006.direct then { form := "hṛdaya", decl := Stump2006.SktDecl.aStem } else { form := "hṛd", decl := Stump2006.SktDecl.consStem }
Instances For
hrdLinkage is the paradigm linkage of HṚD(AYA), whose stem alternation "is not the effect
of any regular rule of inflectional exponence, but is instead simply stipulated in HṚD(AYA)'s
lexical entry" (p. 282). HṚD(AYA) is neuter, and its property sets map by f₁.
Equations
- Stump2006.hrdLinkage = { realize := fun (x : Stump2006.SktNoun) (σ : Stump2006.SktCell) => {Stump2006.hrdStem σ}, pm := fun (x : Stump2006.SktNoun) => Stump2006.f₁ Stump2006.SktGender.neut }
Instances For
hrdClass σ is the declension that the cell σ of HṚD(AYA) inflects in.
Equations
- Stump2006.hrdClass σ = (Stump2006.hrdStem σ).decl
Instances For
HṚD(AYA) is heteroclite.
HṚD(AYA)'s stems also differ in form, its heteroclisis being an effect of stem suppletion,
unlike PRAMEN's (segments_invariant).
HṚD(AYA)'s paradigm is cloven, as the paper counts it (p. 313), with case as its absolute correlate, for "in Sanskrit, for example, cloven noun paradigms have case as their absolute correlate" (p. 310).
Sanskrit stem grades (§3.2) #
"In instances of morphosyntactically conditioned heteroclisis, the choice of inflection class in the realization of a paradigm's individual cells is directly determined by the morphosyntactic property sets expressed by those cells; in instances of morphologically conditioned heteroclisis, the choice of inflection class in the realization of a paradigm's individual cells is instead determined by an independently observable pattern of stem alternation" (p. 293). PRAMEN's is of the first sort. In Sanskrit, rules (20a,b) give each cell of an alternating nominal its Strong, Middle or Weakest stem by the strength (19) of its property set and by the ending that follows; they make PRATYAÑC 'westerly' alternate among stems of one declension and AHAN 'day' among stems of two.
Equations
- Stump2006.instDecidableEqGrade x✝ y✝ = if h : x✝.ctorIdx = y✝.ctorIdx then isTrue ⋯ else isFalse ⋯
Equations
- Stump2006.instFintypeGrade = { elems := { val := ↑Stump2006.Grade.enumList, nodup := Stump2006.Grade.enumList_nodup }, complete := Stump2006.instFintypeGrade._proof_1 }
Equations
- Stump2006.instReprGrade.repr Stump2006.Grade.strong prec✝ = Repr.addAppParen (Std.Format.nest (if prec✝ ≥ 1024 then 1 else 2) (Std.Format.text "Stump2006.Grade.strong")).group prec✝
- Stump2006.instReprGrade.repr Stump2006.Grade.middle prec✝ = Repr.addAppParen (Std.Format.nest (if prec✝ ≥ 1024 then 1 else 2) (Std.Format.text "Stump2006.Grade.middle")).group prec✝
- Stump2006.instReprGrade.repr Stump2006.Grade.weakest prec✝ = Repr.addAppParen (Std.Format.nest (if prec✝ ≥ 1024 then 1 else 2) (Std.Format.text "Stump2006.Grade.weakest")).group prec✝
Instances For
Equations
- Stump2006.instReprGrade = { reprPrec := Stump2006.instReprGrade.repr }
A property set is strong or weak, as (19) defines.
Instances For
Equations
- Stump2006.instDecidableEqStrength x✝ y✝ = if h : x✝.ctorIdx = y✝.ctorIdx then isTrue ⋯ else isFalse ⋯
Equations
- Stump2006.instReprStrength.repr Stump2006.Strength.strong prec✝ = Repr.addAppParen (Std.Format.nest (if prec✝ ≥ 1024 then 1 else 2) (Std.Format.text "Stump2006.Strength.strong")).group prec✝
- Stump2006.instReprStrength.repr Stump2006.Strength.weak prec✝ = Repr.addAppParen (Std.Format.nest (if prec✝ ≥ 1024 then 1 else 2) (Std.Format.text "Stump2006.Strength.weak")).group prec✝
Instances For
Equations
- Stump2006.instReprStrength = { reprPrec := Stump2006.instReprStrength.repr }
Clause (19a) makes strong the direct-case property sets of a masculine and the direct-case plural ones of a neuter.
Equations
- Stump2006.rule19a g = { dom := {σ : Stump2006.SktCell | ↑σ.1 ∈ Stump2006.direct ∧ (g = Stump2006.SktGender.masc ∨ ↑σ.2 = Number.plural)}, exponent := Stump2006.Strength.strong }
Instances For
Clause (19b) makes weak the accusative plural property set of a masculine.
Equations
- Stump2006.rule19b g = { dom := {σ : Stump2006.SktCell | g = Stump2006.SktGender.masc ∧ ↑σ.1 = Case.acc ∧ ↑σ.2 = Number.plural}, exponent := Stump2006.Strength.weak }
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Clause (19b) is narrower than (19a), for "because 19b is the more narrowly applicable of the two clauses, it overrides 19a, in accordance with Pāṇini's principle" (n. 19).
The strength of a property set is given by (19) (p. 294), which reads "Where α is masculine or feminine, β is any direct case (nominative, vocative, or accusative), and γ is any number (singular, dual, or plural), a. instances of {α β γ} and {neuter β plural} are strong by default; b. but instances of {α accusative plural} are weak; in addition, c. any gender/case/number combination that is not strong according to (a) is weak." Clause (19b) overrides (19a) by Pāṇini's principle, and (19c) is the default.
Equations
- Stump2006.strength g σ = Morphology.Exponence.RuleSet.realizeMinimalD [Stump2006.rule19a g, Stump2006.rule19b g] (fun (x : Stump2006.SktCell) => Stump2006.Strength.weak) σ
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weak g is the set of weak property sets of a lexeme of gender g.
Equations
- Stump2006.weak g = {σ : Stump2006.SktCell | Stump2006.strength g σ = Stump2006.Strength.weak}
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A Sanskrit row expresses the concept pid in the gender g at the cell σ.
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- One or more equations did not get rendered due to their size.
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sktRows pid g σ are the Sanskrit rows expressing the concept pid in the gender g at the
cell σ, those of Tables 9 and 10.
Equations
- Stump2006.sktRows pid g σ = List.filter (Stump2006.SktRow pid g σ) Stump2006.Forms.all
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The ending of a row is what follows its stem alternant, nothing for a bare stem.
Equations
- Stump2006.endingOf f = List.drop 1 f.segments
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d.exemplar is the concept whose rows exemplify the declension d, PRATYAÑC 'westerly' for
the general consonant-stem declension and, for the neuter an-stem and as-stem declensions, NĀMAN
'name' and MANAS 'mind', which Table 10 sets beside AHAN. The tables print no a-stem paradigm.
Equations
- Stump2006.SktDecl.aStem.exemplar = none
- Stump2006.SktDecl.consStem.exemplar = some "westerly"
- Stump2006.SktDecl.anStem.exemplar = some "name"
- Stump2006.SktDecl.asStem.exemplar = some "mind"
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The row realizing a form case is that of the case itself, or of the nominative for the join
[nominative ∨ accusative], the accusative row agreeing with it (sktEndings_nomAcc).
Equations
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sktEndings d g τ are the endings of the declension d for the gender g at the form property
set τ, those of its exemplar's row.
Equations
- Stump2006.sktEndings d g τ = match d.exemplar with | some pid => List.map Stump2006.endingOf (Stump2006.sktRows pid g (τ.1.rowCase, τ.2)) | none => []
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The neuter nominative and accusative rows of every exemplar share their endings.
sktVowels are the vowels of Sanskrit.
Equations
- Stump2006.sktVowels = ["a", "ā", "i", "ī", "u", "ū", "ṛ", "ṝ", "ḷ", "e", "ai", "o", "au"]
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An ending is vowel-initial when its first segment begins with a vowel.
Equations
- Stump2006.VowelInitial e = ∃ s ∈ e.head?, ∃ v ∈ Stump2006.sktVowels, v.toList <+: s.toList
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The lexemes of §3.2 are the adjective PRATYAÑC 'westerly' and the noun AHAN 'day'. PRATYAÑC's masculine and neuter paradigms (Table 9) are indexed separately, gender being lexical for the nouns that share their cells.
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Equations
- Stump2006.instDecidableEqSktLex x✝ y✝ = if h : x✝.ctorIdx = y✝.ctorIdx then isTrue ⋯ else isFalse ⋯
Equations
- Stump2006.instFintypeSktLex = { elems := { val := ↑Stump2006.SktLex.enumList, nodup := Stump2006.SktLex.enumList_nodup }, complete := Stump2006.instFintypeSktLex._proof_1 }
Equations
- Stump2006.instReprSktLex.repr Stump2006.SktLex.pratyancM prec✝ = Repr.addAppParen (Std.Format.nest (if prec✝ ≥ 1024 then 1 else 2) (Std.Format.text "Stump2006.SktLex.pratyancM")).group prec✝
- Stump2006.instReprSktLex.repr Stump2006.SktLex.pratyancN prec✝ = Repr.addAppParen (Std.Format.nest (if prec✝ ≥ 1024 then 1 else 2) (Std.Format.text "Stump2006.SktLex.pratyancN")).group prec✝
- Stump2006.instReprSktLex.repr Stump2006.SktLex.ahan prec✝ = Repr.addAppParen (Std.Format.nest (if prec✝ ≥ 1024 then 1 else 2) (Std.Format.text "Stump2006.SktLex.ahan")).group prec✝
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Equations
- Stump2006.instReprSktLex = { reprPrec := Stump2006.instReprSktLex.repr }
A lexical entry records a lexeme's gender, its root, the Strong stem, and whichever of a Middle and a Weakest coradical it has, for "some alternating nominals possess only two stems: a Strong stem and a single Weak stem. Others have a Strong stem and two Weak stems" (p. 293).
- gender : SktGender
genderis the lexeme's gender. - root : SktStem
rootis the lexeme's Strong stem. - middle : Option SktStem
middleis the lexeme's Middle coradical, if it has one. - weakest : Option SktStem
weakestis the lexeme's Weakest coradical, if it has one.
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Equations
- One or more equations did not get rendered due to their size.
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Equations
- Stump2006.instReprSktEntry = { reprPrec := Stump2006.instReprSktEntry.repr }
Equations
- One or more equations did not get rendered due to their size.
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sktEntry l is the lexical entry of l. PRATYAÑC's root is its Strong stem pratyañc, and
pratyac and pratīc are its Middle and Weakest coradicals, all three following "the general
consonant-stem declension" (p. 294). For AHAN, "ahan is identified as AHAN's root (= its Strong
stem), ahas as its Middle coradical, and ahn as its Weakest coradical", where "ahan and its
zero-grade counterpart ahn inflect according to the neuter an-stem declension, while ahas
inflects according to the neuter as-stem declension" (p. 295).
Equations
- One or more equations did not get rendered due to their size.
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A Sanskrit rule of paradigm linkage gives the cells of its domain form correspondents built on its exponent, a stem.
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Rule (20a) (p. 294) reads "Where L is a nominal lexeme having s_w as its Weakest coradical and σ is a weak property set, if the realization of the form-cell ⟨s_w, f₁(σ)⟩ is s_w[vowel]X, then the content-cell ⟨L, σ⟩ has ⟨s_w, f₁(σ)⟩ as its form-correspondent." Its domain is read off the endings of s_w's declension rather than listed.
Equations
- One or more equations did not get rendered due to their size.
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Rule (20b) (p. 294) reads "If L is a nominal lexeme having s_m as its Middle coradical and σ is a weak property set, then the content-cell ⟨L, σ⟩ has ⟨s_m, f₁(σ)⟩ as its form-correspondent."
Equations
- Stump2006.rule20b e = Option.map (fun (x : Stump2006.SktStem) => { dom := Stump2006.weak e.gender, exponent := x }) e.middle
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The rules (20a,b) that apply to a lexeme are those whose coradicals it has. The Sanskrit
default (12) is not among them: it is the root that Exponence.RuleSet.realizeMinimalD falls
back on.
Equations
- Stump2006.sktRulesFor e = (Stump2006.rule20a e).toList ++ (Stump2006.rule20b e).toList
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sktRoot l is the root of l, the stem that the Sanskrit rule of paradigm linkage (12)
(p. 289) gives every cell that no rule of l reaches: "Where L is a nominal lexeme having r as
its root, the content-cell ⟨L, σ⟩ has ⟨r, f₁(σ)⟩ as its form-correspondent."
Equations
- Stump2006.sktRoot l = (Stump2006.sktEntry l).root
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The stem of a cell is the one Pāṇini's principle selects, by which "20a will, as the narrower of the two rules, override 20b in any instance in which the former rule is applicable" (p. 295).
Equations
- Stump2006.sktStem l σ = Morphology.Exponence.RuleSet.realizeMinimalD (Stump2006.sktRules l) (fun (x : Stump2006.SktCell) => Stump2006.sktRoot l) σ
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The Sanskrit paradigm linkage gives each content cell the stem its rules select, with the
form property set that f₁ maps its property set to.
Equations
- One or more equations did not get rendered due to their size.
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The grade of a stem in an entry is weakest for its Weakest coradical, middle for its Middle coradical, and strong for its root.
Equations
- e.gradeOf z = if e.weakest = some z then Stump2006.Grade.weakest else if e.middle = some z then Stump2006.Grade.middle else Stump2006.Grade.strong
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grade l σ is the grade of the stem that the rules select at the cell σ of l.
Equations
- Stump2006.grade l σ = (Stump2006.sktEntry l).gradeOf (Stump2006.sktStem l σ)
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sktClass l σ is the declension that the cell σ of l inflects in.
Equations
- Stump2006.sktClass l σ = (Stump2006.sktStem l σ).decl
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The rules against Tables 9 and 10 #
l.paramId is the concept that the forms of l express in the forms data.
Equations
- Stump2006.SktLex.pratyancM.paramId = "westerly"
- Stump2006.SktLex.pratyancN.paramId = "westerly"
- Stump2006.SktLex.ahan.paramId = "day"
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l.analyses σ are the paper's analyses of the rows of the forms data for the cell σ of
l.
Equations
- l.analyses σ = List.filter (fun (x : Stump2006.Forms.Analysis) => Stump2006.SktRow l.paramId (Stump2006.sktEntry l).gender σ x.form) Stump2006.Forms.analyses
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Every lexeme's Weakest coradical has one exemplar row at each cell, so the vowel test of (20a) never fails for want of a row.
The rules (19) and (20a,b) give every cell of PRATYAÑC's masculine and neuter paradigms the grade that Table 9 (p. 294) shades it with, each cell having one row.
The rules give every cell of AHAN the stem that Table 10 (p. 296) and p. 295 build it on, each cell having one row.
Heteroclisis from stem alternation #
The exponent of a rule of an entry is one of its stems.
A lexeme of §3.2 is heteroclite exactly when two of its cells differ in class.
Neither of PRATYAÑC's paradigms is heteroclite, since "the coradicals pratyac and pratīc belong to the same declension as the root pratyañc" (p. 318), so that "all of their forms follow the general consonant-stem declension" (p. 294).
AHAN is heteroclite, since of the three stems its paradigm is built on, "ahan and its zero-grade counterpart ahn inflect according to the neuter an-stem declension, while ahas inflects according to the neuter as-stem declension" (p. 295).
AHAN's cells have the grades of neuter PRATYAÑC's, though (20a) tests the an-stem endings for the one and the consonant-stem endings for the other: the rules "independently motivated by the need to account for the pattern of stem alternation in nonheteroclite paradigms such as the masculine and neuter paradigms of PRATYAÑC ... also account for the patterns of declension-class alternation exhibited by heteroclite nouns such as AHAN" (p. 295).
Fourteen of AHAN's cells inflect in the neuter an-stem declension and ten in the neuter as-stem declension.
AHAN's degree of case correlation is .71 (= 17/24), as Table 21 (p. 312) prints it, and its degree of number correlation, which the paper does not print, is 7/12.
AHAN's paradigm is fractured, as Table 25 (p. 317) classes it.
Case is the maximal correlate of AHAN's heteroclisis, as Table 21 (p. 312) has it.
PRATYAÑC's masculine paradigm preserves property sets, f₁ mapping every masculine
property set to its identically specified form property set.
The nominative and accusative cells of a neuter lexeme share their form correspondents,
f₁ joining their property sets and the rules selecting one stem for both.
The Sanskrit linkage is syncretic, AHAN's nominative and accusative singular sharing their form correspondent.
The Sanskrit linkage is unfaithful, the nominative singular of a neuter mapping to a form property set with the joined case [nominative ∨ accusative].
The privileged category restriction in Sanskrit #
The Sanskrit nominals considered are HṚD(AYA) and the lexemes of §3.2.
Equations
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sktClasses n σ is the declension that the cell σ of the nominal n inflects in.
Equations
- Stump2006.sktClasses = Sum.elim (fun (x : Stump2006.SktNoun) => Stump2006.hrdClass) Stump2006.sktClass
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The rules of paradigm linkage of a nominal are those of (20a,b) it instantiates, and none for HṚD(AYA), whose stem alternation is "simply stipulated in HṚD(AYA)'s lexical entry" (p. 282).
Equations
- Stump2006.sktNominalRules = Sum.elim (fun (x : Stump2006.SktNoun) => []) Stump2006.sktRules
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Case is privileged for Sanskrit nominals, "a privileged inflectional category for Sanskrit nouns" (p. 318), as the absolute correlate of HṚD(AYA)'s cloven paradigm.
Number is not privileged for Sanskrit nominals, since HṚD(AYA)'s absolute correlate is case, PRATYAÑC is not heteroclite and AHAN's paradigm is fractured.
Rules (20a,b) are sensitive to case, for "in the inflection of Sanskrit PRATYAÑC, the rules 20a,b assigning form-correspondents containing the Middle and Weakest coradicals pratyac and pratīc are sensitive to case, a privileged inflectional category for Sanskrit nouns" (p. 318).
Rules (20a,b) are sensitive to number as well as to case.
The Sanskrit rules satisfy (40), since each, though sensitive to number as well, is sensitive to case, which is privileged.
Russian MAT' (Table 5) #
The Russian numbers are the singular and the plural.
Equations
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A Russian content cell pairs one of the six cases with a number; the prepositional is the locative.
Equations
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Equations
- Stump2006.instDecidableEqRuNoun x✝ y✝ = if h : x✝.ctorIdx = y✝.ctorIdx then isTrue ⋯ else isFalse ⋯
Equations
- Stump2006.instFintypeRuNoun = { elems := { val := ↑Stump2006.RuNoun.enumList, nodup := Stump2006.RuNoun.enumList_nodup }, complete := Stump2006.instFintypeRuNoun._proof_1 }
Equations
- Stump2006.instReprRuNoun.repr Stump2006.RuNoun.mat prec✝ = Repr.addAppParen (Std.Format.nest (if prec✝ ≥ 1024 then 1 else 2) (Std.Format.text "Stump2006.RuNoun.mat")).group prec✝
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Equations
- Stump2006.instReprRuNoun = { reprPrec := Stump2006.instReprRuNoun.repr }
MAT' has "a radical stem mat' in the singular direct-case forms and an extended stem mater' elsewhere" (p. 283).
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Equations
- Stump2006.instDecidableEqRuStem x✝ y✝ = if h : x✝.ctorIdx = y✝.ctorIdx then isTrue ⋯ else isFalse ⋯
Equations
- Stump2006.instFintypeRuStem = { elems := { val := ↑Stump2006.RuStem.enumList, nodup := Stump2006.RuStem.enumList_nodup }, complete := Stump2006.instFintypeRuStem._proof_1 }
Equations
- Stump2006.instReprRuStem = { reprPrec := Stump2006.instReprRuStem.repr }
Equations
- Stump2006.instReprRuStem.repr Stump2006.RuStem.mat prec✝ = Repr.addAppParen (Std.Format.nest (if prec✝ ≥ 1024 then 1 else 2) (Std.Format.text "Stump2006.RuStem.mat")).group prec✝
- Stump2006.instReprRuStem.repr Stump2006.RuStem.mater prec✝ = Repr.addAppParen (Std.Format.nest (if prec✝ ≥ 1024 then 1 else 2) (Std.Format.text "Stump2006.RuStem.mater")).group prec✝
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Both stems of MAT' follow the third declension (p. 283).
Equations
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matLinkage builds MAT' on mat' in the nominative and accusative singular and on
mater' elsewhere.
Equations
- One or more equations did not get rendered due to their size.
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MAT' is suppletive but not heteroclite, for "suppletion in itself does not necessitate heteroclisis" (p. 283).