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---1 Abstract Syntax for Multilingual Resource Grammar
---
--- Aarne Ranta 2002 -- 2003
---
--- Although concrete syntax differs a lot between different languages,
--- many structures can be found that are common, on a certain level
--- of abstraction. What we will present in the following is an abstract 
--- syntax that has been successfully defined for English, Finnish, French, German, 
--- Italian, Russian, and Swedish. It has been applied to define language
--- fragments on technical or near-to-technical domains: database queries,
--- video recorder dialogue systems, software specifications, and a 
--- health-related phrase book. Each new application helped to identify some
--- missing structures in the resource and suggested some additions, but the
--- number of them was usually small.
--- 
--- To use the resource in applications, you need the following 
--- $cat$ and $fun$ rules in $oper$ form, completed by taking the
--- $lincat$ and $lin$ judgements of a particular language. This is done
--- by using the $reuse$ module with the desired concrete syntax of
--- $ResAbs$ as argument.
-
-
---2 Categories
---
--- The categories of this resource grammar are mostly 'standard' categories
--- of linguistics. Their is no claim that they correspond to semantic categories
--- definable in type theory: to define such correspondences is the business
--- of applications grammars.
---
--- Categories that may look special are $Adj2$, $Fun$, and $TV$. They are all
--- instances of endowing another category with a complement, which can be either
--- a direct object (whose case may vary) or a prepositional phrase. This, together
--- with the category $Adv$, removes the need of a category of 
--- 'prepositional phrases', which is too language-dependent to make sense
--- on this level of abstraction.
---
-
-abstract ResAbs = {
-
---3 Nouns and noun phrases
---
-
-cat
-  N ;      -- simple common noun,    e.g. "car"
-  CN ;     -- common noun phrase,    e.g. "red car", "car that John owns"
-  NP ;     -- noun phrase,           e.g. "John", "all cars", "you"
-  PN ;     -- proper name,           e.g. "John", "New York"
-  Det ;    -- determiner,            e.g. "every", "all"
-  Fun ;    -- function word,         e.g. "mother (of)"
-  Fun2 ;   -- two-place function,    e.g. "flight (from) (to)"
-
---3 Adjectives and adjectival phrases
---
-
-  Adj1 ;   -- one-place adjective,   e.g. "even"
-  Adj2 ;   -- two-place adjective,   e.g. "divisible (by)"
-  AdjDeg ; -- degree adjective,      e.g. "big/bigger/biggest"
-  AP ;     -- adjective phrase,      e.g. "divisible by two", "bigger than John"
-
---3 Verbs and verb phrases
---
-
-  V ;      -- one-place verb,        e.g. "walk"
-  TV ;     -- two-place verb,        e.g. "love", "wait (for)", "switch on"
-  V3 ;     -- three-place verb,      e.g. "give", "prefer (stg) (to stg)"
-  VS ;     -- sentence-compl. verb,  e.g. "say", "prove"
-  VP ;     -- verb phrase,           e.g. "switch the light on"
-
---3 Adverbials
---
-
-  AdV ;    -- adverbial              e.g. "now", "in the house"
-  AdA ;    -- ad-adjective           e.g. "very"
-  AdS ;    -- sentence adverbial     e.g. "therefore", "otherwise"
-
---3 Sentences and relative clauses
---
-
-  S ;      -- sentence,              e.g. "John walks"
-  Slash ;  -- sentence without NP,   e.g. "John waits for (...)"
-  RP ;     -- relative pronoun,      e.g. "which", "the mother of whom"
-  RC ;     -- relative clause,       e.g. "who walks", "that I wait for"
-
---3 Questions and imperatives
---
-
-  IP ;     -- interrogative pronoun, e.g. "who", "whose mother", "which yellow car"
-  IAdv ;   -- interrogative adverb., e.g. "when", "why" 
-  Qu ;     -- question,              e.g. "who walks"
-  Imp ;    -- imperative,            e.g. "walk!"
-
---3 Coordination and subordination
---
-
-  Conj ;   -- conjunction,           e.g. "and"
-  ConjD ;  -- distributed conj.      e.g. "both - and"
-  Subj ;   -- subjunction,           e.g. "if", "when"
-
-  ListS ;  -- list of sentences
-  ListAP ; -- list of adjectival phrases
-  ListNP ; -- list of noun phrases
-
---3 Complete utterances
---
-
-  Phr ;    -- full phrase,           e.g. "John walks.","Who walks?", "Wait for me!"
-  Text ;   -- sequence of phrases    e.g. "One is odd. Therefore, two is even."
-
-
---2 Rules
---
--- This set of rules is minimal, in the sense of defining the simplest combinations
--- of categories and not having redundant rules.
--- When the resource grammar is used as a library, it will often be useful to
--- access it through an intermediate library that defines more rules as 
--- 'macros' for combinations of the ones below.
-
---3 Nouns and noun phrases
---
-
-fun 
-  UseN : N -> CN ;                         -- "car"
-  ModAdj : AP -> CN -> CN ;                -- "red car"
-  DetNP : Det -> CN -> NP ;                -- "every car"
-  IndefOneNP, IndefManyNP : CN -> NP ;     -- "a car", "cars"
-  DefOneNP, DefManyNP : CN -> NP ;         -- "the car", "the cars"
-  ModGenOne, ModGenMany : NP -> CN -> NP ; -- "John's car", "John's cars"
-  UsePN : PN -> NP ;                       -- "John"
-  UseFun : Fun -> CN ;                     -- "successor"
-  AppFun : Fun -> NP -> CN ;               -- "successor of zero"
-  AppFun2 : Fun2 -> NP -> Fun ;            -- "flight from Paris"
-  CNthatS : CN -> S -> CN ;                -- "idea that the Earth is flat"
-
---3 Adjectives and adjectival phrases
---
-
-  AdjP1 : Adj1 -> AP ;                     -- "red"
-  ComplAdj : Adj2 -> NP -> AP ;            -- "divisible by two"
-  PositAdjP : AdjDeg -> AP ;               -- "old"
-  ComparAdjP : AdjDeg -> NP -> AP ;        -- "older than John"
-  SuperlNP : AdjDeg -> CN -> NP ;          -- "the oldest man"
-
---3 Verbs and verb phrases
---
-
-  PosV, NegV : V -> VP ;                   -- "walk", "doesn't walk"
-  PosA, NegA : AP -> VP ;                  -- "is old", "isn't old"
-  PosCN, NegCN : CN -> VP ;                -- "is a man", "isn't a man"
-  PosTV, NegTV : TV -> NP -> VP ;          -- "sees John", "doesn't see John"
-  PosPassV, NegPassV : V -> VP ;           -- "is seen", "is not seen"
-  PosNP, NegNP : NP -> VP ;                -- "is John", "is not John"
-  PosVS, NegVS : VS -> S -> VP ;           -- "says that I run", "doesn't say..."
-  PosV3, NegV3 : V3 -> NP -> NP -> VP ;    -- "prefers wine to beer"
-  VTrans : TV -> V ;                       -- "loves"
-
---3 Adverbials
---
-
-  AdvVP : VP -> AdV -> VP ;                -- "always walks", "walks in the park" 
-  LocNP : NP -> AdV ;                      -- "in London"
-  AdvCN : CN -> AdV -> CN ;                -- "house in London", "house today"
-
-  AdvAP : AdA -> AP -> AP ;                -- "very good"
-
-
---3 Sentences and relative clauses
---
-
-  PredVP : NP -> VP -> S ;                     -- "John walks"
-  PosSlashTV, NegSlashTV : NP -> TV -> Slash ; -- "John sees", "John doesn's see"
-  OneVP : VP -> S ;                            -- "one walks"
-
-  IdRP : RP ;                              -- "which"
-  FunRP : Fun -> RP -> RP ;                -- "the successor of which"
-  RelVP : RP -> VP -> RC ;                 -- "who walks"
-  RelSlash : RP -> Slash -> RC ;           -- "that I wait for"/"for which I wait" 
-  ModRC : CN -> RC -> CN ;                 -- "man who walks"
-  RelSuch : S -> RC ;                      -- "such that it is even"
-
---3 Questions and imperatives
---
-
-  WhoOne, WhoMany : IP ;                   -- "who (is)", "who (are)"
-  WhatOne, WhatMany : IP ;                 -- "what (is)", "what (are)"
-  FunIP : Fun -> IP -> IP ;                -- "the mother of whom"
-  NounIPOne, NounIPMany : CN -> IP ;       -- "which car", "which cars"
-
-  QuestVP : NP -> VP -> Qu ;               -- "does John walk"
-  IntVP : IP -> VP -> Qu ;                 -- "who walks"
-  IntSlash : IP -> Slash -> Qu ;           -- "whom does John see"
-  QuestAdv : IAdv -> NP -> VP -> Qu ;      -- "why do you walk"
-
-  ImperVP : VP -> Imp ;                    -- "be a man"
-
-  IndicPhrase : S -> Phr ;                 -- "I walk."
-  QuestPhrase : Qu -> Phr ;                -- "Do I walk?"
-  ImperOne, ImperMany : Imp -> Phr ;       -- "Be a man!", "Be men!"
-
-  AdvS : AdS -> S -> Phr ;                 -- "Therefore, 2 is prime."
-
---3 Coordination
---
--- We consider "n"-ary coordination, with "n" > 1. To this end, we have introduced
--- a *list category* $ListX$ for each category $X$ whose expressions we want to
--- conjoin. Each list category has two constructors, the base case being $TwoX$.
-
--- We have not defined coordination of all possible categories here,
--- since it can be tricky in many languages. For instance, $VP$ coordination
--- is linguistically problematic in German because $VP$ is a discontinuous
--- category.
-
-  ConjS  : Conj -> ListS -> S ;            -- "John walks and Mary runs"
-  ConjAP : Conj -> ListAP -> AP ;          -- "even and prime"
-  ConjNP : Conj -> ListNP -> NP ;          -- "John or Mary"
-
-  ConjDS  : ConjD -> ListS -> S ;          -- "either John walks or Mary runs"
-  ConjDAP : ConjD -> ListAP -> AP ;        -- "both even and prime"
-  ConjDNP : ConjD -> ListNP -> NP ;        -- "either John or Mary"
-
-  TwoS  : S -> S -> ListS ;
-  ConsS : ListS -> S -> ListS ;
-
-  TwoAP  : AP -> AP -> ListAP ;
-  ConsAP : ListAP -> AP -> ListAP ;
-
-  TwoNP  : NP -> NP -> ListNP ;
-  ConsNP : ListNP -> NP -> ListNP ;
-
---3 Subordination
---
--- Subjunctions are different from conjunctions, but form
--- a uniform category among themselves.
-
-  SubjS     : Subj -> S -> S -> S ;        -- "if 2 is odd, 3 is even"
-  SubjImper : Subj -> S -> Imp -> Imp ;    -- "if it is hot, use a glove!"
-  SubjQu    : Subj -> S -> Qu -> Qu ;      -- "if you are new, who are you?"
-  SubjVP    : VP -> Subj -> S -> VP ;      -- "(a man who) sings when he runs"
-
---2 One-word utterances
---
--- These are, more generally, *one-phrase utterances*. The list below
--- is very incomplete.
-
-  PhrNP : NP -> Phr ;                      -- "Some man.", "John."
-  PhrOneCN, PhrManyCN : CN -> Phr ;        -- "A car.", "Cars."
-  PhrIP : IAdv -> Phr ;                    -- "Who?"
-  PhrIAdv : IAdv -> Phr ;                  -- "Why?"
-
---2 Text formation
---
--- A text is a sequence of phrases. It is defined like a non-empty list.
-  
-  OnePhr  : Phr -> Text ;
-  ConsPhr : Phr -> Text -> Text ;
-
---2 Examples of structural words
--- 
--- Here we have some words belonging to closed classes and appearing
--- in all languages we have considered.
--- Sometimes they are not really meaningful, e.g. $TheyNP$ in French
--- should really be replaced by masculine and feminine variants.
-
-  EveryDet, AllDet, WhichDet, MostDet : Det ; -- every, all, which, most
-  INP, ThouNP, HeNP, SheNP, ItNP : NP ;       -- personal pronouns in singular
-  WeNP, YeNP, TheyNP : NP ;                   -- personal pronouns in plural
-  YouNP : NP ;                                -- the polite you
-  WhenIAdv,WhereIAdv,WhyIAdv,HowIAdv : IAdv ; -- when, where, why, how
-  AndConj, OrConj : Conj ;                    -- and, or
-  BothAnd, EitherOr, NeitherNor : ConjD ;     -- both-and, either-or, neither-nor
-  IfSubj, WhenSubj : Subj ;                   -- if, when
-  PhrYes, PhrNo : Phr ;                       -- yes, no
-  VeryAdv, TooAdv : AdA ;                     -- very, too
-  OtherwiseAdv, ThereforeAdv : AdS ;          -- therefore, otherwise            
-} ;
-