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+--1 A Small Predication Library
+--
+-- (c) Aarne Ranta 2003 under Gnu GPL.
+--
+-- This library is built on a language-independent API of
+-- resource grammars. It has a common part, the type signatures
+-- (defined here), and language-dependent parts. The user of
+-- the library should only have to look at the type signatures.
+
+resource Predication = open Deutsch in {
+
+-- We first define a set of predication patterns.
+
+oper
+  predV1 : V -> NP -> S ;             -- one-place verb: "John walks"
+  predV2 : TV -> NP -> NP -> S ;      -- two-place verb: "John loves Mary"
+  predVColl : V -> NP -> NP -> S ;    -- collective verb: "John and Mary fight"
+  predA1 : Adj1 -> NP -> S ;          -- one-place adjective: "John is old"
+  predA2 : Adj2 -> NP -> NP -> S ;    -- two-place adj: "John is married to Mary"
+  predAComp : AdjDeg -> NP -> NP -> S ; -- compar adj: "John is older than Mary"
+  predAColl : Adj1 -> NP -> NP -> S ; -- collective adj: "John and Mary are married"
+  predN1 : N -> NP -> S ;             -- one-place noun: "John is a man"
+  predN2 : Fun -> NP -> NP -> S ;     -- two-place noun: "John is a lover of Mary"
+  predNColl : N -> NP -> NP -> S ;    -- collective noun: "John and Mary are lovers"
+
+-- Individual-valued function applications.
+
+  appFun1 : Fun -> NP -> NP ;          -- one-place function: "the successor of x"
+  appFun2 : Fun -> NP -> NP -> NP ;    -- two-place function: "the line from x to y"
+  appFunColl : Fun -> NP -> NP -> NP ; -- collective function: "the sum of x and y"
+
+-- Families of types, expressed by common nouns depending on arguments.
+
+  appFam1 : Fun -> NP -> CN ;          -- one-place family: "divisor of x"
+  appFam2 : Fun -> NP -> NP -> CN ;    -- two-place family: "line from x to y"
+  appFamColl : Fun -> NP -> NP -> CN ; -- collective family: "path between x and y"
+
+-- Type constructor, similar to a family except that the argument is a type.
+
+  constrTyp1 : Fun -> CN -> CN ;
+
+-- Logical connectives on two sentences.
+
+  conjS : S -> S -> S ;
+  disjS : S -> S -> S ;
+  implS : S -> S -> S ;
+
+-- As an auxiliary, we need two-place conjunction of names ("John and Mary"), 
+-- used in collective predication.
+
+  conjNP : NP -> NP -> NP ;
+
+
+-----------------------------
+
+---- what follows should be an implementation of the preceding
+
+oper
+  predV1 = \F, x -> PredVP x (PosV F) ;
+  predV2 = \F, x, y -> PredVP x (PosTV F y) ;
+  predVColl = \F, x, y -> PredVP (conjNP x y) (PosV F) ;
+  predA1 = \F, x -> PredVP x (PosA F) ;
+  predA2 = \F, x, y -> PredVP x (PosA (ComplAdj F y)) ;
+  predAComp = \F, x, y -> PredVP x (PosA (ComparAdjP F y)) ;
+  predAColl = \F, x, y -> PredVP (conjNP x y) (PosA F) ;
+  predN1 = \F, x -> PredVP x (PosCN (UseN F)) ;
+  predN2 = \F, x, y -> PredVP x (PosCN (AppFun F y)) ;
+  predNColl = \F, x, y -> PredVP (conjNP x y) (PosCN (UseN F)) ;
+
+  appFun1 = \f, x -> DefOneNP (AppFun f x) ;
+  appFun2 = \f, x, y -> DefOneNP (AppFun (AppFun2 f x) y) ;
+  appFunColl = \f, x, y -> DefOneNP (AppFun f (conjNP x y)) ;
+
+  appFam1 = \F, x -> AppFun F x ;
+  appFam2 = \F, x, y -> AppFun (AppFun2 F x) y ;
+  appFamColl = \F, x, y -> AppFun F (conjNP x y) ;
+
+  conjS = \A, B -> ConjS AndConj (TwoS A B) ;
+  disjS = \A, B -> ConjS OrConj (TwoS A B) ;
+  implS = \A, B -> SubjS IfSubj A B ;
+
+  constrTyp1 = \F, A -> AppFun F (IndefManyNP A) ;
+
+  conjNP = \x, y -> ConjNP AndConj (TwoNP x y) ;
+
+} ;