MAth

lib/resource/abstract/Math.gf

@@ -0,0 +1,52 @@
+
+
+abstract Math = Categories ** {
+
+--3 Noun phrases with symbols
+
+fun
+  SymbPN      : String -> PN ;             -- "x"
+  IntPN       : Int -> PN ;                -- "27"
+  IntNP       : CN -> Int -> NP ;          -- "level 53"
+
+  IndefSymbNumNP : Num -> CN -> SymbList -> NP ;         -- "(2) numbers x and y"
+  DefSymbNumNP   : Num -> CN -> SymbList -> NP ;         -- "the (2) numbers x and y"
+  NDetSymbNP     : NDet -> Num -> CN -> SymbList -> NP ; -- "some (3) points x, y and z"
+
+--3 Symbol lists
+
+-- A symbol list has at least two elements. The last two are separated
+-- by a conjunction ("and" in English), the others by commas.
+-- This produces "x, y and z", in English. 
+
+cat
+  SymbList ;
+
+fun
+  SymbTwo  : String -> String   -> SymbList ;
+  SymbMore : String -> SymbList -> SymbList ;
+
+--3 Special forms of expression
+
+-- These expression forms are typical of mathematical texts.
+
+  LetCN    : String   -> CN -> Imp ;         -- Let x be a number.
+  LetNumCN : SymbList -> Num -> CN -> Imp ;  -- Let x and y be (2) numbers.
+
+-- This rule is slightly overgenerating: "there exists every number x". 
+-- The problem seems to be of semantic nature. By this we avoid having many rules.
+
+  ExistNP : NP -> Cl ;  -- there exist (2) number(s) x and y
+
+--3 Rules moved from $Rules$.
+
+-- This rule is powerful but overgenerating.
+
+  SymbCN      : CN -> String -> CN ;       -- "number x"
+
+-- This rule is simply wrong, and will be deprecated: the correct
+-- value type is $NP$.
+
+  IntCN       : CN -> Int -> CN ;          -- "level 53"
+
+}