Founding the newly structured GF2.0 cvs archive.

grammars/logic/LogicEng.gf

@@ -0,0 +1,59 @@
+concrete LogicEng of Logic = open LogicResEng in {
+
+flags lexer=vars ; unlexer=text ;
+
+lincat 
+  Dom = {s : Num => Str} ;
+  Prop, Elem = {s : Str} ;
+
+lin 
+Statement A = {s = A.s ++ "."} ;
+ThmWithProof A a = {s = ["Theorem ."] ++ A.s ++ [". <p> Proof ."] ++ a.s ++ "."} ;
+ThmWithTrivialProof A a = 
+  {s = "Theorem" ++ "." ++ A.s ++ [". <p> Proof . Trivial ."]} ;
+Disj A B = {s = A.s ++ "or" ++ B.s} ;
+Conj A B = {s = A.s ++ "and" ++ B.s} ;
+Impl A B = {s = "if" ++ A.s ++ "then" ++ B.s} ;
+Univ A B = {s = ["for all"] ++ A.s ! pl ++ B.$0 ++ "," ++ B.s} ;
+Exist A B =
+  {s = ["there exists"] ++ indef ++ A.s ! sg ++ B.$0 ++ ["such that"] ++ B.s} ;
+Abs = {s = ["we have a contradiction"]} ;
+Neg A = {s = ["it is not the case that"] ++ A.s} ;
+ImplP A B = {s = "if" ++ A.s ++ "then" ++ B.s} ;
+ConjI A B a b = {s = a.s ++ "." ++ b.s ++ [". Hence"] ++ A.s ++ "and" ++ B.s} ;
+ConjEl A B c = {s = c.s ++ [". A fortiori ,"] ++ A.s} ;
+ConjEr A B c = {s = c.s ++ [". A fortiori ,"] ++ B.s} ;
+DisjIl A B a = {s = a.s ++ [". A fortiori ,"] ++ A.s ++ "or" ++ B.s} ;
+DisjIr A B b = {s = b.s ++ [". A fortiori ,"] ++ A.s ++ "or" ++ B.s} ;
+DisjE A B C c d e = {s = 
+  c.s ++ 
+  [". There are two possibilities . First , assume"] ++ 
+  A.s ++ "(" ++ d.$0 ++ ")" ++ "." ++ d.s ++ 
+  [". Second , assume"] ++ B.s ++ "(" ++ e.$0 ++ ")" ++ "." ++ e.s ++ 
+  [". Thus"] ++ C.s ++ ["in both cases"]} ;
+ImplI A B b = {s = 
+  "assume" ++ A.s ++ "(" ++ b.$0 ++ ")" ++ "." ++ 
+  b.s ++ [". Hence , if"] ++ A.s ++ "then" ++ B.s} ;
+ImplE A B c a = {s = a.s ++ [". But"] ++ c.s ++ [". Hence"] ++ B.s} ;
+NegI A b = {s = 
+  "assume" ++ A.s ++ "(" ++ b.$0 ++ ")" ++ "." ++ b.s ++ 
+  [". Hence, it is not the case that"] ++ A.s} ;
+NegE A c a =
+  {s = a.s ++ [". But"] ++ c.s ++ [". We have a contradiction"]} ;
+UnivI A B b = {s = 
+  ["consider an arbitrary"] ++ A.s ! sg ++ b.$0 ++ "." ++ b.s ++ 
+  [". Hence, for all"] ++ A.s ! pl ++ B.$0 ++ "," ++ B.s} ;
+UnivE A B c a =
+  {s = c.s ++ [". Hence"] ++ B.s ++ "for" ++ B.$0 ++ ["set to"] ++ a.s} ;
+ExistI A B a b = {s = 
+  b.s ++ [". Hence, there exists"] ++ indef ++ 
+  A.s ! sg ++ B.$0 ++ ["such that"] ++ B.s} ;
+ExistE A B C c d = {s = 
+  c.s ++ [". Consider an arbitrary"] ++ d.$0 ++ 
+  ["and assume that"] ++ B.s ++ "(" ++ d.$1 ++ ")" ++ "." ++ d.s ++ 
+  [". Hence"] ++ C.s ++ ["independently of"] ++ d.$0} ;
+AbsE C c = {s = c.s ++ [". We may conclude"] ++ C.s} ;
+Hypo A a = {s = ["by the hypothesis"] ++ a.s ++ "," ++ A.s} ;
+Pron _ _ = {s = "it"} ;
+
+} ;