++<term>  ::= "\" var "."<term>  | n |<term><term>  | "("<term>")"

Aha. Instead of 1. from
http://en.wikipedia.org/wiki/Lambda_calculus#Definition
i.e. "If x is a variable then x\in\Lambda", you use the deBruijn index "n". Good to know. But it should appear at the place where you define your representation.

And what you describe above is a grammar for the input. That's interesting for parsing an input string, but not for representation.

It still doesn't describe why you have this

  Rep := Union(_
         boundTerm:Record(varBound:NNI),_
         freeTerm:UT,_
         compoundTerm:Record(c1:%, c2:%),_
         lambdaTerm:Record(c3:%, nm:UT)_
         )

as representation.

Ralf

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