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\begin{letter}

\signature {Zena M. Ariola \\
 Computer \& Information Science Dept.  \\
 University of Oregon                 \\
 Eugene, OR 97403-1202               \\
 USA - e-mail: ariola@cs.uoregon.edu}

Reference: TCSB 119 


\opening{Dear Mr Kok,}

We have revised our paper and have incorporated all comments from both
the reviewers.  After listing the major changes, we will point to the
places in the revised version where specific comments of the referees
have been addressed.

{\bf Major changes:}

We have decided to restrict this paper to only Functional GRSs, that
is, any discussion of I-structures has been dropped. This has lead to
considerable shortening of the paper (from 48 pages to 35 pages) and a
new title.

The major technical change is that now we do garbage collection in our
terms, {\it i.e.,} we drop the subterms that are not reachable from the
root.  (This was not possible in the presence of I-structures). This
change has required adjustments to almost all the proofs in the
paper. We have also broken down proofs into smaller
steps and more propositions.
We hope that the new proofs are tighter and clearer.



{\bf Comments of A. (The typed review)}

\begin{itemize}
\item[1.]
Comment about Garbage Collection is no longer applicable. 
See Definition 3.6 (Canonical form)

\item[2.] Unboxed constants: See  the discussion in the lower half of page 3.

\item[3.] Each rule is restricted to rewrite one node. Rewriting 
several nodes simultaneously is useful for modeling several compiler
optimizations. However, we did not have any results for such a system
and did not want to complicate the notation unnecessarily.

\item[4.] Infinite term versus an infinite set of finite terms: Both ideas 
can be made to work. We chose the latter for  technical convenience.
We think this is really a question of taste.

\item[5.] {\bf ERRORS: }
\begin{itemize}
   \item[5.1] The technical difference between lower and upper case variable
       names has been dropped.

   \item[5.2] Our old definition was Correct. The definition suggested by the 
referee is wrong because $x$ can be in $\{x_1, ... x_p\}$.
(see Def 3.3 on page 6-7) in the new version. 

   \item[5.3] non-duplicative: fixed. See Remark 3.23 at the bottom of page 13.

   \item[5.4] The old remark 5.2 was indeed wrong. However, the definition of
       omega-ordering was not. The problem pointed out by the refree goes away
       if Garbage collection is required. See the new definition omega-ordering
       (def 3.13, page 10), noting the new definition of canonical form.

   \item[5.5] The definition of ideal has been fixed. See page page 26 - lower half.
\end{itemize}
\end{itemize}

\newpage
{\bf Comments of B. (The hand-written review)}

Most of the confusion for the referee was due to I-structures.
Since these have been deleted, we hope there is less room for confusion.
We now deal with the canonicalization step in every proof explicitly.

Comparison with Barendregt: See - second paragraph page 2; the last
paragraph of secion 2 on page 5; the discussion after Corollary 4.9 on pafe 17.

{\bf ERRORS}:
\begin{itemize}
\item[1.] The mistake in the statement of old Theorem 6.8 has been corrected. See
theorem 4.8 on page 15.

\item[2.] Old Theorem 6.10 has been deleted.

\item[3.] The definition of ideal has been fixed. See page page 26 - lower half.

\item[4.] The definition of  Root has become much simpler. See def 3.2 on page 6.
\end{itemize}

\closing {Yours Sincerely,}

\end{letter}

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