**(1)**- Note that model-theoretic conservativeness of an extension implies consequence-theoretic conservativeness, but not vice versa, see [Vel92]. However, if we consider the consequence relation between specifications, model-theoretic and consequence-theoretic conservativeness become equivalent.
**(2)**- Technically, this means that the reduct functor is bijective on objects, i.e. both specifications have the "same" model class. An abstract axiomatization of definitional extensions can be found in [Sri97].
**(3)**- Would the annotations also make sense within architectural specifications?
**(4)**- We do not propose an annotation
for intended consequences as in the Larch Shared Language
[GHG
93], since we think it is better to include the intended consequences in the specification, and use a %^{+}**cons**annotation to express that they follow already from the rest of the specification (namely the part that is being extended). **(5)**- An Alternative would be to allow the predefined precedences to be overridden. However, we found this too confusing.
**(6)**- There are no built-in precedences for particular operation symbols. The usual precedences between the arithmetic operations are defined in the standard library for numbers [RM99].
**(7)**- Note that the sort
*List[Elem]*in the type construct of the specification List is already generated. Of course one can mix up sort generation and the**brackets**declaration in principle. **(8)**- This problem can
be overcome by allowing views to specify derived specification
morphisms, as in OBJ3, where constants may be mapped to terms.
One objection against derived signature morphisms has been that
the corresponding category is not cocomplete. However, if we
consider the category of derived
*specification*morphisms, we can retain cocompleteness, see [Sri97] for a completeness proof. **(9)**- We omit here the non interesting
cases of multiple signs as e.g.
*-+d*_{1}:: d_{2}:: ...:: d_{n}.

CoFI Note: L-11 -- Version: 0.1 -- 11 March 1999.

Comments to roba@informatik.uni-bremen.de