allowing a name to be introduced ``twice''

Sometimes an event will announce that it is ``redundant'', meaning that the the form is not evaluated because ACL2 determines that its effect is already incorporated into the logical world. Thus, when this happens, no change to the logical world takes place. This feature permits two independent books, each of which defines some name, to be included sequentially provided they use exactly the same definition.

Note that by the definition above, a form can have no effect on the logical world yet not be considered to be redundant. Here is an example of such a form.

(value-triple (cw "Hello world.~%"))

When are two logical-name definitions considered ``the same''? It depends upon the kind of name being defined. We consider these below in alphabetical order. See also the Notes below.

A defabsstobj is redundant if there is already an identical defabsstobj event in the logical world.

A defattach event is never redundant. Note that it doesn't define any name.

A defaxiom or defthm event is redundant if there is already an axiom or theorem of the given name and both the formula (after macroexpansion) and the rule-classes are syntactically identical. Note that a defaxiom can make a subsequent defthm redundant, and a defthm can make a subsequent defaxiom redundant as well.

A defconst is redundant if the name is already defined either with a syntactically identical defconst event or one that defines it to have the same value.

A defdoc event is never redundant because it doesn't define any name.

A deflabel event is never redundant. This means that if you have a deflabel in a book and that book has been included (without error), then references to that label denote the point in history at which the book introduced the label. See the note about shifting logical names, below.

A defmacro event is redundant if there is already a macro defined with the same name and syntactically identical arguments, guard, and body.

A defpkg event is redundant if a package of the same name with exactly the same imports has been defined.

A defstobj event is redundant if there is already a defstobj event with the same name that has exactly the same field descriptors (see defstobj), in the same order, and with the same :renaming value if :renaming is supplied for either event.

A defthm event is redundant according to the criterion given above in the discussion of defaxiom.

A deftheory is never redundant. The ``natural'' notion of equivalent deftheory forms is that the names and values of the two theory expressions are the same. But since most theory expressions are sensitive to the context in which they occur, it seems unlikely to us that two deftheorys coming from two sequentially included books will ever have the same values. So we prohibit redundant theory definitions. If you try to define the same theory name twice, you will get a ``name in use'' error.

A defun, defuns, or mutual-recursion event is redundant if for each function to be introduced, there has already been introduced a function with the same name, the same formals, and syntactically identical :guard, :measure, type declarations, stobjs declarations and body (before macroexpansion), and an appropriate mode (see the ``Note About Appropriate Modes'' below). Moreover, the order of the combined :guard and type declarations must be the same in both cases. Exceptions:
(1) If either definition is declared :non-executable (see defun-nx), then the two events must be identical.
(2) It is permissible for one definition to have a :guard of t and the other to have no explicit guard (hence, the guard is implicitly t).
(3) The :measure check is avoided if we are skipping proofs (for example, during include-book), and otherwise, the new definition may have a :measure of (:? v1 ... vk), where (v1 ... vk) enumerates the variables occurring in the measure stored for the old definition.
(4) If either the old or new event is a mutual-recursion event, then redundancy requires that both are mutual-recursion events that define the same set of function symbols.

An encapsulate event is most commonly redundant when a syntactically identical encapsulate has already been executed under the same default-defun-mode, default-ruler-extenders, and default-verify-guards-eagerness. The full criterion for redundancy of encapsulate events is more complex, for example ignoring contents of local events; see encapsulate.

An in-theory event is never redundant. Note that it doesn't define any name.

An include-book event is redundant if the book has already been included.

A call of make-event is never redundant, as its argument is always evaluated to obtain the make-event expansion. However, that expansion may of course be redundant.

A mutual-recursion event is redundant according to the criteria in the discussion above for the case of a defun event.

A progn event is never redundant: its subsidiary events are always considered. Of course, its sub-events may themselves be redundant. If all of its sub-events are redundant -- or more generally, if none of the sub-events changes the logical world -- then the progn event also won't change the world.

A push-untouchable event is redundant if every name supplied is already a member of the corresponding list of untouchable symbols.

A regenerate-tau-database event is never redundant. Note that it doesn't define any name.

A remove-untouchable event is redundant if no name supplied is a member of the corresponding list of untouchable symbols.

A reset-prehistory event is redundant if it does not cause any change.

A set-body event is redundant if the indicated body is already the current body.

A table event not define any name. It is redundant when it sets the value already associated with a key of the table, or when it sets an entire table (using keyword :clear) to its existing value; see table.

A verify-guards event is redundant if the function has already had its guards verified.

Note About Built-in (Predefined) Functions and Macros:

Redundancy is restricted for built-in macros and functions that have special raw Lisp code. Such redundancy is only legal in the context of LOCAL. This restriction is needed for soundness, for technical reasons omitted here (details may be found in a long comment about redundant-events in source function chk-acceptable-defuns-redundancy).

Note About Appropriate Modes:

Suppose a function is being redefined and that the formals, guards, types, stobjs, and bodies are identical. When are the modes (:program or :logic) ``appropriate?'' Identical modes are appropriate. But what if the old mode was :program and the new mode is :logic? This is appropriate, provided the definition meets the requirements of the logical definitional principle. That is, you may redefine ``redundantly'' a :program mode function as a :logic mode function provide the measure conjectures can be proved. This is what verify-termination does. Now consider the reverse style of redefinition. Suppose the function was defined in :logic mode and is being identically redefined in :program mode. ACL2 will treat the redefinition as redundant, provided the appropriate criteria are met (as though it were in :logic mode).

Note About Shifting Logical Names:

Suppose a book defines a function fn and later uses fn as a logical name in a theory expression. Consider the value of that theory expression in two different sessions. In session A, the book is included in a world in which fn is not already defined, i.e., in a world in which the book's definition of fn is not redundant. In session B, the book is included in a world in which fn is already identically defined. In session B, the book's definition of fn is redundant. When fn is used as a logical name in a theory expression, it denotes the point in history at which fn was introduced. Observe that those points are different in the two sessions. Hence, it is likely that theory expressions involving fn will have different values in session A than in session B.

This may adversely affect the user of your book. For example, suppose your book creates a theory via deftheory that is advertised just to contain the names generated by the book. But suppose you compute the theory as the very last event in the book using:

(set-difference-theories (universal-theory :here)
                         (universal-theory fn))
where fn is the very first event in the book and happens to be a defun event. This expression returns the advertised set if fn is not already defined when the book is included. But if fn were previously (identically) defined, the theory is larger than advertised.

The moral of this is simple: when building books that other people will use, it is best to describe your theories in terms of logical names that will not shift around when the books are included. The best such names are those created by deflabel.

Note About Unfortunate Redundancies.

Notice that our syntactic criterion for redundancy of defun events may not allow redefinition to take effect unless there is a syntactic change in the definition. The following example shows how an attempt to redefine a function can fail to make any change.

(set-ld-redefinition-action '(:warn . :overwrite) state)
(defmacro mac (x) x)
(defun foo (x) (mac x))
(defmacro mac (x) (list 'car x))
(set-ld-redefinition-action nil state)
(defun foo (x) (mac x)) ; redundant, unfortunately; foo does not change
(thm (equal (foo 3) 3)) ; succeeds, showing that redef of foo didn't happen
The call of macro mac was expanded away before storing the first definition of foo for the theorem prover. Therefore, the new definition of mac does not affect the expansion of foo by the theorem prover, because the new definition of foo is ignored.

One workaround is first to supply a different definition of foo, just before the last definition of foo above. Then that final definition will no longer be redundant. However, as a courtesy to users, we strengthen the redundancy check for function definitions when redefinition is active. If in the example above we remove the form (set-ld-redefinition-action nil state), then the problem goes away:

(set-ld-redefinition-action '(:warn . :overwrite) state)
(defmacro mac (x) x)
(defun foo (x) (mac x))
(defmacro mac (x) (list 'car x))
(defun foo (x) (mac x)) ; no longer redundant
(thm (equal (foo 3) 3)) ; fails, as we would like

To summarize: If a defun form is submitted that meets the usual redundancy criteria, then it may be considered redundant even if a macro called in the definition has since been redefined. The analogous problem applie to constants, i.e., symbols defined by defconst that occur in the definition body. However, if redefinition is currently active the problem goes away: that is, the redundancy check is strengthened to check the ``translated'' body, in which macro calls and constants defined by defconst are expanded away.

The above discussion for defun forms applies to defconst forms as well. However, for defmacro forms ACL2 always checks translated bodies, so such bogus redundancy does not occur.

Here is more complex example illustrating the limits of redefinition, based on one supplied by Grant Passmore.

(defun n3 () 0)
(defun n4 () 1)
(defun n5 () (> (n3) (n4))) ; body is normalized to nil
(thm (equal (n5) nil)) ; succeeds, trivially
(set-ld-redefinition-action '(:warn . :overwrite) state)
(defun n3 () 2)
(thm (equal (n5) nil)) ; still succeeds, sadly
We may expect the final thm call to fail because of the following reasoning: (n5) = (> (n3) (n4)) = (> 2 1) = t. Unfortunatly, the body of n5 was simplified (``normalized'') to nil when n5 was admitted, so the redefinition of n3 is ignored during the final thm call. (Such normalization can be avoided; see the brief discussion of :normalize in the documentation for defun.) So, given this unfortunate situation, one might expect at this point simply to redefine n5 using the same definition as before, in order to pick up the new definition of n3. Such ``redefinition'' would, however, be redundant, for the same reason as in the previous example: no syntactic change was made to the definition. Even with redefinition active, there is no change in the body of n5, even with macros and constants (defined by defconst) expanded; there are none such! The same workaround applies as before: redefine n5 to be something different, and then redefine n5 again to be as desired.

A related phenomenon can occur for encapsulate. As explained above, an encapsulate event is redundant if it is identical to one already in the database. Consider then the following contrived example.

(defmacro mac (x) x)
(encapsulate () (defun foo (x) (mac x)))
(set-ld-redefinition-action '(:warn . :overwrite) state)
(defmacro mac (x) (list 'car x))
(encapsulate () (defun foo (x) (mac x)))
The last encapsulate event is redundant because it meets the criterion for redundancy: it is identical to the earlier encapsulate event. Even though redefinition is active, and hence ACL2 ``should'' be able to see that the new defun of foo is not truly redundant, nevertheless the criterion for redundancy of encapsulate allows the new encapsulate form to be redundant.

A workaround can be to add something trivial to the encapsulate, for example:

(encapsulate ()
  (deflabel try2) ; ``Increment'' to try3 next time, and so on.
  (defun foo (x) x))