allowing a name to be introduced ``twice''

Sometimes an event will announce that it is ``redundant''. When this happens, no change to the logical world has occurred. This happens when the logical name being defined is already defined and has exactly the same definition, from the logical point of view. This feature permits two independent books, each of which defines some name, to be included sequentially provided they use exactly the same definition.

When are two logical-name definitions considered exactly the same? It depends upon the kind of name being defined.

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 defun or mutual-recursion (or defuns) 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, type declarations, stobjs declarations and body (before macroexpansion), and an appropriate mode. Exception: if either definition is declared :non-executable (see xargs), then the two events must be identical. We discuss the situation with ``appropriate modes'' below.

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

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 has been defined to have the same value.

A defstobj is never redundant. Blah blah...

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

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

A deftheory is never redundant. The ``natural'' notion of equivalent deftheorys 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.

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

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

Table and defdoc events are never redundant because they don't define any name.

An encapsulate event is redundant if and only if a syntactically identical encapsulate has already been executed under the same default-defun-mode.

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

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. This is inappropriate. We do not permit the downgrading of a function from :logic mode to :program mode, since that might produce a logical world in which there were theorems about a :program mode function, violating one of ACL2's basic assumptions.

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.