extra arguments, for example to give hints to defun

Common Lisp's defun function does not easily allow one to pass extra arguments such as ``hints''. ACL2 therefore supports a peculiar new declaration (see declare) designed explicitly for passing additional arguments to defun via a keyword-like syntax. This declaration can also be used with defmacro, but only for xargs keyword :GUARD; so we restrict attention below to use of xargs in defun events.

The following declaration is nonsensical but does illustrate all of the xargs keywords for defun (which are the members of the list *xargs-keywords*).

(declare (xargs :guard (symbolp x)
                :guard-hints (("Goal" :in-theory (theory batch1)))
                :guard-debug t
                :hints (("Goal" :in-theory (theory batch1)))
                :measure (- i j)
                :ruler-extenders :basic
                :mode :logic
                :non-executable t
                :normalize nil
                :otf-flg t
                :stobjs ($s)
                :verify-guards t
                :split-types t
                :well-founded-relation my-wfr))

General Form:
(xargs :key1 val1 ... :keyn valn)
where the keywords and their respective values are as shown below. Note that once ``inside'' the xargs form, the ``extra arguments'' to defun are passed exactly as though they were keyword arguments.

Value is a term involving only the formals of the function being defined. The actual guard used for the definition is the conjunction of all the guards and types (see declare) declared.

Value: hints (see hints), to be used during the guard verification proofs as opposed to the termination proofs of the defun.

Value: nil by default, else directs ACL2 to decorate each guard proof obligation with hypotheses indicating its sources. See guard-debug.

Value: hints (see hints), to be used during the termination proofs as opposed to the guard verification proofs of the defun.

Value is a term involving only the formals of the function being defined. This term is indicates what is getting smaller in the recursion. The well-founded relation with which successive measures are compared is o<. Also allowed is a special case, (:? v1 ... vk), where (v1 ... vk) enumerates a subset of the formal parameters such that some valid measure involves only those formal parameters. However, this special case is only allowed for definitions that are redundant (see redundant-events) or are executed when skipping proofs (see skip-proofs). Another special case is :MEASURE nil, which is treated the same as if :MEASURE is omitted.

For recursive definitions (possibly mutually recursive), value controls termination analysis and the resulting stored induction scheme. See ruler-extenders for a discussion of legal values and their effects.

Value is :program or :logic, indicating the defun mode of the function introduced. See defun-mode. If unspecified, the defun mode defaults to the default defun mode of the current world. To convert a function from :program mode to :logic mode, see verify-termination.

Value is normally t or nil (the default). Rather than stating :non-executable t directly, which requires :logic mode and that the definitional body has a certain form, we suggest using the macro defun-nx or defund-nx; see defun-nx. A third value of :non-executable for advanced users is :program, which is generated by expansion of defproxy forms; see defproxy. For another way to deal with non-executability, see non-exec.

Value is a flag telling defun whether to propagate if tests upward. Since the default is to do so, the value supplied is only of interest when it is nil. (See defun).

Value is a flag indicating ``onward through the fog'' (see otf-flg).

Value is either a single stobj name or a true list of stobj names (see stobj and see defstobj, and perhaps see defabsstobj). Every stobj name among the formals of the function must be listed, if the corresponding actual is to be treated as a stobj. That is, if a function uses a stobj name as a formal parameter but the name is not declared among the :stobjs then the corresponding argument is treated as ordinary. The only exception to this rule is state: whether you include it or not, state is always treated as a single-threaded object. This declaration has two effects. One is to enforce the syntactic restrictions on single-threaded objects. The other is to strengthen the guard of the function being defined so that it includes conjuncts specifying that each declared single-threaded object argument satisfies the recognizer for the corresponding single-threaded object.

Value is t or nil, indicating whether or not guards are to be verified upon completion of the termination proof. This flag should only be t if the :mode is unspecified but the default defun mode is :logic, or else the :mode is :logic.

Value is t or nil, indicating whether or not types are to be proved from the guards. The default is nil, indicating that type declarations (see declare) contribute to the guards. If the value is t, then instead, the expressions corresponding to the type declarations (see type-spec) are conjoined into a ``split-type expression,'' and guard verification insists that this term is implied by the specified :guard. Suppose for example that a definition has the following declare form.

  (declare (xargs :guard (p x y) :split-types t)
           (type integer x)
           (type (satisfies good-bar-p) y))
Then for guard verification, (p x y) is assumed, and in addition to the usual proof obligations derived from the body of the definition, guard verification requires a proof that (p x y) implies both (integerp x) and (good-bar-p y). See community book demos/split-types-examples.lisp for small examples.

Value is a function symbol that is known to be a well-founded relation in the sense that a rule of class :well-founded-relation has been proved about it. See well-founded-relation.