ACL2 property lists and the ACL2 logical data base

A ``world'' is a list of triples, each of the form (sym prop . val), implementing the ACL2 notion of property lists. ACL2 permits the simultaneous existence of many property list worlds. ``The world'' is often used as a shorthand for ``the ACL2 logical world'' which is the particular property list world used within the ACL2 system to maintain the data base of rules.

Common Lisp provides the notion of ``property lists'' by which one can attach ``properties'' and their corresponding ``values'' to symbols. For example, one can arrange for the 'color property of the symbol 'box-14 to be 'purple and the 'color property of the symbol 'triangle-7 to be 'yellow. Access to property lists is given via the Common Lisp function get. Thus, (get 'box-14 'color) might return 'purple. Property lists can be changed via the special form setf. Thus, (setf (get 'box-14 'color) 'blue) changes the Common Lisp property list configuration so that (get 'box-14 'color) returns 'blue. It should be obvious that ACL2 cannot provide this facility, because Common Lisp's get ``function'' is not a function of its argument, but instead a function of some implicit state object representing the property list settings for all symbols.

ACL2 provides the functions getprop and putprop which allow one to mimic the Common Lisp property list facility. However, ACL2's getprop takes as one of its arguments a list that is a direct encoding of what was above called the ``state object representing the property list settings for all symbols.'' Because ACL2 already has a notion of ``state'' that is quite distinct from that used here, we call this property list object a ``world.'' A world is just a true list of triples. Each triple is of the form (sym prop . val). This world can be thought of as a slightly elaborated form of association list and getprop is a slightly elaborated form of assoc that takes two keys. When getprop is called on a symbol, s, property p, and world, w, it scans w for the first triple whose sym is s and prop is p and returns the corresponding val. Getprop has two additional arguments, one of which that controls what it returns if no such sym and prop exist in w, and other other of which allows an extremely efficient implementation. To set some property's value for some symbol, ACL2 provides putprop. (putprop sym prop val w) merely returns a new world, w', in which (sym prop . val) has been consed onto the front of w, thus ``overwriting'' the prop value of sym in w to val and leaving all other properties in w unchanged.

One aspect of ACL2's property list arrangment is that it is possible to have many different property list worlds. For example, 'box-14 can have 'color 'purple in one world and can have 'color 'yes in another, and these two worlds can exist simultaneously because getprop is explicitly provided the world from which the property value is to be extracted.

The efficiency alluded to above stems from the fact that Common Lisp provides property lists. Using Common Lisp's provisions behind the scenes, ACL2 can ``install'' the properties of a given world into the Common Lisp property list state so as to make retrieval via getprop very fast in the special case that the world provided to getprop has been installed. To permit multiple installed worlds, each of which is permitted to be changed via putprop, ACL2 requires that worlds be named and these names are used to distinquish installed versions of the various worlds. At the moment we do not further document getprop and putprop.

However, the ACL2 system uses a property list world, named 'current-acl2-world, in which to store the succession of user commands and their effects on the logic. This world is often referred to in our documentation as ``the world'' though it should be stressed that the user is permitted to have worlds and ACL2's is in no way distinguished except that the user is not permitted to modify it except via event commands. The ACL2 world is part of the ACL2 state and may be obtained via (w state).

Warning: The ACL2 world is very large. Its length as of this writing (Version 2.5) is over 40,000 and it grows with each release. Furthermore, some of the values stored in it are pointers to old versions of itself. Printing (w state) is something you should avoid because you likely will not have the patience to await its completion. For these practical reasons, the only thing you should do with (w state) is provide it to getprop, as in the form

  (getprop sym prop default 'current-acl2-world (w state))
to inspect properties within it, or to pass it to ACL2 primitives, such as theory functions, where it is expected.

Some ACL2 command forms, such as theory expressions (see theories) and the values to be stored in tables (see table), are permitted to use the variable symbol world freely with the understanding that when these forms are evaluated that variable is bound to (w state). Theoretically, this gives those forms complete knowledge of the current logical configuration of ACL2. However, at the moment, few world scanning functions have been documented for the ACL2 user. Instead, supposedly convenient macro forms have been created and documented. For example, (current-theory :here), which is the theory expression which returns the currently enabled theory, actually macroexpands to (current-theory-fn :here world). When evaluated with world bound to (w state), current-theory-fn scans the current ACL2 world and computes the set of runes currently enabled in it.


ld without state -- a short-cut to a parallel universe

Example Form:
(wormhole t 'interactive-break nil '(value 'hi!))
                             ; Enters a recursive read-eval-print loop
                             ; on a copy of the ``current state'' and
                             ; returns nil!

General Form: (wormhole pseudo-flg name input form :current-package ... ; known package name :ld-skip-proofsp ... ; t, nil or 'include-book :ld-redefinition-action ; nil or '(:a . :b) :ld-prompt ... ; nil, t, or some prompt printer fn :ld-keyword-aliases ... ; an alist pairing keywords to parse info :ld-pre-eval-filter ... ; :all, :query, or some new name :ld-pre-eval-print ... ; nil, t, or :never :ld-post-eval-print ... ; nil, t, or :command-conventions :ld-evisc-tuple ... ; nil or '(alist nil nil level length) :ld-error-triples ... ; nil or t :ld-error-action ... ; :continue, :return, or :error :ld-query-control-alist ; alist supplying default responses :ld-verbose ...) ; nil or t

The keyword arguments above are exactly those of ld (see ld) except that three of ld's keyword arguments are missing: the three that specify the channels standard-oi, standard-co and proofs-co. Essentially wormhole is just a call of ld on the current state with the given keyword arguments. Wormhole always returns nil. The amazing thing about wormhole is that it calls ld and interacts with the user even though state is not available as an argument!

Wormhole does this by manufacturing a ``wormhole state,'' a copy of the ``current state'' (whatever that is) modified so as to contain some of the wormhole arguments. Ld is called on that wormhole state with the three ld channels directed to ACL2's ``comment window.'' At the moment, the comment window is overlaid on the terminal and you cannot tell when output is going to *standard-co* and when it is going to the comment window. But we imagine that eventually a different window will pop up on your screen. In any case, the interaction provided by this call of ld does not modify the state ``from which'' wormhole was called, it modifies the copied state. When ld exits (e.g., in response to :q being typed in the comment window) the wormhole state evaporates and wormhole returns nil. Logically and actually (from the perspective of the ongoing computation) nothing has happened except that a ``no-op'' function was called and returned nil.

The name wormhole is meant to suggest the idea that the function provides easy access to state in situations where it is apparently impossible to get state. Thus, for example, if you define the factorial function, say, except that you sprinkled into its body appropriate calls of wormhole, then the execution of (factorial 6) would cause interactive breaks in the comment window. During those breaks you would apparently be able to inspect the ``current state'' even though factorial does not take state as an argument. The whole notion of there being a ``current state'' during the evaluation of (factorial 6) is logically ill-defined. And yet, we know from practical experience with the sequential computing machines upon which ACL2 is implemented that there is a ``current state'' (to which the factorial function is entirely insensitive) and that is the state to which wormhole ``tunnels.'' A call of wormhole from within factorial can pass factorial-specific information that is embedded in the wormhole state and made available for inspection by the user in an interactive setting. But no information ever flows out of a wormhole state: wormhole always returns nil.

There are some restrictions about what can be done inside a wormhole. As you may imagine, we really do not ``copy the current state'' but rather just keep track of how we modified it and undo those modifications upon exit. An error is signalled if you try to modify state in an unsupported way. For this same reason, wormholes do not allow updating of any user-defined single-threaded objects. See stobj.

There are four arguments to wormhole that need further explanation: pseudo-flg, name, input, and form. Roughly speaking, the value of pseudo-flg should be t or nil and indicates whether we are actually to enter a wormhole or just return nil immediately. The actual handling of pseudo-flg is more sophisticated and is explained in detail at the end of this documentation.

Name and input are used as follows. Recall that wormhole copies the ``current state'' and then modifies it slightly to obtain the state upon which ld is called. We now describe the modifications. First, the state global variable 'wormhole-name is set to name, which may be any non-nil ACL2 object but is usually a symbol. Then, 'wormhole-input is set to input, which may be any ACL2 object. Finally, and inexplicably, 'wormhole-output is set to the value of 'wormhole-output the last time a wormhole named name was exited (or nil if this is the first time a wormhole named name was entered). This last aspect of wormholes, namely the preservation of 'wormhole-output, allows all the wormholes of a given name to communicate with each other.

We can now explain how form is used. The modified state described above is the state on which ld is called. However, standard-oi -- the input channel from which ld reads commands -- is set so that the first command that ld reads and evaluates is form. If form returns an error triple with value :q, i.e., form returns via (value :q), then no further commands are read, ld exits, and the wormhole exits and returns nil. But if form returns any other value (or is not an error triple), then subsequent commands are read from the comment window.

As usual, the ld-specials affect whether a herald is printed upon entry, whether form is printed before evaluation, whether a prompt is printed, how errors are handled, etc. The ld-specials can be specified with the corresponding arguments to wormhole. It is standard practice to call wormhole so that the entry to ld and the evaluation of form are totally silent. Then, tests in form can inspect the state and decide whether user interaction is desired. If so, form can appropriately set ld-prompt, ld-error-action, etc., print a herald, and then return (value :invisible). Recall (see ld) that (value :invisible) causes ld not to print a value for the just executed form. The result of this arrangement is that whether interaction occurs can be based on tests that are performed on the wormhole state after (@ wormhole-input) and the last (@ wormhole-output) are available for inspection. This is important because outside the wormhole you can access wormhole-input (you are passing it into the wormhole) but you may not be able to access the current state (because you might be in factorial) and you definitely cannot access the wormhole-output of the last wormhole because it is not part of the ACL2 state. Thus, if the condition under which you wish to interact depends upon the state or that part of it preserved from the last wormhole interaction, that condition can only be tested from within the wormhole, via form.

It is via this mechanism that break-rewrite (see break-rewrite) is implemented. To be more precise, the list of monitored runes is maintained as part of the preserved wormhole-output of the break-rewrite wormhole. Because it is not part of the normal state, it may be changed by the user during proofs. That is what allows you to install new monitors while debugging proofs. But that means that the list of monitored runes cannot be inspected from outside the wormhole. Therefore, to decide whether a break is to occur when a given rule is applied, the rewriter must enter the break-rewrite wormhole, supplying a form that causes interaction if the given rule's break condition is satisfied. The user perceives this as though the wormhole was conditionally entered -- a perception that is happily at odds with the informed user's knowledge that the list of monitored runes is not part of the state. In fact, the wormhole was unconditionally entered and the condition was checked from within the wormhole, that being the only state in which the condition is known.

Another illustrative example is available in the implemention of the monitor command. How can we add a new rune to the list of monitored runes while in the normal ACL2 state (i.e., while not in a wormhole)? The answer is: by getting into a wormhole. In particular, when you type (monitor rune expr) at the top-level of ACL2, monitor enters the break-rewrite wormhole with a cleverly designed first form. That form adds rune and expr to the list of monitored runes -- said list only being available in break-rewrite wormhole states. Then the first form returns (value :q), which causes us to exit the wormhole. By using ld-specials that completely suppress all output during the process, it does not appear to the user that a wormhole was entered. The moral here is rather subtle: the first form supplied to wormhole may be the entire computation you want to perform in the wormhole; it need not just be a predicate that decides if interaction is to occur. Using wormholes of different names you can maintain a variety of ``hidden'' data structures that are always accessible (whether passed in or not). This appears to violate completely the applicative semantics of ACL2, but it does not: because these data structures are only accessible via wormholes, it is impossible for them to affect any ACL2 computation (except in the comment window).

As one might imagine, there is some overhead associated with entering a wormhole because of the need to copy the current state. This brings us back to pseudo-flg. Ostensibly, wormhole is a function and hence all of its argument expressions are evaluated outside the function (and hence, outside the wormhole it creates) and then their values are passed into the function where an appropriate wormhole is created. In fact, wormhole is a macro that permits the pseudo-flg expression to peer dimly into the wormhole that will be created before it is created. In particular, pseudo-flg allows the user to access the wormhole-output that will be used to create the wormhole state.

This is done by allowing the user to mention the (apparently unbound) variable wormhole-output in the first argument to wormhole. Logically, wormhole is a macro that wraps

(let ((wormhole-output nil)) ...)
around the expression supplied as its first argument. So logically, wormhole-output is always nil when the expression is evaluated. However, actually, wormhole-output is bound to the value of (@ wormhole-output) on the last exit from a wormhole of the given name (or nil if this is the first entrance). Thus, the pseudo-flg expression, while having to handle the possibility that wormhole-output is nil, will sometimes see non-nil values. The next question is, of course, ``But how can you get away with saying that logically wormhole-output is always nil but actually it is not? That doesn't appear to be sound.'' But it is sound because whether pseudo-flg evaluates to nil or non-nil doesn't matter, since in either case wormhole returns nil. To make that point slightly more formal, imagine that wormhole did not take pseudo-flg as an argument. Then it could be implemented by writing
(if pseudo-flg (wormhole name input form ...) nil).
Now since wormhole always returns nil, this expression is equivalent to (if pseudo-flg nil nil) and we see that the value of pseudo-flg is irrelevant. So we could in fact allow the user to access arbitrary information to decide which branch of this if to take. We allow access to wormhole-output because it is often all that is needed. We don't allow access to state (unless state is available at the level of the wormhole call) for technical reasons having to do with the difficulty of overcoming translate's prohibition of the sudden appearance of the variable state.

We conclude with an example of the use of pseudo-flg. This example is a simplification of our implementation of break-rewrite. To enter break-rewrite at the beginning of the attempted application of a rule, rule, we use

 (and (f-get-global 'brr-mode state)
      (member-equal (access rewrite-rule rule :rune)
                    (cdr (assoc-eq 'monitored-runes wormhole-output))))
The function in which this call of wormhole occurs has state as a formal. The pseudo-flg expression can therefore refer to state to determine whether 'brr-mode is set. But the pseudo-flg expression above mentions the variable wormhole-output; this variable is not bound in the context of the call of wormhole; if wormhole were a simple function symbol, this expression would be illegal because it mentions a free variable.

However, it is useful to think of wormhole as a simple function that evaluates all of its arguments but to also imagine that somehow wormhole-output is magically bound around the first argument so that wormhole-output is the output of the last break-rewrite wormhole. If we so imagine, then the pseudo-flg expression above evaluates either to nil or non-nil and we will enter the wormhole named break-rewrite in the latter case.

Now what does the pseudo-flg expression above actually test? We know the format of our own wormhole-output because we are responsible for maintaining it. In particular, we know that the list of monitored runes can be obtained via

(cdr (assoc-eq 'monitored-runes wormhole-output)).
Using that knowledge we can design a pseudo-flg expression which tests whether (a) we are in brr-mode and (b) the rune of the current rule is a member of the monitored runes. Question (a) is answered by looking into the current state. Question (b) is answered by looking into that part of the about-to-be-created wormhole state that will differ from the current state. To reiterate the reason we can make wormhole-output available here even though it is not in the current state: logically speaking the value of wormhole-output is irrelevant because it is only used to choose between two identical alternatives. This example also makes it clear that pseudo-flg provides no additional functionality. The test made in the pseudo-flg expression could be moved into the first form evaluated by the wormhole -- changing the free variable wormhole-output to (@ wormhole-output) and arranging for the first form to return (value :q) when the pseudo-flg expression returns nil. The only reason we provide the pseudo-flg feature is because it allows the test to be carried out without the overhead of entering the wormhole.

Wormholes can be used not only in :program mode definitions but also in :logic mode definitions. Thus, it is possible (though somewhat cumbersome without investing in macro support) to annotate logical functions with output facilities that do not require state. These facilities do not complicate proof obligations. Suppose then that one doctored a simple function, e.g., APP, so as to do some printing and then proved that APP is associative. The proof may generate extraneous output due to the doctoring. Furthermore, contrary to the theorem proved, execution of the function appears to affect *standard-co*. To see what the function ``really'' does when evaluated, enter raw lisp and set the global variable *inhibit-wormhole-activityp* to t.


giving 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.

The following declaration is nonsensical but does illustrate all of the xargs keywords:

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

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 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 e0-ord-<.

Value is either a single stobj name or a true list of stobj names. 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. :WELL-FOUNDED-RELATION
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.

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

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

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).