THEORY-INVARIANT.html -- ACL2 Version 6.3

## THEORY-INVARIANT

user-specified invariants on theories

    Major Section:  EVENTS

    Examples:
    (theory-invariant (not (and (active-runep '(:rewrite left-to-right))
                                (active-runep '(:rewrite right-to-left))))
                      :key my-invariant
                      :error nil)

    ; Equivalent to the above:
    (theory-invariant (incompatible (:rewrite left-to-right)
                                    (:rewrite right-to-left))
                      :key my-invariant
                      :error nil)

    General Form:
    (theory-invariant term &key key error)

where:

> o `term` is a term that uses no variables other than `ens` and `state`;

> o `key` is an arbitrary ``name'' for this invariant (if omitted, an integer is generated and used); and

> o `:error` specifies the action to be taken when an invariant is violated -- either `nil` if a warning is to be printed, else `t` (the default) if an error is to be caused.

`Theory-invariant` is an event that adds to or modifies the table of user-supplied theory invariants that are checked each time a theory expression is evaluated.

The theory invariant mechanism is provided via a table (see table) named `theory-invariant-table`. In fact, the `theory-invariant` ``event'' is just a macro that expands into a use of the `table` event. More general access to the `theory-invariant` table is provided by `table` itself. For example, the table can be inspected or cleared with `table`; you can clear an individual theory invariant by setting the invariant to `t`, or eliminate all theory invariants with the command `(table theory-invariant-table nil nil :clear)`.

`Theory-invariant-table` maps arbitrary keys to records containing terms that mention, at most, the variables `ens` and `state`. Every time an alleged theory expression is evaluated, e.g., in the `in-theory` event or `:``in-theory` hint, each of the terms in `theory-invariant-table` is evaluated with `ens` bound to a so-called ``enabled structure'' obtained from the theory expression and `state` bound to the current ACL2 state (see state). Users generally need not know about the enabled structure, other than that it can be accessed using the macros `active-runep` and `incompatible`; see active-runep and see incompatible. If the result is `nil`, a message is printed and an error occurs (except, only a warning occurs if `:error nil` is specified). Thus, the table can be thought of as a list of conjuncts. Each `term` in the table has a ``name,'' which is just the key under which the term is stored. When a theory violates the restrictions specified by some term, both the name and the term are printed. By calling `theory-invariant` with a new term but the same name, you can overwrite that conjunct of the theory invariant; but see the Local Redefinition Caveat at the end of this note. You may want to avoid using explicit names, since otherwise the subsequent inclusion of another book that defines a theory invariant with the same name will override your theory invariant.

Theory invariants are particularly useful in the context of large rule sets intended for re-use. Such sets often contain conflicting rules, e.g., rules that are to be enabled when certain function symbols are disabled, rules that rewrite in opposite directions and thus loop if simultaneously enabled, groups of rules which should be enabled in concert, etc. The developer of such rule sets understands these restrictions and probably documents them. The theory invariant mechanism allows the developer to codify his restrictions so that the user is alerted when they are violated.

Since theory invariants are arbitrary terms, macros may be used to express commonly used restrictions. For example, executing the event

    (theory-invariant (incompatible (:rewrite left-to-right)
                                    (:rewrite right-to-left)))

would subsequently cause an error any time the current theory contained both of the two runes shown. Of course, incompatible is just defined as a macro. Its definition may be inspected with `:pe incompatible`.

In order for a `theory-invariant` event to be accepted, the proposed theory invariant must be satisfied by the current theory (see current-theory). The value returned upon successful execution of the event is the key (whether user-supplied or generated).

Local Redefinition Caveat. Care needs to be taken when redefining a theory invariant in a local context. Consider the following example.

    (theory-invariant
     (active-runep '(:definition binary-append))
     :key app-inv)

    (encapsulate
     ()
     (local (theory-invariant t :key app-inv))
     (in-theory (disable binary-append))
     (defthm ...))

The second pass of the `encapsulate` will fail, because the `in-theory` event violates the original `theory-invariant` and the `local` `theory-invariant` is skipped in the second pass of the `encapsulate`. Of course, `local` `theory-invariant`s in books can cause the analogous problem in the second (`include-book`) pass of a `certify-book`. In both cases, though, the theory invariants are only checked at the conclusion of the (`include-book` or `encapsulate`) event. Indeed, theory invariants are checked at the end of every event related to theories, including `defun`, `defthm`, `in-theory`, `encapsulate`, and `include-book`, except for events executed on behalf of an `include-book` or the second pass of an `encapsulate`.