Major Section: MISCELLANEOUS
General Form of :hints: (hint1 hint2 ... hintk)Each element, hinti, must be either a common hint or a computed hint.
A common hint is of the form
(goal-spec :key1 val1 ... :keyn valn)
where goal-spec is as specified in goal-spec and each
:keyi and vali is as specified in hints.
A computed hint is either a function symbol, fn, of three or four
arguments or is a term involving, at most, the four free variables
ID, CLAUSE, WORLD and STABLE-UNDER-SIMPLIFICATIONP.
The function symbol case is treated as an abbreviation of the term
(fn ID CLAUSE WORLD) or
(fn ID CLAUSE WORLD STABLE-UNDER-SIMPLIFICATIONP), as appropriate
for the arity of fn. (Note that
this tells you which argument of fn is which.) In the discussion
below we assume all computed hints are of the term form.
The evaluation of the term (in a context in which its variables are
bound as described below) should be either nil, indicating that
the hint is not applicable to the clause in question, or else the
value is an alternating list of :keyi vali ``pairs.''
Except possibly for the first keyword, the :keyi vali pairs
should be as specified in hints. That is, those elements of the
result should be hint settings as you might have typed in a common
hint. The first keyword is allowed to be :COMPUTED-HINT-REPLACEMENT.
Its value should be nil, t, or a list of terms. If this
keyword is not present, the default value of nil is provided.
The evaluation of a hint term is done with guard checking turned off
(see set-guard-checking); e.g., the form (car 23) in a
computed hint returns nil as per the axioms.
When a non-nil value is returned, the keyword/value pairs (other
than the optional :COMPUTED-HINT-REPLACEMENT) are used as the
hint for the subgoal in question. Thus, your job as the programmer
of computed hints is to generate the list of keys and values you
would have typed had you supplied a common hint for the subgoal. (In
particular, any theory expressions in it are evaluated with respect
to the global current-theory, not whatever theory is active at the
subgoal in question.) If the generated list of keywords and values
is illegal, an error will be signaled and the proof attempt will be
aborted.
The purpose of the :COMPUTED-HINT-REPLACEMENT keyword and its
value, chr, is to change the list of hints. If chr is nil,
then the hint which was applied is removed from the list of hints that
is passed down to the children of the subgoal in question. This is
the default. If chr is t, then the hint is left in list of
hints. This means that the same hint may act on the children of the
subgoal. Otherwise, chr must be a list of terms, each of which
is treated as a computed hint. The hint which was applied is deleted
from the list of hints and the hints in chr are added to the list
of hints passed to the children of the subgoal. The ability to compute
new hints and pass them down allows strange and wonderful behavior.
For these purposes, the goals produced by induction and the top-level goals of forcing rounds are not considered children; all original hints are available to them.
After a computed hint is applied to a goal and before the goal is
processed, the remaining applicable computed hints are applied.
For hint settings, such as :USE, that modify the goal, the effect
of multiple applicable hints just compounds. But for hint settings,
such as :IN-THEORY that determine the context of the subsequent
goal processing, only the last applicable hint is effective.
It remains only to describe the bindings of the four variables.
Suppose the theorem prover is working on some clause, clause, named
by some goal-spec, e.g., "Subgoal *1/2'''" in some logical
world, world. Corresponding to the printed goal-spec is an
internal data structure called a ``clause identifier'' id.
See clause-identifier.
In the case of a common hint, the hint applies if the goal-spec of the hint is the same as the goal-spec of the clause in question.
In the case of a computed hint, the variable ID is bound to the
clause id, the variable CLAUSE is bound to the (translated form
of the) clause, and the variable WORLD is bound to the current
ACL2 world. The variable STABLE-UNDER-SIMPLIFICATIONP is bound
to t or nil. It is bound to t only if the clause
is known to be stable under simplification. That is, the simplifier
has been applied to the clause and did not change it. Such a clause
is sometimes known as a ``simplification checkpoint.'' It is
frequently useful to inject hints (e.g., to enable a rule or provide
a :use hint) only when the goal in question has stabilized. If
a hint is provided, the processing of the clause starts over with
simplification.
For some instruction about how to use computed hints,
see using-computed-hints.