Major Section: RULE-CLASSES
See rule-classes for a general discussion of rule classes, including how they are used to build rules from formulas and a discussion of the various keywords in a rule class description.
Example Rule Class:
(:type-set-inverter
:corollary (equal (and (counting-number x) (not (equal x 0)))
(and (integerp x) (< 0 x)))
:type-set 2)
General Forms of Rule Class:
:type-set-inverter, or
(:type-set-inverter :type-set n)
General Form of Theorem or Corollary:
(EQUAL new-expr old-expr)
where n is a type-set (see type-set) and old-expr is the term
containing x as a free variable that ACL2 currently uses to
recognize type-set n. For a given n, the exact form of old-expr is
generated by
(convert-type-set-to-term 'x n (ens state) (w state) nil)].
If the :type-set field of the rule-class is omitted, we attempt to
compute it from the right-hand side, old-expr, of the corollary.
That computation is done by type-set-implied-by-term
(see type-set). However, it is possible that the type-set we
compute from lhs does not have the required property that when
inverted with convert-type-set-to-term the result is lhs. If you
omit :type-set and an error is caused because lhs has the incorrect
form, you should manually specify both :type-set and the lhs
generated by convert-type-set-to-term.
The rule generated will henceforth make new-expr be the term used by
ACL2 to recognize type-set n. If this rule is created by a defthm
event named name then the rune of the rule is
(:type-set-inverter name) and by disabling that rune you can
prevent its being used to decode type-sets.
Type-sets are inverted when forced assumptions are turned into
formulas to be proved. In their internal form, assumptions are
essentially pairs consisting of a context and a goal term, which was
forced. Abstractly a context is just a list of hypotheses which may
be assumed while proving the goal term. But actually contexts are
alists which pair terms with type-sets, encoding the current
hypotheses. For example, if the original conjecture contained the
hypothesis (integerp x) then the context used while working on that
conjecture will include the assignment to x of the type-set
*ts-integer*.