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Rule-classes

Type-set-inverter

Exhibit a new decoding for an ACL2 type-set

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. Also see type-reasoning for basic background on type reasoning in ACL2.

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*.