TYPE-SET-INVERTER.html -- ACL2 Version 6.3

## TYPE-SET-INVERTER

exhibit a new decoding for an ACL2 type-set

    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*`.