		Search-engine friendly clone of the ACL2 documentation.

Syntax-abstraction

Abs-integer-alt

Signature
(abs-integer-alt tree) → int
Arguments: tree — Guard (abnf::treep tree).
Returns: int — Type (integerp int).

Definitions and Theorems

Function: abs-integer-alt

(defun abs-integer-alt (tree)
 (declare (xargs :guard (abnf::treep tree)))
 (declare (xargs :guard (cst-matchp tree "integer")))
 (let ((__function__ 'abs-integer-alt))
   (declare (ignorable __function__))
   (let
      ((int-or-err
            (b* (((okf (abnf::tree-list-tuple2 sub))
                  (check-tree-nonleaf-2 tree "integer"))
                 ((okf optional-minus-tree)
                  (check-tree-list-1 sub.1st))
                 ((okf has-minus-sign?)
                  (check-optional-minus-sign-p optional-minus-tree))
                 ((okf numeral-tree)
                  (check-tree-list-1 sub.2nd))
                 ((okf nat-value)
                  (abs-numeral numeral-tree)))
              (if has-minus-sign? (- nat-value)
                nat-value))))
     (b* (((when (integerp int-or-err))
           int-or-err)
          (- (er hard? 'top-level
                 "problem in abs-integer-alt: ~x0"
                 tree)))
       0))))

Theorem: integerp-of-abs-integer-alt

(defthm integerp-of-abs-integer-alt
  (b* ((int (abs-integer-alt tree)))
    (integerp int))
  :rule-classes :rewrite)

Theorem: abs-integer-alt-of-tree-fix-tree

(defthm abs-integer-alt-of-tree-fix-tree
  (equal (abs-integer-alt (abnf::tree-fix tree))
         (abs-integer-alt tree)))

Theorem: abs-integer-alt-tree-equiv-congruence-on-tree

(defthm abs-integer-alt-tree-equiv-congruence-on-tree
  (implies (abnf::tree-equiv tree tree-equiv)
           (equal (abs-integer-alt tree)
                  (abs-integer-alt tree-equiv)))
  :rule-classes :congruence)