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Syntax-abstraction

Abs-integer

Abstract an integer to an ACL2 int.

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

Definitions and Theorems

Function: abs-integer

(defun abs-integer (tree)
  (declare (xargs :guard (abnf::treep tree)))
  (let ((__function__ 'abs-integer))
    (declare (ignorable __function__))
    (b* (((okf (abnf::tree-list-tuple2 sub))
          (abnf::check-tree-nonleaf-2 tree "integer"))
         ((okf optional-minus-tree)
          (abnf::check-tree-list-1 sub.1st))
         ((okf has-minus-sign?)
          (check-optional-minus-sign-p optional-minus-tree))
         ((okf numeral-tree)
          (abnf::check-tree-list-1 sub.2nd))
         ((okf nat-value)
          (abs-numeral numeral-tree)))
      (if has-minus-sign? (- nat-value)
        nat-value))))

Theorem: integer-resultp-of-abs-integer

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

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

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

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

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