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Max-index-clause

Maximum index of any identifier used anywhere in a clause.

Signature

(max-index-clause clause) → max

Arguments

clause — Guard (lit-listp clause).

Returns

max — Type (natp max).

Definitions and Theorems

Function: max-index-clause

(defun max-index-clause (clause)
  (declare (xargs :guard (lit-listp clause)))
  (let ((__function__ 'max-index-clause))
    (declare (ignorable __function__))
    (mbe :logic
         (if (atom clause)
             0
           (max (lit->var (car clause))
                (max-index-clause (cdr clause))))
         :exec (fast-max-index-clause clause 0))))

Theorem: natp-of-max-index-clause

(defthm natp-of-max-index-clause
  (b* ((max (max-index-clause clause)))
    (natp max))
  :rule-classes :type-prescription)

Theorem: fast-max-index-clause-removal

(defthm fast-max-index-clause-removal
  (equal (fast-max-index-clause clause max)
         (max (nfix max)
              (max-index-clause clause))))

Theorem: max-index-clause-of-lit-list-fix-clause

(defthm max-index-clause-of-lit-list-fix-clause
  (equal (max-index-clause (lit-list-fix clause))
         (max-index-clause clause)))

Theorem: max-index-clause-lit-list-equiv-congruence-on-clause

(defthm max-index-clause-lit-list-equiv-congruence-on-clause
  (implies (lit-list-equiv clause clause-equiv)
           (equal (max-index-clause clause)
                  (max-index-clause clause-equiv)))
  :rule-classes :congruence)

Subtopics

Fast-max-index-clause

Tail-recursive version of max-index-clause.