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Computation-states

Compustate-scopes-numbers-aux

Signature
(compustate-scopes-numbers-aux frames) → ns
Arguments: frames — Guard (frame-listp frames).
Returns: ns — Type (pos-listp ns).

Definitions and Theorems

Function: compustate-scopes-numbers-aux

(defun compustate-scopes-numbers-aux (frames)
  (declare (xargs :guard (frame-listp frames)))
  (let ((__function__ 'compustate-scopes-numbers-aux))
    (declare (ignorable __function__))
    (cond ((endp frames) nil)
          (t (cons (len (frame->scopes (car frames)))
                   (compustate-scopes-numbers-aux (cdr frames)))))))

Theorem: pos-listp-of-compustate-scopes-numbers-aux

(defthm pos-listp-of-compustate-scopes-numbers-aux
  (b* ((ns (compustate-scopes-numbers-aux frames)))
    (pos-listp ns))
  :rule-classes :rewrite)

Theorem: len-of-compustate-scopes-numbers-aux

(defthm len-of-compustate-scopes-numbers-aux
  (b* ((?ns (compustate-scopes-numbers-aux frames)))
    (equal (len ns) (len frames))))

Theorem: consp-of-compustate-scopes-numbers-aux

(defthm consp-of-compustate-scopes-numbers-aux
  (b* ((?ns (compustate-scopes-numbers-aux frames)))
    (equal (consp ns) (consp frames))))

Theorem: car-of-compustate-scopes-numbers-aux

(defthm car-of-compustate-scopes-numbers-aux
  (b* ((?ns (compustate-scopes-numbers-aux frames)))
    (implies (> (len frames) 0)
             (equal (car ns)
                    (len (frame->scopes (car frames)))))))

Theorem: compustate-scopes-numbers-aux-of-append

(defthm compustate-scopes-numbers-aux-of-append
  (equal (compustate-scopes-numbers-aux (append frames1 frames2))
         (append (compustate-scopes-numbers-aux frames1)
                 (compustate-scopes-numbers-aux frames2))))

Theorem: compustate-scopes-numbers-aux-of-rev

(defthm compustate-scopes-numbers-aux-of-rev
  (equal (compustate-scopes-numbers-aux (rev frames))
         (rev (compustate-scopes-numbers-aux frames))))

Theorem: compustate-scopes-numbers-aux-of-update-nth

(defthm compustate-scopes-numbers-aux-of-update-nth
 (implies
  (< (nfix i) (len frames))
  (equal (compustate-scopes-numbers-aux (update-nth i frame frames))
         (update-nth i (len (frame->scopes frame))
                     (compustate-scopes-numbers-aux frames)))))

Theorem: update-nth-of-nth-and-compustate-scopes-numbers-aux

(defthm update-nth-of-nth-and-compustate-scopes-numbers-aux
 (implies
  (< (nfix i)
     (len (compustate->frames compst)))
  (equal
   (update-nth
        i
        (len (frame->scopes (nth i (compustate->frames compst))))
        (compustate-scopes-numbers-aux (compustate->frames compst)))
   (compustate-scopes-numbers-aux (compustate->frames compst)))))

Theorem: compustate-scopes-numbers-aux-of-frame-list-fix-frames

(defthm compustate-scopes-numbers-aux-of-frame-list-fix-frames
  (equal (compustate-scopes-numbers-aux (frame-list-fix frames))
         (compustate-scopes-numbers-aux frames)))

Theorem: compustate-scopes-numbers-aux-frame-list-equiv-congruence-on-frames

(defthm
 compustate-scopes-numbers-aux-frame-list-equiv-congruence-on-frames
 (implies (frame-list-equiv frames frames-equiv)
          (equal (compustate-scopes-numbers-aux frames)
                 (compustate-scopes-numbers-aux frames-equiv)))
 :rule-classes :congruence)