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Computation-states

Compustate-scopes-numbers

Ordered list of the numbers of scopes in the call stack frames.

Signature
(compustate-scopes-numbers compst) → ns
Arguments: compst — Guard (compustatep compst).
Returns: ns — Type (pos-listp ns).

Each frame in the call stack has a number of scopes. This function returns these numbers, in the same order as the frames in the stack.

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)

Function: compustate-scopes-numbers

(defun compustate-scopes-numbers (compst)
  (declare (xargs :guard (compustatep compst)))
  (let ((__function__ 'compustate-scopes-numbers))
    (declare (ignorable __function__))
    (compustate-scopes-numbers-aux (compustate->frames compst))))

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

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

Theorem: len-of-compustate-scopes-numbers

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

Theorem: consp-of-compustate-scopes-numbers

(defthm consp-of-compustate-scopes-numbers
  (implies (> (compustate-frames-number compst) 0)
           (b* ((?ns (compustate-scopes-numbers compst)))
             (consp ns)))
  :rule-classes :type-prescription)

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

(defthm posp-of-car-of-compustate-scopes-numbers
  (implies (> (compustate-frames-number compst) 0)
           (b* ((?ns (compustate-scopes-numbers compst)))
             (posp (car ns))))
  :rule-classes :type-prescription)

Theorem: car-of-compustate-scopes-numbers-lower-bound

(defthm car-of-compustate-scopes-numbers-lower-bound
  (implies (> (compustate-frames-number compst) 0)
           (b* ((?ns (compustate-scopes-numbers compst)))
             (> (car ns) 0)))
  :rule-classes :linear)

Theorem: car-of-compustate-scopes-numbers

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

Theorem: compustate-scopes-numbers-of-push-frame

(defthm compustate-scopes-numbers-of-push-frame
  (equal (compustate-scopes-numbers (push-frame frame compst))
         (cons (len (frame->scopes frame))
               (compustate-scopes-numbers compst))))

Theorem: compustate-scopes-numbers-of-pop-frame

(defthm compustate-scopes-numbers-of-pop-frame
  (equal (compustate-scopes-numbers (pop-frame compst))
         (cdr (compustate-scopes-numbers compst))))

Theorem: compustate-scopes-numbers-of-compustate-fix-compst

(defthm compustate-scopes-numbers-of-compustate-fix-compst
  (equal (compustate-scopes-numbers (compustate-fix compst))
         (compustate-scopes-numbers compst)))

Theorem: compustate-scopes-numbers-compustate-equiv-congruence-on-compst

(defthm
    compustate-scopes-numbers-compustate-equiv-congruence-on-compst
  (implies (compustate-equiv compst compst-equiv)
           (equal (compustate-scopes-numbers compst)
                  (compustate-scopes-numbers compst-equiv)))
  :rule-classes :congruence)