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• R1cs-bridge

R1cs-constraints-to-pfcs

Translate a list of R1CS constraints to a list of PFCS constraints.

Signature

(r1cs-constraints-to-pfcs x) → pconstrs

Returns

pconstrs — Type (constraint-listp pconstrs).

These are translated element-wise.

Definitions and Theorems

Function: r1cs-constraints-to-pfcs-exec

(defun r1cs-constraints-to-pfcs-exec (x acc)
  (declare (xargs :guard (r1cs::r1cs-constraint-listp x)))
  (let ((__function__ 'r1cs-constraints-to-pfcs-exec))
    (declare (ignorable __function__))
    (if (consp x)
        (r1cs-constraints-to-pfcs-exec
             (cdr x)
             (cons (r1cs-constraint-to-pfcs (car x))
                   acc))
      acc)))

Function: r1cs-constraints-to-pfcs-nrev

(defun r1cs-constraints-to-pfcs-nrev (x acl2::nrev)
 (declare (xargs :stobjs (acl2::nrev)))
 (declare (xargs :guard (r1cs::r1cs-constraint-listp x)))
 (let ((__function__ 'r1cs-constraints-to-pfcs-nrev))
  (declare (ignorable __function__))
  (if (atom x)
      (acl2::nrev-fix acl2::nrev)
    (let
     ((acl2::nrev (acl2::nrev-push (r1cs-constraint-to-pfcs (car x))
                                   acl2::nrev)))
     (r1cs-constraints-to-pfcs-nrev (cdr x)
                                    acl2::nrev)))))

Function: r1cs-constraints-to-pfcs

(defun r1cs-constraints-to-pfcs (x)
  (declare (xargs :guard (r1cs::r1cs-constraint-listp x)))
  (let ((__function__ 'r1cs-constraints-to-pfcs))
    (declare (ignorable __function__))
    (mbe :logic
         (if (consp x)
             (cons (r1cs-constraint-to-pfcs (car x))
                   (r1cs-constraints-to-pfcs (cdr x)))
           nil)
         :exec
         (if (atom x)
             nil
           (acl2::with-local-nrev
                (r1cs-constraints-to-pfcs-nrev x acl2::nrev))))))

Theorem: constraint-listp-of-r1cs-constraints-to-pfcs

(defthm constraint-listp-of-r1cs-constraints-to-pfcs
  (b* ((pconstrs (r1cs-constraints-to-pfcs x)))
    (constraint-listp pconstrs))
  :rule-classes :rewrite)

Theorem: r1cs-constraints-to-pfcs-of-take

(defthm r1cs-constraints-to-pfcs-of-take
  (implies (<= (nfix acl2::n) (len acl2::x))
           (equal (r1cs-constraints-to-pfcs (take acl2::n acl2::x))
                  (take acl2::n
                        (r1cs-constraints-to-pfcs acl2::x))))
  :rule-classes ((:rewrite)))

Theorem: set-equiv-congruence-over-r1cs-constraints-to-pfcs

(defthm set-equiv-congruence-over-r1cs-constraints-to-pfcs
  (implies (set-equiv acl2::x acl2::y)
           (set-equiv (r1cs-constraints-to-pfcs acl2::x)
                      (r1cs-constraints-to-pfcs acl2::y)))
  :rule-classes ((:congruence)))

Theorem: subsetp-of-r1cs-constraints-to-pfcs-when-subsetp

(defthm subsetp-of-r1cs-constraints-to-pfcs-when-subsetp
  (implies (subsetp acl2::x acl2::y)
           (subsetp (r1cs-constraints-to-pfcs acl2::x)
                    (r1cs-constraints-to-pfcs acl2::y)))
  :rule-classes ((:rewrite)))

Theorem: member-of-r1cs-constraint-to-pfcs-in-r1cs-constraints-to-pfcs

(defthm
      member-of-r1cs-constraint-to-pfcs-in-r1cs-constraints-to-pfcs
  (implies (member acl2::k acl2::x)
           (member (r1cs-constraint-to-pfcs acl2::k)
                   (r1cs-constraints-to-pfcs acl2::x)))
  :rule-classes ((:rewrite)))

Theorem: r1cs-constraints-to-pfcs-nrev-removal

(defthm r1cs-constraints-to-pfcs-nrev-removal
  (equal (r1cs-constraints-to-pfcs-nrev acl2::x acl2::nrev)
         (append acl2::nrev
                 (r1cs-constraints-to-pfcs acl2::x)))
  :rule-classes ((:rewrite)))

Theorem: r1cs-constraints-to-pfcs-exec-removal

(defthm r1cs-constraints-to-pfcs-exec-removal
  (equal (r1cs-constraints-to-pfcs-exec acl2::x acl2::acc)
         (revappend (r1cs-constraints-to-pfcs acl2::x)
                    acl2::acc))
  :rule-classes ((:rewrite)))

Theorem: r1cs-constraints-to-pfcs-of-rev

(defthm r1cs-constraints-to-pfcs-of-rev
  (equal (r1cs-constraints-to-pfcs (rev acl2::x))
         (rev (r1cs-constraints-to-pfcs acl2::x)))
  :rule-classes ((:rewrite)))

Theorem: r1cs-constraints-to-pfcs-of-list-fix

(defthm r1cs-constraints-to-pfcs-of-list-fix
  (equal (r1cs-constraints-to-pfcs (list-fix acl2::x))
         (r1cs-constraints-to-pfcs acl2::x))
  :rule-classes ((:rewrite)))

Theorem: r1cs-constraints-to-pfcs-of-append

(defthm r1cs-constraints-to-pfcs-of-append
  (equal (r1cs-constraints-to-pfcs (append acl2::a acl2::b))
         (append (r1cs-constraints-to-pfcs acl2::a)
                 (r1cs-constraints-to-pfcs acl2::b)))
  :rule-classes ((:rewrite)))

Theorem: cdr-of-r1cs-constraints-to-pfcs

(defthm cdr-of-r1cs-constraints-to-pfcs
  (equal (cdr (r1cs-constraints-to-pfcs acl2::x))
         (r1cs-constraints-to-pfcs (cdr acl2::x)))
  :rule-classes ((:rewrite)))

Theorem: car-of-r1cs-constraints-to-pfcs

(defthm car-of-r1cs-constraints-to-pfcs
  (equal (car (r1cs-constraints-to-pfcs acl2::x))
         (and (consp acl2::x)
              (r1cs-constraint-to-pfcs (car acl2::x))))
  :rule-classes ((:rewrite)))

Theorem: r1cs-constraints-to-pfcs-under-iff

(defthm r1cs-constraints-to-pfcs-under-iff
  (iff (r1cs-constraints-to-pfcs acl2::x)
       (consp acl2::x))
  :rule-classes ((:rewrite)))

Theorem: consp-of-r1cs-constraints-to-pfcs

(defthm consp-of-r1cs-constraints-to-pfcs
  (equal (consp (r1cs-constraints-to-pfcs acl2::x))
         (consp acl2::x))
  :rule-classes ((:rewrite)))

Theorem: len-of-r1cs-constraints-to-pfcs

(defthm len-of-r1cs-constraints-to-pfcs
  (equal (len (r1cs-constraints-to-pfcs acl2::x))
         (len acl2::x))
  :rule-classes ((:rewrite)))

Theorem: true-listp-of-r1cs-constraints-to-pfcs

(defthm true-listp-of-r1cs-constraints-to-pfcs
  (true-listp (r1cs-constraints-to-pfcs acl2::x))
  :rule-classes :type-prescription)

Theorem: r1cs-constraints-to-pfcs-when-not-consp

(defthm r1cs-constraints-to-pfcs-when-not-consp
  (implies (not (consp acl2::x))
           (equal (r1cs-constraints-to-pfcs acl2::x)
                  nil))
  :rule-classes ((:rewrite)))

Theorem: r1cs-constraints-to-pfcs-of-cons

(defthm r1cs-constraints-to-pfcs-of-cons
  (equal (r1cs-constraints-to-pfcs (cons acl2::a acl2::b))
         (cons (r1cs-constraint-to-pfcs acl2::a)
               (r1cs-constraints-to-pfcs acl2::b)))
  :rule-classes ((:rewrite)))

Theorem: r1cs-constraint-listp-of-r1cs-constraints-to-pfcs

(defthm r1cs-constraint-listp-of-r1cs-constraints-to-pfcs
  (b* ((pconstrs (r1cs-constraints-to-pfcs x)))
    (r1cs-constraint-listp pconstrs))
  :rule-classes :rewrite)