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Param

Param-fix

Fixing function for param structures.

Signature
(param-fix x) → new-x
Arguments: x — Guard (paramp x).
Returns: new-x — Type (paramp new-x).

Definitions and Theorems

Function: param-fix$inline

(defun param-fix$inline (x)
 (declare (xargs :guard (paramp x)))
 (let ((__function__ 'param-fix))
  (declare (ignorable __function__))
  (mbe
   :logic
   (b*
    ((prime (prime-fix (cdr (std::da-nth 0 x))))
     (rate (acl2::pos-fix (cdr (std::da-nth 1 x))))
     (capacity (acl2::pos-fix (cdr (std::da-nth 2 x))))
     (alpha (ifix (cdr (std::da-nth 3 x))))
     (full-rounds-half (nfix (cdr (std::da-nth 4 x))))
     (partial-rounds (nfix (cdr (std::da-nth 5 x))))
     (constants (cdr (std::da-nth 6 x)))
     (mds (cdr (std::da-nth 7 x)))
     (rate-then-capacity-p (acl2::bool-fix (cdr (std::da-nth 8 x))))
     (ascending-p (acl2::bool-fix (cdr (std::da-nth 9 x))))
     (partial-first-p (acl2::bool-fix (cdr (std::da-nth 10 x)))))
    (let
       ((constants
             (if (and (fe-list-listp constants prime)
                      (all-len-equal-p constants (+ rate capacity))
                      (equal (len constants)
                             (+ (* 2 full-rounds-half)
                                partial-rounds)))
                 constants
               (repeat (+ (* 2 full-rounds-half)
                          partial-rounds)
                       (repeat (+ rate capacity) 0))))
        (mds (if (and (fe-list-listp mds prime)
                      (all-len-equal-p mds (+ rate capacity))
                      (equal (len mds) (+ rate capacity)))
                 mds
               (repeat (+ rate capacity)
                       (repeat (+ rate capacity) 0)))))
      (list (cons 'prime prime)
            (cons 'rate rate)
            (cons 'capacity capacity)
            (cons 'alpha alpha)
            (cons 'full-rounds-half
                  full-rounds-half)
            (cons 'partial-rounds partial-rounds)
            (cons 'constants constants)
            (cons 'mds mds)
            (cons 'rate-then-capacity-p
                  rate-then-capacity-p)
            (cons 'ascending-p ascending-p)
            (cons 'partial-first-p
                  partial-first-p))))
   :exec x)))

Theorem: paramp-of-param-fix

(defthm paramp-of-param-fix
  (b* ((new-x (param-fix$inline x)))
    (paramp new-x))
  :rule-classes :rewrite)

Theorem: param-fix-when-paramp

(defthm param-fix-when-paramp
  (implies (paramp x)
           (equal (param-fix x) x)))

Function: param-equiv$inline

(defun param-equiv$inline (acl2::x acl2::y)
  (declare (xargs :guard (and (paramp acl2::x)
                              (paramp acl2::y))))
  (equal (param-fix acl2::x)
         (param-fix acl2::y)))

Theorem: param-equiv-is-an-equivalence

(defthm param-equiv-is-an-equivalence
  (and (booleanp (param-equiv x y))
       (param-equiv x x)
       (implies (param-equiv x y)
                (param-equiv y x))
       (implies (and (param-equiv x y)
                     (param-equiv y z))
                (param-equiv x z)))
  :rule-classes (:equivalence))

Theorem: param-equiv-implies-equal-param-fix-1

(defthm param-equiv-implies-equal-param-fix-1
  (implies (param-equiv acl2::x x-equiv)
           (equal (param-fix acl2::x)
                  (param-fix x-equiv)))
  :rule-classes (:congruence))

Theorem: param-fix-under-param-equiv

(defthm param-fix-under-param-equiv
  (param-equiv (param-fix acl2::x)
               acl2::x)
  :rule-classes (:rewrite :rewrite-quoted-constant))

Theorem: equal-of-param-fix-1-forward-to-param-equiv

(defthm equal-of-param-fix-1-forward-to-param-equiv
  (implies (equal (param-fix acl2::x) acl2::y)
           (param-equiv acl2::x acl2::y))
  :rule-classes :forward-chaining)

Theorem: equal-of-param-fix-2-forward-to-param-equiv

(defthm equal-of-param-fix-2-forward-to-param-equiv
  (implies (equal acl2::x (param-fix acl2::y))
           (param-equiv acl2::x acl2::y))
  :rule-classes :forward-chaining)

Theorem: param-equiv-of-param-fix-1-forward

(defthm param-equiv-of-param-fix-1-forward
  (implies (param-equiv (param-fix acl2::x)
                        acl2::y)
           (param-equiv acl2::x acl2::y))
  :rule-classes :forward-chaining)

Theorem: param-equiv-of-param-fix-2-forward

(defthm param-equiv-of-param-fix-2-forward
  (implies (param-equiv acl2::x (param-fix acl2::y))
           (param-equiv acl2::x acl2::y))
  :rule-classes :forward-chaining)