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Pnumber

Pnumber-fix

Fixing function for pnumber structures.

Signature
(pnumber-fix x) → new-x
Arguments: x — Guard (pnumberp x).
Returns: new-x — Type (pnumberp new-x).

Definitions and Theorems

Function: pnumber-fix$inline

(defun pnumber-fix$inline (x)
 (declare (xargs :guard (pnumberp x)))
 (mbe
  :logic
  (case (pnumber-kind x)
   (:digit (b* ((digit (acl2::char-fix (std::da-nth 0 (cdr x)))))
             (let ((digit (if (dec-digit-char-p digit)
                              digit
                            #\0)))
               (cons :digit (list digit)))))
   (:dot-digit
        (b* ((digit (acl2::char-fix (std::da-nth 0 (cdr x)))))
          (let ((digit (if (dec-digit-char-p digit)
                           digit
                         #\0)))
            (cons :dot-digit (list digit)))))
   (:number-digit
        (b* ((number (pnumber-fix (std::da-nth 0 (cdr x))))
             (digit (acl2::char-fix (std::da-nth 1 (cdr x)))))
          (let ((digit (if (dec-digit-char-p digit)
                           digit
                         #\0)))
            (cons :number-digit (list number digit)))))
   (:number-nondigit
        (b* ((number (pnumber-fix (std::da-nth 0 (cdr x))))
             (nondigit (acl2::char-fix (std::da-nth 1 (cdr x)))))
          (let ((nondigit (if (str::letter/uscore-char-p nondigit)
                              nondigit
                            #\_)))
            (cons :number-nondigit (list number nondigit)))))
   (:number-locase-e-sign
        (b* ((number (pnumber-fix (std::da-nth 0 (cdr x))))
             (sign (sign-fix (std::da-nth 1 (cdr x)))))
          (cons :number-locase-e-sign (list number sign))))
   (:number-upcase-e-sign
        (b* ((number (pnumber-fix (std::da-nth 0 (cdr x))))
             (sign (sign-fix (std::da-nth 1 (cdr x)))))
          (cons :number-upcase-e-sign (list number sign))))
   (:number-locase-p-sign
        (b* ((number (pnumber-fix (std::da-nth 0 (cdr x))))
             (sign (sign-fix (std::da-nth 1 (cdr x)))))
          (cons :number-locase-p-sign (list number sign))))
   (:number-upcase-p-sign
        (b* ((number (pnumber-fix (std::da-nth 0 (cdr x))))
             (sign (sign-fix (std::da-nth 1 (cdr x)))))
          (cons :number-upcase-p-sign (list number sign))))
   (:number-dot (b* ((number (pnumber-fix (std::da-nth 0 (cdr x)))))
                  (cons :number-dot (list number)))))
  :exec x))

Theorem: pnumberp-of-pnumber-fix

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

Theorem: pnumber-fix-when-pnumberp

(defthm pnumber-fix-when-pnumberp
  (implies (pnumberp x)
           (equal (pnumber-fix x) x)))

Function: pnumber-equiv$inline

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

Theorem: pnumber-equiv-is-an-equivalence

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

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

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

Theorem: pnumber-fix-under-pnumber-equiv

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

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

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

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

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

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

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

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

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

Theorem: pnumber-kind$inline-of-pnumber-fix-x

(defthm pnumber-kind$inline-of-pnumber-fix-x
  (equal (pnumber-kind$inline (pnumber-fix x))
         (pnumber-kind$inline x)))

Theorem: pnumber-kind$inline-pnumber-equiv-congruence-on-x

(defthm pnumber-kind$inline-pnumber-equiv-congruence-on-x
  (implies (pnumber-equiv x x-equiv)
           (equal (pnumber-kind$inline x)
                  (pnumber-kind$inline x-equiv)))
  :rule-classes :congruence)

Theorem: consp-of-pnumber-fix

(defthm consp-of-pnumber-fix
  (consp (pnumber-fix x))
  :rule-classes :type-prescription)

Theorem: pnumber-fix$inline-of-pnumber-fix-x

(defthm pnumber-fix$inline-of-pnumber-fix-x
  (equal (pnumber-fix$inline (pnumber-fix x))
         (pnumber-fix$inline x)))

Theorem: pnumber-fix$inline-pnumber-equiv-congruence-on-x

(defthm pnumber-fix$inline-pnumber-equiv-congruence-on-x
  (implies (pnumber-equiv x x-equiv)
           (equal (pnumber-fix$inline x)
                  (pnumber-fix$inline x-equiv)))
  :rule-classes :congruence)