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Console

Console-fix

Fixing function for console structures.

Signature
(console-fix x) → new-x
Arguments: x — Guard (consolep x).
Returns: new-x — Type (consolep new-x).

Definitions and Theorems

Function: console-fix$inline

(defun console-fix$inline (x)
 (declare (xargs :guard (consolep x)))
 (let ((__function__ 'console-fix))
  (declare (ignorable __function__))
  (mbe
   :logic
   (case (console-kind x)
    (:assert (b* ((arg (expression-fix (std::da-nth 0 (cdr x)))))
               (cons :assert (list arg))))
    (:error
         (b* ((string (char-list-fix (std::da-nth 0 (cdr x))))
              (exprs (expression-list-fix (std::da-nth 1 (cdr x)))))
           (cons :error (list string exprs))))
    (:log
         (b* ((string (char-list-fix (std::da-nth 0 (cdr x))))
              (exprs (expression-list-fix (std::da-nth 1 (cdr x)))))
           (cons :log (list string exprs)))))
   :exec x)))

Theorem: consolep-of-console-fix

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

Theorem: console-fix-when-consolep

(defthm console-fix-when-consolep
  (implies (consolep x)
           (equal (console-fix x) x)))

Function: console-equiv$inline

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

Theorem: console-equiv-is-an-equivalence

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

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

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

Theorem: console-fix-under-console-equiv

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

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

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

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

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

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

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

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

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

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

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

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

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

Theorem: consp-of-console-fix

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