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Jliteral

Jliteral-fix

Fixing function for jliteral structures.

Signature
(jliteral-fix x) → new-x
Arguments: x — Guard (jliteralp x).
Returns: new-x — Type (jliteralp new-x).

Definitions and Theorems

Function: jliteral-fix$inline

(defun jliteral-fix$inline (x)
 (declare (xargs :guard (jliteralp x)))
 (let ((__function__ 'jliteral-fix))
  (declare (ignorable __function__))
  (mbe
   :logic
   (case (jliteral-kind x)
    (:integer
         (b* ((get (integer-literal-fix (std::da-nth 0 (cdr x)))))
           (cons :integer (list get))))
    (:floating (b* ((value (nfix (std::da-nth 0 (cdr x)))))
                 (cons :floating (list value))))
    (:boolean (b* ((value (acl2::bool-fix (std::da-nth 0 (cdr x)))))
                (cons :boolean (list value))))
    (:character
         (b* ((value (acl2::char-fix (std::da-nth 0 (cdr x)))))
           (cons :character (list value))))
    (:string (b* ((value (str-fix (std::da-nth 0 (cdr x)))))
               (cons :string (list value))))
    (:null (cons :null (list))))
   :exec x)))

Theorem: jliteralp-of-jliteral-fix

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

Theorem: jliteral-fix-when-jliteralp

(defthm jliteral-fix-when-jliteralp
  (implies (jliteralp x)
           (equal (jliteral-fix x) x)))

Function: jliteral-equiv$inline

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

Theorem: jliteral-equiv-is-an-equivalence

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

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

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

Theorem: jliteral-fix-under-jliteral-equiv

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

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

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

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

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

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

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

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

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

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

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

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

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

Theorem: consp-of-jliteral-fix

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