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Simple-escape

Simple-escape-fix

Fixing function for simple-escape structures.

Signature
(simple-escape-fix x) → new-x
Arguments: x — Guard (simple-escapep x).
Returns: new-x — Type (simple-escapep new-x).

Definitions and Theorems

Function: simple-escape-fix$inline

(defun simple-escape-fix$inline (x)
  (declare (xargs :guard (simple-escapep x)))
  (let ((__function__ 'simple-escape-fix))
    (declare (ignorable __function__))
    (mbe :logic
         (case (simple-escape-kind x)
           (:squote (cons :squote (list)))
           (:dquote (cons :dquote (list)))
           (:qmark (cons :qmark (list)))
           (:bslash (cons :bslash (list)))
           (:a (cons :a (list)))
           (:b (cons :b (list)))
           (:f (cons :f (list)))
           (:n (cons :n (list)))
           (:r (cons :r (list)))
           (:t (cons :t (list)))
           (:v (cons :v (list)))
           (:percent (cons :percent (list))))
         :exec x)))

Theorem: simple-escapep-of-simple-escape-fix

(defthm simple-escapep-of-simple-escape-fix
  (b* ((new-x (simple-escape-fix$inline x)))
    (simple-escapep new-x))
  :rule-classes :rewrite)

Theorem: simple-escape-fix-when-simple-escapep

(defthm simple-escape-fix-when-simple-escapep
  (implies (simple-escapep x)
           (equal (simple-escape-fix x) x)))

Function: simple-escape-equiv$inline

(defun simple-escape-equiv$inline (acl2::x acl2::y)
  (declare (xargs :guard (and (simple-escapep acl2::x)
                              (simple-escapep acl2::y))))
  (equal (simple-escape-fix acl2::x)
         (simple-escape-fix acl2::y)))

Theorem: simple-escape-equiv-is-an-equivalence

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

Theorem: simple-escape-equiv-implies-equal-simple-escape-fix-1

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

Theorem: simple-escape-fix-under-simple-escape-equiv

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

Theorem: equal-of-simple-escape-fix-1-forward-to-simple-escape-equiv

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

Theorem: equal-of-simple-escape-fix-2-forward-to-simple-escape-equiv

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

Theorem: simple-escape-equiv-of-simple-escape-fix-1-forward

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

Theorem: simple-escape-equiv-of-simple-escape-fix-2-forward

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

Theorem: simple-escape-kind$inline-of-simple-escape-fix-x

(defthm simple-escape-kind$inline-of-simple-escape-fix-x
  (equal (simple-escape-kind$inline (simple-escape-fix x))
         (simple-escape-kind$inline x)))

Theorem: simple-escape-kind$inline-simple-escape-equiv-congruence-on-x

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

Theorem: consp-of-simple-escape-fix

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