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• Path

Path-fix

Fixing function for path structures.

Signature

(path-fix x) → new-x

Arguments

x — Guard (path-p x).

Returns

new-x — Type (path-p new-x).

Definitions and Theorems

Function: path-fix$inline

(defun path-fix$inline (x)
  (declare (xargs :guard (path-p x)))
  (let ((__function__ 'path-fix))
    (declare (ignorable __function__))
    (mbe :logic
         (case (path-kind x)
           (:wire (b* ((name (name-fix x))) name))
           (:scope (b* ((subpath (path-fix (cdr x)))
                        (namespace (name-fix (car x))))
                     (cons namespace subpath))))
         :exec x)))

Theorem: path-p-of-path-fix

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

Theorem: path-fix-when-path-p

(defthm path-fix-when-path-p
  (implies (path-p x)
           (equal (path-fix x) x)))

Function: path-equiv$inline

(defun path-equiv$inline (x y)
  (declare (xargs :guard (and (path-p x) (path-p y))))
  (equal (path-fix x) (path-fix y)))

Theorem: path-equiv-is-an-equivalence

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

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

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

Theorem: path-fix-under-path-equiv

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

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

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

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

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

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

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

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

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

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

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

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

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