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• Config

Config-fix

Fixing function for config structures.

Signature

(config-fix x) → new-x

Arguments

x — Guard (configp x).

Returns

new-x — Type (configp new-x).

Definitions and Theorems

Function: config-fix$inline

(defun config-fix$inline (x)
  (declare (xargs :guard (configp x)))
  (let ((__function__ 'config-fix))
    (declare (ignorable __function__))
    (mbe :logic
         (b* ((comms (comm-list-fix (std::da-nth 0 (cdr x))))
              (env (env-fix (std::da-nth 1 (cdr x)))))
           (cons :config (list comms env)))
         :exec x)))

Theorem: configp-of-config-fix

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

Theorem: config-fix-when-configp

(defthm config-fix-when-configp
  (implies (configp x)
           (equal (config-fix x) x)))

Function: config-equiv$inline

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

Theorem: config-equiv-is-an-equivalence

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

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

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

Theorem: config-fix-under-config-equiv

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

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

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

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

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

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

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

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

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