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Command

Command-fix

Fixing function for command structures.

Signature
(command-fix x) → new-x
Arguments: x — Guard (commandp x).
Returns: new-x — Type (commandp new-x).

Definitions and Theorems

Function: command-fix$inline

(defun command-fix$inline (x)
 (declare (xargs :guard (commandp x)))
 (let ((__function__ 'command-fix))
  (declare (ignorable __function__))
  (mbe
   :logic
   (case (command-kind x)
     (:increment (b* ((map (identifier-fix (std::da-nth 0 (cdr x))))
                      (key (operand-fix (std::da-nth 1 (cdr x))))
                      (value (operand-fix (std::da-nth 2 (cdr x)))))
                   (cons :increment (list map key value))))
     (:decrement (b* ((map (identifier-fix (std::da-nth 0 (cdr x))))
                      (key (operand-fix (std::da-nth 1 (cdr x))))
                      (value (operand-fix (std::da-nth 2 (cdr x)))))
                   (cons :decrement (list map key value))))
     (:instruction
          (b* ((get (instruction-fix (std::da-nth 0 (cdr x)))))
            (cons :instruction (list get)))))
   :exec x)))

Theorem: commandp-of-command-fix

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

Theorem: command-fix-when-commandp

(defthm command-fix-when-commandp
  (implies (commandp x)
           (equal (command-fix x) x)))

Function: command-equiv$inline

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

Theorem: command-equiv-is-an-equivalence

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

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

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

Theorem: command-fix-under-command-equiv

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

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

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

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

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

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

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

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

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

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

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

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

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

Theorem: consp-of-command-fix

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