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• Program

Program-fix

Fixing function for program structures.

Signature

(program-fix x) → new-x

Arguments

x — Guard (programp x).

Returns

new-x — Type (programp new-x).

Definitions and Theorems

Function: program-fix$inline

(defun
 program-fix$inline (x)
 (declare (xargs :guard (programp x)))
 (let
  ((__function__ 'program-fix))
  (declare (ignorable __function__))
  (mbe :logic (b* ((packages (package-list-fix (std::da-nth 0 x)))
                   (functions (function-set-fix (std::da-nth 1 x))))
                  (list packages functions))
       :exec x)))

Theorem: programp-of-program-fix

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

Theorem: program-fix-when-programp

(defthm program-fix-when-programp
        (implies (programp x)
                 (equal (program-fix x) x)))

Function: program-equiv$inline

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

Theorem: program-equiv-is-an-equivalence

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

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

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

Theorem: program-fix-under-program-equiv

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

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

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

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

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

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

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

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

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