Fixing function for fty-type structures.
(fty-type-fix x) → new-x
Function:
(defun fty-type-fix$inline (x) (declare (xargs :guard (fty-type-p x))) (let ((acl2::__function__ 'fty-type-fix)) (declare (ignorable acl2::__function__)) (mbe :logic (case (fty-type-kind x) (:prod (b* ((fields (fty-field-alist-fix (std::da-nth 0 (cdr x))))) (cons :prod (list fields)))) (:list (b* ((elt-type (symbol-fix (std::da-nth 0 (cdr x))))) (cons :list (list elt-type)))) (:alist (b* ((key-type (symbol-fix (std::da-nth 0 (cdr x)))) (val-type (symbol-fix (std::da-nth 1 (cdr x))))) (cons :alist (list key-type val-type)))) (:option (b* ((some-type (symbol-fix (std::da-nth 0 (cdr x))))) (cons :option (list some-type))))) :exec x)))
Theorem:
(defthm fty-type-p-of-fty-type-fix (b* ((new-x (fty-type-fix$inline x))) (fty-type-p new-x)) :rule-classes :rewrite)
Theorem:
(defthm fty-type-fix-when-fty-type-p (implies (fty-type-p x) (equal (fty-type-fix x) x)))
Function:
(defun fty-type-equiv$inline (acl2::x acl2::y) (declare (xargs :guard (and (fty-type-p acl2::x) (fty-type-p acl2::y)))) (equal (fty-type-fix acl2::x) (fty-type-fix acl2::y)))
Theorem:
(defthm fty-type-equiv-is-an-equivalence (and (booleanp (fty-type-equiv x y)) (fty-type-equiv x x) (implies (fty-type-equiv x y) (fty-type-equiv y x)) (implies (and (fty-type-equiv x y) (fty-type-equiv y z)) (fty-type-equiv x z))) :rule-classes (:equivalence))
Theorem:
(defthm fty-type-equiv-implies-equal-fty-type-fix-1 (implies (fty-type-equiv acl2::x x-equiv) (equal (fty-type-fix acl2::x) (fty-type-fix x-equiv))) :rule-classes (:congruence))
Theorem:
(defthm fty-type-fix-under-fty-type-equiv (fty-type-equiv (fty-type-fix acl2::x) acl2::x) :rule-classes (:rewrite :rewrite-quoted-constant))
Theorem:
(defthm equal-of-fty-type-fix-1-forward-to-fty-type-equiv (implies (equal (fty-type-fix acl2::x) acl2::y) (fty-type-equiv acl2::x acl2::y)) :rule-classes :forward-chaining)
Theorem:
(defthm equal-of-fty-type-fix-2-forward-to-fty-type-equiv (implies (equal acl2::x (fty-type-fix acl2::y)) (fty-type-equiv acl2::x acl2::y)) :rule-classes :forward-chaining)
Theorem:
(defthm fty-type-equiv-of-fty-type-fix-1-forward (implies (fty-type-equiv (fty-type-fix acl2::x) acl2::y) (fty-type-equiv acl2::x acl2::y)) :rule-classes :forward-chaining)
Theorem:
(defthm fty-type-equiv-of-fty-type-fix-2-forward (implies (fty-type-equiv acl2::x (fty-type-fix acl2::y)) (fty-type-equiv acl2::x acl2::y)) :rule-classes :forward-chaining)
Theorem:
(defthm fty-type-kind$inline-of-fty-type-fix-x (equal (fty-type-kind$inline (fty-type-fix x)) (fty-type-kind$inline x)))
Theorem:
(defthm fty-type-kind$inline-fty-type-equiv-congruence-on-x (implies (fty-type-equiv x x-equiv) (equal (fty-type-kind$inline x) (fty-type-kind$inline x-equiv))) :rule-classes :congruence)
Theorem:
(defthm consp-of-fty-type-fix (consp (fty-type-fix x)) :rule-classes :type-prescription)