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Tyspecseq

Tyspecseq-fix

Fixing function for tyspecseq structures.

Signature
(tyspecseq-fix x) → new-x
Arguments: x — Guard (tyspecseqp x).
Returns: new-x — Type (tyspecseqp new-x).

Definitions and Theorems

Function: tyspecseq-fix$inline

(defun tyspecseq-fix$inline (x)
 (declare (xargs :guard (tyspecseqp x)))
 (let ((__function__ 'tyspecseq-fix))
  (declare (ignorable __function__))
  (mbe
   :logic
   (case (tyspecseq-kind x)
    (:void (cons :void (list)))
    (:char (cons :char (list)))
    (:schar (cons :schar (list)))
    (:uchar (cons :uchar (list)))
    (:sshort (b* ((signed (acl2::bool-fix (std::da-nth 0 (cdr x))))
                  (int (acl2::bool-fix (std::da-nth 1 (cdr x)))))
               (cons :sshort (list signed int))))
    (:ushort (b* ((int (acl2::bool-fix (std::da-nth 0 (cdr x)))))
               (cons :ushort (list int))))
    (:sint (b* ((signed (acl2::bool-fix (std::da-nth 0 (cdr x))))
                (int (acl2::bool-fix (std::da-nth 1 (cdr x)))))
             (let ((signed (if (not int) t signed))
                   (int (if (not signed) t int)))
               (cons :sint (list signed int)))))
    (:uint (b* ((int (acl2::bool-fix (std::da-nth 0 (cdr x)))))
             (cons :uint (list int))))
    (:slong (b* ((signed (acl2::bool-fix (std::da-nth 0 (cdr x))))
                 (int (acl2::bool-fix (std::da-nth 1 (cdr x)))))
              (cons :slong (list signed int))))
    (:ulong (b* ((int (acl2::bool-fix (std::da-nth 0 (cdr x)))))
              (cons :ulong (list int))))
    (:sllong (b* ((signed (acl2::bool-fix (std::da-nth 0 (cdr x))))
                  (int (acl2::bool-fix (std::da-nth 1 (cdr x)))))
               (cons :sllong (list signed int))))
    (:ullong (b* ((int (acl2::bool-fix (std::da-nth 0 (cdr x)))))
               (cons :ullong (list int))))
    (:bool (cons :bool (list)))
    (:float (b* ((complex (acl2::bool-fix (std::da-nth 0 (cdr x)))))
              (cons :float (list complex))))
    (:double
         (b* ((complex (acl2::bool-fix (std::da-nth 0 (cdr x)))))
           (cons :double (list complex))))
    (:ldouble
         (b* ((complex (acl2::bool-fix (std::da-nth 0 (cdr x)))))
           (cons :ldouble (list complex))))
    (:struct (b* ((tag (ident-fix (std::da-nth 0 (cdr x)))))
               (cons :struct (list tag))))
    (:union (b* ((tag (ident-fix (std::da-nth 0 (cdr x)))))
              (cons :union (list tag))))
    (:enum (b* ((tag (ident-fix (std::da-nth 0 (cdr x)))))
             (cons :enum (list tag))))
    (:typedef (b* ((name (ident-fix (std::da-nth 0 (cdr x)))))
                (cons :typedef (list name)))))
   :exec x)))

Theorem: tyspecseqp-of-tyspecseq-fix

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

Theorem: tyspecseq-fix-when-tyspecseqp

(defthm tyspecseq-fix-when-tyspecseqp
  (implies (tyspecseqp x)
           (equal (tyspecseq-fix x) x)))

Function: tyspecseq-equiv$inline

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

Theorem: tyspecseq-equiv-is-an-equivalence

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

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

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

Theorem: tyspecseq-fix-under-tyspecseq-equiv

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

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

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

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

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

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

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

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

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

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

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

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

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