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• Floating-point-value

Floating-point-value-fix

Fixing function for floating-point-value structures.

Signature

(floating-point-value-fix acl2::x) → new-x

Arguments

acl2::x — Guard (floating-point-valuep acl2::x).

Returns

new-x — Type (floating-point-valuep new-x).

Definitions and Theorems

Function: floating-point-value-fix$inline

(defun floating-point-value-fix$inline (acl2::x)
  (declare (xargs :guard (floating-point-valuep acl2::x)))
  (let ((__function__ 'floating-point-value-fix))
    (declare (ignorable __function__))
    (mbe :logic
         (case (floating-point-value-kind acl2::x)
           (:float (b* ((get (float-value-fix acl2::x)))
                     get))
           (:double (b* ((get (double-value-fix acl2::x)))
                      get)))
         :exec acl2::x)))

Theorem: floating-point-valuep-of-floating-point-value-fix

(defthm floating-point-valuep-of-floating-point-value-fix
  (b* ((new-x (floating-point-value-fix$inline acl2::x)))
    (floating-point-valuep new-x))
  :rule-classes :rewrite)

Theorem: floating-point-value-fix-when-floating-point-valuep

(defthm floating-point-value-fix-when-floating-point-valuep
  (implies (floating-point-valuep acl2::x)
           (equal (floating-point-value-fix acl2::x)
                  acl2::x)))

Function: floating-point-value-equiv$inline

(defun floating-point-value-equiv$inline (acl2::x acl2::y)
  (declare (xargs :guard (and (floating-point-valuep acl2::x)
                              (floating-point-valuep acl2::y))))
  (equal (floating-point-value-fix acl2::x)
         (floating-point-value-fix acl2::y)))

Theorem: floating-point-value-equiv-is-an-equivalence

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

Theorem: floating-point-value-equiv-implies-equal-floating-point-value-fix-1

(defthm
 floating-point-value-equiv-implies-equal-floating-point-value-fix-1
 (implies (floating-point-value-equiv acl2::x x-equiv)
          (equal (floating-point-value-fix acl2::x)
                 (floating-point-value-fix x-equiv)))
 :rule-classes (:congruence))

Theorem: floating-point-value-fix-under-floating-point-value-equiv

(defthm floating-point-value-fix-under-floating-point-value-equiv
  (floating-point-value-equiv (floating-point-value-fix acl2::x)
                              acl2::x)
  :rule-classes (:rewrite :rewrite-quoted-constant))

Theorem: equal-of-floating-point-value-fix-1-forward-to-floating-point-value-equiv

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

Theorem: equal-of-floating-point-value-fix-2-forward-to-floating-point-value-equiv

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

Theorem: floating-point-value-equiv-of-floating-point-value-fix-1-forward

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

Theorem: floating-point-value-equiv-of-floating-point-value-fix-2-forward

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

Theorem: floating-point-value-kind$inline-of-floating-point-value-fix-x

(defthm
     floating-point-value-kind$inline-of-floating-point-value-fix-x
  (equal (floating-point-value-kind$inline
              (floating-point-value-fix acl2::x))
         (floating-point-value-kind$inline acl2::x)))

Theorem: floating-point-value-kind$inline-floating-point-value-equiv-congruence-on-x

(defthm
 floating-point-value-kind$inline-floating-point-value-equiv-congruence-on-x
 (implies (floating-point-value-equiv acl2::x x-equiv)
          (equal (floating-point-value-kind$inline acl2::x)
                 (floating-point-value-kind$inline x-equiv)))
 :rule-classes :congruence)

Theorem: consp-of-floating-point-value-fix

(defthm consp-of-floating-point-value-fix
  (consp (floating-point-value-fix acl2::x))
  :rule-classes :type-prescription)