		Search-engine friendly clone of the ACL2 documentation.

Primitive-values

Floatx-value-fns

Recognizer, fixer, constructor, and destructor of Java float values in the float-extended-exponent value set [JLS.4.2.3].

We define the recognizer analogously to the one of the fixtypes of other Java primitive values, by tagging the underlying values introduced in floatx-value-abs. The recognizer is non-empty if and only if floatx-param is non-nil. We define a conditional fixer, but we cannot define a fixtype because the recognizer may be empty. We also define a conditional constructor and a conditional destructor, analogous to the ones of the fixtypes of other Java primitive values.

Definitions and Theorems

Function: floatx-valuep

(defun floatx-valuep (x)
  (declare (xargs :guard t))
  (let ((__function__ 'floatx-valuep))
    (declare (ignorable __function__))
    (and (tuplep 2 x)
         (eq (first x) :floatx)
         (floatx-value-abs-p (second x)))))

Theorem: booleanp-of-floatx-valuep

(defthm booleanp-of-floatx-valuep
  (b* ((yes/no (floatx-valuep x)))
    (booleanp yes/no))
  :rule-classes :rewrite)

Theorem: no-floatx-value-when-unsupported

(defthm no-floatx-value-when-unsupported
  (implies (not (floatx-param))
           (not (floatx-valuep x))))

Function: floatx-value-fix

(defun floatx-value-fix (x)
  (declare (xargs :guard (floatx-valuep x)))
  (let ((__function__ 'floatx-value-fix))
    (declare (ignorable __function__))
    (mbe :logic
         (if (floatx-valuep x)
             x
           (list :floatx (floatx-value-abs-pos-zero)))
         :exec x)))

Theorem: floatx-valuep-of-floatx-value-fix

(defthm floatx-valuep-of-floatx-value-fix
  (implies (floatx-param)
           (b* ((fixed-x (floatx-value-fix x)))
             (floatx-valuep fixed-x)))
  :rule-classes :rewrite)

Theorem: floatx-value-fix-when-floatx-valuep

(defthm floatx-value-fix-when-floatx-valuep
  (implies (floatx-valuep x)
           (equal (floatx-value-fix x) x)))

Function: floatx-value

(defun floatx-value (x)
  (declare (xargs :guard (floatx-value-abs-p x)))
  (let ((__function__ 'floatx-value))
    (declare (ignorable __function__))
    (list :floatx (floatx-value-abs-fix x))))

Theorem: floatx-valuep-of-floatx-value

(defthm floatx-valuep-of-floatx-value
  (implies (floatx-param)
           (b* ((value (floatx-value x)))
             (floatx-valuep value)))
  :rule-classes :rewrite)

Function: floatx-value->floatx

(defun floatx-value->floatx (value)
  (declare (xargs :guard (floatx-valuep value)))
  (let ((__function__ 'floatx-value->floatx))
    (declare (ignorable __function__))
    (second (floatx-value-fix value))))

Theorem: floatx-value-abs-p-of-floatx-value->floatx

(defthm floatx-value-abs-p-of-floatx-value->floatx
  (implies (floatx-param)
           (b* ((x (floatx-value->floatx value)))
             (floatx-value-abs-p x)))
  :rule-classes :rewrite)

Theorem: floatx-value->floatx-of-floatx-value

(defthm floatx-value->floatx-of-floatx-value
  (implies (floatx-param)
           (equal (floatx-value->floatx (floatx-value x))
                  (floatx-value-abs-fix x))))

Subtopics

Floatx-valuep: Recognizer of Java float values in the float-extended-exponent value set.
Floatx-value->floatx: Destructor of Java float values in the float-extended-exponent value set.
Floatx-value-fix: Fixer of Java float values in the float-extended-exponent value set.
Floatx-value: Constructor of Java float values in the float-extended-exponent value set.