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Floating-point-literals

Floating-point-literal

Fixtype of Java floating-point literals.

For now we model them via a predicate constrained to be non-empty so that a fixing function and a fixtype can be defined.

Definition: floating-point-literalp

(encapsulate (((floating-point-literalp *) acl2::=> *)
              ((floating-point-literal-witness)
               acl2::=> *))
  (local (value-triple :elided))
  (local (value-triple :elided))
  (defthm booleanp-of-floating-point-literalp
    (booleanp (floating-point-literalp x))
    :rule-classes (:rewrite :type-prescription))
  (defthm floating-point-literalp-of-floating-point-literal-witness
    (floating-point-literalp (floating-point-literal-witness))))

Definition: floating-point-literal-witness

(encapsulate (((floating-point-literalp *) acl2::=> *)
              ((floating-point-literal-witness)
               acl2::=> *))
  (local (value-triple :elided))
  (local (value-triple :elided))
  (defthm booleanp-of-floating-point-literalp
    (booleanp (floating-point-literalp x))
    :rule-classes (:rewrite :type-prescription))
  (defthm floating-point-literalp-of-floating-point-literal-witness
    (floating-point-literalp (floating-point-literal-witness))))

Definitions and Theorems

Theorem: booleanp-of-floating-point-literalp

(defthm booleanp-of-floating-point-literalp
  (booleanp (floating-point-literalp x))
  :rule-classes (:rewrite :type-prescription))

Theorem: floating-point-literalp-of-floating-point-literal-witness

(defthm floating-point-literalp-of-floating-point-literal-witness
  (floating-point-literalp (floating-point-literal-witness)))

Function: floating-point-literal-fix

(defun floating-point-literal-fix (x)
  (declare (xargs :guard (floating-point-literalp x)))
  (mbe :logic
       (if (floating-point-literalp x)
           x
         (floating-point-literal-witness))
       :exec x))

Theorem: floating-point-literalp-of-floating-point-literal-fix

(defthm floating-point-literalp-of-floating-point-literal-fix
  (b* ((fixed-x (floating-point-literal-fix x)))
    (floating-point-literalp fixed-x))
  :rule-classes :rewrite)

Theorem: floating-point-literal-fix-when-floating-point-literalp

(defthm floating-point-literal-fix-when-floating-point-literalp
  (implies (floating-point-literalp x)
           (equal (floating-point-literal-fix x)
                  x)))

Function: floating-point-literal-equiv$inline

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

Subtopics

Floating-point-literal-fix: Fixer for floating-point-literal.