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• Vl-consteval

Vl-consteval-binop

Signature

(vl-consteval-binop op aval bval) → ans

Arguments

op — Guard (member op '(:vl-binary-plus :vl-binary-minus :vl-binary-times :vl-binary-div :vl-binary-rem :vl-binary-bitand :vl-binary-bitor :vl-binary-xor :vl-binary-xnor)) .

aval — Guard (natp aval).

bval — Guard (natp bval).

Returns

ans — Type (integerp ans).

Definitions and Theorems

Function: vl-consteval-binop

(defun vl-consteval-binop (op aval bval)
 (declare
  (xargs
   :guard
   (and (member op
                '(:vl-binary-plus :vl-binary-minus :vl-binary-times
                                  :vl-binary-div :vl-binary-rem
                                  :vl-binary-bitand :vl-binary-bitor
                                  :vl-binary-xor :vl-binary-xnor))
        (natp aval)
        (natp bval))))
 (declare
   (xargs
        :guard (implies (member op '(:vl-binary-div :vl-binary-rem))
                        (posp bval))))
 (let ((__function__ 'vl-consteval-binop))
   (declare (ignorable __function__))
   (b* ((aval (lnfix aval))
        (bval (lnfix bval)))
     (case op (:vl-binary-plus (+ aval bval))
           (:vl-binary-minus (- aval bval))
           (:vl-binary-times (* aval bval))
           (:vl-binary-div (truncate aval bval))
           (:vl-binary-rem (rem aval bval))
           (:vl-binary-bitand (logand aval bval))
           (:vl-binary-bitor (logior aval bval))
           (:vl-binary-xor (logxor aval bval))
           (:vl-binary-xnor (lognot (logxor aval bval)))
           (otherwise (progn$ (impossible) 0))))))

Theorem: integerp-of-vl-consteval-binop

(defthm integerp-of-vl-consteval-binop
  (b* ((ans (vl-consteval-binop op aval bval)))
    (integerp ans))
  :rule-classes :type-prescription)

Theorem: vl-consteval-binop-of-nfix-aval

(defthm vl-consteval-binop-of-nfix-aval
  (equal (vl-consteval-binop op (nfix aval) bval)
         (vl-consteval-binop op aval bval)))

Theorem: vl-consteval-binop-nat-equiv-congruence-on-aval

(defthm vl-consteval-binop-nat-equiv-congruence-on-aval
  (implies (acl2::nat-equiv aval aval-equiv)
           (equal (vl-consteval-binop op aval bval)
                  (vl-consteval-binop op aval-equiv bval)))
  :rule-classes :congruence)

Theorem: vl-consteval-binop-of-nfix-bval

(defthm vl-consteval-binop-of-nfix-bval
  (equal (vl-consteval-binop op aval (nfix bval))
         (vl-consteval-binop op aval bval)))

Theorem: vl-consteval-binop-nat-equiv-congruence-on-bval

(defthm vl-consteval-binop-nat-equiv-congruence-on-bval
  (implies (acl2::nat-equiv bval bval-equiv)
           (equal (vl-consteval-binop op aval bval)
                  (vl-consteval-binop op aval bval-equiv)))
  :rule-classes :congruence)