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• Vl-svstmt.lisp

Sv::svar->lhs-by-mask

Given a variable and a mask of bits, create an LHS that covers those bits.

Signature

(sv::svar->lhs-by-mask acl2::x sv::mask) → sv::lhs

Arguments

acl2::x — Guard (sv::svar-p acl2::x).

sv::mask — Guard (sv::4vmask-p sv::mask).

Returns

sv::lhs — Type (sv::lhs-p sv::lhs).

Fails by returning an empty LHS if the mask is negative, i.e. an ~ infinite range of bits should be written.

Definitions and Theorems

Function: svar->lhs-by-mask

(defun sv::svar->lhs-by-mask (acl2::x sv::mask)
 (declare (xargs :guard (and (sv::svar-p acl2::x)
                             (sv::4vmask-p sv::mask))))
 (let ((__function__ 'sv::svar->lhs-by-mask))
  (declare (ignorable __function__))
  (and
   (bitops::sparseint-< 0 (sv::4vmask-fix sv::mask))
   (list
        (sv::make-lhrange
             :w (bitops::sparseint-length (sv::4vmask-fix sv::mask))
             :atom (sv::make-lhatom-var :name acl2::x
                                        :rsh 0))))))

Theorem: lhs-p-of-svar->lhs-by-mask

(defthm sv::lhs-p-of-svar->lhs-by-mask
  (b* ((sv::lhs (sv::svar->lhs-by-mask acl2::x sv::mask)))
    (sv::lhs-p sv::lhs))
  :rule-classes :rewrite)

Theorem: vars-of-svar->lhs-by-mask

(defthm sv::vars-of-svar->lhs-by-mask
 (implies
  (not (equal sv::v (sv::svar-fix acl2::x)))
  (not
    (member
         sv::v
         (sv::lhs-vars (sv::svar->lhs-by-mask acl2::x sv::mask))))))

Theorem: svar->lhs-by-mask-of-svar-fix-x

(defthm sv::svar->lhs-by-mask-of-svar-fix-x
  (equal (sv::svar->lhs-by-mask (sv::svar-fix acl2::x)
                                sv::mask)
         (sv::svar->lhs-by-mask acl2::x sv::mask)))

Theorem: svar->lhs-by-mask-svar-equiv-congruence-on-x

(defthm sv::svar->lhs-by-mask-svar-equiv-congruence-on-x
  (implies (sv::svar-equiv acl2::x sv::x-equiv)
           (equal (sv::svar->lhs-by-mask acl2::x sv::mask)
                  (sv::svar->lhs-by-mask sv::x-equiv sv::mask)))
  :rule-classes :congruence)

Theorem: svar->lhs-by-mask-of-4vmask-fix-mask

(defthm sv::svar->lhs-by-mask-of-4vmask-fix-mask
  (equal (sv::svar->lhs-by-mask acl2::x (sv::4vmask-fix sv::mask))
         (sv::svar->lhs-by-mask acl2::x sv::mask)))

Theorem: svar->lhs-by-mask-4vmask-equiv-congruence-on-mask

(defthm sv::svar->lhs-by-mask-4vmask-equiv-congruence-on-mask
  (implies (sv::4vmask-equiv sv::mask sv::mask-equiv)
           (equal (sv::svar->lhs-by-mask acl2::x sv::mask)
                  (sv::svar->lhs-by-mask acl2::x sv::mask-equiv)))
  :rule-classes :congruence)