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• Vl-expr-wildelim

Vl-wildeq-replacement-expr

Construct the expression to replace lhs ==? rhs.

Signature

(vl-wildeq-replacement-expr lhs care-mask zapped atts) → new-x

Arguments

lhs — Left hand side of some lhs ==? rhs expression.
    Guard (vl-expr-p lhs).

care-mask — Care mask computed for rhs; see vl-wildeq-decompose-rhs.
    Guard (vl-expr-p care-mask).

zapped — Zapped version of rhs; see vl-wildeq-decompose-rhs.
    Guard (vl-expr-p zapped).

atts — Attributes for the new expression.
    Guard (vl-atts-p atts).

Returns

new-x — Type (vl-expr-p new-x).

LHS could be anything, but since X is well-typed we know that its width is positive and that its signedness agrees with the signedness of RHS. Moreover we constructed the care-mask and zap-expr in such a way that they also agree on this width and signedness. Hence, everything lines up perfectly and we're ready to go.

In the ==? case, we want to make sure that LHS agrees with RHS on all of the care bits, i.e., that

(LHS & CARE-MASK) == (RHS & CARE-MASK)

It is perhaps nicer to write RHS & CARE-MASK as ZAPPED, since that is just a constant integer. So this is just:

(LHS & CARE-MASK) == ZAPPED

Except that, per oprewrite, we would rather write this as:

& (  (LHS & CARE-MASK) ~^ ZAPPED )

Definitions and Theorems

Function: vl-wildeq-replacement-expr

(defun vl-wildeq-replacement-expr (lhs care-mask zapped atts)
  (declare (xargs :guard (and (vl-expr-p lhs)
                              (vl-expr-p care-mask)
                              (vl-expr-p zapped)
                              (vl-atts-p atts))))
  (declare (xargs :guard (and (vl-expr-welltyped-p lhs)
                              (vl-expr-welltyped-p care-mask)
                              (vl-expr-welltyped-p zapped)
                              (posp (vl-expr->finalwidth lhs))
                              (equal (vl-expr->finalwidth care-mask)
                                     (vl-expr->finalwidth lhs))
                              (equal (vl-expr->finalwidth zapped)
                                     (vl-expr->finalwidth lhs))
                              (vl-expr->finaltype lhs)
                              (equal (vl-expr->finaltype care-mask)
                                     (vl-expr->finaltype lhs))
                              (equal (vl-expr->finaltype zapped)
                                     (vl-expr->finaltype lhs)))))
  (let ((__function__ 'vl-wildeq-replacement-expr))
    (declare (ignorable __function__))
    (b* ((width (vl-expr->finalwidth lhs))
         (type (vl-expr->finaltype lhs))
         (masked-lhs (make-vl-nonatom :op :vl-binary-bitand
                                      :args (list lhs care-mask)
                                      :finalwidth width
                                      :finaltype type))
         (inner-iff (make-vl-nonatom :op :vl-binary-xnor
                                     :args (list masked-lhs zapped)
                                     :finalwidth width
                                     :finaltype type)))
      (make-vl-nonatom :op :vl-unary-bitand
                       :args (list inner-iff)
                       :finalwidth 1
                       :finaltype :vl-unsigned
                       :atts atts))))

Theorem: vl-expr-p-of-vl-wildeq-replacement-expr

(defthm vl-expr-p-of-vl-wildeq-replacement-expr
  (b*
    ((new-x (vl-wildeq-replacement-expr lhs care-mask zapped atts)))
    (vl-expr-p new-x))
  :rule-classes :rewrite)

Theorem: vl-expr-welltyped-p-of-vl-wildeq-replacement-expr

(defthm vl-expr-welltyped-p-of-vl-wildeq-replacement-expr
 (implies
   (and (force (vl-expr-p lhs))
        (force (vl-expr-p care-mask))
        (force (vl-expr-p zapped))
        (force (vl-atts-p atts))
        (force (vl-expr-welltyped-p lhs))
        (force (vl-expr-welltyped-p care-mask))
        (force (vl-expr-welltyped-p zapped))
        (force (posp (vl-expr->finalwidth$inline lhs)))
        (force (equal (vl-expr->finalwidth$inline care-mask)
                      (vl-expr->finalwidth$inline lhs)))
        (force (equal (vl-expr->finalwidth$inline zapped)
                      (vl-expr->finalwidth$inline lhs)))
        (force (vl-expr->finaltype$inline lhs))
        (force (equal (vl-expr->finaltype$inline care-mask)
                      (vl-expr->finaltype$inline lhs)))
        (force (equal (vl-expr->finaltype$inline zapped)
                      (vl-expr->finaltype$inline lhs))))
   (b*
    ((new-x (vl-wildeq-replacement-expr lhs care-mask zapped atts)))
    (vl-expr-welltyped-p new-x)))
 :rule-classes :rewrite)

Theorem: vl-wildeq-replacement-expr-basics

(defthm vl-wildeq-replacement-expr-basics
  (b*
    ((new-x (vl-wildeq-replacement-expr lhs care-mask zapped atts)))
    (and (equal (vl-expr->finalwidth new-x) 1)
         (equal (vl-expr->finaltype new-x)
                :vl-unsigned)))
  :rule-classes :rewrite)

Theorem: vl-wildeq-replacement-expr-of-vl-expr-fix-lhs

(defthm vl-wildeq-replacement-expr-of-vl-expr-fix-lhs
  (equal (vl-wildeq-replacement-expr (vl-expr-fix lhs)
                                     care-mask zapped atts)
         (vl-wildeq-replacement-expr lhs care-mask zapped atts)))

Theorem: vl-wildeq-replacement-expr-vl-expr-equiv-congruence-on-lhs

(defthm vl-wildeq-replacement-expr-vl-expr-equiv-congruence-on-lhs
 (implies
  (vl-expr-equiv lhs lhs-equiv)
  (equal
      (vl-wildeq-replacement-expr lhs care-mask zapped atts)
      (vl-wildeq-replacement-expr lhs-equiv care-mask zapped atts)))
 :rule-classes :congruence)

Theorem: vl-wildeq-replacement-expr-of-vl-expr-fix-care-mask

(defthm vl-wildeq-replacement-expr-of-vl-expr-fix-care-mask
  (equal (vl-wildeq-replacement-expr lhs (vl-expr-fix care-mask)
                                     zapped atts)
         (vl-wildeq-replacement-expr lhs care-mask zapped atts)))

Theorem: vl-wildeq-replacement-expr-vl-expr-equiv-congruence-on-care-mask

(defthm
   vl-wildeq-replacement-expr-vl-expr-equiv-congruence-on-care-mask
 (implies
  (vl-expr-equiv care-mask care-mask-equiv)
  (equal
      (vl-wildeq-replacement-expr lhs care-mask zapped atts)
      (vl-wildeq-replacement-expr lhs care-mask-equiv zapped atts)))
 :rule-classes :congruence)

Theorem: vl-wildeq-replacement-expr-of-vl-expr-fix-zapped

(defthm vl-wildeq-replacement-expr-of-vl-expr-fix-zapped
 (equal
      (vl-wildeq-replacement-expr lhs care-mask (vl-expr-fix zapped)
                                  atts)
      (vl-wildeq-replacement-expr lhs care-mask zapped atts)))

Theorem: vl-wildeq-replacement-expr-vl-expr-equiv-congruence-on-zapped

(defthm
      vl-wildeq-replacement-expr-vl-expr-equiv-congruence-on-zapped
 (implies
  (vl-expr-equiv zapped zapped-equiv)
  (equal
      (vl-wildeq-replacement-expr lhs care-mask zapped atts)
      (vl-wildeq-replacement-expr lhs care-mask zapped-equiv atts)))
 :rule-classes :congruence)

Theorem: vl-wildeq-replacement-expr-of-vl-atts-fix-atts

(defthm vl-wildeq-replacement-expr-of-vl-atts-fix-atts
  (equal (vl-wildeq-replacement-expr
              lhs care-mask zapped (vl-atts-fix atts))
         (vl-wildeq-replacement-expr lhs care-mask zapped atts)))

Theorem: vl-wildeq-replacement-expr-vl-atts-equiv-congruence-on-atts

(defthm vl-wildeq-replacement-expr-vl-atts-equiv-congruence-on-atts
 (implies
  (vl-atts-equiv atts atts-equiv)
  (equal
      (vl-wildeq-replacement-expr lhs care-mask zapped atts)
      (vl-wildeq-replacement-expr lhs care-mask zapped atts-equiv)))
 :rule-classes :congruence)