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Substitution

Vl-module-subst

Substitute into a vl-module-p.

Signature
(vl-module-subst x sigma) → new-x
Arguments: x — Guard (vl-module-p x).; sigma — Guard (vl-sigma-p sigma).
Returns: new-x — Type (vl-module-p new-x).

Definitions and Theorems

Function: vl-module-subst

(defun vl-module-subst (x sigma)
  (declare (xargs :guard (and (vl-module-p x)
                              (vl-sigma-p sigma))))
  (declare (ignorable x sigma))
  (let ((__function__ 'vl-module-subst))
    (declare (ignorable __function__))
    (b* (((vl-module x) x))
      (change-vl-module
           x
           :ports (vl-portlist-subst x.ports sigma)
           :portdecls (vl-portdecllist-subst x.portdecls sigma)
           :assigns (vl-assignlist-subst x.assigns sigma)
           :vardecls (vl-vardecllist-subst x.vardecls sigma)
           :fundecls (vl-fundecllist-subst x.fundecls sigma)
           :paramdecls (vl-paramdecllist-subst x.paramdecls sigma)
           :modinsts (vl-modinstlist-subst x.modinsts sigma)
           :gateinsts (vl-gateinstlist-subst x.gateinsts sigma)
           :alwayses (vl-alwayslist-subst x.alwayses sigma)
           :initials (vl-initiallist-subst x.initials sigma)))))

Theorem: vl-module-p-of-vl-module-subst

(defthm vl-module-p-of-vl-module-subst
  (b* ((new-x (vl-module-subst x sigma)))
    (vl-module-p new-x))
  :rule-classes :rewrite)

Theorem: vl-module-subst-of-vl-module-fix-x

(defthm vl-module-subst-of-vl-module-fix-x
  (equal (vl-module-subst (vl-module-fix x)
                          sigma)
         (vl-module-subst x sigma)))

Theorem: vl-module-subst-vl-module-equiv-congruence-on-x

(defthm vl-module-subst-vl-module-equiv-congruence-on-x
  (implies (vl-module-equiv x x-equiv)
           (equal (vl-module-subst x sigma)
                  (vl-module-subst x-equiv sigma)))
  :rule-classes :congruence)

Theorem: vl-module-subst-of-vl-sigma-fix-sigma

(defthm vl-module-subst-of-vl-sigma-fix-sigma
  (equal (vl-module-subst x (vl-sigma-fix sigma))
         (vl-module-subst x sigma)))

Theorem: vl-module-subst-vl-sigma-equiv-congruence-on-sigma

(defthm vl-module-subst-vl-sigma-equiv-congruence-on-sigma
  (implies (vl-sigma-equiv sigma sigma-equiv)
           (equal (vl-module-subst x sigma)
                  (vl-module-subst x sigma-equiv)))
  :rule-classes :congruence)