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• Alias-norm.lisp

Assigns-subst

Signature

(assigns-subst x aliases svexarr) → xx

Arguments

x — Guard (assigns-p x).

Returns

xx — Type (assigns-p xx).

Definitions and Theorems

Function: assigns-subst

(defun assigns-subst (x aliases svexarr)
 (declare (xargs :stobjs (aliases svexarr)))
 (declare (xargs :guard (assigns-p x)))
 (declare
    (xargs :guard (and (svarlist-boundedp (assigns-vars x)
                                          (aliass-length aliases))
                       (svarlist-boundedp (assigns-vars x)
                                          (svexs-length svexarr)))))
 (let ((__function__ 'assigns-subst))
  (declare (ignorable __function__))
  (mbe
   :logic
   (b* ((x (assigns-fix x))
        ((when (atom x)) nil)
        ((cons lhs (driver rhs)) (car x))
        (lhs (lhs-alias-norm lhs aliases))
        (val (svex-subst-from-svexarr rhs.value svexarr)))
     (cons (cons lhs (change-driver rhs :value val))
           (assigns-subst (cdr x)
                          aliases svexarr)))
   :exec
   (if (atom x)
       nil
    (with-local-stobj
     nrev
     (mv-let (ans nrev)
             (b* ((nrev (assigns-subst-nrev x aliases svexarr nrev))
                  ((mv ans nrev)
                   (acl2::nrev-finish nrev)))
               (mv ans nrev))
       ans))))))

Theorem: assigns-p-of-assigns-subst

(defthm assigns-p-of-assigns-subst
  (b* ((xx (assigns-subst x aliases svexarr)))
    (assigns-p xx))
  :rule-classes :rewrite)

Theorem: assigns-subst-of-assigns-fix-x

(defthm assigns-subst-of-assigns-fix-x
  (equal (assigns-subst (assigns-fix x)
                        aliases svexarr)
         (assigns-subst x aliases svexarr)))

Theorem: assigns-subst-assigns-equiv-congruence-on-x

(defthm assigns-subst-assigns-equiv-congruence-on-x
  (implies (assigns-equiv x x-equiv)
           (equal (assigns-subst x aliases svexarr)
                  (assigns-subst x-equiv aliases svexarr)))
  :rule-classes :congruence)

Theorem: assigns-subst-of-lhslist-fix-aliases

(defthm assigns-subst-of-lhslist-fix-aliases
  (equal (assigns-subst x (lhslist-fix aliases)
                        svexarr)
         (assigns-subst x aliases svexarr)))

Theorem: assigns-subst-lhslist-equiv-congruence-on-aliases

(defthm assigns-subst-lhslist-equiv-congruence-on-aliases
  (implies (lhslist-equiv aliases aliases-equiv)
           (equal (assigns-subst x aliases svexarr)
                  (assigns-subst x aliases-equiv svexarr)))
  :rule-classes :congruence)

Theorem: svarlist-addr-p-of-assigns-subst

(defthm svarlist-addr-p-of-assigns-subst
  (implies (and (svarlist-addr-p (svexarr-vars svexarr))
                (svarlist-addr-p (aliases-vars aliases)))
           (svarlist-addr-p
                (assigns-vars (assigns-subst x aliases svexarr)))))