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Svex-alist-truncate-by-var-decls

Signature

(svex-alist-truncate-by-var-decls x var-decls acc) → new-x

Arguments

x — Guard (svex-alist-p x).

var-decls — Guard (var-decl-map-p var-decls).

acc — Guard (svex-alist-p acc).

Returns

new-x — Type (svex-alist-p new-x).

Definitions and Theorems

Function: svex-alist-truncate-by-var-decls

(defun svex-alist-truncate-by-var-decls (x var-decls acc)
  (declare (xargs :guard (and (svex-alist-p x)
                              (var-decl-map-p var-decls)
                              (svex-alist-p acc))))
  (let ((__function__ 'svex-alist-truncate-by-var-decls))
    (declare (ignorable __function__))
    (b* (((when (atom x)) (svex-alist-fix acc))
         ((unless (mbt (and (consp (car x))
                            (svar-p (caar x)))))
          (svex-alist-truncate-by-var-decls (cdr x)
                                            var-decls acc))
         ((cons var val) (car x))
         (wire (cdr (hons-get var (var-decl-map-fix var-decls))))
         ((unless wire)
          (svex-alist-truncate-by-var-decls (cdr x)
                                            var-decls acc))
         ((wire wire))
         (acc (cons (cons var (svex-concat wire.width val 0))
                    (svex-alist-fix acc))))
      (svex-alist-truncate-by-var-decls (cdr x)
                                        var-decls acc))))

Theorem: svex-alist-p-of-svex-alist-truncate-by-var-decls

(defthm svex-alist-p-of-svex-alist-truncate-by-var-decls
  (b* ((new-x (svex-alist-truncate-by-var-decls x var-decls acc)))
    (svex-alist-p new-x))
  :rule-classes :rewrite)

Theorem: vars-of-svex-alist-truncate-by-var-decls

(defthm vars-of-svex-alist-truncate-by-var-decls
  (b* ((?new-x (svex-alist-truncate-by-var-decls x var-decls acc)))
    (implies (and (svarlist-addr-p (svex-alist-vars x))
                  (svarlist-addr-p (svex-alist-vars acc)))
             (svarlist-addr-p (svex-alist-vars new-x)))))

Theorem: keys-of-svex-alist-truncate-by-var-decls

(defthm keys-of-svex-alist-truncate-by-var-decls
  (b* ((?new-x (svex-alist-truncate-by-var-decls x var-decls acc)))
    (implies (and (not (svex-lookup v x))
                  (not (svex-lookup v acc)))
             (not (svex-lookup v new-x)))))

Theorem: no-duplicate-keys-of-svex-alist-truncate-by-var-decls

(defthm no-duplicate-keys-of-svex-alist-truncate-by-var-decls
  (b* ((?new-x (svex-alist-truncate-by-var-decls x var-decls acc)))
    (implies (and (no-duplicatesp-equal (svex-alist-keys acc))
                  (no-duplicatesp-equal (svex-alist-keys x))
                  (not (intersectp-equal (svex-alist-keys x)
                                         (svex-alist-keys acc))))
             (no-duplicatesp-equal (svex-alist-keys new-x)))))

Theorem: svex-alist-truncate-by-var-decls-of-svex-alist-fix-x

(defthm svex-alist-truncate-by-var-decls-of-svex-alist-fix-x
  (equal (svex-alist-truncate-by-var-decls (svex-alist-fix x)
                                           var-decls acc)
         (svex-alist-truncate-by-var-decls x var-decls acc)))

Theorem: svex-alist-truncate-by-var-decls-svex-alist-equiv-congruence-on-x

(defthm
  svex-alist-truncate-by-var-decls-svex-alist-equiv-congruence-on-x
 (implies
   (svex-alist-equiv x x-equiv)
   (equal (svex-alist-truncate-by-var-decls x var-decls acc)
          (svex-alist-truncate-by-var-decls x-equiv var-decls acc)))
 :rule-classes :congruence)

Theorem: svex-alist-truncate-by-var-decls-of-var-decl-map-fix-var-decls

(defthm
     svex-alist-truncate-by-var-decls-of-var-decl-map-fix-var-decls
 (equal
    (svex-alist-truncate-by-var-decls x (var-decl-map-fix var-decls)
                                      acc)
    (svex-alist-truncate-by-var-decls x var-decls acc)))

Theorem: svex-alist-truncate-by-var-decls-var-decl-map-equiv-congruence-on-var-decls

(defthm
 svex-alist-truncate-by-var-decls-var-decl-map-equiv-congruence-on-var-decls
 (implies
   (var-decl-map-equiv var-decls var-decls-equiv)
   (equal (svex-alist-truncate-by-var-decls x var-decls acc)
          (svex-alist-truncate-by-var-decls x var-decls-equiv acc)))
 :rule-classes :congruence)

Theorem: svex-alist-truncate-by-var-decls-of-svex-alist-fix-acc

(defthm svex-alist-truncate-by-var-decls-of-svex-alist-fix-acc
  (equal (svex-alist-truncate-by-var-decls
              x var-decls (svex-alist-fix acc))
         (svex-alist-truncate-by-var-decls x var-decls acc)))

Theorem: svex-alist-truncate-by-var-decls-svex-alist-equiv-congruence-on-acc

(defthm
 svex-alist-truncate-by-var-decls-svex-alist-equiv-congruence-on-acc
 (implies
   (svex-alist-equiv acc acc-equiv)
   (equal (svex-alist-truncate-by-var-decls x var-decls acc)
          (svex-alist-truncate-by-var-decls x var-decls acc-equiv)))
 :rule-classes :congruence)