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Svar-map-truncate-by-var-decls

Signature

(svar-map-truncate-by-var-decls x var-decls acc) → new-x

Arguments

x — Guard (svar-map-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: svar-map-truncate-by-var-decls

(defun svar-map-truncate-by-var-decls (x var-decls acc)
 (declare (xargs :guard (and (svar-map-p x)
                             (var-decl-map-p var-decls)
                             (svex-alist-p acc))))
 (let ((__function__ 'svar-map-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)))))
        (svar-map-truncate-by-var-decls (cdr x)
                                        var-decls acc))
       ((cons delay-var var) (car x))
       (wire (cdr (hons-get (svar-fix var)
                            (var-decl-map-fix var-decls))))
       ((unless wire)
        (svar-map-truncate-by-var-decls (cdr x)
                                        var-decls acc))
       ((wire wire))
       (acc (cons (cons delay-var
                        (svcall zerox (svex-quote (2vec wire.width))
                                (svex-var var)))
                  (svex-alist-fix acc))))
    (svar-map-truncate-by-var-decls (cdr x)
                                    var-decls acc))))

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

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

Theorem: vars-of-svar-map-truncate-by-var-decls

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

Theorem: keys-of-svar-map-truncate-by-var-decls

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

Theorem: svar-map-truncate-by-var-decls-of-svar-map-fix-x

(defthm svar-map-truncate-by-var-decls-of-svar-map-fix-x
  (equal (svar-map-truncate-by-var-decls (svar-map-fix x)
                                         var-decls acc)
         (svar-map-truncate-by-var-decls x var-decls acc)))

Theorem: svar-map-truncate-by-var-decls-svar-map-equiv-congruence-on-x

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

Theorem: svar-map-truncate-by-var-decls-of-var-decl-map-fix-var-decls

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

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

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

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

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

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

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