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• Svex-env

Svex-env-reduce

Restrict an svex-env to only particular variables. Variables that are present in keys but not env will be left unbound.

Signature

(svex-env-reduce keys env) → sub-env

Arguments

keys — Variables to keep.
    Guard (svarlist-p keys).

env — Original environment to filter. Need not be fast.
    Guard (svex-env-p env).

Returns

sub-env — Restriction of env to keys. Slow alist.
    Type (svex-env-p sub-env).

Definitions and Theorems

Function: svex-env-reduce

(defun svex-env-reduce (keys env)
 (declare (xargs :guard (and (svarlist-p keys)
                             (svex-env-p env))))
 (let ((__function__ 'svex-env-reduce))
  (declare (ignorable __function__))
  (mbe :logic
       (if (atom keys)
           nil
         (b* ((key (svar-fix (car keys)))
              (look (hons-get key (svex-env-fix env))))
           (if look (cons (cons key (cdr look))
                          (svex-env-reduce (cdr keys) env))
             (svex-env-reduce (cdr keys) env))))
       :exec (with-fast-alist env (svex-env-reduce-aux keys env)))))

Theorem: svex-env-p-of-svex-env-reduce

(defthm svex-env-p-of-svex-env-reduce
  (b* ((sub-env (svex-env-reduce keys env)))
    (svex-env-p sub-env))
  :rule-classes :rewrite)

Theorem: svex-env-lookup-of-svex-env-reduce

(defthm svex-env-lookup-of-svex-env-reduce
  (equal (svex-env-lookup v (svex-env-reduce vars env))
         (if (member (svar-fix v)
                     (svarlist-fix vars))
             (svex-env-lookup v env)
           (4vec-x))))

Theorem: svex-env-boundp-of-svex-env-reduce

(defthm svex-env-boundp-of-svex-env-reduce
  (iff (svex-env-boundp key (svex-env-reduce vars x))
       (and (member-equal (svar-fix key)
                          (svarlist-fix vars))
            (svex-env-boundp key x))))

Theorem: svex-eval-reduce-var-superset

(defthm svex-eval-reduce-var-superset
  (implies (subsetp (svex-vars x)
                    (svarlist-fix vars))
           (equal (svex-eval x (svex-env-reduce vars env))
                  (svex-eval x env))))

Theorem: svexlist-eval-reduce-var-superset

(defthm svexlist-eval-reduce-var-superset
  (implies (subsetp (svexlist-vars x)
                    (svarlist-fix vars))
           (equal (svexlist-eval x (svex-env-reduce vars env))
                  (svexlist-eval x env))))

Theorem: svex-alist-eval-of-reduce-var-supserset

(defthm svex-alist-eval-of-reduce-var-supserset
  (implies (subsetp (svexlist-vars (svex-alist-vals x))
                    (svarlist-fix vars))
           (equal (svex-alist-eval x (svex-env-reduce vars env))
                  (svex-alist-eval x env))))

Theorem: alist-keys-of-svex-env-reduce

(defthm alist-keys-of-svex-env-reduce
  (equal (alist-keys (svex-env-reduce vars env))
         (intersection-equal (svarlist-fix vars)
                             (alist-keys (svex-env-fix env)))))

Theorem: svex-env-reduce-when-alist-keys-equal

(defthm svex-env-reduce-when-alist-keys-equal
  (implies (and (equal (alist-keys (svex-env-fix x))
                       keys)
                (no-duplicatesp keys))
           (equal (svex-env-reduce keys x)
                  (svex-env-fix x))))

Theorem: hons-assoc-equal-of-svex-env-reduce

(defthm hons-assoc-equal-of-svex-env-reduce
  (equal (hons-assoc-equal v (svex-env-reduce keys x))
         (and (member v (svarlist-fix keys))
              (hons-assoc-equal v (svex-env-fix x)))))

Theorem: svex-env-reduce-of-superset

(defthm svex-env-reduce-of-superset
  (implies (subsetp (svarlist-fix keys)
                    (svarlist-fix keys2))
           (equal (svex-env-reduce keys (svex-env-reduce keys2 x))
                  (svex-env-reduce keys x))))

Theorem: svex-env-extract-of-subset-of-env-reduce

(defthm svex-env-extract-of-subset-of-env-reduce
  (implies (subsetp (svarlist-fix keys)
                    (svarlist-fix keys2))
           (equal (svex-env-extract keys (svex-env-reduce keys2 x))
                  (svex-env-extract keys x))))

Theorem: svex-env-reduce-redef

(defthm svex-env-reduce-redef
  (equal (svex-env-reduce keys env)
         (if (atom keys)
             nil
           (if (svex-env-boundp (car keys) env)
               (cons (cons (svar-fix (car keys))
                           (svex-env-lookup (car keys) env))
                     (svex-env-reduce (cdr keys) env))
             (svex-env-reduce (cdr keys) env))))
  :rule-classes :definition)

Theorem: svex-env-reduce-of-svarlist-fix-keys

(defthm svex-env-reduce-of-svarlist-fix-keys
  (equal (svex-env-reduce (svarlist-fix keys)
                          env)
         (svex-env-reduce keys env)))

Theorem: svex-env-reduce-svarlist-equiv-congruence-on-keys

(defthm svex-env-reduce-svarlist-equiv-congruence-on-keys
  (implies (svarlist-equiv keys keys-equiv)
           (equal (svex-env-reduce keys env)
                  (svex-env-reduce keys-equiv env)))
  :rule-classes :congruence)

Theorem: svex-env-reduce-of-svex-env-fix-env

(defthm svex-env-reduce-of-svex-env-fix-env
  (equal (svex-env-reduce keys (svex-env-fix env))
         (svex-env-reduce keys env)))

Theorem: svex-env-reduce-svex-env-equiv-congruence-on-env

(defthm svex-env-reduce-svex-env-equiv-congruence-on-env
  (implies (svex-env-equiv env env-equiv)
           (equal (svex-env-reduce keys env)
                  (svex-env-reduce keys env-equiv)))
  :rule-classes :congruence)

Subtopics

Svex-env-reduce-aux