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• Svex-env

Svex-env-extract

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

Signature

(svex-env-extract 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-extract

(defun svex-env-extract (keys env)
 (declare (xargs :guard (and (svarlist-p keys)
                             (svex-env-p env))))
 (let ((__function__ 'svex-env-extract))
  (declare (ignorable __function__))
  (mbe
      :logic
      (if (atom keys)
          nil
        (cons (cons (svar-fix (car keys))
                    (svex-env-fastlookup (car keys) env))
              (svex-env-extract (cdr keys) env)))
      :exec (with-fast-alist env (svex-env-extract-aux keys env)))))

Theorem: svex-env-p-of-svex-env-extract

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

Theorem: svex-env-lookup-of-svex-env-extract

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

Theorem: svex-eval-extract-var-superset

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

Theorem: svexlist-eval-extract-var-superset

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

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

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

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

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

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

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

Theorem: svex-env-extract-of-superset

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

Theorem: svex-env-boundp-of-svex-env-extract

(defthm svex-env-boundp-of-svex-env-extract
  (b* ((?sub-env (svex-env-extract keys env)))
    (iff (svex-env-boundp k sub-env)
         (member-equal (svar-fix k)
                       (svarlist-fix keys)))))

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

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

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

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

Theorem: svex-env-extract-of-svex-env-fix-env

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

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

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

Subtopics

Svex-env-extract-aux