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• Svex-composition

Svex-compose*

Compose an svex with a substitution alist. Variables not in the substitution are left in place.

Signature

(svex-compose* x a) → xa

Arguments

x — Guard (svex-p x).

a — Guard (svex-alist-p a).

Returns

xa — x composed with a, unbound variables preserved.
    Type (svex-p xa).

Theorem: return-type-of-svex-compose*.xa

(defthm return-type-of-svex-compose*.xa
  (b* ((?xa (svex-compose* x a)))
    (svex-p xa))
  :rule-classes :rewrite)

Theorem: return-type-of-svexlist-compose*.xa

(defthm return-type-of-svexlist-compose*.xa
  (b* ((?xa (svexlist-compose* x a)))
    (svexlist-p xa))
  :rule-classes :rewrite)

Theorem: svex-compose*-of-svex-fix-x

(defthm svex-compose*-of-svex-fix-x
  (equal (svex-compose* (svex-fix x) a)
         (svex-compose* x a)))

Theorem: svex-compose*-of-svex-alist-fix-a

(defthm svex-compose*-of-svex-alist-fix-a
  (equal (svex-compose* x (svex-alist-fix a))
         (svex-compose* x a)))

Theorem: svexlist-compose*-of-svexlist-fix-x

(defthm svexlist-compose*-of-svexlist-fix-x
  (equal (svexlist-compose* (svexlist-fix x) a)
         (svexlist-compose* x a)))

Theorem: svexlist-compose*-of-svex-alist-fix-a

(defthm svexlist-compose*-of-svex-alist-fix-a
  (equal (svexlist-compose* x (svex-alist-fix a))
         (svexlist-compose* x a)))

Theorem: svex-compose*-svex-equiv-congruence-on-x

(defthm svex-compose*-svex-equiv-congruence-on-x
  (implies (svex-equiv x x-equiv)
           (equal (svex-compose* x a)
                  (svex-compose* x-equiv a)))
  :rule-classes :congruence)

Theorem: svex-compose*-svex-alist-equiv-congruence-on-a

(defthm svex-compose*-svex-alist-equiv-congruence-on-a
  (implies (svex-alist-equiv a a-equiv)
           (equal (svex-compose* x a)
                  (svex-compose* x a-equiv)))
  :rule-classes :congruence)

Theorem: svexlist-compose*-svexlist-equiv-congruence-on-x

(defthm svexlist-compose*-svexlist-equiv-congruence-on-x
  (implies (svexlist-equiv x x-equiv)
           (equal (svexlist-compose* x a)
                  (svexlist-compose* x-equiv a)))
  :rule-classes :congruence)

Theorem: svexlist-compose*-svex-alist-equiv-congruence-on-a

(defthm svexlist-compose*-svex-alist-equiv-congruence-on-a
  (implies (svex-alist-equiv a a-equiv)
           (equal (svexlist-compose* x a)
                  (svexlist-compose* x a-equiv)))
  :rule-classes :congruence)

Theorem: len-of-svexlist-compose*

(defthm len-of-svexlist-compose*
  (equal (len (svexlist-compose* x a))
         (len x)))

Theorem: svex-eval-of-svex-compose*

(defthm svex-eval-of-svex-compose*
  (equal (svex-eval (svex-compose* x a) env)
         (svex-eval x
                    (append (svex-alist-eval a env) env))))

Theorem: svexlist-eval-of-svexlist-compose*

(defthm svexlist-eval-of-svexlist-compose*
  (equal (svexlist-eval (svexlist-compose* x a)
                        env)
         (svexlist-eval x
                        (append (svex-alist-eval a env) env))))

Theorem: vars-of-svex-compose*

(defthm vars-of-svex-compose*
  (implies (and (not (member v (svex-vars x)))
                (not (member v (svex-alist-vars a))))
           (not (member v (svex-vars (svex-compose* x a))))))

Theorem: vars-of-svexlist-compose*

(defthm vars-of-svexlist-compose*
  (implies (and (not (member v (svexlist-vars x)))
                (not (member v (svex-alist-vars a))))
           (not (member v
                        (svexlist-vars (svexlist-compose* x a))))))

Theorem: vars-of-svex-compose*-strong

(defthm vars-of-svex-compose*-strong
  (implies (and (not (member v (svex-alist-vars a)))
                (or (member v (svex-alist-keys a))
                    (not (member v (svex-vars x)))))
           (not (member v (svex-vars (svex-compose* x a))))))

Theorem: vars-of-svexlist-compose*-strong

(defthm vars-of-svexlist-compose*-strong
  (implies (and (not (member v (svex-alist-vars a)))
                (or (member v (svex-alist-keys a))
                    (not (member v (svexlist-vars x)))))
           (not (member v
                        (svexlist-vars (svexlist-compose* x a))))))

Function: svex-compose*-memoize-condition

(defun svex-compose*-memoize-condition (x a)
  (declare (ignorable x a)
           (xargs :guard (if (svex-p x) (svex-alist-p a) 'nil)))
  (eq (svex-kind x) :call))

Subtopics

Svexlist-compose*