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• Svex-select

Svex-selects-merge

Apply one select operation to the result of another.

Signature

(svex-selects-merge outer inner) → composition

Arguments

outer — Guard (svex-select-p outer).

inner — Guard (svex-select-p inner).

Returns

composition — Type (svex-select-p composition).

Definitions and Theorems

Function: svex-selects-merge

(defun svex-selects-merge (outer inner)
 (declare (xargs :guard (and (svex-select-p outer)
                             (svex-select-p inner))))
 (let ((__function__ 'svex-selects-merge))
  (declare (ignorable __function__))
  (svex-select-case
      outer
      :var (svex-select-fix inner)
      :part (change-svex-select-part
                 outer
                 :subexp (svex-selects-merge outer.subexp inner)))))

Theorem: svex-select-p-of-svex-selects-merge

(defthm svex-select-p-of-svex-selects-merge
  (b* ((composition (svex-selects-merge outer inner)))
    (svex-select-p composition))
  :rule-classes :rewrite)

Theorem: svex-select->width-of-svex-select-merge

(defthm svex-select->width-of-svex-select-merge
  (implies
       (equal (svex-select-inner-width outer)
              (svex-select->width inner))
       (equal (svex-select->width (svex-selects-merge outer inner))
              (svex-select->width outer))))

Theorem: svex-selects-merge-is-svex-compose

(defthm svex-selects-merge-is-svex-compose
 (b* nil
  (b* ((inner-var (svex-select-inner-var outer)))
   (implies
    (and (not (member inner-var
                      (svexlist-vars (svex-select->indices outer))))
         (equal (svex-select-inner-width outer)
                (svex-select->width inner)))
    (equal
       (svex-eval
            (svex-select-to-svex (svex-selects-merge outer inner))
            env)
       (svex-eval (svex-select-to-svex outer)
                  (cons (cons inner-var
                              (svex-eval (svex-select-to-svex inner)
                                         env))
                        env)))))))

Theorem: svex-select->indices-of-svex-selects-merge

(defthm svex-select->indices-of-svex-selects-merge
  (b* ((?composition (svex-selects-merge outer inner)))
    (equal (svex-select->indices composition)
           (append (svex-select->indices outer)
                   (svex-select->indices inner)))))

Theorem: svex-selects-merge-of-svex-select-fix-outer

(defthm svex-selects-merge-of-svex-select-fix-outer
  (equal (svex-selects-merge (svex-select-fix outer)
                             inner)
         (svex-selects-merge outer inner)))

Theorem: svex-selects-merge-svex-select-equiv-congruence-on-outer

(defthm svex-selects-merge-svex-select-equiv-congruence-on-outer
  (implies (svex-select-equiv outer outer-equiv)
           (equal (svex-selects-merge outer inner)
                  (svex-selects-merge outer-equiv inner)))
  :rule-classes :congruence)

Theorem: svex-selects-merge-of-svex-select-fix-inner

(defthm svex-selects-merge-of-svex-select-fix-inner
  (equal (svex-selects-merge outer (svex-select-fix inner))
         (svex-selects-merge outer inner)))

Theorem: svex-selects-merge-svex-select-equiv-congruence-on-inner

(defthm svex-selects-merge-svex-select-equiv-congruence-on-inner
  (implies (svex-select-equiv inner inner-equiv)
           (equal (svex-selects-merge outer inner)
                  (svex-selects-merge outer inner-equiv)))
  :rule-classes :congruence)