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• Sv::vl-expr.lisp

Vttree-join

Signature

(vttree-join x y) → join

Arguments

x — Guard (vttree-p x).

y — Guard (vttree-p y).

Returns

join — Type (vttree-p join).

Definitions and Theorems

Function: vttree-join

(defun vttree-join (x y)
  (declare (xargs :guard (and (vttree-p x) (vttree-p y))))
  (let ((__function__ 'vttree-join))
    (declare (ignorable __function__))
    (cond ((vttree-case x :none) (vttree-fix y))
          ((vttree-case y :none) (vttree-fix x))
          (t (make-vttree-branch :left x
                                 :right y)))))

Theorem: vttree-p-of-vttree-join

(defthm vttree-p-of-vttree-join
  (b* ((join (vttree-join x y)))
    (vttree-p join))
  :rule-classes :rewrite)

Theorem: vttree->warnings-of-vttree-join

(defthm vttree->warnings-of-vttree-join
  (b* ((?join (vttree-join x y)))
    (equal (vttree->warnings join)
           (append (vttree->warnings x)
                   (vttree->warnings y)))))

Theorem: vttree->constraints-of-vttree-join

(defthm vttree->constraints-of-vttree-join
  (b* ((?join (vttree-join x y)))
    (equal (vttree->constraints join)
           (append (vttree->constraints x)
                   (vttree->constraints y)))))

Theorem: vttree-join-of-vttree-fix-x

(defthm vttree-join-of-vttree-fix-x
  (equal (vttree-join (vttree-fix x) y)
         (vttree-join x y)))

Theorem: vttree-join-vttree-equiv-congruence-on-x

(defthm vttree-join-vttree-equiv-congruence-on-x
  (implies (vttree-equiv x x-equiv)
           (equal (vttree-join x y)
                  (vttree-join x-equiv y)))
  :rule-classes :congruence)

Theorem: vttree-join-of-vttree-fix-y

(defthm vttree-join-of-vttree-fix-y
  (equal (vttree-join x (vttree-fix y))
         (vttree-join x y)))

Theorem: vttree-join-vttree-equiv-congruence-on-y

(defthm vttree-join-vttree-equiv-congruence-on-y
  (implies (vttree-equiv y y-equiv)
           (equal (vttree-join x y)
                  (vttree-join x y-equiv)))
  :rule-classes :congruence)