• Top
  • Documentation
  • Books
  • Recursion-and-induction
  • Boolean-reasoning
    • Ipasir
    • Aignet
    • Aig
    • Satlink
    • Truth
    • Ubdds
      • Equal-by-eval-bdds
      • Ubdd-constructors
        • Q-and
        • Q-ite
        • Q-or
        • Q-implies
        • Q-iff
        • Q-and-c2
        • Q-and-c1
        • Q-or-c2
        • Q-not
        • Q-ite-fn
        • Q-xor
        • Q-and-is-nil
        • Cheap-and-expensive-arguments
        • Q-compose-list
        • Q-compose
        • Qv
        • Q-and-is-nilc2
        • Q-nor
        • Q-nand
      • Eval-bdd
      • Ubddp
      • Ubdd-fix
      • Q-sat
      • Bdd-sat-dfs
      • Eval-bdd-list
      • Qcdr
      • Qcar
      • Q-sat-any
      • Canonicalize-to-q-ite
      • Ubdd-listp
      • Qcons
    • Bdd
    • Faig
    • Bed
    • 4v
  • Debugging
  • Projects
  • Std
  • Proof-automation
  • Macro-libraries
  • ACL2
  • Interfacing-tools
  • Hardware-verification
  • Software-verification
  • Testing-utilities
  • Math

• Ubdd-constructors

Qv

(qv i) constructs a UBDD which evaluates to true exactly when the ith BDD variable is true.

Definitions and Theorems

Function: qv

(defun qv (i)
       (declare (xargs :guard t))
       (if (posp i)
           (let ((prev (qv (1- i))))
                (hons prev prev))
           (hons t nil)))

Theorem: ubddp-qv

(defthm ubddp-qv (ubddp (qv i)))

Theorem: eval-bdd-of-qv-and-nil

(defthm eval-bdd-of-qv-and-nil
        (not (eval-bdd (qv i) nil)))

Theorem: eval-bdd-of-qv

(defthm eval-bdd-of-qv
        (equal (eval-bdd (qv i) lst)
               (if (nth i lst) t nil)))

Theorem: qvs-equal

(defthm qvs-equal
        (equal (equal (qv i) (qv j))
               (equal (nfix i) (nfix j))))