• Top
  • Documentation
  • Books
  • Boolean-reasoning
    • Ipasir
    • Aignet
    • Aig
    • Satlink
    • Truth
    • Ubdds
    • Bdd
    • Faig
    • Bed
    • 4v
      • 4v-sexprs
      • 4v-monotonicity
      • 4v-operations
        • 4v-ite
        • 4v-res
        • 4v-not-list
        • 4v-unfloat
        • 4v-wand
        • 4v-wor
        • 4v-tristate
        • 4v-zif
        • 4v-xdet
        • 4v-xor
        • 4v-iff
        • 4v-and
        • 4v-or
        • 4v-not
        • 4v-pullup
        • 4v-and-list
        • 4v-ite*
      • Why-4v-logic
      • 4v-<=
      • 4vp
      • 4vcases
      • 4v-fix
      • 4v-lookup
  • Projects
  • Debugging
  • Std
  • Proof-automation
  • Macro-libraries
  • ACL2
  • Interfacing-tools
  • Hardware-verification
  • Software-verification
  • Math
  • Testing-utilities

• 4v-operations

4v-wor

Four-valued semantics for a wired or.

(4v-wor a b) returns:

• T when either input is T, or
• Z when both inputs are Z, or
• F when one input is F and the other is F/Z, or
• X otherwise.

We use this to model what happens when multiple signals are connected in a wired-or arrangement.

The full truth table is shown below. It intentionally corresponds to the Verilog semantics for wired ors (Section 4.6.2 of the Verilog specification).

     |   F   T   X   Z  |
-----+------------------+
  F  |   F   T   X   F  |
  T  |   T   T   T   T  |
  X  |   X   T   X   X  |
  Z  |   F   T   X   Z  |
-----+------------------+

Definitions and Theorems

Function: 4v-wor

(defun 4v-wor (a b)
  (declare (xargs :guard t))
  (mbe :logic (4vcases a (t (4vt))
                       (f (4vcases b (z (4vf)) (& (4v-fix b))))
                       (z (4v-fix b))
                       (& (4vcases b (t (4vt)) (& (4vx)))))
       :exec (cond ((eq a (4vt)) (4vt))
                   ((eq b (4vt)) (4vt))
                   ((eq a (4vf))
                    (if (or (eq b (4vf)) (eq b (4vz)))
                        (4vf)
                      (4vx)))
                   ((eq a (4vz))
                    (if (or (eq b (4vf)) (eq b (4vz)))
                        b
                      (4vx)))
                   (t (4vx)))))

Theorem: 4v-wor-truth-table

(defthm 4v-wor-truth-table
  (and (equal (4v-wor (4vf) (4vf)) (4vf))
       (equal (4v-wor (4vf) (4vt)) (4vt))
       (equal (4v-wor (4vf) (4vx)) (4vx))
       (equal (4v-wor (4vf) (4vz)) (4vf))
       (equal (4v-wor (4vt) (4vf)) (4vt))
       (equal (4v-wor (4vt) (4vt)) (4vt))
       (equal (4v-wor (4vt) (4vx)) (4vt))
       (equal (4v-wor (4vt) (4vz)) (4vt))
       (equal (4v-wor (4vx) (4vf)) (4vx))
       (equal (4v-wor (4vx) (4vt)) (4vt))
       (equal (4v-wor (4vx) (4vx)) (4vx))
       (equal (4v-wor (4vx) (4vz)) (4vx))
       (equal (4v-wor (4vz) (4vf)) (4vf))
       (equal (4v-wor (4vz) (4vt)) (4vt))
       (equal (4v-wor (4vz) (4vx)) (4vx))
       (equal (4v-wor (4vz) (4vz)) (4vz)))
  :rule-classes nil)