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4v-operations

4v-pullup

Four-valued semantics for a pullup resistor.

(4v-pullup a) acts just like a buffer except that, if its input is floating, it instead produces true. That is, it returns the value specified by the following truth table:

  a  |  out
-----+-------
  F  |   F
  T  |   T
  X  |   X
  Z  |   T

Definitions and Theorems

Function: 4v-pullup

(defun 4v-pullup (a)
  (declare (xargs :guard t))
  (4vcases a (t (4vt))
           (z (4vt))
           (f (4vf))
           (& (4vx))))

Theorem: 4v-equiv-implies-equal-4v-pullup-1

(defthm 4v-equiv-implies-equal-4v-pullup-1
  (implies (4v-equiv a a-equiv)
           (equal (4v-pullup a)
                  (4v-pullup a-equiv)))
  :rule-classes (:congruence))