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A4vec-operations

A4vec-syntactic-3vec-p

Try to cheaply, statically determine whether an a4vec always evaluates to a 3vec, i.e., whether it has no Z bits.

Signature
(a4vec-syntactic-3vec-p x) → *
Arguments: x — Guard (a4vec-p x).

This is used mainly in a3vec-fix: when we know that there are no Z bits, we can avoid building AIGs to do unfloating.

Definitions and Theorems

Function: a4vec-syntactic-3vec-p

(defun a4vec-syntactic-3vec-p (x)
  (declare (xargs :guard (a4vec-p x)))
  (let ((__function__ 'a4vec-syntactic-3vec-p))
    (declare (ignorable __function__))
    (b* (((a4vec x)))
      (a4vec-syntactic-3vec-p-rec x.upper x.lower))))

Theorem: a4vec-syntactic-3vec-p-correct

(defthm a4vec-syntactic-3vec-p-correct
  (implies (a4vec-syntactic-3vec-p x)
           (3vec-p (a4vec-eval x env))))

Theorem: a4vec-syntactic-3vec-p-of-a4vec-fix-x

(defthm a4vec-syntactic-3vec-p-of-a4vec-fix-x
  (equal (a4vec-syntactic-3vec-p (a4vec-fix x))
         (a4vec-syntactic-3vec-p x)))

Theorem: a4vec-syntactic-3vec-p-a4vec-equiv-congruence-on-x

(defthm a4vec-syntactic-3vec-p-a4vec-equiv-congruence-on-x
  (implies (a4vec-equiv x x-equiv)
           (equal (a4vec-syntactic-3vec-p x)
                  (a4vec-syntactic-3vec-p x-equiv)))
  :rule-classes :congruence)

Subtopics

A4vec-syntactic-3vec-p-rec: Make sure there is no pair of bits with Xi == 0 while Yi == 1.