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      • Index-permute-shrink
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• Truth

Permute-shrink

Signature

(permute-shrink n count mask truth numvars) → perm-truth

Arguments

n — Guard (natp n).

mask — Guard (natp mask).

truth — Guard (integerp truth).

numvars — Guard (natp numvars).

Returns

perm-truth — Type (natp perm-truth).

Definitions and Theorems

Function: permute-shrink

(defun permute-shrink (n count mask truth numvars)
  (declare (xargs :guard (and (natp n)
                              (natp mask)
                              (integerp truth)
                              (natp numvars))))
  (declare
       (xargs :guard (and (<= n numvars)
                          (eql count (logcount (loghead n mask))))))
  (let ((__function__ 'permute-shrink))
    (declare (ignorable __function__))
    (b* (((when (mbe :logic (zp (- (nfix numvars) (nfix n)))
                     :exec (eql n numvars)))
          (truth-norm truth numvars))
         (n (lnfix n))
         (count (mbe :logic (logcount (loghead n (lnfix mask)))
                     :exec count))
         (bit (logbit n (lnfix mask)))
         (truth (if (eql bit 1)
                    (permute-var-down count n truth numvars)
                  truth)))
      (permute-shrink (1+ n)
                      (+ bit count)
                      mask truth numvars))))

Theorem: natp-of-permute-shrink

(defthm natp-of-permute-shrink
  (b* ((perm-truth (permute-shrink n count mask truth numvars)))
    (natp perm-truth))
  :rule-classes :type-prescription)

Theorem: normalize-count-of-permute-shrink

(defthm normalize-count-of-permute-shrink
 (b* nil
  (implies (syntaxp (not (equal count ''nil)))
           (equal (permute-shrink n count mask truth numvars)
                  (let ((count nil))
                    (permute-shrink n count mask truth numvars))))))

Theorem: eval-of-permute-shrink-with-env-permute-shrink

(defthm eval-of-permute-shrink-with-env-permute-shrink
 (b* ((?perm-truth (permute-shrink n count mask truth numvars)))
  (implies
    (<= (nfix n) (nfix numvars))
    (equal (truth-eval perm-truth
                       (env-permute-shrink n count mask env numvars)
                       numvars)
           (truth-eval truth env numvars)))))

Theorem: eval-of-permute-shrink

(defthm eval-of-permute-shrink
 (b* ((?perm-truth (permute-shrink n count mask truth numvars)))
  (implies
   (<= (nfix n) (nfix numvars))
   (equal (truth-eval perm-truth env numvars)
          (truth-eval truth
                      (env-permute-stretch n count mask env numvars)
                      numvars)))))

Theorem: size-of-permute-shrink

(defthm size-of-permute-shrink
  (b* ((?perm-truth (permute-shrink n count mask truth numvars)))
    (implies (and (natp size)
                  (<= (ash 1 (nfix numvars)) size))
             (unsigned-byte-p size perm-truth))))

Theorem: depends-on-of-permute-shrink

(defthm depends-on-of-permute-shrink
 (implies
  (and (natp numvars)
       (< (nfix n) numvars)
       (not (depends-on (index-permute-stretch 0 nil mask n numvars)
                        truth numvars)))
  (not (depends-on n
                   (permute-shrink 0 count mask truth numvars)
                   numvars))))

Theorem: permute-shrink-of-truth-norm

(defthm permute-shrink-of-truth-norm
  (equal (permute-shrink n count mask (truth-norm truth numvars)
                         numvars)
         (permute-shrink n count mask truth numvars)))

Theorem: permute-shrink-of-nfix-n

(defthm permute-shrink-of-nfix-n
  (equal (permute-shrink (nfix n)
                         count mask truth numvars)
         (permute-shrink n count mask truth numvars)))

Theorem: permute-shrink-nat-equiv-congruence-on-n

(defthm permute-shrink-nat-equiv-congruence-on-n
 (implies (nat-equiv n n-equiv)
          (equal (permute-shrink n count mask truth numvars)
                 (permute-shrink n-equiv count mask truth numvars)))
 :rule-classes :congruence)

Theorem: permute-shrink-of-nfix-mask

(defthm permute-shrink-of-nfix-mask
  (equal (permute-shrink n count (nfix mask)
                         truth numvars)
         (permute-shrink n count mask truth numvars)))

Theorem: permute-shrink-nat-equiv-congruence-on-mask

(defthm permute-shrink-nat-equiv-congruence-on-mask
 (implies (nat-equiv mask mask-equiv)
          (equal (permute-shrink n count mask truth numvars)
                 (permute-shrink n count mask-equiv truth numvars)))
 :rule-classes :congruence)

Theorem: permute-shrink-of-ifix-truth

(defthm permute-shrink-of-ifix-truth
  (equal (permute-shrink n count mask (ifix truth)
                         numvars)
         (permute-shrink n count mask truth numvars)))

Theorem: permute-shrink-int-equiv-congruence-on-truth

(defthm permute-shrink-int-equiv-congruence-on-truth
 (implies (int-equiv truth truth-equiv)
          (equal (permute-shrink n count mask truth numvars)
                 (permute-shrink n count mask truth-equiv numvars)))
 :rule-classes :congruence)

Theorem: permute-shrink-of-nfix-numvars

(defthm permute-shrink-of-nfix-numvars
  (equal (permute-shrink n count mask truth (nfix numvars))
         (permute-shrink n count mask truth numvars)))

Theorem: permute-shrink-nat-equiv-congruence-on-numvars

(defthm permute-shrink-nat-equiv-congruence-on-numvars
 (implies (nat-equiv numvars numvars-equiv)
          (equal (permute-shrink n count mask truth numvars)
                 (permute-shrink n count mask truth numvars-equiv)))
 :rule-classes :congruence)