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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)