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• Truth

Permute-polarity

Signature

(permute-polarity n mask truth numvars) → new-truth

Arguments

n — Guard (natp n).

mask — Guard (integerp mask).

truth — Guard (integerp truth).

numvars — Guard (natp numvars).

Returns

new-truth — Type (integerp new-truth).

Definitions and Theorems

Function: permute-polarity

(defun permute-polarity (n mask truth numvars)
  (declare (xargs :guard (and (natp n)
                              (integerp mask)
                              (integerp truth)
                              (natp numvars))))
  (declare (xargs :guard (<= n numvars)))
  (let ((__function__ 'permute-polarity))
    (declare (ignorable __function__))
    (b* (((when (mbe :logic (zp (- (nfix numvars) (nfix n)))
                     :exec (eql n numvars)))
          (truth-norm truth numvars))
         (truth (if (logbitp n mask)
                    (swap-polarity n truth numvars)
                  truth)))
      (permute-polarity (1+ (lnfix n))
                        mask truth numvars))))

Theorem: integerp-of-permute-polarity

(defthm integerp-of-permute-polarity
  (b* ((new-truth (permute-polarity n mask truth numvars)))
    (integerp new-truth))
  :rule-classes :type-prescription)

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

(defthm eval-of-permute-polarity-with-env-permute-polarity
  (b* ((?new-truth (permute-polarity n mask truth numvars)))
    (equal (truth-eval new-truth
                       (env-permute-polarity n mask env numvars)
                       numvars)
           (truth-eval truth env numvars))))

Theorem: eval-of-permute-polarity

(defthm eval-of-permute-polarity
  (b* ((?new-truth (permute-polarity n mask truth numvars)))
    (equal (truth-eval new-truth env numvars)
           (truth-eval truth
                       (env-permute-polarity n mask env numvars)
                       numvars))))

Theorem: permute-polarity-size-basic

(defthm permute-polarity-size-basic
  (b* ((?new-truth (permute-polarity n mask truth numvars)))
    (unsigned-byte-p (ash 1 (nfix numvars))
                     new-truth)))

Theorem: permute-polarity-size

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

Theorem: permute-polarity-identity

(defthm permute-polarity-identity
  (b* nil
    (equal (permute-polarity n 0 truth numvars)
           (truth-norm truth numvars))))

Theorem: permute-polarity-of-truth-norm

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

Theorem: permute-polarity-of-nfix-n

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

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

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

Theorem: permute-polarity-of-ifix-mask

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

Theorem: permute-polarity-int-equiv-congruence-on-mask

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

Theorem: permute-polarity-of-ifix-truth

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

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

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

Theorem: permute-polarity-of-nfix-numvars

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

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

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