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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)