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• Bool-formats

Bool-format-wfp

Check if a _Bool format is well-formed.

Signature

(bool-format-wfp bool-format uchar-format) → yes/no

Arguments

bool-format — Guard (bool-formatp bool-format).

uchar-format — Guard (uchar-formatp uchar-format).

Returns

yes/no — Type (booleanp yes/no).

The index of the value bit must be within the range of indices of the bits that form the _Bool object. This depends on the number of bits in a bit, which is defined by the unsigned char format. So we need a separate predicate (this one) to express this condition, which could not be part of the bool-format fixtype.

Definitions and Theorems

Function: bool-format-wfp

(defun bool-format-wfp (bool-format uchar-format)
  (declare (xargs :guard (and (bool-formatp bool-format)
                              (uchar-formatp uchar-format))))
  (< (bool-format->value-index bool-format)
     (* (bool-format->byte-size bool-format)
        (uchar-format->size uchar-format))))

Theorem: booleanp-of-bool-format-wfp

(defthm booleanp-of-bool-format-wfp
  (b* ((yes/no (bool-format-wfp bool-format uchar-format)))
    (booleanp yes/no))
  :rule-classes :rewrite)

Theorem: bool-format-wfp-of-bool-format-fix-bool-format

(defthm bool-format-wfp-of-bool-format-fix-bool-format
  (equal (bool-format-wfp (bool-format-fix bool-format)
                          uchar-format)
         (bool-format-wfp bool-format uchar-format)))

Theorem: bool-format-wfp-bool-format-equiv-congruence-on-bool-format

(defthm bool-format-wfp-bool-format-equiv-congruence-on-bool-format
  (implies (bool-format-equiv bool-format bool-format-equiv)
           (equal (bool-format-wfp bool-format uchar-format)
                  (bool-format-wfp bool-format-equiv uchar-format)))
  :rule-classes :congruence)

Theorem: bool-format-wfp-of-uchar-format-fix-uchar-format

(defthm bool-format-wfp-of-uchar-format-fix-uchar-format
  (equal (bool-format-wfp bool-format
                          (uchar-format-fix uchar-format))
         (bool-format-wfp bool-format uchar-format)))

Theorem: bool-format-wfp-uchar-format-equiv-congruence-on-uchar-format

(defthm
      bool-format-wfp-uchar-format-equiv-congruence-on-uchar-format
  (implies (uchar-format-equiv uchar-format uchar-format-equiv)
           (equal (bool-format-wfp bool-format uchar-format)
                  (bool-format-wfp bool-format uchar-format-equiv)))
  :rule-classes :congruence)