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Bitwise-operations

Op-bitand

Leo bitwise-and operation

Signature
(op-bitand left right) → result
Arguments: left — Guard (valuep left).; right — Guard (valuep right).
Returns: result — Type (value-resultp result).

This and operation operates on integers in a bitwise fashion and on booleans where both arguments are evaluated.

Definitions and Theorems

Function: op-bitand

(defun op-bitand (left right)
  (declare (xargs :guard (and (valuep left) (valuep right))))
  (let ((__function__ 'op-bitand))
    (declare (ignorable __function__))
    (b* ((err (list :op-bitand (value-fix left)
                    (value-fix right))))
      (cond ((and (value-case left :bool)
                  (value-case right :bool))
             (let ((leftval (value-bool->get left))
                   (rightval (value-bool->get right)))
               (value-bool (and leftval rightval))))
            ((and (value-case left :u8)
                  (value-case right :u8))
             (value-u8 (logand (value-u8->get left)
                               (value-u8->get right))))
            ((and (value-case left :u16)
                  (value-case right :u16))
             (value-u16 (logand (value-u16->get left)
                                (value-u16->get right))))
            ((and (value-case left :u32)
                  (value-case right :u32))
             (value-u32 (logand (value-u32->get left)
                                (value-u32->get right))))
            ((and (value-case left :u64)
                  (value-case right :u64))
             (value-u64 (logand (value-u64->get left)
                                (value-u64->get right))))
            ((and (value-case left :u128)
                  (value-case right :u128))
             (value-u128 (logand (value-u128->get left)
                                 (value-u128->get right))))
            ((and (value-case left :i8)
                  (value-case right :i8))
             (value-i8 (logand (value-i8->get left)
                               (value-i8->get right))))
            ((and (value-case left :i16)
                  (value-case right :i16))
             (value-i16 (logand (value-i16->get left)
                                (value-i16->get right))))
            ((and (value-case left :i32)
                  (value-case right :i32))
             (value-i32 (logand (value-i32->get left)
                                (value-i32->get right))))
            ((and (value-case left :i64)
                  (value-case right :i64))
             (value-i64 (logand (value-i64->get left)
                                (value-i64->get right))))
            ((and (value-case left :i128)
                  (value-case right :i128))
             (value-i128 (logand (value-i128->get left)
                                 (value-i128->get right))))
            (t (reserrf err))))))

Theorem: value-resultp-of-op-bitand

(defthm value-resultp-of-op-bitand
  (b* ((result (op-bitand left right)))
    (value-resultp result))
  :rule-classes :rewrite)

Theorem: op-bitand-of-value-fix-left

(defthm op-bitand-of-value-fix-left
  (equal (op-bitand (value-fix left) right)
         (op-bitand left right)))

Theorem: op-bitand-value-equiv-congruence-on-left

(defthm op-bitand-value-equiv-congruence-on-left
  (implies (value-equiv left left-equiv)
           (equal (op-bitand left right)
                  (op-bitand left-equiv right)))
  :rule-classes :congruence)

Theorem: op-bitand-of-value-fix-right

(defthm op-bitand-of-value-fix-right
  (equal (op-bitand left (value-fix right))
         (op-bitand left right)))

Theorem: op-bitand-value-equiv-congruence-on-right

(defthm op-bitand-value-equiv-congruence-on-right
  (implies (value-equiv right right-equiv)
           (equal (op-bitand left right)
                  (op-bitand left right-equiv)))
  :rule-classes :congruence)