def truncate_half_year(datetime):
    '''
    Truncates the datetime to the first day of the half year for this date.

    :params datetime: an initialized datetime object
    :return: `datetime` with the month set to the first month of this half year
    :rtype: :py:mod:`datetime` datetime object
    '''
    datetime = truncate(datetime, 'month')

    month = datetime.month

    if 1 <= month <= 6:
        return datetime.replace(month=1)
    elif 7 <= month <= 12:
        return datetime.replace(month=7)