How to check if a plugin (WooCommerce) is active?

I am trying to modify the head and foot of my WooCommerce pages. I have an if statement that is supposed to target the shop and cart of WooCommerce, but it isn’t. If I modify the PHP after the if statement nothing changes. But if I modify the PHP in the else statement is works:

This doesn’t work:

<?php if (function_exists('woocommerce')): ?>
    <?php if (is_cart() || is_shop()): ?>
        <?php get_template_part('inc/CHANGE'); ?>
    <?php endif ?>
<?php else: ?>
    <?php get_template_part('inc/page-header'); ?>
<?php endif ?>

This does work:

<?php if (function_exists('woocommerce')): ?>
    <?php if (is_cart() || is_shop()): ?>
        <?php get_template_part('inc/page-header'); ?>
    <?php endif ?>
<?php else: ?>
    <?php get_template_part('inc/CHANGE'); ?>
<?php endif ?>

I think the function WooCommerce might not be properly defined, because this also works:

<?php if (is_cart() || is_shop()): ?>
        <?php get_template_part('inc/header-shop'); ?>
    <?php else: ?>
        <?php get_template_part('inc/page-header'); ?>
    <?php endif ?>

Your edit got me to this idea, there indeed is no function called »woocommerce«, there is a class »WooCommerce« though. One thing to be aware of is, that the check has to late enough, so that plug-ins are actually initialized, otherwise – obviously – the class won’t exists and the check returns false. So your check should look like this:

if ( class_exists( 'WooCommerce' ) ) {
  // some code
} else {
  / more code
}

On the WooCommerce documentation page »Creating a plugin for WooCommerce« I have found this:

/**
 * Check if WooCommerce is active
 **/
if ( 
  in_array( 
    'woocommerce/woocommerce.php', 
    apply_filters( 'active_plugins', get_option( 'active_plugins' ) ) 
  ) 
) {
    // Put your plugin code here
}

Personally I think it is not nearly as reliable as checking for the class. For obvious reasons, what if the folder/file name is different, but should work just fine too. Besides if you do it like this, then there is an API function you can use, fittingly named is_plugin_active(). But because it is normally only available on admin pages, you have to make it available by including wp-admin/includes/plugin.php, where the function resides. Using it the check would look like this:

include_once( ABSPATH . 'wp-admin/includes/plugin.php' );
if ( is_plugin_active( 'woocommerce/woocommerce.php' ) ) {
  // some code
} else {
  / more code
}