"Undefined function" fatal error with Views caching, when calling functions in Setup Code

When Views caching is turned on for a View with a Views PHP field, functions defined in the Setup Code section of the Views PHP field cannot be used in the Output Code section.

Instead, going to the View shows a white screen with a PHP error like Fatal error: Call to undefined function foo() in sites/all/modules/contrib/views_php/plugins/views/views_php_handler_field.inc(207) : runtime-created function on line 2

Steps to replicate:

1. Create a View page showing "unformatted fields" for a list of nodes. E.g. show a list of nodes with the "Article" content type, at the URI /article-list.
2. In the Fields section of the View config, add the Title field, and a Views PHP field. Go to the settings for the Views PHP field.
3. In the Setup Code section of the Views PHP field settings, define a function. Example code:
   

   function foo($str) {return $str . ' foo';}

4. In the Output Code section of the Views PHP field settings, call the function. Example code:
   

   <?php print foo($row->title); ?>

5. In the "Advanced" section of the View config, go to "Caching", and set it to "Time-based", use the default "1 hour" cache time.
6. Save the View.
7. Browse to the View page URI e.g. /article-list .
8. You will see a white screen with an error similar to Fatal error: Call to undefined function foo() in sites/all/modules/contrib/views_php/plugins/views/views_php_handler_field.inc(207) : runtime-created function on line 2

Example View producing the error

Below is an exported View of a list of Article nodes, using a Views PHP field, which produces this error.

$view = new view();
$view->name = 'article_list';
$view->description = '';
$view->tag = 'default';
$view->base_table = 'node';
$view->human_name = 'Article list';
$view->core = 7;
$view->api_version = '3.0';
$view->disabled = FALSE; /* Edit this to true to make a default view disabled initially */

/* Display: Master */
$handler = $view->new_display('default', 'Master', 'default');
$handler->display->display_options['title'] = 'Article list';
$handler->display->display_options['use_more_always'] = FALSE;
$handler->display->display_options['access']['type'] = 'perm';
$handler->display->display_options['cache']['type'] = 'time';
$handler->display->display_options['cache']['results_lifespan'] = '3600';
$handler->display->display_options['cache']['results_lifespan_custom'] = '0';
$handler->display->display_options['cache']['output_lifespan'] = '3600';
$handler->display->display_options['cache']['output_lifespan_custom'] = '0';
$handler->display->display_options['query']['type'] = 'views_query';
$handler->display->display_options['exposed_form']['type'] = 'basic';
$handler->display->display_options['pager']['type'] = 'full';
$handler->display->display_options['pager']['options']['items_per_page'] = '10';
$handler->display->display_options['style_plugin'] = 'default';
$handler->display->display_options['row_plugin'] = 'fields';
/* Field: Content: Title */
$handler->display->display_options['fields']['title']['id'] = 'title';
$handler->display->display_options['fields']['title']['table'] = 'node';
$handler->display->display_options['fields']['title']['field'] = 'title';
$handler->display->display_options['fields']['title']['label'] = '';
$handler->display->display_options['fields']['title']['alter']['word_boundary'] = FALSE;
$handler->display->display_options['fields']['title']['alter']['ellipsis'] = FALSE;
/* Field: Global: PHP */
$handler->display->display_options['fields']['php']['id'] = 'php';
$handler->display->display_options['fields']['php']['table'] = 'views';
$handler->display->display_options['fields']['php']['field'] = 'php';
$handler->display->display_options['fields']['php']['use_php_setup'] = 1;
$handler->display->display_options['fields']['php']['php_setup'] = 'function foo($str) {
  return $str . \' foo\';
}';
$handler->display->display_options['fields']['php']['php_output'] = '<?php
print foo($row->title);
?>';
$handler->display->display_options['fields']['php']['use_php_click_sortable'] = '0';
$handler->display->display_options['fields']['php']['php_click_sortable'] = '';
/* Sort criterion: Content: Post date */
$handler->display->display_options['sorts']['created']['id'] = 'created';
$handler->display->display_options['sorts']['created']['table'] = 'node';
$handler->display->display_options['sorts']['created']['field'] = 'created';
$handler->display->display_options['sorts']['created']['order'] = 'DESC';
/* Filter criterion: Content: Published */
$handler->display->display_options['filters']['status']['id'] = 'status';
$handler->display->display_options['filters']['status']['table'] = 'node';
$handler->display->display_options['filters']['status']['field'] = 'status';
$handler->display->display_options['filters']['status']['value'] = 1;
$handler->display->display_options['filters']['status']['group'] = 1;
$handler->display->display_options['filters']['status']['expose']['operator'] = FALSE;
/* Filter criterion: Content: Type */
$handler->display->display_options['filters']['type']['id'] = 'type';
$handler->display->display_options['filters']['type']['table'] = 'node';
$handler->display->display_options['filters']['type']['field'] = 'type';
$handler->display->display_options['filters']['type']['value'] = array(
  'article' => 'article',
);

/* Display: Page */
$handler = $view->new_display('page', 'Page', 'page');
$handler->display->display_options['path'] = 'article-list';
$translatables['article_list'] = array(
  t('Master'),
  t('Article list'),
  t('more'),
  t('Apply'),
  t('Reset'),
  t('Sort by'),
  t('Asc'),
  t('Desc'),
  t('Items per page'),
  t('- All -'),
  t('Offset'),
  t('« first'),
  t('‹ previous'),
  t('next ›'),
  t('last »'),
  t('PHP'),
  t('Page'),
);