gistfile1.php

function create_post_types() {
	register_post_type('degrees-and-programs', [
	        'labels' => [
		    	'name' => 'Degrees and Programs',
		    	'all_items' => 'All Degrees/Programs'
		],
	        'public' => true,
	        'has_archive' => true,
		'rewrite' => ['slug' => 'degrees-and-programs'],
		'hierarchical' => true,
		'supports' => ['title', 'thumbnail', 'excerpt', 'page-attributes'],
		'exclude_from_search' => false
    	]);
}

function create_taxonomies() {

    	register_taxonomy('program-categories', ['degrees-and-programs'], [
		'labels' => [
		    'name' => 'Program Categories'
	],
        'show_ui' => true,
	'show_tagcloud' => false,
	'hierarchical' => true,
	'rewrite' => [
	    	'slug' => 'programs'
	]
    ]);
}

function taxonomy_slug_rewrite(&$wp_rewrite) {
    
    $rules = [];
    $taxonomies = get_taxonomies(['_builtin' => false], 'objects');
    $post_types = get_post_types(['public' => true, '_builtin' => false], 'names');


    foreach ($post_types as $post_type) {
		foreach ($taxonomies as $taxonomy) {
		    if ($taxonomy->object_type[0] == $post_type) {
                	$category_settings = ['type' => $post_type, 'taxonomy' => $taxonomy->name, 'hide_empty' => 0, 'category_parent'=>0];
			$categories = get_categories($category_settings);
			foreach ($categories as $category) {
				$rules[$post_type . '/' . $category->slug . '/?$'] = 'index.php?' . $category->taxonomy . '=' . $category->slug;
			}
		    }
		}
  	}

    $wp_rewrite->rules = $rules + $wp_rewrite->rules;
}

add_action( 'generate_rewrite_rules', 'taxonomy_slug_rewrite' );