public function test_check_nested_bookends()
{
$this->assertTrue(stack_utils::check_nested_bookends(''));
$this->assertTrue(stack_utils::check_nested_bookends('x+1'));
$this->assertTrue(stack_utils::check_nested_bookends('(sin(x)+1)'));
$this->assertTrue(stack_utils::check_nested_bookends('[sin(x)+1]'));
$this->assertTrue(stack_utils::check_nested_bookends('{}[]()'));
$this->assertTrue(stack_utils::check_nested_bookends('{[()]}'));
$this->assertTrue(stack_utils::check_nested_bookends('{[()(()[(){}((){})])]}'));
$this->assertFalse(stack_utils::check_nested_bookends('('));
$this->assertFalse(stack_utils::check_nested_bookends(')'));
$this->assertFalse(stack_utils::check_nested_bookends('x+1)'));
$this->assertFalse(stack_utils::check_nested_bookends('(sin(x+1)'));
$this->assertFalse(stack_utils::check_nested_bookends('[sin(x]+1)'));
$this->assertFalse(stack_utils::check_nested_bookends('{}[()'));
$this->assertFalse(stack_utils::check_nested_bookends('{[()(()[(){}((){})]))]}'));
}
private function validate($security = 's', $syntax = true, $insertstars = 0, $allowwords = '')
{
if (!('s' === $security || 't' === $security)) {
throw new stack_exception('stack_cas_casstring: security level, must be "s" or "t" only.');
}
if (!is_bool($syntax)) {
throw new stack_exception('stack_cas_casstring: syntax, must be Boolean.');
}
if (!is_int($insertstars)) {
throw new stack_exception('stack_cas_casstring: insertstars, must be an integer.');
}
$this->valid = true;
$this->casstring = $this->rawcasstring;
$cmd = $this->rawcasstring;
// CAS strings must be non-empty.
if (trim($this->casstring) == '') {
$this->answernote[] = 'empty';
$this->valid = false;
return false;
}
// CAS strings may not contain @ or $.
if (strpos($cmd, '@') !== false || strpos($cmd, '$') !== false) {
$this->add_error(stack_string('illegalcaschars'));
$this->answernote[] = 'illegalcaschars';
$this->valid = false;
return false;
}
// Check for matching string delimiters.
$cmdsafe = str_replace('\\"', '', $cmd);
if (stack_utils::check_matching_pairs($cmdsafe, '"') == false) {
$this->errors .= stack_string('stackCas_MissingString');
$this->answernote[] = 'MissingString';
$this->valid = false;
}
// Now remove any strings from the $cmd.
list($cmd, $strings) = $this->strings_remove($cmd);
// Search for HTML fragments. This is hard to do because < is an infix operator!
// We cannot search for arbitrary closing tags, e.g. for the pattern '</' because
// we pass back strings with HTML in when we have already evaluated plots!
$htmlfragments = array('<span', '</span>', '<p>', '</p>');
foreach ($htmlfragments as $frag) {
if (strpos($cmd, $frag) !== false) {
$this->add_error(stack_string('htmlfragment') . ' <pre>' . $this->strings_replace($cmd, $strings) . '</pre>');
$this->answernote[] = 'htmlfragment';
$this->valid = false;
return false;
}
}
// If student, check for spaces between letters or numbers in expressions.
if ($security != 't') {
$pat = "|([A-Za-z0-9\\(\\)]+) ([A-Za-z0-9\\(\\)]+)|";
// Special case - allow students to type in expressions such as "x>1 and x<4".
$cmdmod = str_replace(' or ', '', $cmd);
$cmdmod = str_replace(' and ', '', $cmdmod);
$cmdmod = str_replace('not ', '', $cmdmod);
if (preg_match($pat, $cmdmod)) {
$cmds = str_replace(' ', '<font color="red">_</font>', $this->strings_replace($cmd, $strings));
$this->add_error(stack_string('stackCas_spaces', array('expr' => stack_maxima_format_casstring($cmds))));
$this->answernote[] = 'spaces';
$this->valid = false;
}
}
// Check for % signs, allow %pi %e, %i, %gamma, %phi but nothing else.
if (strstr($cmd, '%') !== false) {
$cmdl = strtolower($cmd);
preg_match_all("(\\%.*)", $cmdl, $found);
foreach ($found[0] as $match) {
if (!(strpos($match, '%e') !== false || strpos($match, '%pi') !== false || strpos($match, '%i') !== false || strpos($match, '%j') !== false || strpos($match, '%gamma') !== false || strpos($match, '%phi') !== false)) {
// Constants %e and %pi are allowed. Any other percentages dissallowed.
$this->add_error(stack_string('stackCas_percent', array('expr' => stack_maxima_format_casstring($this->strings_replace($cmd, $strings)))));
$this->answernote[] = 'percent';
$this->valid = false;
}
}
}
$inline = stack_utils::check_bookends($cmd, '(', ')');
if ($inline !== true) {
// The method check_bookends does not return false.
$this->valid = false;
if ($inline == 'left') {
$this->answernote[] = 'missingLeftBracket';
$this->add_error(stack_string('stackCas_missingLeftBracket', array('bracket' => '(', 'cmd' => stack_maxima_format_casstring($this->strings_replace($cmd, $strings)))));
} else {
$this->answernote[] = 'missingRightBracket';
$this->add_error(stack_string('stackCas_missingRightBracket', array('bracket' => ')', 'cmd' => stack_maxima_format_casstring($this->strings_replace($cmd, $strings)))));
}
}
$inline = stack_utils::check_bookends($cmd, '{', '}');
if ($inline !== true) {
// The method check_bookends does not return false.
$this->valid = false;
if ($inline == 'left') {
$this->answernote[] = 'missingLeftBracket';
$this->add_error(stack_string('stackCas_missingLeftBracket', array('bracket' => '{', 'cmd' => stack_maxima_format_casstring($this->strings_replace($cmd, $strings)))));
} else {
$this->answernote[] = 'missingRightBracket';
$this->add_error(stack_string('stackCas_missingRightBracket', array('bracket' => '}', 'cmd' => stack_maxima_format_casstring($this->strings_replace($cmd, $strings)))));
}
}
$inline = stack_utils::check_bookends($cmd, '[', ']');
if ($inline !== true) {
// The method check_bookends does not return false.
$this->valid = false;
if ($inline == 'left') {
$this->answernote[] = 'missingLeftBracket';
$this->add_error(stack_string('stackCas_missingLeftBracket', array('bracket' => '[', 'cmd' => stack_maxima_format_casstring($this->strings_replace($cmd, $strings)))));
} else {
$this->answernote[] = 'missingRightBracket';
$this->add_error(stack_string('stackCas_missingRightBracket', array('bracket' => ']', 'cmd' => stack_maxima_format_casstring($this->strings_replace($cmd, $strings)))));
}
}
if (!stack_utils::check_nested_bookends($cmd)) {
$this->valid = false;
$this->add_error(stack_string('stackCas_bracketsdontmatch', array('cmd' => stack_maxima_format_casstring($this->strings_replace($cmd, $strings)))));
}
if ($security == 's') {
// Check for apostrophes if a student.
if (strpos($cmd, "'") !== false) {
$this->add_error(stack_string('stackCas_apostrophe'));
$this->answernote[] = 'apostrophe';
$this->valid = false;
}
// Check new lines.
if (strpos($cmd, "\n") !== false) {
$this->add_error(stack_string('stackCas_newline'));
$this->answernote[] = 'newline';
$this->valid = false;
}
}
if ($security == 's') {
// Check for bad looking trig functions, e.g. sin^2(x) or tan*2*x
// asin etc, will be included automatically, so we don't need them explicitly.
$triglist = array('sin', 'cos', 'tan', 'sinh', 'cosh', 'tanh', 'sec', 'cosec', 'cot', 'csc', 'coth', 'csch', 'sech');
$funlist = array('log', 'ln', 'lg', 'exp', 'abs', 'sqrt');
foreach (array_merge($triglist, $funlist) as $fun) {
if (strpos($cmd, $fun . '^') !== false) {
$this->add_error(stack_string('stackCas_trigexp', array('forbid' => stack_maxima_format_casstring($fun . '^'))));
$this->answernote[] = 'trigexp';
$this->valid = false;
break;
}
if (strpos($cmd, $fun . '[') !== false) {
$this->add_error(stack_string('stackCas_trigparens', array('forbid' => stack_maxima_format_casstring($fun . '(x)'))));
$this->answernote[] = 'trigparens';
$this->valid = false;
break;
}
$opslist = array('*', '+', '-', '/');
foreach ($opslist as $op) {
if (strpos($cmd, $fun . $op) !== false) {
$this->add_error(stack_string('stackCas_trigop', array('trig' => stack_maxima_format_casstring($fun), 'forbid' => stack_maxima_format_casstring($fun . $op))));
$this->answernote[] = 'trigop';
$this->valid = false;
break;
}
}
}
foreach ($triglist as $fun) {
if (strpos($cmd, 'arc' . $fun) !== false) {
$this->add_error(stack_string('stackCas_triginv', array('badinv' => stack_maxima_format_casstring('arc' . $fun), 'goodinv' => stack_maxima_format_casstring('a' . $fun))));
$this->answernote[] = 'triginv';
$this->valid = false;
break;
}
}
}
// Only permit the following characters to be sent to the CAS.
$cmd = trim($cmd);
$allowedcharsregex = '~[^' . preg_quote(self::$allowedchars, '~') . ']~u';
// Check for permitted characters.
if (preg_match_all($allowedcharsregex, $cmd, $matches)) {
$invalidchars = array();
foreach ($matches as $match) {
$badchar = $match[0];
if (!array_key_exists($badchar, $invalidchars)) {
$invalidchars[$badchar] = $badchar;
}
}
$this->add_error(stack_string('stackCas_forbiddenChar', array('char' => implode(", ", array_unique($invalidchars)))));
$this->answernote[] = 'forbiddenChar';
$this->valid = false;
}
// Check for disallowed final characters, / * + - ^ £ # = & ~ |, ? : ;.
$disallowedfinalcharsregex = '~[' . preg_quote(self::$disallowedfinalchars, '~') . ']$~u';
if (preg_match($disallowedfinalcharsregex, $cmd, $match)) {
$this->valid = false;
$a = array();
$a['char'] = $match[0];
$a['cmd'] = stack_maxima_format_casstring($this->strings_replace($cmd, $strings));
$this->add_error(stack_string('stackCas_finalChar', $a));
$this->answernote[] = 'finalChar';
}
// Check for empty parentheses `()`.
if (strpos($cmd, '()') !== false) {
$this->valid = false;
$this->add_error(stack_string('stackCas_forbiddenWord', array('forbid' => stack_maxima_format_casstring('()'))));
$this->answernote[] = 'forbiddenWord';
}
// Check for spurious operators.
$spuriousops = array('<>', '||', '&', '..', ',,', '/*', '*/');
foreach ($spuriousops as $op) {
if (substr_count($cmd, $op) > 0) {
$this->valid = false;
$a = array();
$a['cmd'] = stack_maxima_format_casstring($op);
$this->add_error(stack_string('stackCas_spuriousop', $a));
$this->answernote[] = 'spuriousop';
}
}
// CAS strings may not contain
// * reversed inequalities, i.e =< is not permitted in place of <=.
// * chained inequalities 1<x<=3.
if (strpos($cmd, '=<') !== false || strpos($cmd, '=>') !== false) {
if (strpos($cmd, '=<') !== false) {
$a['cmd'] = stack_maxima_format_casstring('=<');
} else {
$a['cmd'] = stack_maxima_format_casstring('=>');
}
$this->add_error(stack_string('stackCas_backward_inequalities', $a));
$this->answernote[] = 'backward_inequalities';
$this->valid = false;
} else {
if (!$this->check_chained_inequalities($cmd)) {
$this->add_error(stack_string('stackCas_chained_inequalities'));
$this->answernote[] = 'chained_inequalities';
$this->valid = false;
}
}
// Commas not inside brackets either should be, or indicate a decimal number not
// using the decimal point. In either case this is problematic.
// For now, we just look for expressions with a comma, but without brackets.
// [TODO]: improve this test to really look for unencapsulated commas.
if (!(false === strpos($cmd, ',')) && !(!(false === strpos($cmd, '(')) || !(false === strpos($cmd, '[')) || !(false === strpos($cmd, '{')))) {
$this->add_error(stack_string('stackCas_unencpsulated_comma'));
$this->answernote[] = 'unencpsulated_comma';
$this->valid = false;
}
$this->check_stars($security, $syntax, $insertstars);
$this->check_security($security, $allowwords);
$this->key_val_split();
return $this->valid;
}
