Question

I’m trying to implement prefix to infix in PHP. The input should be for example something like this:

prefix  * + 3 2 4
infix   ((3+2)*4)

I want to convert prefix expression like (* + 3 2 4) into infix expression using PHP or JavaScript (((3+2)*4)).

Answer 1

An exemplary object oriented AST and parser:

$prefix = '* + 3 2 4';
$parser = new InfixPrefixParser($prefix);
$node = $parser->parse();
echo $node, "\n"; # ((3 + 2) * 4)
echo ' = ', $node->evaluate(), "\n"; # 20

The parser:

class InfixPrefixParser extends IteratorIterator
{
    public function __construct($prefix)
    {
        $tokens = new ArrayIterator(preg_split('/\s/', $prefix, 0, PREG_SPLIT_NO_EMPTY));
        parent::__construct($tokens);
    }

    /**
     * @return InfixNode
     */
    public function current()
    {
        $string = parent::current();
        parent::next();
        $operators = array('*' => 'Mult', '+' => 'Plus');
        $class = 'InfixNode' . (isset($operators[$string]) ? 'Operator' . $operators[$string] : 'Value');
        $node = new $class($string);
        if ($node instanceof InfixNodeOperator) {
            $node->setLeft($this->current());
            $node->setRight($this->current());
        }
        return $node;
    }

    public function __toString()
    {
        return (string)$this->parse();
    }

    public function parse()
    {
        $this->rewind();
        return $this->current();
    }
}

The object model for the AST

abstract class InfixNode
{
    abstract function evaluate();
}

abstract class InfixNodeOperator extends InfixNode
{
    private $operator;
    protected $left;
    protected $right;

    public function __construct($operator)
    {
        $this->operator = $operator;
    }

    public function setLeft(InfixNode $node)
    {
        $this->left = $node;
    }

    public function getLeft()
    {
        return $this->left;
    }

    public function setRight(InfixNode $node)
    {
        $this->right = $node;
    }

    public function getRight()
    {
        return $this->right;
    }

    public function __toString()
    {
        return sprintf('(%s %s %s)', $this->left, $this->operator, $this->right);
    }
}

class InfixNodeOperatorMult extends InfixNodeOperator
{
    public function evaluate()
    {
        return $this->left->evaluate() * $this->right->evaluate();
    }
}

class InfixNodeOperatorPlus extends InfixNodeOperator
{
    public function evaluate()
    {
        return $this->left->evaluate() + $this->right->evaluate();
    }
}

class InfixNodeValue extends InfixNode
{
    private $value;

    public function __construct($value)
    {
        $this->value = $value;
    }

    public function __toString()
    {
        return (string)$this->value;
    }

    public function evaluate()
    {
        return $this->value;
    }
}

I’m not very confident with the wording, because the nodes aren’t exactly fully related to infix, large parts of them could be used for prefix or postfix as well, only the __toString() functions are infix related actually.

---

(old version) Some PHP code, using some recursive parse function and an object model for the nodes. Usage:

$prefix = '* + 3 2 4';

$tokens = new ArrayIterator(preg_split('/\s/', $prefix, 0, PREG_SPLIT_NO_EMPTY));

$parse = function() use ($tokens, &$parse) {
    $string = $tokens->current(); $tokens->next();
    $isOperator = in_array($string, array('*', '+'));
    $class = 'InfixNode' . ($isOperator ? 'Operator' : 'Value');
    $node = new $class($string);
    if ($node instanceof InfixNodeOperator) {
        $node->setLeft($parse());
        $node->setRight($parse());
    }
    return $node;
};

echo $parse(); # ((3 + 2) * 4)

The node classes:

class InfixNode {}

class InfixNodeOperator extends InfixNode
{
    private $operator;
    private $left;
    private $right;
    public function __construct($operator) {
        $this->operator = $operator;
    }
    public function setLeft(InfixNode $node) {
        $this->left = $node;
    }
    public function getLeft() {
        return $this->left;
    }
    public function setRight(InfixNode $node) {
        $this->right = $node;
    }
    public function getRight() {
        return $this->right;
    }
    public function __toString() {
        return sprintf('(%s %s %s)', $this->left, $this->operator, $this->right);
    }
}

class InfixNodeValue extends InfixNode
{
    private $value;
    public function __construct($value) {
        $this->value = $value;
    }
    public function __toString() {
        return (string) $this->value;
    }
}