Many variations upon the theme of parser combinators have been proposed, too many to list here, but the main idea is simple: A parser for phrases of type α is a function that takes an input string and produces results (x, rest), where x is a value of type α, and rest is the remainder of the input after the phrase with value x has been consumed. The results are often arranged into a list, because this allows a parser to signal failure with the empty list of results, an unambiguous success with one result, or multiple possibilities with a longer ‘list of successes’.