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Even higher-order functions for parsing or Why would anyone ever want to use a sixth-order function?

1998; Cambridge University Press; Volume: 8; Issue: 2 Linguagem: Inglês

10.1017/s0956796898003001

1469-7653

Chris Okasaki,

Formal Methods in Verification

A higher-order function is a function that takes another function as an argument or returns another function as a result. More specifically, a first-order function takes and returns base types, such as integers or lists. A k th-order function takes or returns a function of order k −1. Currying often artificially inflates the order of a function, so we will ignore all inessential currying. (Whether a particular instance of currying is essential or inessential is open to debate, but we expect that our choices will be uncontroversial.) In addition, when calculating the order of a polymorphic function, we instantiate all type variables with base types. Under these assumptions, most common higher-order functions, such as map and foldr , are second-order, so beginning functional programmers often wonder: What good are functions of order three or above? We illustrate functions of up to sixth-order with examples taken from a combinator parsing library. Combinator parsing is a classic application of functional programming, dating back to at least Burge (1975). Most combinator parsers are based on Wadler's list-of-successes technique (Wadler, 1985). Hutton (1992) popularized the idea in his excellent tutorial Higher-Order Functions for Parsing . In spite of the title, however, he considered only functions of up to order three.