Author: Andreas Rossberg
Last revised: September 21, 2015
Status: proposed
Discussion:issue #6

signature FNstructure Fn :> FN

TheFn structure provides various combinators to aid computing with function values.

val id       : 'a -> 'aval const    : 'a -> 'b -> 'aval apply    : ('a -> 'b) * 'a -> 'bval o        : ('b -> 'c) * ('a -> 'b) -> ('a -> 'c)val curry    : ('a * 'b -> 'c) -> ('a -> 'b -> 'c)val uncurry  : ('a -> 'b -> 'c) -> ('a * 'b -> 'c)val flip     : ('a * 'b -> 'c) -> ('b * 'a -> 'c)val repeat   : int -> ('a -> 'a) -> ('a -> 'a)val equal    : ''a -> ''a -> boolval notEqual : ''a -> ''a -> bool

• id x
  returns the valuex (id is the polymorphic identity function).

• const x y
  returns the value x.

• apply (f, x)
  applies the functionf tox. Thus, it is equivalent tof a.

• f o g
  is the function composition off andg. Thus,(f o g) x is equivalent tof (g x).This function is the same as the globalo operator and is also part of theGeneral structure.

• curry f x y
  is equivalent tof (x, y);i.e.,curry f transforms the binary functionf into curried form.

• uncurry f (x, y)
  is equivalent tof x y;i.e.,uncurry f transforms the curried functionf into a binary function.This function is the inverse ofcurry.

• flip f (x, y)
  is equivalent tof (y, x);i.e.,flip f flips the argument order of the binary functionf.

• repeat n f
  returns the n-fold composition off.Ifn is zero, thenrepeat n f returns the identity function.Ifn is negative, then it raises the exceptionDomain.

• equal a b
  a curried version of the polymorphic equality function (=).

• notEqual a b
  a curried version of the polymorphic inequality function (<>).

Other combinators could be added. These are the ones that I have needed most in practice.

Adopting this proposal should not affect existing programs.

The need for basic higher-order functions likeid andconst arises all the time in combination with other functionals.So far, the SML Basis has lacked any of these functions, although they are standard in the libraries of most other functional programming languages.

This module also provides a more natural home for the existingo operator, but it would alsoremain in theGeneral structure for backward compatibility.

• [2015-09-21] Addedequal andnotEqual functions as proposed byMichael Norrishin thediscussion.[JHR].

• [2015-08-21] Reworked function descriptions to follow standard style[JHR].

• [2015-08-16] Proposed