list comprehension

list comprehension
set abstraction
set comprehension

   <functional programming> An expression in a {functional
   language} denoting the results of some operation on (selected)
   elements of one or more lists.  An example in {Haskell}:

   [ (x,y) | x <- [1 .. 6], y <- [1 .. x], x+y < 10]

   This returns all pairs of numbers (x,y) where x and y are
   elements of the list 1, 2, ..., 10, y <= x and their sum is
   less than 10.

   A list comprehension is simply "{syntactic sugar}" for a
   combination of applications of the functions, concat, map and
   filter.  For instance the above example could be written:

   	filter p (concat (map (\ x -> map (\ y -> (x,y))
   			 [1..x]) [1..6]))
   	where
   	p (x,y) = x+y < 10

   According to a note by Rishiyur Nikhil <[email protected]>,
   (August 1992), the term itself seems to have been coined by
   Phil Wadler circa 1983-5, although the programming construct
   itself goes back much further (most likely Jack Schwartz and
   the SETL language).

   The term "list comprehension" appears in the references below.

   The earliest reference to the notation is in Rod Burstall and
   John Darlington's description of their language, NPL.

   David Turner subsequently adopted this notation in his
   languages SASL, KRC and Miranda, where he has called them "{ZF
   expressions}", set abstractions and list abstractions (in his
   1985 FPCA paper [Miranda: A Non-Strict Functional Language
   with Polymorphic Types]).

   ["The OL Manual" Philip Wadler, Quentin Miller and Martin
   Raskovsky, probably 1983-1985].

   ["How to Replace Failure by a List of Successes" FPCA
   September 1985, Nancy, France, pp. 113-146].

   (1995-02-22)