On Wednesday 18 May 2005 17:57, Matt Fowles wrote: > All~ > > What does the reduce metaoperator do with an empty list?

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Here is the last answer from Ken Iverson, who invented reduce in the 1950s, and died recently. file:///usr/share/j504/system/extras/help/dictionary/intro28.htm Identity Functions and Neutral The monads 0&+ and 1&* are identity functions, and 0 and 1 are said to be identity elements or neutrals of the dyads + and * respectively. Insertion on an empty list yields the neutral of the dyad inserted. For example: +/ i.0 +/'' +/0{. 2 3 5 0 0 0 */i.0 */'' */0{. 2 3 5 1 1 1 > my @a; > [+] @a; # 0? exception? > [*] @a; # 1? exception? > [<] @a; # false? > [||] @a; # false? > [&&] @a; # true? > > Also if it magically supplies some correct like the above, how > does it know what that value is? > > Thanks, > Matt The page file:///usr/share/j504/system/extras/help/dictionary/d420.htm gives examples, unfortunately not easily readable ones. "If y has no items (that is, 0=#y), the result of u/y is the neutral or identity element of the function u. A neutral of a function u is a value e such that x u e â x or e u x â x, for every x in the domain (or some significant sub-domain such as boolean) of u . This definition of insertion over an argument having zero items extends partitioning identities of the form u/y â (u/k{.y) u (u/k}.y) to the cases k e. 0,#y . "The identity function of u is a function ifu such that ifu y â u/y if 0=#y ." [The following table is greatly simplified by listing identity elements rather than identity functions. Some are only left identities, and some only right identities.] Identity element For 0 < > + - +. ~: | (2 4 5 6 b.) 1 = <: >: * % *. %: ^ ! (1 9 11 13 b.) _ <. __ >. '' , [and a few more that I will not explain here] Glossary J Description +. or ~: objects are identical | remainder, defined so that 0|N is N b. Boolean functions from table <: less than or equal, restricted to Booleans here (1<:0 is 0, 1<:1 is 1) >: greater than or equal, restricted to Booleans here * times, restricted to Booleans here % divide *. and %: root ^ exponential ! combinations <. minimum >. maximum '' empty vector, list of length 0 , catenate, join lists _ infinity __ negative infinity So (_ <. N) is N, as is (__ >. N). All of these functions are defined in detail but quite tersely in the J Dictionary, indexed on the page file:///usr/share/j504/system/extras/help/dictionary/vocabul.htm For examuple, the Boolean function b. is defined on the page file:///usr/share/j504/system/extras/help/dictionary/dbdotn.htm -- Edward Cherlin Generalist & activist--Linux, languages, literacy and more "A knot! Oh, do let me help to undo it!" --Alice in Wonderland http://cherlin.blogspot.com