| 释义 |
recursively, adv.|rɪˈkɜːsɪvlɪ|
[f. prec. + -ly2.]
In a recursive manner: esp. recursively defined, having a recursive definition; recursively enumerable, (of a set of natural numbers) generated by a general recursive function having one parameter which ranges through all possible values.
1934Kleene & Rosser Gödel's Undecidable Propositions Formal Math. Syst. (typescript) 21 These are arithmetic propositions which involve only recursively defined functions. 1943,1944[see recursive a. 2 a]. 1944Bull. Amer. Math. Soc. L. 285 A set of positive integers is said to be recursively enumerable if there is a recursive function f(x) of one positive integral variable whose values for positive integral values of x, constitute the given set. 1961Commun. Assoc. Computing Machinery IV. 10/2 Many of the constituents of the Algol language are defined recursively. 1962B. Meltzer tr. Gödel's Formally Undecidable Propositions 46 A number-theoretic function ϕ(x1, x2,{ddd}xn) is said to be recursively defined by the number-theoretic functions ψ(x1, x2,{ddd}xn - 1) and µ(x1, x2,{ddd}xn - 1) if for all x2,{ddd}xn, k the following hold: ϕ(0, x2,{ddd}xn) = ψ(x2,{ddd}xn), ϕ(k + 1, x2,{ddd}xn) = µ(k, ϕ(k, x2,{ddd}xn), x2,{ddd}xn). 1964Mem. Amer. Math. Soc. LI. 8 An index of ϕ2 is obtainable primitive recursively from an index of ϕ1, and vice versa. 1968[see nest v. 4 b]. 1968Language XLIV. 571 The set of all sets of integers is non-denumerable; the set of all Turing machines is denumerable; each recursively enumerable set corresponds to a Turing machine; therefore there are sets of integers which are not recursively enumerable. 1970Ibid. XLVI. 787 Sentence margins are slots where nuclear sentence patterns may recursively be embedded within other sentences. 1970Eilenberg & Elgot Recursiveness 84 The class of all recursively enumerable sets is countable. 1974Kernighan & Plauger Elem. Programming Style iii. 54 Learning to think recursively takes some effort, but that is repaid with smaller and simpler programs... Use recursive procedures for recursively-defined data structures. |