| 释义 |
recursion|rɪˈkɜːʃən|
[ad. L. recursiōn-em, n. of action f. recurrĕre to recur.]
1. A backward movement, return. Now rare or Obs.
1616Bullokar Eng. Expos., Recursion, a running backe. 1660Boyle New Exp. Phys. Mech. xxvi. 203 The Recursions of that Pendulum which was swinging within the Receiver. 1677Gilpin Demonol. (1867) 237 Our passions in their workings do depend upon the fluctuations, excursions, and recursions of the blood and animal spirits. 1720–1Lett. fr. Mist's Jrnl. (1722) II. 33 The present melancholy Prospect of the Recursion of the South-Sea Tide. 1830T. Taylor Argts. Celsus 23 The doctrine..that in long periods of time, recursions and concursions of the stars, conflagrations and deluges take place.
2. a. The application or use of a recursive procedure or definition; primitive recursion [tr. G. primitive rekursion (R. Péter 1934, in Math. Ann. CX. 613)], definition of a function of natural numbers by induction on a single argument or (equivalently) by simple recursion formulæ; recursion formula, an equation relating the value of a function for a given value of its argument (or arguments) to its values for other values of the argument(s).
[1871Math. Annalen IV. 113 Man hat also für die Funktion Rm, ν folgende Recursionsformel: 2(ν - 1)/z·Rm, ν = Rm + 1, ν - 1 + Rm - 1, ν + 1.] 1930Proc. London Math. Soc. XXX. 267 For other values of r we define f(r, n, k) by recursion formulae. 1933Ann. Math. XXXIV. 863 The recursion formulas, m + 1 = S(m), and m + (k + 1) = S(m + k). 1934,1974[see recursive a. 2 a]. 1943Trans. Amer. Math. Soc. LIII. 42 Schema (I) introduces the successor function,..and Schema (V) the schema of primitive recursion. 1961Commun. Assoc. Computing Machinery IV. 65/1 The growing extent and direction of application of recursion in programming research. 1964E. Bach Introd. Transformational Gram. iii. 46 Care must be taken to ensure that unwanted recursion (looping) does not occur. 1967Klerer & Korn Digital Computer User's Handbk. i. 167 Even if recursive procedures are explicitly outlawed,..recursion can take place unwittingly. 1972R. A. Palmatier Gloss. Eng. Transformational Gram. 142 Recursion is restricted to the transformational component of the grammar. 1973C. W. Gear Introd. Computer Sci. v. 232 Fortran does not allow recursion. 1975F. R. Palmer in W. F. Bolton Eng. Lang. i. 34 The structure of language involves ‘recursion’ of the kind illustrated by ‘This is the house that Jack built’, ‘This is the mouse that lived in the house that Jack built’ and so on—if necessary ad infinitum.
b. A recursive definition.
1936Math. Ann. CXII. 727 There are other definitions of this sort, e.g. certain recursions with respect to two or more variables simultaneously, which cannot be reduced to a succession of substitutions and ordinary recursions. 1963W. V. Quine Set Theory §11. 79 There are the familiar so-called recursive definitions or recursions. 1966N. Chomsky Topics Theory Generative Gram. ii. 33 An utterly fantastic proposal, namely, that a grammar should contain no recursions in its system of rules. 1971Computers & Humanities V. 155 algol is more powerful in that it allows recursions, has block structure, and permits expressions in many places. |