recursiveadj.n.

Brit.

/rᵻˈkəːsɪv/, U.S.

/rəˈkərsɪv/,

/riˈkərsɪv/

Origin: A borrowing from Latin, combined with an English element. Etymons: Latin recurs- , recurrere , -ive suffix.

Etymology: < classical Latin recurs-, past participial stem of recurrere recur v. + -ive suffix. In sense A. 2a after similar uses of German rekurrent (D. Hilbert 1904, in Verhandl. des dritten Internat. Math. Kongr.), rekursiv (K. Gödel 1931, in Monatshefte f. Math. u. Physik 38 179). Compare earlier recursion n. and also recurse v. Compare also earlier recurrent adj.

A. adj.

1. Repeatedly or continually recurring; recurrent. Now rare.

ΘΚΠ

the world > time > frequency > [adjective] > periodical or recurring at regular intervals

continualc1530

periodical1585

termly1594

clock-like1609

terminal1610

stated1611

regular1639

periodic1661

clockwork1679

recursive1766

clockwork-like1875

tidal1876

seasonal1880

1766 R. Andrews tr. Virgil Georgics i, in Wks. i. 49 While her song eludes the painful hours, Let your wife's shuttle shrill recursive glide [L. percurrit].

1790 Loiterer 13 Mar. 7 Till your ear be so attuned to one particular measure, that your ideas may be spontaneously absorbed into the same revolving eddy of recursive harmony.

1877 Galaxy Sept. 346/1 Had not the newspapers been filled for weeks with recursive dissertations upon the animals concerned in the ceremony?

1961 Times 22 Aug. 13/6 These balances are subject to recursive shrinkages as a result of precautionary and speculative conversions into gold.

a. Mathematics and Logic. Designating a repeated procedure such that the required result at each step is defined in terms of the results of previous steps according to a particular rule (the result of an initial step being specified).general, partial, primitive recursive: see the first element.

ΘΚΠ

the world > relative properties > number > mathematics > [adjective] > relating to mathematical enquiry > of calculation > using repeated procedure

iterative1924

recursive1943

1916 Science 4 Feb. 154/1 Conditions that exhibit a recursive law of formation in one domain of rationality are quite certain to do the same in a different domain.

1943 Mind 52 268 Elementary theorems, requiring for their proofs recursive arguments to take care of the indefinite number of variables involved.

1964 E. Mendelson Introd. Math. Logic 125 Relations obtained from primitive recursive (or recursive) relations by means of the propositional connectives and the bounded quantifiers are also primitive recursive (or recursive).

1974 A. Kenny tr. Wittgenstein Philos. Gram. 34 Is there a further step from writing the recursive proof to the generalization? Doesn't the recursion schema already say all that is to be said?

2007 Jrnl. Functional Anal. 244 289 We derive new recursive formulas for principal series Whittaker functions.

b. Linguistics. Designating a rule which can be reapplied to a form or construction that is itself partly or wholly derived by that rule. Also: designating a grammatical structure generated, or language characterized, by such rules. Also in extended use.

ΘΚΠ

the mind > language > linguistics > study of grammar > syntax or word order > syntactic relations > [adjective] > change of word order or position > specifically in transformational grammar > specific features of

recursive1955

unary1965

postcyclic1967

post-cyclical1967

1955 N. Chomsky Logical Struct. Ling. Theory (microfilm, Mass. Inst. Technol.) vi. 248 We will find many other reasons to question the validity of the extension of the notion of production to recursive production.

1957 N. Chomsky in Janua Linguarum 4 57 Bar-Hillel has suggested..that Pike's proposals can be formalized without the circularity that many sense in them by the use of recursive definitions.

1968 J. Lyons Introd. Theoret. Linguistics vii. 326 The adverb is a recursive category..in the sense that one adverb may modify another.

1970 J. Lyons Chomsky viii. 90 It will be observed that rules (2), (3) and (4) are recursive, but in different ways. Rule (2) is left recursive; rule (3) is right recursive; and rule (4) is self-embedding.

1984 C. Hookway Minds, Machines & Evol. (BNC) (1987) 73 The phenomenon of recursive syntax may bear on the intentional ingredient in human communication.

2006 S. Shukla & J. Connor-Linton in R. Fasold & J. Connor-Linton Introd. Lang. & Linguistics viii. 279 Humans may have developed a simple protolanguage..thousands of years before developing the hierarchical, recursive syntax of modern human language.

c. Computing. Designating a statement, definition, subroutine, etc., some part of which requires application of the whole, so that its explicit interpretation requires in general many successive executions; relating to or involving such a statement, etc.Quot. 1958 uses the word in a context where ‘iterative’ would now be usual.

ΘΚΠ

society > computing and information technology > programming language > program or code > [adjective] > self-referential

recursive1958

1958 Communications Assoc. Computing Machinery 1 10 The idea of recursive curve fitting has been in use for some time as a graphical technique for fitting curves ‘by eye’ to observational data.

1959 Numerische Math. 1 45 The definition of expressions, and their constituents, is necessarily recursive.

1960 Numerische Math. 2 312 It is then impossible to call in a subroutine while one or more previous activations of the same subroutine have not yet come to an end... We intend to describe..a means of removing the..restriction..; hence the name ‘recursive programming’.

1979 E. S. Page & L. B. Wilson Introd. Computational Combinatorics vi. 136 Since backtrack programming is closely related to tree searching we can consider using recursive techniques in our implementations.

1993 Computing 2 Sept. 26/1 A recursive program is one which contains a subroutine which calls itself at least once.

2004 ‘Dr. K.’ Hackers' Tales v. 97 When they finally taught me about recursion, the first program I wrote was a recursive version of the Ten Green Bottles program.

3. Phonetics. Designating a consonant accompanied by glottal closure or implosion. See also sense B.

ΘΚΠ

the mind > language > linguistics > study of speech sound > speech sound > speech sound by place or organ > [adjective] > glottal

recursive1934

glottalic1942

1934 Webster's New Internat. Dict. Eng. Lang. Recursive, adj.,..formed with an inward movement of air caused by lowering the larynx with closed glottis;—said of certain consonants in Sindhi (g, j, d, b).

1974 Encycl. Brit. Macropædia IX. 448/1 One major feature distinguishing Sindhi from the rest of the northwest group is the development of a series of imploded stops (also called suction stops and recursive stops), for b, d, j, and g.

1995 G. L. Campbell Conc. Compend. World's Langs. 461 Implosive or recursive stops: ɓ, ɗ.

B. n.

Phonetics. A recursive consonant. Cf. sense A. 3.

ΘΚΠ

the mind > language > linguistics > study of speech sound > speech sound > speech sound by place or organ > [noun] > glottal

catch1788

glottal catch (also stop1877

glottid1883

coup de glotte1909

recursive1924

stød1954

1924 R. L. Turner in Bull. School Oriental Stud. 3 304 According to one of my informants, an m accompanied by glottal closure and distinguished from ordinary m, exists in Magarkurā, one of the Mongolian languages of Nepal. Prince Troubetzkoy refers to consonants in the Caucasian languages accompanied by complete closure of the glottis. These he calls ‘recoursives’, a convenient term I have anglicized as ‘recursives’; he indicates them by a dot above or below the letter.

1984 Bull. School Oriental & Afr. Stud. 47 543 His publications..were devoted to clearing up outstanding difficulties in the languages of the North West, beginning with the much debated development of Sindhi recursives..and Sindhi cerebrals.

2007 Chicago Tribune (Midwest ed.) 10 June i. 22/2 Everett..reported that the Brazilian tribe he was studying didn't use recursives.

Compounds

recursive definition n. Mathematics, Logic, and Computing definition of a function of the natural numbers in which its value for a given value of its argument is defined in terms of its values for other arguments; definition (of a function, word, etc.) by recursion; an instance of this.

ΘΚΠ

the world > relative properties > number > algebra > [noun] > expression > function > property of

discontinuity1803

functionality1857

self-conjugation1866

covariance1878

symmetry1888

monogeneity1906

recursion1913

recursive definition1935

holomorphy1957

unateness1960

1935 Mind 44 394 The metamathematician may use mathematical induction for the recursive definition of simple functions.

1962 R. B. Braithwaite in B. Meltzer tr. K. Gödel Formally Undecidable Propositions 12 Recursive definition enables every number in a recursively defined infinite sequence to be constructed according to a rule, so that a remark about the infinite sequence can be construed as a remark about the rule of construction and not as a remark about a given infinite totality.

2007 Theoret. Computer Sci. 387 98 The second inequality follows from the recursive definition of Stirling numbers of the second kind.

recursive function n. Mathematics, Logic, and Computing a function which has or which may be given a recursive definition; also in extended use.

ΘΚΠ

the world > relative properties > number > algebra > [noun] > expression > function

function1758

exponential1784

potential function1828

syzygy1850

permutant1852

Green function1863

theta-function1871

Greenian1876

Gudermannian1876

discriminoid1877

Weierstrassian function1878

gradient1887

beta function1888

distribution function1889

Riemann zeta function1899

Airy integral1903

Poisson bracket1904

Stirling approximation1908

functional1915

metric1921

Fourier transform1923

recursive function1934

utility function1934

Airy function1939

transfer function1948

objective function1949

restriction1949

multifunction1954

restriction mapping1956

scalar function1956

Langevin function1960

mass function1961

1934 S. C. Kleene & J. B. Rosser Gödel's Undecidable Propositions Formal Math. Syst. (typescript) 3 We define the class of recursive functions to be the totality of functions which can be generated by substitution..and recursion..from the successor function x + 1, constant functions.., and identity functions.

1970 Nature 19 Dec. 1234/1 Turing formulated his concept of an abstract computing machine; the functions computable by these machines are exactly the recursive functions.

1994 Denver Post 15 Dec. b11/3 The president has become what mathematicians call a recursive function—a machine that moves in endless, repeated cycles.

2000 A. Brennecke in R. Rojas & U. Hashagen First Computers i. 54 Theoretical computer science has developed notions like μ-recursive functions, primitive recursive functions and the Chomsky hierarchy to describe the potential of computing devices.

recursive relation n. Mathematics and Logic a property of, or relation between, natural numbers whose truth value for all arguments is a recursive function; a relation that can be expressed by a recursive function.

ΘΚΠ

the world > relative properties > number > mathematical number or quantity > [noun] > relationship between quantities > other

finite difference1807

inverse1837

reciprocator1874

power law1919

recursive relation1934

1934 S. C. Kleene & J. B. Rosser Gödel's Undecidable Propositions Formal Math. Syst. (typescript) 3 A relation R shall be recursive if the representing function is recursive... Recursive relations (classes) are decidable in the sense that, for each given set of natural numbers, it can be determined by a finite procedure whether the relation holds or does not hold... The functions x + y, xy, x^y and x! are clearly recursive.

1989 G. M. Edelman Remembered Present x. 179 Given the recursive relation between recombinatorial conceptual capabilities and speech production and recognition, it is perhaps not surprising that an enormous extension of conceptual power rapidly emerged as a result of the evolution of language.

2000 J. R. Lucas Conceptual Roots Math. iv. 205 The three rules of inference—the rule of substitution, the rule of generalisation and the rule of Modus Ponens—can be represented by Primitive Recursive Relations between the Gödel numbers of the premises and the Gödel numbers of the conclusions.

recursive set n. Mathematics and Logic a set of natural numbers, or of elements that each corresponds to a natural number, generated by a recursive procedure.

ΘΚΠ

the world > relative properties > number > mathematical number or quantity > numerical arrangement > [noun] > set

set1857

interval1902

intersection1909

union1912

lattice1933

matroid1935

closure1937

Steiner triple or triplet system1939

recursive set1943

convex hull1951

power set1953

convex envelope1964

Steiner system1966

Julia set1976

Mandelbrot set1984

1943 Amer. Jrnl. Math. 65 201 We may note this interchange of primary and secondary concept as compared with the Church development; for normal set corresponds to recursively enumerable set, binormal set to (general) recursive set.

1989 R. Penrose Emperor's New Mind iv. 120 A set which has the property that both it and its complementary set are recursively enumerable is called a recursive set.

2006 Jrnl. Complexity 22 748 A recursive binary tree T which has A but no recursive set as an infinite branch is constructed.

This entry has been updated (OED Third Edition, June 2009; most recently modified version published online June 2022).

单词	recursive
释义	recursiveadj.n. Brit. /rᵻˈkəːsɪv/, U.S. /rəˈkərsɪv/, /riˈkərsɪv/ Origin: A borrowing from Latin, combined with an English element. Etymons: Latin recurs- , recurrere , -ive suffix. Etymology: < classical Latin recurs-, past participial stem of recurrere recur v. + -ive suffix. In sense A. 2a after similar uses of German rekurrent (D. Hilbert 1904, in Verhandl. des dritten Internat. Math. Kongr.), rekursiv (K. Gödel 1931, in Monatshefte f. Math. u. Physik 38 179). Compare earlier recursion n. and also recurse v. Compare also earlier recurrent adj. A. adj. 1. Repeatedly or continually recurring; recurrent. Now rare. ΘΚΠ the world > time > frequency > [adjective] > periodical or recurring at regular intervals continualc1530 periodical1585 termly1594 clock-like1609 terminal1610 stated1611 regular1639 periodic1661 clockwork1679 recursive1766 clockwork-like1875 tidal1876 seasonal1880 1766 R. Andrews tr. Virgil Georgics i, in Wks. i. 49 While her song eludes the painful hours, Let your wife's shuttle shrill recursive glide [L. percurrit]. 1790 Loiterer 13 Mar. 7 Till your ear be so attuned to one particular measure, that your ideas may be spontaneously absorbed into the same revolving eddy of recursive harmony. 1877 Galaxy Sept. 346/1 Had not the newspapers been filled for weeks with recursive dissertations upon the animals concerned in the ceremony? 1961 Times 22 Aug. 13/6 These balances are subject to recursive shrinkages as a result of precautionary and speculative conversions into gold. 2. a. Mathematics and Logic. Designating a repeated procedure such that the required result at each step is defined in terms of the results of previous steps according to a particular rule (the result of an initial step being specified).general, partial, primitive recursive: see the first element. ΘΚΠ the world > relative properties > number > mathematics > [adjective] > relating to mathematical enquiry > of calculation > using repeated procedure iterative1924 recursive1943 1916 Science 4 Feb. 154/1 Conditions that exhibit a recursive law of formation in one domain of rationality are quite certain to do the same in a different domain. 1943 Mind 52 268 Elementary theorems, requiring for their proofs recursive arguments to take care of the indefinite number of variables involved. 1964 E. Mendelson Introd. Math. Logic 125 Relations obtained from primitive recursive (or recursive) relations by means of the propositional connectives and the bounded quantifiers are also primitive recursive (or recursive). 1974 A. Kenny tr. Wittgenstein Philos. Gram. 34 Is there a further step from writing the recursive proof to the generalization? Doesn't the recursion schema already say all that is to be said? 2007 Jrnl. Functional Anal. 244 289 We derive new recursive formulas for principal series Whittaker functions. b. Linguistics. Designating a rule which can be reapplied to a form or construction that is itself partly or wholly derived by that rule. Also: designating a grammatical structure generated, or language characterized, by such rules. Also in extended use. ΘΚΠ the mind > language > linguistics > study of grammar > syntax or word order > syntactic relations > [adjective] > change of word order or position > specifically in transformational grammar > specific features of recursive1955 unary1965 postcyclic1967 post-cyclical1967 1955 N. Chomsky Logical Struct. Ling. Theory (microfilm, Mass. Inst. Technol.) vi. 248 We will find many other reasons to question the validity of the extension of the notion of production to recursive production. 1957 N. Chomsky in Janua Linguarum 4 57 Bar-Hillel has suggested..that Pike's proposals can be formalized without the circularity that many sense in them by the use of recursive definitions. 1968 J. Lyons Introd. Theoret. Linguistics vii. 326 The adverb is a recursive category..in the sense that one adverb may modify another. 1970 J. Lyons Chomsky viii. 90 It will be observed that rules (2), (3) and (4) are recursive, but in different ways. Rule (2) is left recursive; rule (3) is right recursive; and rule (4) is self-embedding. 1984 C. Hookway Minds, Machines & Evol. (BNC) (1987) 73 The phenomenon of recursive syntax may bear on the intentional ingredient in human communication. 2006 S. Shukla & J. Connor-Linton in R. Fasold & J. Connor-Linton Introd. Lang. & Linguistics viii. 279 Humans may have developed a simple protolanguage..thousands of years before developing the hierarchical, recursive syntax of modern human language. c. Computing. Designating a statement, definition, subroutine, etc., some part of which requires application of the whole, so that its explicit interpretation requires in general many successive executions; relating to or involving such a statement, etc.Quot. 1958 uses the word in a context where ‘iterative’ would now be usual. ΘΚΠ society > computing and information technology > programming language > program or code > [adjective] > self-referential recursive1958 1958 Communications Assoc. Computing Machinery 1 10 The idea of recursive curve fitting has been in use for some time as a graphical technique for fitting curves ‘by eye’ to observational data. 1959 Numerische Math. 1 45 The definition of expressions, and their constituents, is necessarily recursive. 1960 Numerische Math. 2 312 It is then impossible to call in a subroutine while one or more previous activations of the same subroutine have not yet come to an end... We intend to describe..a means of removing the..restriction..; hence the name ‘recursive programming’. 1979 E. S. Page & L. B. Wilson Introd. Computational Combinatorics vi. 136 Since backtrack programming is closely related to tree searching we can consider using recursive techniques in our implementations. 1993 Computing 2 Sept. 26/1 A recursive program is one which contains a subroutine which calls itself at least once. 2004 ‘Dr. K.’ Hackers' Tales v. 97 When they finally taught me about recursion, the first program I wrote was a recursive version of the Ten Green Bottles program. 3. Phonetics. Designating a consonant accompanied by glottal closure or implosion. See also sense B. ΘΚΠ the mind > language > linguistics > study of speech sound > speech sound > speech sound by place or organ > [adjective] > glottal recursive1934 glottalic1942 1934 Webster's New Internat. Dict. Eng. Lang. Recursive, adj.,..formed with an inward movement of air caused by lowering the larynx with closed glottis;—said of certain consonants in Sindhi (g, j, d, b). 1974 Encycl. Brit. Macropædia IX. 448/1 One major feature distinguishing Sindhi from the rest of the northwest group is the development of a series of imploded stops (also called suction stops and recursive stops), for b, d, j, and g. 1995 G. L. Campbell Conc. Compend. World's Langs. 461 Implosive or recursive stops: ɓ, ɗ. B. n. Phonetics. A recursive consonant. Cf. sense A. 3. ΘΚΠ the mind > language > linguistics > study of speech sound > speech sound > speech sound by place or organ > [noun] > glottal catch1788 glottal catch (also stop1877 glottid1883 coup de glotte1909 recursive1924 stød1954 1924 R. L. Turner in Bull. School Oriental Stud. 3 304 According to one of my informants, an m accompanied by glottal closure and distinguished from ordinary m, exists in Magarkurā, one of the Mongolian languages of Nepal. Prince Troubetzkoy refers to consonants in the Caucasian languages accompanied by complete closure of the glottis. These he calls ‘recoursives’, a convenient term I have anglicized as ‘recursives’; he indicates them by a dot above or below the letter. 1984 Bull. School Oriental & Afr. Stud. 47 543 His publications..were devoted to clearing up outstanding difficulties in the languages of the North West, beginning with the much debated development of Sindhi recursives..and Sindhi cerebrals. 2007 Chicago Tribune (Midwest ed.) 10 June i. 22/2 Everett..reported that the Brazilian tribe he was studying didn't use recursives. Compounds recursive definition n. Mathematics, Logic, and Computing definition of a function of the natural numbers in which its value for a given value of its argument is defined in terms of its values for other arguments; definition (of a function, word, etc.) by recursion; an instance of this. ΘΚΠ the world > relative properties > number > algebra > [noun] > expression > function > property of discontinuity1803 functionality1857 self-conjugation1866 covariance1878 symmetry1888 monogeneity1906 recursion1913 recursive definition1935 holomorphy1957 unateness1960 1935 Mind 44 394 The metamathematician may use mathematical induction for the recursive definition of simple functions. 1962 R. B. Braithwaite in B. Meltzer tr. K. Gödel Formally Undecidable Propositions 12 Recursive definition enables every number in a recursively defined infinite sequence to be constructed according to a rule, so that a remark about the infinite sequence can be construed as a remark about the rule of construction and not as a remark about a given infinite totality. 2007 Theoret. Computer Sci. 387 98 The second inequality follows from the recursive definition of Stirling numbers of the second kind. recursive function n. Mathematics, Logic, and Computing a function which has or which may be given a recursive definition; also in extended use. ΘΚΠ the world > relative properties > number > algebra > [noun] > expression > function function1758 exponential1784 potential function1828 syzygy1850 permutant1852 Green function1863 theta-function1871 Greenian1876 Gudermannian1876 discriminoid1877 Weierstrassian function1878 gradient1887 beta function1888 distribution function1889 Riemann zeta function1899 Airy integral1903 Poisson bracket1904 Stirling approximation1908 functional1915 metric1921 Fourier transform1923 recursive function1934 utility function1934 Airy function1939 transfer function1948 objective function1949 restriction1949 multifunction1954 restriction mapping1956 scalar function1956 Langevin function1960 mass function1961 1934 S. C. Kleene & J. B. Rosser Gödel's Undecidable Propositions Formal Math. Syst. (typescript) 3 We define the class of recursive functions to be the totality of functions which can be generated by substitution..and recursion..from the successor function x + 1, constant functions.., and identity functions. 1970 Nature 19 Dec. 1234/1 Turing formulated his concept of an abstract computing machine; the functions computable by these machines are exactly the recursive functions. 1994 Denver Post 15 Dec. b11/3 The president has become what mathematicians call a recursive function—a machine that moves in endless, repeated cycles. 2000 A. Brennecke in R. Rojas & U. Hashagen First Computers i. 54 Theoretical computer science has developed notions like μ-recursive functions, primitive recursive functions and the Chomsky hierarchy to describe the potential of computing devices. recursive relation n. Mathematics and Logic a property of, or relation between, natural numbers whose truth value for all arguments is a recursive function; a relation that can be expressed by a recursive function. ΘΚΠ the world > relative properties > number > mathematical number or quantity > [noun] > relationship between quantities > other finite difference1807 inverse1837 reciprocator1874 power law1919 recursive relation1934 1934 S. C. Kleene & J. B. Rosser Gödel's Undecidable Propositions Formal Math. Syst. (typescript) 3 A relation R shall be recursive if the representing function is recursive... Recursive relations (classes) are decidable in the sense that, for each given set of natural numbers, it can be determined by a finite procedure whether the relation holds or does not hold... The functions x + y, xy, x^y and x! are clearly recursive. 1989 G. M. Edelman Remembered Present x. 179 Given the recursive relation between recombinatorial conceptual capabilities and speech production and recognition, it is perhaps not surprising that an enormous extension of conceptual power rapidly emerged as a result of the evolution of language. 2000 J. R. Lucas Conceptual Roots Math. iv. 205 The three rules of inference—the rule of substitution, the rule of generalisation and the rule of Modus Ponens—can be represented by Primitive Recursive Relations between the Gödel numbers of the premises and the Gödel numbers of the conclusions. recursive set n. Mathematics and Logic a set of natural numbers, or of elements that each corresponds to a natural number, generated by a recursive procedure. ΘΚΠ the world > relative properties > number > mathematical number or quantity > numerical arrangement > [noun] > set set1857 interval1902 intersection1909 union1912 lattice1933 matroid1935 closure1937 Steiner triple or triplet system1939 recursive set1943 convex hull1951 power set1953 convex envelope1964 Steiner system1966 Julia set1976 Mandelbrot set1984 1943 Amer. Jrnl. Math. 65 201 We may note this interchange of primary and secondary concept as compared with the Church development; for normal set corresponds to recursively enumerable set, binormal set to (general) recursive set. 1989 R. Penrose Emperor's New Mind iv. 120 A set which has the property that both it and its complementary set are recursively enumerable is called a recursive set. 2006 Jrnl. Complexity 22 748 A recursive binary tree T which has A but no recursive set as an infinite branch is constructed. This entry has been updated (OED Third Edition, June 2009; most recently modified version published online June 2022). < adj.n.1766
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