Hartley RogersJr., Gödel numberings of partial recursive functions. The journal of symbolic logic, vol. 23 no. 3 (for 1958, pub. 1959), pp. 331–341.

1964 ◽  
Vol 29 (3) ◽  
pp. 146-146
Author(s):  
Martin Davis
Keyword(s):  
Symbolic Logic ◽  
Recursive Functions ◽  
Partial Recursive Functions

Preliminaries

2017 ◽  
Author(s):  
David J. Lobina
Keyword(s):  
Data Structures ◽  
Production Systems ◽  
Specific Data ◽  
Recursive Functions ◽  
Recursive Solution ◽  
Partial Recursive Functions ◽  
Recursive Structures ◽  
Recursive Data Structures ◽  
Recursive Data ◽  
The Relationship

Recursion, or the capacity of ‘self-reference’, has played a central role within mathematical approaches to understanding the nature of computation, from the general recursive functions of Alonzo Church to the partial recursive functions of Stephen C. Kleene and the production systems of Emil Post. Recursion has also played a significant role in the analysis and running of certain computational processes within computer science (viz., those with self-calls and deferred operations). Yet the relationship between the mathematical and computer versions of recursion is subtle and intricate. A recursively specified algorithm, for example, may well proceed iteratively if time and space constraints permit; but the nature of specific data structures—viz., recursive data structures—will also return a recursive solution as the most optimal process. In other words, the correspondence between recursive structures and recursive processes is not automatic; it needs to be demonstrated on a case-by-case basis.

scholarly journals Recursive density types and Nerode extensions of arithmetic

1975 ◽  
Vol 20 (2) ◽  
pp. 146-158 ◽  
Author(s):  
P. Aczel
Keyword(s):  
Equivalence Classes ◽  
Partial Functions ◽  
Recursive Functions ◽  
Cardinal Numbers ◽  
Partial Recursive Functions

The notion of a recursive density type (R.D.T.) was introduced by Medvedev and developed by Pavlova (1961). More recently the algebra of R.D.T.'s was initiated by Gonshor and Rice (1969). The R.D.T.'s are equivalence classes of sets of integers, similar in many respects to the R.E.T.'s. They may both be thought of as effective analogues of the cardinal numbers. While the equivalence relationfor R.E.T.'s is defined in terms of partial recursive functions, that for R.D.T.'s may be characterized in terms of recursively bounded partial functions (see 4.22a).

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