Enumeration and Universality of the Computable Functions

1982 ◽  
pp. 45-74
Author(s):  
A. J. Kfoury ◽  
Robert N. Moll ◽  
Michael A. Arbib
Keyword(s):  
Computable Functions

scholarly journals The Limits of Computation

Axiomathes ◽  
2021 ◽  
Author(s):  
Andrew Powell
Keyword(s):  
Natural Number ◽  
Set Theory ◽  
Lambda Calculus ◽  
Second Order ◽  
Functional Interpretation ◽  
Arbitrary Type ◽  
Computable Functions

AbstractThis article provides a survey of key papers that characterise computable functions, but also provides some novel insights as follows. It is argued that the power of algorithms is at least as strong as functions that can be proved to be totally computable in type-theoretic translations of subsystems of second-order Zermelo Fraenkel set theory. Moreover, it is claimed that typed systems of the lambda calculus give rise naturally to a functional interpretation of rich systems of types and to a hierarchy of ordinal recursive functionals of arbitrary type that can be reduced by substitution to natural number functions.

Primitive program algebras of computable functions

Cybernetics ◽  
1988 ◽  
Vol 23 (3) ◽  
pp. 368-377
Author(s):  
D. B. Bui ◽  
I. V. Red'ko
Keyword(s):  
Computable Functions

A characterization of log-space computable functions

1973 ◽  
Vol 5 (3) ◽  
pp. 26-29 ◽  
Author(s):  
John Lind ◽  
Albert R. Meyer
Keyword(s):  
Computable Functions

scholarly journals Simple section interchange and properties of non-computable functions

2010 ◽  
Vol 75 (11) ◽  
pp. 1142-1164
Author(s):  
Ward Douglas Maurer
Keyword(s):  
Computable Functions

Hierarchies of Provably Computable Functions

1990 ◽  
pp. 211-220 ◽  
Author(s):  
S. S. Wainer
Keyword(s):  
Computable Functions

scholarly journals A combinatory account of internal structure

2011 ◽  
Vol 76 (3) ◽  
pp. 807-826 ◽  
Author(s):  
Barry Jay ◽  
Thomas Given-Wilson
Keyword(s):  
Normal Form ◽  
Internal Structure ◽  
Pattern Matching ◽  
Normal Forms ◽  
Expressive Power ◽  
Combinatory Logic ◽  
Natural Numbers ◽  
Type Information ◽  
Computable Functions

AbstractTraditional combinatory logic uses combinators S and K to represent all Turing-computable functions on natural numbers, but there are Turing-computable functions on the combinators themselves that cannot be so represented, because they access internal structure in ways that S and K cannot. Much of this expressive power is captured by adding a factorisation combinator F. The resulting SF-calculus is structure complete, in that it supports all pattern-matching functions whose patterns are in normal form, including a function that decides structural equality of arbitrary normal forms. A general characterisation of the structure complete, confluent combinatory calculi is given along with some examples. These are able to represent all their Turing-computable functions whose domain is limited to normal forms. The combinator F can be typed using an existential type to represent internal type information.

Local Induction and Provably Total Computable Functions: A Case Study

2012 ◽  
pp. 440-449
Author(s):  
Andrés Cordón–Franco ◽  
F. Félix Lara–Martín
Keyword(s):  
Computable Functions
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