scholarly journals Finding parallel functional pearls: Automatic parallel recursion scheme detection in Haskell functions via anti-unification

2018 ◽  
Vol 79 ◽  
pp. 669-686 ◽  
Author(s):  
Adam D. Barwell ◽  
Christopher Brown ◽  
Kevin Hammond
Keyword(s):  
Recursion Scheme

Simplifications of the recursion scheme

1971 ◽  
Vol 36 (4) ◽  
pp. 653-665 ◽  
Author(s):  
M. D. Gladstone
Keyword(s):  
Recursion Scheme ◽  
Projection Functions ◽  
Primitive Recursive

This paper resolves 3 problems left open by R. M. Robinson in [3].We recall that the set of primitive recursive functions is the closure under (i) substitution (or “composition”), and (ii) recursion, of the set P consisting of the zero, successor and projection functions (see any textbook, for instance p. 120 of [2]).

scholarly journals RELATIVE PREDICATIVITY AND DEPENDENT RECURSION IN SECOND-ORDER SET THEORY AND HIGHER-ORDER THEORIES

2014 ◽  
Vol 79 (3) ◽  
pp. 712-732 ◽  
Author(s):  
SATO KENTARO
Keyword(s):  
Number Theory ◽  
Set Theory ◽  
Higher Order ◽  
Second Order ◽  
Order Number ◽  
Recursion Scheme ◽  
Transfinite Recursion ◽  
The Given ◽  
The Universe ◽  
Order Set

AbstractThis article reports that some robustness of the notions of predicativity and of autonomous progression is broken down if as the given infinite total entity we choose some mathematical entities other than the traditional ω. Namely, the equivalence between normal transfinite recursion scheme and new dependent transfinite recursion scheme, which does hold in the context of subsystems of second order number theory, does not hold in the context of subsystems of second order set theory where the universe V of sets is treated as the given totality (nor in the contexts of those of n+3-th order number or set theories, where the class of all n+2-th order objects is treated as the given totality).

A predicative approach to the classification problem

2001 ◽  
Vol 11 (1) ◽  
pp. 95-116 ◽  
Author(s):  
SALVATORE CAPORASO ◽  
EMANUELE COVINO ◽  
GIOVANNI PANI
Keyword(s):  
Time Complexity ◽  
Classification Problem ◽  
Elementary Level ◽  
Complexity Classes ◽  
Elementary Functions ◽  
Recursion Scheme ◽  
Slow Growing

We harmonize many time-complexity classes DTIMEF(f(n)) (f(n) [ges ] n) with the PR functions (at and above the elementary level) in a transfinite hierarchy of classes of functions [Tscr ]α. Class [Tscr ]α is obtained by means of unlimited operators, namely: a variant Π of the predicative or safe recursion scheme, introduced by Leivant, and by Bellantoni and Cook, if α is a successor; and constructive diagonalization if α is a limit. Substitution (SBST) is discarded because the time complexity classes are not closed under this scheme. [Tscr ]α is a structure for the PR functions finer than [Escr ]α, to the point that we have [Tscr ]ε0 = [Escr ]3 (elementary functions). Although no explicit use is made of hierarchy functions, it is proved that f(n) ∈ [Tscr ]α implies f(n) [les ] nGα(n), where Gα belongs to the slow growing hierarchy (of functions) studied, in particular, by Girard and Wainer.

scholarly journals Generating of Nonisospectral Integrable Hierarchies via the Lie-Algebraic Recursion Scheme

Mathematics ◽  
2020 ◽  
Vol 8 (4) ◽  
pp. 621
Author(s):  
Haifeng Wang ◽  
Yufeng Zhang
Keyword(s):  
Lie Algebra ◽  
Efficient Method ◽  
Integrable Hierarchies ◽  
Loop Algebra ◽  
Integrable Hierarchy ◽  
Conserved Quantities ◽  
Recursion Scheme

In the paper, we introduce an efficient method for generating non-isospectral integrable hierarchies, which can be used to derive a great many non-isospectral integrable hierarchies. Based on the scheme, we derive a non-isospectral integrable hierarchy by using Lie algebra and the corresponding loop algebra. It follows that some symmetries of the non-isospectral integrable hierarchy are also studied. Additionally, we also obtain a few conserved quantities of the isospectral integrable hierarchies.

The application of the analytical recursion scheme method on soft ground sites

2012 ◽  
pp. 409-413
Author(s):  
Qi Jingjing ◽  
You Shaoyan ◽  
yin Zhiqing ◽  
Li Dahua
Keyword(s):  
Soft Ground ◽  
Recursion Scheme
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