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Subrecursive programming languages II on program size

1971
*
Journal of computer and system sciences (Print)
*

*Programming*

*languages*which express

*programs*

*for*all computable (recursive) functions are called universal, those expressing

*programs*only

*for*

*a*subset are called

*subrecursive*

*programming*

*languages*, SPL's ... Blum has shown that

*for*certain SPL's any universal

*programming*

*language*(UPL) contains

*programs*which are arbitrarily shorter and nearly

*as*efficient

*as*the shortest SPL

*program*

*for*the same function. ... Finally, we add an iterative type statement:

*Subrecursive*

*Programming*

*Languages*

*As*

*for*UPL's, our results apply to

*a*wide class of

*subrecursive*formalisms (such

*as*primitive recursive equations)

*as*...

##
###
Page 3188 of Mathematical Reviews Vol. , Issue 98E
[page]

1998
*
Mathematical Reviews
*

{

*For*the entire collection see MR 98c:68003b. } 98e:68024 68N15 03D15 03D20 68Q15 Voda, Paul J. (SK-K MSK-IC; Bratislava)*Subrecursion**as**a**basis**for**a**feasible**programming**language*. ... Summary: “Motivated by the desire to find*a*good*basis**for*the semantics of*programming**languages*, we investigate small classes in*subrecursive*hierarchies of functions. ...##
###
Obstacles to a totally functional programming style

2004
*
2004 Australian Software Engineering Conference. Proceedings.
*

The obstacles that currently prevent the immediate uptake of TFP

doi:10.1109/aswec.2004.1290470
dblp:conf/aswec/BailesK04
fatcat:bomub3ewbjeorn347bnylninxi
*as**a*style within functional*programming*equally indicate future research directions in the areas of theoretical foundations, supporting ... TFP is motivated by observations from practice in*language*extensibility and functional*programming*. ...*Programming**as**language*extension. Conversely,*programming*is*a*kind of*language*design and thereby*a*kind of*language*extension,*as*follows. ...##
###
Page 2545 of Mathematical Reviews Vol. , Issue 98D
[page]

1998
*
Mathematical Reviews
*

Voda,

*Subrecursion**as**a**basis**for**a**feasible**programming*lan- guage (324-338); Roy L. Crole and Andrew D. ... - 368); David Lester and Sava Mintchev, Towards machine-checked compiler correctness*for*higher-order pure functional*languages*(369-381); Yiannis N. ...##
###
On characterizations of the basic feasible functionals, Part I

2001
*
Journal of functional programming
*

We introduce

doi:10.1017/s0956796800003841
fatcat:jmzob42u6zdb5m443h2citli3a
*a*typed*programming*formalism, type-2 inflationary tiered loop*programs*or ITLP 2 , that characterizes the type-2 basic*feasible*functionals. ... BC92] and Leivant's [Lei95] type-theoretic characterization of polynomial-time and turns out to be closely related to Kapron and Cook's [KC91, KC96] machine-based characterization of the type-2 basic*feasible*... We happily acknowledge the influence of Neil Jones's text [Jon97] that provided us with an extended example of how to carefully mesh*programming**language*and complexity-theoretic concerns. ...##
###
Finitely stratified polymorphism

1991
*
Information and Computation
*

The latter has great expressive power, well beyond current

doi:10.1016/0890-5401(91)90053-5
fatcat:nr2cayee5zgthi3dhsa2g4r6z4
*programming*needs, but it is probably too powerful to allow computationally*feasible*user friendly facilities, such*as*type inference. ... ., the class &*a*in Grzegorczyk's*subrecursive*hierarchy. ...##
###
Non-Obfuscated Unprovable Programs & Many Resultant Subtleties

2016
*
Logical Methods in Computer Science
*

The International Obfuscated C Code Contest was

doi:10.2168/lmcs-12(2:2)2016
fatcat:c4silpe5cfctfhf5eemuhxmppm
*a**programming*contest*for*the most creatively obfuscated yet succinct C code. ... : the existence of the control structure composition is provable*for*it, but anything about true I/O-*program*equivalence*for*syntactically unequal*programs*is not provable. ... Acknowledgement We are very grateful*for*the anonymous referees' hard work, helpful suggestions, and corrections. NON-OBFUSCATED YET UNPROVABLE*PROGRAMS*...##
###
Mathematical Logic in Computer Science
[article]

2018
*
arXiv
*
pre-print

Type theory emerged

arXiv:1802.03292v1
fatcat:bqajf55ih5aw3mxxo6tt5tjzkq
*as**a*unifying conceptual framework*for*the design, analysis, and implementation of*programming**languages*. ... It turned out to be an extremely productive correspondence, the*basis*of*a*totally different approach to the design of typed*programming**languages*, among other deep changes in both proof theory and*programming*...##
###
Hypercomputation by definition

2004
*
Theoretical Computer Science
*

It is not recursive, although

doi:10.1016/j.tcs.2003.12.011
fatcat:d3faa6rvkrf2nj3bhywab3nr54
*for*each given number n, its equations in n variables form*a*recursive set. ... Hypercomputation is therefore required*for*an algorithmic answer to the membership problem of such*a*theory. Yet Alfred Tarski declared these theories to be decidable. ... of this paper, to Jack Copeland*for*fostering*a*broader interest in hypercomputation and historical computers and*for*proposing speciÿc projects in both, to Carol Cleland*for*encouraging expression of ...##
###
Hypercomputation by definition

2004
*
Theoretical Computer Science
*

It is not recursive, although

doi:10.1016/s0304-3975(03)00638-8
fatcat:p5hy7ivycja6fpah3ouorspogq
*for*each given number n, its equations in n variables form*a*recursive set. ... Hypercomputation is therefore required*for*an algorithmic answer to the membership problem of such*a*theory. Yet Alfred Tarski declared these theories to be decidable. ... of this paper, to Jack Copeland*for*fostering*a*broader interest in hypercomputation and historical computers and*for*proposing speciÿc projects in both, to Carol Cleland*for*encouraging expression of ...##
###
Page 103 of Mathematical Reviews Vol. , Issue Index
[page]

*
Mathematical Reviews
*

*Subrecursion*

*as*

*a*

*basis*

*for*

*a*

*feasible*

*programming*

*language*. ...

*Subrecursion*

*as*

*a*

*basis*

*for*

*a*

*feasible*

*programming*

*language*. (English summary) 98e:68024 Volimer, Heribert (with Wagner, Klaus W.) ...

##
###
The Prospects for Mathematical Logic in the Twenty-First Century

2001
*
Bulletin of Symbolic Logic
*

The areas of recursion theory, proof theory and logic

doi:10.2307/2687773
fatcat:mdamfnfy55atzalpnh7ul3xv6m
*for*computer science, model theory, and set theory are discussed independently. ... I am grateful to Yiannis Moschovakis, Richard Shore, John Steel, and Hugh Woodin*for*their comments on an earlier draft of this section. ... Here the beginnings of recursion theory have already played an important role, e.g. the Turing machine model*as**a*basic one*for*computation and the*A*-calculus*as*one*for**programming**languages*both abstract ...##
###
Subject index volumes 1–200

1999
*
Theoretical Computer Science
*

-, 207
graph, subgraph homeomorphism
problem

doi:10.1016/s0304-3975(98)00319-3
fatcat:s22ud3iiqjht7lfbtc3zctk7zm
*for**a*-, 152 fixed number of parallel processes, 1137*program*variables, 352 sortings, 2726 variables, factorization*for*polynomials in*a*-, 661 fixed ...*for*e-unification, 1276 good sets of*basis*-, 256 in schemes, equivalent -, 1343 mto specialized*programs*, 1670 linear-time -, 2726 maligness preserving -, 3477 method of -, 1276 normalizing -. 2072 transformations ...##
###
The prospects for mathematical logic in the twenty-first century
[article]

2002
*
arXiv
*
pre-print

The areas of recursion theory, proof theory and logic

arXiv:cs/0205003v1
fatcat:i3rpwamx6nfdzi5kqkrt34twkq
*for*computer science, model theory, and set theory are discussed independently. ... I am grateful to Yiannis Moschovakis, Richard Shore, John Steel, and Hugh Woodin*for*their comments on an earlier draft of this section. ... Here the beginnings of recursion theory have already played an important role, e.g. the Turing machine model*as**a*basic one*for*computation and the λ-calculus*as*one*for**programming**languages*both abstract ...##
###
The bounded arithmetic hierarchy

1978
*
Information and Control
*

The bounded arithmetic predicates are

doi:10.1016/s0019-9958(78)90257-7
fatcat:aslt6dyy7fbk3l6xnzmzva4zk4
*a*small subset of the recursively enumerable, but theY include most of the standard examples from recursive function theory and form*a**basis**for*the r.e. sets. ... Although the existence of*a*strict hierarchy is not established, necessary and sufficient conditions*for*the hierarchy to be strict are shown. ... ACKNOWLEDGMENTS The author would like to thank Martin Davis*for*originally suggesting the question of*a*bounded arithmetic hierarchy, Sheldon Finkelstein*for*his careful reading of the manuscript and simplification ...
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