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Subrecursive programming languages II on program size

Robert L. Constable
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  ... 
doi:10.1016/s0022-0000(71)80039-9 fatcat:esyuvfhcujfdvm5qus43x2atua

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

P. Bailes, C. Kemp
2004 2004 Australian Software Engineering Conference. Proceedings.  
The obstacles that currently prevent the immediate uptake of TFP 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.  ... 
doi:10.1109/aswec.2004.1290470 dblp:conf/aswec/BailesK04 fatcat:bomub3ewbjeorn347bnylninxi

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

ROBERT J. IRWIN, JAMES S. ROYER, BRUCE M. KAPRON
2001 Journal of functional programming  
We introduce 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.  ... 
doi:10.1017/s0956796800003841 fatcat:jmzob42u6zdb5m443h2citli3a

Finitely stratified polymorphism

Daniel Leivant
1991 Information and Computation  
The latter has great expressive power, well beyond current 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.  ... 
doi:10.1016/0890-5401(91)90053-5 fatcat:nr2cayee5zgthi3dhsa2g4r6z4

Non-Obfuscated Unprovable Programs & Many Resultant Subtleties

John Case, Michael Ralston, Ulrich Kohlenbach
2016 Logical Methods in Computer Science  
The International Obfuscated C Code Contest was 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  ... 
doi:10.2168/lmcs-12(2:2)2016 fatcat:c4silpe5cfctfhf5eemuhxmppm

Mathematical Logic in Computer Science [article]

Assaf Kfoury
2018 arXiv   pre-print
Type theory emerged 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  ... 
arXiv:1802.03292v1 fatcat:bqajf55ih5aw3mxxo6tt5tjzkq

Hypercomputation by definition

Benjamin Wells
2004 Theoretical Computer Science  
It is not recursive, although 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  ... 
doi:10.1016/j.tcs.2003.12.011 fatcat:d3faa6rvkrf2nj3bhywab3nr54

Hypercomputation by definition

B WELLS
2004 Theoretical Computer Science  
It is not recursive, although 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  ... 
doi:10.1016/s0304-3975(03)00638-8 fatcat:p5hy7ivycja6fpah3ouorspogq

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

Samuel R. Buss, Alexander S. Kechris, Anand Pillay, Richard A. Shore
2001 Bulletin of Symbolic Logic  
The areas of recursion theory, proof theory and logic 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  ... 
doi:10.2307/2687773 fatcat:mdamfnfy55atzalpnh7ul3xv6m

Subject index volumes 1–200

1999 Theoretical Computer Science  
-, 207 graph, subgraph homeomorphism problem 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  ... 
doi:10.1016/s0304-3975(98)00319-3 fatcat:s22ud3iiqjht7lfbtc3zctk7zm

The prospects for mathematical logic in the twenty-first century [article]

Samuel R. Buss and Alexander S. Kechris and Anand Pillay and Richard A. Shore
2002 arXiv   pre-print
The areas of recursion theory, proof theory and logic 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  ... 
arXiv:cs/0205003v1 fatcat:i3rpwamx6nfdzi5kqkrt34twkq

The bounded arithmetic hierarchy

Keith Harrow
1978 Information and Control  
The bounded arithmetic predicates are 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  ... 
doi:10.1016/s0019-9958(78)90257-7 fatcat:aslt6dyy7fbk3l6xnzmzva4zk4
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