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Abstract: In previous work the author has introduced a lambda calculus SLR with modal and linear types which serves as an extension of Bellantoni-Cook's function algebra BC to higher types. It is a step towards a functional programming language in which all programs run in polynomial time. In this paper we develop a semantics of SLR using BCK-algebras consisting of certain polynomial-time algorithms. It will follow from this semantics that safe recursion with arbitrary result type built up from N and (... (Update)
Context of citations to this paper: More
...of logical systems. Systems with recursion in all nite types characterizing polynomial time were given by Bellantoni et al. 5] and Hofmann [12], based on the rst order system of Bellantoni and Cook [4] We de ne an analogous system that characterizes NC while allowing an...
.... bounded arithmetic [2] polynomial time subsytems of G odel s T [6, 1] and systems for other complexity classes [4] In our own work [14, 13, 18, 17, 16] we substantially extended these systems to encompass higher order functions and datatypes such as lists and trees. The key...
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9: A New Recursion-Theoretic Characterization of the Polytime Functions (context) - Bellantoni, Cook - 1992
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BibTeX entry: (Update)
Martin Hofmann. Safe recursion with higher types and bck-algebra. Annals of Pure and Applied Logic, 2000. to appear. http://citeseer.ist.psu.edu/hofmann00safe.html More
@article{ hofmann00safe,
author = "Hofmann",
title = "Safe Recursion with Higher Types and {BCK}-algebra",
journal = "ANNALSPAL: Annals of Pure and Applied Logic",
volume = "104",
year = "2000",
url = "citeseer.ist.psu.edu/hofmann00safe.html" }
Citations (may not include all citations):562 Categories for the Working Mathematician (context) - Lane - 1971
359 Introduction to Higher-Order Categorical Logic (context) - Lambek, Scott - 1986
96 New recursion-theoretic characterization of the polytime fun.. (context) - Bellantoni, Cook - 1992
58 Linear types and non size-increasing polynomial time computa.. - Hofmann - 1999
38 The intrinsic computational difficulty of functions (context) - Cobham - 1965
38 Ramified Recurrence and Computational Complexity IV: Predica.. (context) - Leivant, Marion - 1997
38 Ramified Recurrence and Computational Complexity II: Substit.. (context) - Leivant, Marion - 1995
30 Information and Control (context) - Statman, the et al. - 1985
15 Syntax and semantics of dependent types - Hofmann - 1997
11 An application of category-theoretic semantics to the charac.. - Hofmann - 1997
9 Equations for Defining Poly-time Functions (context) - Caseiro - 1997
7 Extensional constructs in intensional type theory (context) - Hofmann - 1997
7 linear lambda calculus with applications to BellantoniCook s.. (context) - Hofmann, modal - 1998
7 Lambda calculus characterisations of polytime (context) - Leivant, Marion - 1993
7 and Linearity in Higher Type Recursion (context) - Bellantoni, Niggl et al. - 1999
5 a modal lambda calculus - Pfenning, Wong - 1995
5 available electronically under http://thelonius (context) - Clote, function - 1996
4 Habilitation thesis (context) - Hofmann, for - 1999
1 modal lambda calculus (context) - Hofmann, linear - 1998
The graph only includes citing articles where the year of publication is known.
Documents on the same site (http://www.dcs.ed.ac.uk/home/mxh/papers.html): More
A Simple Model for Quotient Types - Hofmann (1995) (Correct)
Type Systems For Polynomial-Time Computation - Hofmann (1998) (Correct)
On the Interpretation of Type Theory in Locally Cartesian Closed.. - Hofmann (1994) (Correct)
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