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Abstract: In this note, we reprove a theorem of Statman that deciding the fij-equality of two firstorder typable -terms is not elementary recursive [Sta79]. The basic idea of our proof, like that of Statman's, is the Henkin quantifier elimination procedure [Hen63]. However, our coding is much simpler, and easy to understand. 1 Introduction A well known theorem of Richard Statman states that if we have two -terms that are first-order typable, deciding whether the terms reduce to the same normal form is... (Update)
Context of citations to this paper: More
...of TLC. That more expressive power is possible follows from the fact that provably hard decision problems can be embedded in TLC, see [37, 33], and that different typings allow exponentiation [19] One way of expressing all of PTIME, while avoiding the anomalies associated...
...the basic expressibility analysis in Section 3. For more details on the analysis of expressibility we refer the reader to [44, 45, 17, 37, 23, 24, 25]. The expressive power of TLC was originally analyzed in terms of computations on simply typed Church numerals (see, e.g. 4,...
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15: The Inherent Computational Complexity of Theories of Ordered Sets (context) - Meyer - 1974
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BibTeX entry: (Update)
H.G. Mairson. A Simple Proof of a Theorem of Statman. TCS, 103 (1992), pp. 387--394. http://citeseer.ist.psu.edu/mairson92simple.html More
@article{ mairson92simple,
author = "Harry G. Mairson",
title = "A simple proof of a theorem of {Statman}",
journal = "Theoretical Computer Science",
volume = "103",
number = "2",
pages = "387--394",
year = "1992",
url = "citeseer.ist.psu.edu/mairson92simple.html" }
Citations (may not include all citations):146 Computers and Intractibility: A Guide to the Theory of NP-Co.. (context) - Garey, Johnson - 1979
137 Introduction to Combinators and -Calculus (context) - Hindley, Seldin - 1986
32 Unification and ML type reconstruction - Kanellakis, Mairson et al. - 1991
24 The complexity of type inference for higher-order typed lamb.. - Henglein, Mairson - 1991
20 The typed -calculus is not elementary recursive (context) - Statman - 1979
18 The inherent computational complexity of theories of ordered.. (context) - Meyer - 1974
17 rd Annual ACM Symposium on the Theory of Computing (context) - Cook, of
13 A theory of propositional types (context) - Henkin - 1963
13 Journal of Symbolic Logic (context) - Statman, invariance - 1982
The graph only includes citing articles where the year of publication is known.
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