NDLI: Computational foundations of basic recursive function theory

Content Provider	IEEE Xplore Digital Library
Author	Constable, R.L. Smith, S.F.
Copyright Year	1988
Description	Author affiliation: Cornell Univ., Ithaca, NY, USA (Constable, R.L.; Smith, S.F.)
Abstract	The theory of computability often called basic recursive function theory is usually motivated and developed using Church's thesis. It is shown that there is an alternative computability theory in which some of the basic results on unsolvability become more absolute. Results on completeness become simpler, and many of the central concepts become more abstract. In this approach computations are viewed as mathematical objects, and the major theorems in recursion theory may be classified according to which axioms about computation are needed to prove them. The theory is a typed theory of functions over the natural numbers, and there are unsolvable problems in this setting independent of the existence of indexings. The unsolvability results are interpreted to show that the partial function concept serves to distinguish between classical and constructive type theories.
Starting Page	360
Ending Page	371
File Size	826905
Page Count	12
File Format	PDF
ISBN	0818608536
DOI	10.1109/LICS.1988.5133
Language	English
Publisher	Institute of Electrical and Electronics Engineers, Inc. (IEEE)
Publisher Date	1988-01-01
Access Restriction	Subscribed
Rights Holder	Institute of Electrical and Electronics Engineers, Inc. (IEEE)
Subject Keyword	Computer science Mathematics Indexing Computational modeling Context modeling Computation theory
Content Type	Text
Resource Type	Article

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