An Evaluation Semantics for Classical Proofs
| dc.contributor.author | Murthy, Chetan R. | en_US |
| dc.date.accessioned | 2007-04-23T17:53:51Z | |
| dc.date.available | 2007-04-23T17:53:51Z | |
| dc.date.issued | 1991-06 | en_US |
| dc.description.abstract | We show how to interpret classical proofs as programs in a way that agrees with the well-known treatment of constructive proofs as programs and moreover extends it to give a computational meaning to proofs claiming the existence of a value satisfying a recursive predicate. Our method turns out to be equivalent to H. Friedman's proof by "A-translation" of the conservative extention of classical over constructive arithmetic for $\Pi^{0}_{2}$ sentences. We show that Friedman's result is a proof-theoretic version of a semantics-preserving CPS-translation from a nonfunctional programming language (with the "control" (C, a relative of call/cc) operator) back to a functional programming language. We present a sound evaluation semantics for proofs in classical number theory (PA) of such sentences, as a modification the standard semantics for proofs in constructive number theory (HA). Our results soundly extend the proofs-as-programs paradigm to classical logics and to programs with C. | en_US |
| dc.format.extent | 1799794 bytes | |
| dc.format.extent | 423983 bytes | |
| dc.format.mimetype | application/pdf | |
| dc.format.mimetype | application/postscript | |
| dc.identifier.citation | http://techreports.library.cornell.edu:8081/Dienst/UI/1.0/Display/cul.cs/TR91-1213 | en_US |
| dc.identifier.uri | https://hdl.handle.net/1813/7053 | |
| dc.language.iso | en_US | en_US |
| dc.publisher | Cornell University | en_US |
| dc.subject | computer science | en_US |
| dc.subject | technical report | en_US |
| dc.title | An Evaluation Semantics for Classical Proofs | en_US |
| dc.type | technical report | en_US |