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摘要
Since it was realized that the Curry-Howard isomorphism can be extended to the case of classical logic as well, several calculi have appeared as candidates for the encodings of proofs in classical logic. One of the most extensively studied among them is the lambda mu-calculus of Parigot [Par.92]. In this paper, based on the result of Xi presented for the lambda-calculus [Xi.99], we give an upper bound for the lengths of the reduction sequences in the lambda mu-calculus extended with the rho- and theta-rules. Surprisingly, our results show that the new terms and the new rules do not add to the computational complexity of the calculus despite the fact that mu-abstraction is able to consume an unbounded number of arguments by virtue of the mu-rule.
- 出版日期2018
