Abstract
We present a quantitative analysis of random combinatory logic terms. Our main goal is to investigate likelihood of semantic properties of random combinators. We show that asymptotically almost all weakly normalizing terms are not strongly normalizing. Moreover, we present a proof that asymptotically almost all strongly normalizing terms are not in normal form. We also prove that asymptotically almost all normal forms in combinatory logic are not typeable.
This work was supported within the grant 2013/11/B/ST6/0095 funded by the Polish National Science Center.
K. Grygiel—This author was supported by funding from the Jagiellonian University within the SET project. The project is co-financed by the European Union.
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Bendkowski, M., Grygiel, K., Zaionc, M. (2015). Asymptotic Properties of Combinatory Logic. In: Jain, R., Jain, S., Stephan, F. (eds) Theory and Applications of Models of Computation. TAMC 2015. Lecture Notes in Computer Science(), vol 9076. Springer, Cham. https://doi.org/10.1007/978-3-319-17142-5_7
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