关于未定义值的类型化函数程序解释算法的不可比性

Proceedings of the YSU A: Physical and Mathematical Sciences Pub Date : 2018-08-15 DOI:10.46991/pysu:a/2018.52.2.109

D. Grigoryan

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摘要

本文研究了类型化函数程序的解释算法。解释算法基于替换、$ \beta $ -约简和规范$ \delta $ -约简。结果表明，对于未定义值($ \perp $ -incomparable)，已知的7种解释算法(FS (full substitution)、PES (parallel external substitution)、LES (left external substitution)、PIS (parallel inner substitution)、LIS (left inner substitution)、ACT (active algorithm)、PAS (passive algorithm))是两两不可比较的。

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ON INCOMPARABILITY OF INTERPRETATION ALGORITHMS OF TYPED FUNCTIONAL PROGRAMS WITH RESPECT TO UNDEFINED VALUE

In the paper the interpretation algorithms of typed functional programs are considered. The interpretation algorithm is based on substitution, $ \beta $-reduction and canonical $ \delta $-reduction. It is shown that seven known interpretation algorithms (FS (of full substitution), PES (of parallel external substitution), LES (of left external substitution), PIS (of parallel inner substitution), LIS (of left inner substitution), ACT (active algorithm), PAS (passive algorithm)) are pairwise incomparable with respect to undefined value ($ \perp $-incomparable).

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Proceedings of the YSU A: Physical and Mathematical Sciences

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