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

Abstract

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).