A NON-DEFINABILITY RESULT FOR A PREDICATIONAL LANGUAGE WITH THE USUAL CONTROL

Abstract

A term calculus corresponding to pure prolog is introduced and extended by an if-then-else construct to obtain the expressiveness of pure prolog + cut. In contrast to functional terms which have a single value the evaluation of predicational terms leads to an enumeration of the several (finite or infinite) solutions. A user can control up to which point this stream of answers is computed and restrict his attention to a special position in this stream. We show that this can not be achieved inside the program. The addition of if-then-else offers the possibility to pick the first answer but this does not carry over to the second or later position. This is proved used the denotational semantics of the predicational language.