An Improved Extensionality Criterion for Higher-Order Logic Programs

Extensional Higher-Order Logic Programming

“…However, the semantics of hoapata programs defined in Bezem [2001] appears to differ significantly from the semantics of H. As it was pointed out to us by one of the reviewers, one important difference can be seen when considering queries with uninstantiated predicate variables. More specifically, given the program: p(Q):-Q(0),Q(s(0)).…”

“…Apart from the results of Wadge [1991] 7 , the only other work that has come to our attention is that of M. Bezem [Bezem 1999[Bezem , 2001, who considers higher-order logic programming languages with syntax similar to that of Wadge [1991].…”

“…In Bezem [2001] a notion of extensionality is defined (called the extensional collapse) and it is demonstrated that many logic programs are extensional under this notion; however, this notion appears to differ from classical extensionality and has a more proof-theoretical flavor.…”

“…The "hoapata" programs defined in Bezem [2001] are higher-order logic programs in which the higher-order arguments (hoa) can only be passed (p), applied (a) and/or thrown away (ta). In particular, all higher-order arguments in the head of a clause, are distinct variables.…”

“…the query ←p(R) will not return any answer under the approach of Bezem [2001]. Under our semantics, we will get basic expressions (representing sets), as discussed in the previous sections.…”