From Higher Order Terms To Circuits

In his lecture at the congress, the first author gave a survey on some recent results relevant for computability theory in the context of partial continuous functionals (cf. (Scott, 1982; Ershov, 1977; Stoltenberg-Hansen et al., 1994)): An abstract definition of totality due to Berger (cf. (Berger, 1990; Berger, 1993) and (Stoltenberg-Hansen et al., 1994, Ch. 8.3)), and applications concerning density and effective density theorems. Bounded fixed points: one can have the flexibility of fixed point definitions and termination at the same time (cf. (Schwichtenberg and Wainer, 1995)). A notion of strict functionals as a tool to prove termination of higher order rewrite systems (cf. (van de Pol and Schwichtenberg, 1995)) .