From Higher Order Terms To Circuits

INTRODUCTION 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)): ffl 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. ffl Bounded fixed points: one can have the flexibility of fixed point definitions and termination at the same time (cf. (Schwichtenberg and Wainer, 1995)). ffl A notion of strict functionals as a tool to prove termination of higher order rewrite systems (cf. (van de Pol and Schwichtenberg, 1995)). Since this work is published already, we do not give details here but rather concentrate on another "appl