Abstract

The aim of this thesis is to give a new understanding of sequential computations in higher types. We present a new computation model for higher types based on a game describing the interaction between a functional and its arguments. The functionals which may be described in this way are called hereditarily sequential. We show that this computation model captures exactly the notion of computability in higher types introduced by Kleene in his pioneering work starting 1959. We study the order structure of the hereditarily sequential functionals and discuss the occurring difficulties. These functionals form a fully abstract model for PCF and we discuss which problems remain still open for a satisfactory solution to the full abstraction problem of PCF. Zusammenfassung Ziel dieser Arbeit ist es, eine neue Beschreibung sequentieller Berechnungen in hoheren Typen zu geben. Wir stellen dazu ein neues Berechnungsmodell fur hohere Typen vor, in dem die Interaktion zwischen einem Funktional und se...

Citations