In [Plol] a powerdomain was defined which was intended as a kind of analogue of the powerset construction, but for (certain kinds) of cpos. For example the power-domain~(S±) of the flat cpo Si, formed from a set S, is the set {X! S~I(X#~) and

Type free lazy -calculus is enriched with angelic parallelism and demonic nondeterminism. Call-by-name and call-by-value abstractions are considered and the operational semantics is stated in terms of a must convergence predicate. We introduce a type assignment system with intersection and union types and we prove that the induced logical semantics is fully abstract.

ion and the operator "!" associate to the right: x oe 1 1 ; x oe 2 2 ; . . . ; x oe n n :M or even more abridged ~x oe stands for x oe 1 1 :x oe 2 2 . . . x oe n n :M and (oe 1 ; . . . ; oe n ) stands for oe 1 !(oe 2 !(. . . !(oe n\Gamma1 !oe n ) . . .)). Define oe n for n 2 N and oe 2 \Sigma by oe 0 := oe and oe n+1 := oe!oe n . ffl Instead of LM 1 . . . M n we mostly use the uncurry-notation L(M 1 ; . . . ; M n ). ffl Greek indices in the right upper corner stand for types. They are omitted, if the type of the term is evident or unmistakable. Obviously, each type can be written in the form oe = (oe 1 ; . . . ; oe n ; oe n+1 ) such that oe n+1 2 \Sigma 0 . 6 2 THE PROGRAMMING LANGUAGE PCF Definition 2.2 1. The set FV (M) of the free occuring variables in a term M is defined as follows: (a) For all x oe i 2 V set FV (x oe i ) := fx oe i g. (b) For all c 2 C set FV (c) := ;. (c) For all M oe!ø and N oe 2 (C ) set FV (MN) := FV (M) [ FV (N). (d) For...