Semantic models are presented for two simple imperative languages with higher order constructs. In the rst language the interesting notion is that of second order assignment x := s, for x a procedure variable and s a statement. The second language extends this idea by a form of higher order communication, with statements c ! s and c ? x, for c a channel. We develop operational and denotational ...

We show that function types which have only initial algebras for regular functors in the domains, i.e. first order function types, can be represented by terminal coalgebras for certain nested functors. The representation exploits properties of ω-limits and local ω-colimits.

Logic programs can be synthesized as a by-product of the planning of their verification proofs. This is achieved by using higher-order variables at the proof planning level, which become instantiated in the course of planning. We illustrate two uses of such variables in proof planning for program synthesis, one for synthesis proper and one for the selection of induction schemes. We demonstrate ...

Fold functions are a general mechanism for computing over recursive data structures. First-order folds compute results bottom-up. With higher-order folds, computations that inherit attributes from above can also be expressed. In this paper, we explore folds over a form of recursive higher-order function, called hyperfunctions, and show that hyperfunctions allow fold computations to coroutine ac...