Unary PCF is Decidable

We show that unary PCF, a very small fragment of Plotkin's PCF [7], has a decidable observational pre-order, and that its fully abstract model is effectively presentable. This is in marked contrast to larger fragments, where corresponding results fail [4]. The techniques used are adaptions of those of Padovani [5], who applied them to the minimal model of the simply typed lambda calculus.