Abstract

. In lazy functional languages, ? is typically an element of every type. While this provides great flexibility, it also comes at a cost. In this paper we explore the consequences of allowing unpointed types in a lazy functional language like Haskell. We use the type (and class) system to keep track of pointedness, and show the consequences for parametricity and for controlling evaluation order and unboxing. 1 Introduction Ever since Scott and others showed how to use pointed CPOs (i.e. with bottoms) to give meaning to general recursion, both over values (including functions), and over types themselves, functional languages seem to have been wedded to the concept. Languages like Haskell [5] model types by appropriate CPOs and, because non-terminating computations can happen at any type, all the CPOs are pointed. This gives significant flexibility. In particular, values of any type may be defined using recursion. 1.1 Parametricity There are associated costs, however. When reason...

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