## Luca Cardelli and Xavier Leroy.
Abstract types and the dot notation.
In M. Broy and C. B. Jones, editors, *Proceedings IFIP TC2
working conference on programming concepts and methods*, pages 479-504.
North-Holland, 1990.

We investigate the use of the dot notation in the context of
abstract types. The dot notation - that is, a.f referring to
the operation f provided by the abstraction a - is used by
programming languages such as Modula-2 and CLU. We compare
this notation with the Mitchell-Plotkin approach, which draws
a parallel between type abstraction and (weak) existential
quantification in constructive logic. The basic operations on
existentials coming from logic give new insights about the
meaning of type abstraction, but differ completely from the
more familiar dot notation. In this paper, we formalize simple
calculi equipped with the dot notation, and relate them to a
more classical calculus a la Mitchell and Plotkin. This work
provides some theoretical foundations for the dot notation,
and suggests some useful extensions.

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