Hidden Signature
Hidden signatures provide the basic vocabulary for describing a system, including the methods and attributes of its objects, and its data values.

A hidden signature (over a data algebra D) is a pair (H,), where H is a set of hidden sorts disjoint from the set V of visible sorts, and is an S = (H V)-sorted signature containing , such that

1. each f in of rank w,s with w in V* and s in V lies in , and
2. each f in of rank w,s has at most one element of H in w.
The first condition expresses data encapsulation, that all operations on data are already given. The second condition, called monadicity, says that operations depend on the state of at most one object: this expresses the locality of states of objects, i.e., that they can interact only through methods and attributes (see below).

We may abbreviate (H,) to just . If w in S* contains a hidden sort, then we call f in of sort s a method if s in H, and an attribute if s is in V.

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11 October 1996