Abstraction and Verification in Alphard: Defining
and Specifying Iteration and Generators
The Alphard "form" provides the programmer with
a great deal of control over the implementation 
of abstract data types.  In this paper the abstraction techniques
are extended from simple data representation 
and function definition to the iteration statement, the
most important poin t of interaction between data 
and the control structure of the language itself.  A
means of specializing Alphard's loops to operate 
on abstract entities without explicit dependence on the
representation of those entities is in troduced. 
 Specification and verification techniques that allow
the properties of the generators for such iterations 
to be expressed in the form of proof rules are developed.
 Results are obtained that for common special 
cases of these loops are essentially identical to the
corresponding constructs in other languages.  A 
means of showing that a generator will terminate is also provided.
CACM August, 1977
Shaw, M.
Wulf, W. A.
