Shape Checking of Array Programs

Shape theory provides a framework for the study of data types in which shape and data can be manipulated separately. This paper is concerned with shape checking, i.e. the detection of shape errors, such as array bound errors, without handling the data. It can be seen as a form of partial evaluation in which data computations are ignored. We construct a simply-typed lambda-calculus that supports a vector type constructor, whose iteration yields types of arrays. It is expressive enough to construct all of the usual array operations. All shape errors in a term t can be detected by evaluating its shape #t which proceeds by rst eliminating all the data, and then evaluating in the usual way. Evaluation of #t will terminate if that of t does.