Data-Oblivious Stream Productivity

Abstract

We are concerned with demonstrating productivity of specifications of infinite streams of data, based on orthogonal rewrite rules. In general, this property is undecidable, but for restricted formats computable sufficient conditions can be obtained. The usual analysis, also adopted here, disregards the identity of data, thus leading to approaches that we call data-oblivious. We present a method that is provably optimal among all such data-oblivious approaches. This means that in order to improve on our algorithm one has to proceed in a data-aware fashion. 3

Well-Definedness of Streams by Termination

“…Another closely related topic is productivity of stream specifications, as studied by [3]. Productive stream specifications are always well-defined.…”

“…Conversely we will give an example (Example 4) of a stream specification that is well-defined, but not productive. Our format of stream specifications is strongly inspired by [3]. In [3] a technique is developed for establishing productivity fully automatically for a restricted class of stream specifications.…”

“…Our format of stream specifications is strongly inspired by [3]. In [3] a technique is developed for establishing productivity fully automatically for a restricted class of stream specifications. In particular, only a very mild type of nesting in the right hand sides of the rule is allowed.…”

A Tool Proving Well-Definedness of Streams Using Termination Tools

“…For instance, productivity of M of the specification M = 1 : even(zip(M, M )) zip(a : s, t) = a : zip(t, s) even(a : s) = a : odd(s) odd(a : s) = even(s) is easily proved by the tool of [1], while our approach fails to prove well-definedness.…”

“…The first is based on the well-known property that productivity implies well-definedness. An approach to prove productivity is given in [1], together with a corresponding tool. The second s by proving equality of two copies of the same specification by the tool Circ [4].…”