Infinitary Algebraic Specifications for Stream Algebras (original) (raw)

. A stream is an infinite sequence of data from a set A. A wide variety of algorithms and architectures operate continuously in time, producing streams of data, for example: systolic arrays, data-flow machines, neural networks and cellular automata. Also many models of real number computation use streams. In this paper we study the construction of an algebra ¯ A of streams over a many-sorted algebra A of data. In particular, we show how an initial algebra specification for ¯ A can be constructed from one for A. One problem is that ¯ A is uncountable even when A is finite. To handle this, we work with infinitary terms called stream terms, and infinitary formulae that generalise conditional equations, called !-conditional stream equations . 0 Introduction A stream ff is an infinite sequence ff(0); ff(1); : : : of data from a set A. A variety of algorithms and architectures operate continuously in time, producing streams of data, for example: systolic arrays, data-flow machines, neur...