ISETL: a language for teaching discrete mathematics (abstract)

Abstract

ISETL is an interactive implementation and extension of SETL1, a programming language built around mathematical notation and objects, primarily sets and functions. Just as an introductory chemistry course uses a laboratory to provide an arena for experimenting, an introductory mathematics class could use ISETL to provide a workplace for its students.When children first begin their study of mathematics — counting and simple arithmetic — it is easy to provide them with concrete examples suitable for manipulation: coins, sheep, apples and oranges. As the level of mathematics increases, however, it becomes harder to provide direct experience. ISETL implements some of the common objects used in mathematics, and so provides a place for students to experiment with immediate feedback. It is important to notice that, unlike the experience gained from most general purpose programming languages, ISETL provides transferrable knowledge, because it uses standard mathematical notations and ideas. E.g., the primes less than 50: {p: p in [2..50] | forall i in [2..p-1] | p mod i/=0}By providing functions as first class objects, both as sets of ordered pairs and as computational objects, ISETL permits students to manipulate functions, providing examples of higher order mathematical structures (such as groups of functions). Aside from its original application as a laboratory for experimentation in Discrete Mathematics, ISETL has been used for teaching calculus, introductory programming, programming languages, and abstract algebra. The first class functions provide support for many of the paradigms of programming in a single familiar context. ISETL is in use in more than 100 schools. ISETL is available for UNIX, VMS, MSDOS, and the Macintosh. Write to the author for more information.