Abstract

Abstract. This paper reports the design and initial implementation of an extensive collection of libraries for automata theory and Turing machines in the functional programming languages SML and Haskell. Such an effort has two benefits: one is conceptual clarity, in the sense that computational concepts and construction algorithms match directly and faithfully to types and functions in the implementation, especially in terms of recursion; the other is conciseness and efficiency brought by the unusual features of these functional programming languages unimaginable in the traditional imperative setting. In SML, we provide a simulation of finite state machines and Turing machines by taking advantage of SML's structures, functors, and exceptional handling mechanism. The simplicity of this implementation makes it valuable for classroom use. In Haskell, we provide an implementation of deterministic and non-deterministic finite state machines, the conversion from the non-deterministic one to a deterministic one, state minimization, and constructions such as union, intersection, concatenation, and Kleene star on non-deterministic machines. Conversion from regular expressions to finite state machines can be achieved straightforwardly in terms of these constructions. The benefit of the Haskell implementation is the great freedom in the representation of actual automata to be used with the package. This freedom has been enhanced by using Multi-Parameter Type Class extensions of the Haskell type system to allow the various constructions to make very few assumptions about the data they use.

Citations