Type inference in stack based languages

We consider a language of operations which pass parameters by means of a stack. An algebra over the set of type signatures is introduced, which allows the type signature of a program to be obtained from the type signatures of its constituent operations.Although the theories apply in principle to any stack based language, they have been evolved with particular regard to the proposed ANSI Standard Forth language, which is currently implemented in a type free manner. We hope this work will stimulate an interest in Forth amongst those applying algebraic techniques in software engineering, and we hope to lay the theoretical foundations for implementing practical type checkers to support Forth.