EPIA'01

#### Abstract

In~\cite{TAH96} it was shown that it is possible to describe the set of normal inhabitants of a given type $\tau$, in the standard simple type system, using an infinitary extension of the concept of context-free grammar, which allows for an infinite number of non-terminal symbols as well as production rules. The set of normal inhabitants of $\tau$ corresponds then to the set of terms generated by this, possibly infinitary, grammar plus all terms obtained from those by $\eta$-reduction. In this paper we show that the set of normal inhabitants of a type $\tau$ can in fact be described using a standard (finite) context-free grammar, and more interestingly that normal inhabitants of types with the same structure are described by identical context-free grammars, up to renaming of symbols.