A Context-Free Grammar Representation for Normal Inhabitants of Types in TAlambda

Authors:
Sabine Broda;Luís Damas
Affiliations:
-;-
Venue:
EPIA '01 Proceedings of the10th Portuguese Conference on Artificial Intelligence on Progress in Artificial Intelligence, Knowledge Extraction, Multi-agent Systems, Logic Programming and Constraint Solving
Year:
2001

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Abstract

In [10] it was shown that it is possible to describe the set of normal inhabitants of a given type Τ, 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 Τ corresponds then to the set of terms generated by this, possibly infinitary, grammar plus all terms obtained from those by η-reduction. In this paper we show that the set of normal inhabitants of a type Τ 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.