New directions in type-theoretic grammars

Abstract

This paper argues for the idea that in describing language we should follow Haskell Curry in distinguishing between the structure of an expression and its appearance or manifestation. It is explained how making this distinction obviates the need for directed types in type-theoretic grammars and a simple grammatical formalism is sketched in which representations at all levels are lambda terms. The lambda term representing the abstract structure of an expression is homomorphically translated to a lambda term representing its manifestation, but also to a lambda term representing its semantics. © 2009 The Author(s).