The Cooper Storage Idiom

Abstract

Cooper storage is a widespread technique for associating sentences with their meanings, used (sometimes implicitly) in diverse linguistic and computational linguistic traditions. This paper encodes the data structures and operations of cooper storage in the simply typed linear $$\lambda $$ -calculus, revealing the rich categorical structure of a graded applicative functor. In the case of finite cooper storage, which corresponds to ideas in current transformational approaches to syntax, the semantic interpretation function can be given as a linear homomorphism acting on a regular set of trees, and thus generation can be done in polynomial time.