Call-by-name linguistic side effects

We propose a typed call-by-name λ-calculus with shift, reset and strict functions and describe its linguistic applications, improving on the previous continuation-based analyses of quantification, binding, raised and in-situ wh-questions, binding in wh-questions, and superiority. The evaluation order is not fixed left-to-right: rather, it is determined by the demand for values exerted by reset and strict functions. Since functions can take general, effectful terms, our analyses need no thunks and similar type raising. The main improvement of the present analyses is in typing: assigning types both to terms and contexts and building types using connectives with clear logical interpretation. Types abstractly interpret operational semantics, and thus concisely describe all the effects that could occur in the evaluation of a term. Our main result is that both typing and call-by-name are necessary to correctly predict superiority and binding in wh-questions with topicalization, without resorting to thunking or type raising and thus maintaining the uniformity of the analyses. We have implemented the calculus including the type checking and mechanically verified all the analyses.