Linear higher-order pre-unification

Higher-Order Abstract Syntax, or HOAS, is a technique for using a higher-order logic as a metalanguage for an object language with binding operators. It avoids formalizing syntactic details related to variable binding. This paper gives an extension to ...

We present a technique for higher-order representation of substructural logics such as linear or modal logic. We show that such logics can be encoded in the (ordinary) Logical Framework, without any linear or modal extensions. Using this encoding, ...

In this paper we define a model theory and give a semantic proof of cut-elimination for ICTT, an intuitionistic formulation of Church's theory of types defined by Miller et al. and the basis for the λProlog programming language. Our approach, extending ...