J-Calc: a typed lambda calculus for intuitionistic justification logic

In this paper we offer a system J-Calc that can be regarded as a typed λ-calculus for the {→, ⊥} fragment of Intuitionistic Justification Logic. We offer different interpretations of J-Calc, in particular, as a two phase proof system in which we proof check the validity of deductions of a theory T based on deductions from a stronger theory T and computationally as a type system for separate compilations. We establish some first metatheoretic results