We introduce a natural deduction formulation for the Logic of Proofs, a refinement of modal logic S4 in which the assertion PA is replaced by [[s]]A whose intended reading is “s...
We study contexts (terms with holes) by proposing a ‘λcalculus with holes’. It is very expressive and can encode programming constructs apparently unrelated to contexts, incl...
Abstract. While many higher-order interactive theorem provers include a choice operator, higher-order automated theorem provers currently do not. As a step towards supporting autom...
—We propose a mathematical framework for step indexed realizability semantics of a call-by-value polymorphic lambda calculus with recursion, existential types and recursive types...
This paper brings together two lines of research: implicit characterization of complexity classes by Linear Logic (LL) on the one hand, and computation over an arbitrary ring in t...