The Intensional Lambda Calculus

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 is a proof of A”. A term calculus for this formulation yields a typed lambda calculus λI that internalises intensional information on how a term is computed. In the same way that the Logic of Proofs internalises its own derivations, λI internalises its own computations. Confluence and strong normalisation of λI is proved. This system serves as the basis for the study of type theories that internalise intensional aspects of computation.

• Type: Conference
• Year: 2007
• Where: LFCS
• Authors: Sergei N. Artëmov, Eduardo Bonelli
• Keywords: LFCS 2007, Modal Logic S4, Natural Deduction Formulation, Typed Lambda Calculus