Abstract
We introduce a natural deduction formulation for the Logic of Proofs, a refinement of modal logic S4 in which the assertion □ A 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 λ I that internalises intensional information on how a term is computed. In the same way that the Logic of Proofs internalises its own derivations, λ I internalises its own computations. Confluence and strong normalisation of λ I is proved. This system serves as the basis for the study of type theories that internalise intensional aspects of computation.
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Artemov, S., Bonelli, E. (2007). The Intensional Lambda Calculus. In: Artemov, S.N., Nerode, A. (eds) Logical Foundations of Computer Science. LFCS 2007. Lecture Notes in Computer Science, vol 4514. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-72734-7_2
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DOI: https://doi.org/10.1007/978-3-540-72734-7_2
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