Le 14 mai 2012, à 14h en salle B311, le séminaire LCR accueille Beniamino Accattoli (LIX).
In some works in collaboration with Stefano Guerrini and Delia Kesner I developed a new approach to explicit substitutions, arising from Linear Logic proof-nets. The idea is to design calculi mimicking closely the dynamics of the graphical cut-elimination rules. Proof-nets and terms have very different notions of locality: this fact induce non-local, "at a distance" rewriting rules on terms. Substitution calculi at a distance are half-way lambda calculus and typical explicit substitution calculi: they retain most of the simplicity of lambda calculus, keeping the subtleties and the finer evaluation of explicit substitutions. In a series of recent works (some of which are joint works with Delia Kesner, Luca Paolini or Ugo Dal Lago) I explored systematically the rewriting theory of these calculi. In the talk I will survey the problems I studied (confluence, preservation of strong normalization, sigma-equivalence, developments, solvability, factorization, standardization, residuals) and the results I obtained, showing how they provide new understandings of classical notions and results - and sometimes even new results - in the theory of lambda-calculus.