A journey through resource control lambda calculi and explicit substitution using intersection types (an account) [article]

Silvia Ghilezan, Jelena Ivetic, Pierre Lescanne, Silvia Likavec
2013 arXiv   pre-print
In this paper we invite the reader to a journey through three lambda calculi with resource control: the lambda calculus, the sequent lambda calculus, and the lambda calculus with explicit substitution. All three calculi enable explicit control of resources due to the presence of weakening and contraction operators. Along this journey, we propose intersection type assignment systems for all three resource control calculi. We recognise the need for three kinds of variables all requiring different
more » ... kinds of intersection types. Our main contribution is the characterisation of strong normalisation of reductions in all three calculi, using the techniques of reducibility, head subject expansion, a combination of well-orders and suitable embeddings of terms.
arXiv:1306.2283v1 fatcat:5d5jdpwuynfavaquqqbpnwzx4q