2013/06/10 by Silvia Ghilezan, Ghilezan, Silvia, Jelena Ivetic +5 · 1 citation
Computer Science · Mathematics · #FOS: Computer and information sciences #FOS: Mathematics #Logic (math.LO) #Logic in Computer Science (cs.LO) #cs.LO #math.LO
paper · pdf · doi:10.48550/arxiv.1306.2283
arXiv admin note: text overlap with arXiv:1112.3455
arxiv created 2013/06/10 · arxiv updated 2013/06/11
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 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.