Foundations of Strong Call by Need

Thibaut Balabonski (LRI, France and University of Paris-Sud, France) gives the third talk in the second panel, Foundations of Higher-Order Programming, on the 2nd day of the ICFP conference. Co-written by Pablo Barenbaum (University of Buenos Aires, Argentina/IRIF, France/University of Paris Diderot, France), Eduardo Bonelli (CONICET, Argentina/Universidad Nacional de Quilmes, Argentina), Delia Kesner (IRIF/University of Paris Diderot, France). We present a call-by-need strategy for computing strong normal forms of open terms (reduction is admitted inside the body of abstractions and substitutions, and the terms may contain free variables), which guarantees that arguments are only evaluated when needed and at most once. The strategy is shown to be complete with respect to beta-reduction to strong normal form. The proof of completeness relies on two key tools: (1) the definition of a strong call-by-need calculus where reduction may be performed inside any context, and (2) the use of non-idempotent intersection types. More precisely, terms admitting a beta-normal form in pure lambda calculus are typable, typability implies (weak) normalisation in the strong call-by-need calculus, and weak normalisation in the strong call-by-need calculus implies normalisation in the strong call-by-need strategy. Our (strong) call-by-need strategy is also shown to be conservative over the standard (weak) call-by-need.