Types by Need

Beniamino Accattoli (1, 2) , Giulio Guerrieri (3) , Maico Leberle (4, 5, 2)

1 PARSIFAL - Proof search and reasoning with logic specifications
2 PARTOUT - Automatisation et ReprésenTation: fOndation du calcUl et de la déducTion
3 Department of Computer Science [Bath]
4 Inria Saclay - Ile de France
5 LIX - Laboratoire d'informatique de l'École polytechnique [Palaiseau]

A cornerstone of the theory of λ-calculus is that intersection types characterise termination properties. They are a flexible tool that can be adapted to various notions of termination, and that also induces adequate denotational models. Since the seminal work of de Carvalho in 2007, it is known that multi types (i.e. non-idempotent intersection types) refine intersection types with quantitative information and a strong connection to linear logic. Typically, type derivations provide bounds for evaluation lengths, and minimal type derivations provide exact bounds. De Carvalho studied call-by-name evaluation, and Kesner used his system to show the termination equivalence of call-by-need and call-by-name. De Carvalho's system, however, cannot provide exact bounds on call-by-need evaluation lengths. In this paper we develop a new multi type system for call-by-need. Our system produces exact bounds and induces a denotational model of call-by-need, providing the first tight quantitative semantics of call-by-need.

Domaines: Logique en informatique [cs.LO]

Beniamino Accattoli, Giulio Guerrieri, Maico Leberle. Types by Need. ESOP 2019 - 28th European Symposium on Programming, Apr 2019, Prague, Czech Republic. ⟨10.1007/978-3-030-17184-1_15⟩. ⟨hal-02415758⟩