Factorization and Normalization, Essentially

Beniamino Accattoli (1, 2) , Claudia Faggian (3) , Giulio Guerrieri (4)

1 PARSIFAL - Proof search and reasoning with logic specifications
2 PARTOUT - Automatisation et ReprésenTation: fOndation du calcUl et de la déducTion
3 IRIF (UMR_8243) - Institut de Recherche en Informatique Fondamentale
4 University of Bath [Bath]

λ-calculi come with no fixed evaluation strategy. Different strategies may then be considered, and it is important that they satisfy some abstract rewriting property, such as factorization or normalization theorems. In this paper we provide simple proof techniques for these theorems. Our starting point is a revisitation of Takahashi's technique to prove factorization for head reduction. Our technique is both simpler and more powerful, as it works in cases where Takahashi's does not. We then pair factorization with two other abstract properties, defining essential systems, and show that normalization follows. Concretely, we apply the technique to four case studies, two classic ones, head and the leftmost-outermost reductions, and two less classic ones, non-deterministic weak call-by-value and least-level reductions.

Domains: Computer Science [cs]

Beniamino Accattoli, Claudia Faggian, Giulio Guerrieri. Factorization and Normalization, Essentially. APLAS 2019 - 17th Asian Symposium on Programming Languages and Systems, Dec 2019, Bali, Indonesia. ⟨10.1007/978-3-030-34175-6_9⟩. ⟨hal-02411556⟩