Probabilistic Termination by Monadic Affine Sized Typing

Ugo Dal Lago (1, 2) , Charles Grellois (1)

1 FOCUS - Foundations of Component-based Ubiquitous Systems
2 UNIBO - Alma Mater Studiorum Università di Bologna = University of Bologna

We introduce a system of monadic affine sized types, which substantially generalise usual sized types, and allows this way to capture probabilistic higher-order programs which terminate almost surely. Going beyond plain, strong normalisation without losing soundness turns out to be a hard task, which cannot be accomplished without a richer, quantitative notion of types, but also without imposing some affinity constraints. The proposed type system is powerful enough to type classic examples of probabilistically terminating programs such as random walks. The way typable programs are proved to be almost surely terminating is based on reducibility, but requires a substantial adaptation of the technique.

Domaines: Logique en informatique [cs.LO]; Langage de programmation [cs.PL]

Ugo Dal Lago, Charles Grellois. Probabilistic Termination by Monadic Affine Sized Typing. ESOP 2017 - 26th European Symposium on Programming, Apr 2017, Uppsala, Sweden. ⟨hal-01635077⟩