Probabilistic Termination by Monadic Affine Sized Typing

Ugo Dal Lago 1, 2 Charles Grellois 3
2 FOCUS - Foundations of Component-based Ubiquitous Systems
CRISAM - Inria Sophia Antipolis - Méditerranée , DISI - Dipartimento di Informatica - Scienza e Ingegneria [Bologna]
Abstract : 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.
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Ugo Dal Lago, Charles Grellois. Probabilistic Termination by Monadic Affine Sized Typing. ACM Transactions on Programming Languages and Systems (TOPLAS), ACM, 2019, 41 (2), pp.1-65. ⟨10.1145/3293605⟩. ⟨hal-02399423⟩

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