Session types guarantee that message-passing processes adhere to predefined communication protocols. Prior work on session types has focused on deterministic languages but many message-passing systems, such as Markov chains and randomized distributed algorithms, are probabilistic. To implement and analyze such systems, this article develops the meta theory of probabilistic session types with an application focus on automatic expected resource analysis. Probabilistic session types describe probability distributions over messages and are a conservative extension of intuitionistic (binary) session types. To send on a probabilistic channel, processes have to utilize internal randomness from a probabilistic branching or external randomness from receiving on a probabilistic channel. The analysis for expected resource bounds is smoothly integrated with the type system and is a variant of automatic amortized resource analysis. Type inference relies on linear constraint solving to automatically derive symbolic bounds for various cost metrics. The technical contributions include the meta theory that is based on a novel nested multiverse semantics and a type-reconstruction algorithm that allows flexible mixing of different sources of randomness without burdening the programmer with complex type annotations. The type system has been implemented in the language NomosPro with linear-time type checking. Experiments demonstrate that NomosPro is applicable in different domains such as cost analysis of randomized distributed algorithms, analysis of Markov chains, probabilistic analysis of amortized data structures and digital contracts. NomosPro is also shown to be scalable by (i) implementing two broadcast and a bounded retransmission protocol where messages are dropped with a fixed probability, and (ii) verifying the limiting distribution of a Markov chain with 64 states and 420 transitions.
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Raising Expectations: Automating Expected Cost Analysis with Types
This article presents a type-based analysis for deriving upper bounds
on the expected execution cost of probabilistic programs.
The analysis is naturally compositional, parametric in the cost
model, and supports higher-order functions and inductive data types.
The derived bounds are multivariate polynomials that are functions of
data structures.
Bound inference is enabled by local type rules that reduce type
inference to linear constraint solving.
The type system is based on the potential method of amortized analysis
and extends automatic amortized resource
analysis (AARA) for deterministic programs.
A main innovation is that bounds can contain symbolic probabilities,
which may appear in data structures and function arguments.
Another contribution is a novel soundness proof that establishes the
correctness of the derived bounds with respect to a distribution-based
operational cost semantics that also includes nontrivial diverging
behavior.
For cost models like time, derived bounds imply termination with
probability one.
To highlight the novel ideas, the presentation focuses on linear
potential and a core language.
However, the analysis is implemented as an extension of Resource Aware
ML and supports polynomial bounds and user defined data structures.
The effectiveness of the technique is evaluated by analyzing the
sample complexity of discrete distributions
and with a novel average-case estimation for deterministic programs
that combines expected cost analysis with statistical methods.
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- NSF-PAR ID:
- 10163967
- Date Published:
- Journal Name:
- Proceedings of the ACM on programming languages
- ISSN:
- 2475-1421
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
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