Confluence in probabilistic rewriting

ALEJANDRO DÍAZ-CARO; GUIDO MARTÍNEZ

Electronic Notes in Theoretical Computer Science

Elsevier

Año: 2018 vol. 338 p. 115 - 131

1571-0661

Driven by the interest of reasoning about probabilistic programming languages, we set out to study a notion of unicity of normal forms for them. To provide a tractable proof method for it, we define a property of distribution confluence which is shown to imply the desired unicity and further properties. We then carry over several criteria from the classical case, such as Newman?s lemma, to simplify proving confluence in concrete languages. Using these criteria, we obtain simple proofs of confluence for lambda1, an affine probabilistic lambda-calculus, and for Q*, a quantum programming language for which a related property has already been proven in the literature. Lastly, we show how distribution confluence implies unicity even for distributions that are only reached asymptotically.