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Latest Articles

Consistent Subtyping for All

Consistent subtyping is employed in some gradual type systems to validate type conversions. The original definition by Siek and Taha serves as a guideline for designing gradual type systems with subtyping. Polymorphic types à la System F also induce a subtyping relation that relates polymorphic types to their instantiations.... (more)

Modular Product Programs

Many interesting program properties like determinism or information flow security are hyperproperties, that is, they relate multiple executions of the same program. Hyperproperties can be verified using relational logics, but these logics require dedicated tool support and are difficult to automate. Alternatively, constructions such as... (more)

Behavioural Equivalence via Modalities for Algebraic Effects

The article investigates behavioural equivalence between programs in a call-by-value functional language extended with a signature of (algebraic)... (more)

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Forthcoming Articles
A Theory of Slicing for Probabilistic Programs

We present a theory for slicing probabilistic imperative programs --containing random assignments, and "observe" statements (for conditioning) --represented as probabilistic control-flow graphs (pCFGs) whose nodes modify probability distributions. We show that such a representation allows direct adaptation of standard machinery such as data and control dependence, postdominators, relevant variables, etc. to the probabilistic setting. We separate the specification of slicing from its implementation: first we develop syntactic conditions that a slice must satisfy; next we prove that any such slice is semantically correct; finally we give an algorithm to compute the least slice. To generate smaller slices, we may in addition take advantage of knowledge that certain loops will terminate (almost) always. A key feature of our syntactic conditions is that they involve two disjoint slices such that the variables of one slice are probabilistically independent of the variables of the other. This leads directly to a proof of correctness of probabilistic slicing. In a companion article we show adequacy of the semantics of pCFGs with respect to the standard semantics of structured probabilistic programs.

Symbolic disintegration with a variety of base measures

Disintegration is a relation on measures and a transformation on programs that generalizes density and conditioning, two operations widely used for exact and approximate probabilistic inference. Existing program transformations that find a disintegration or density automatically are limited to a fixed base measure that is an independent product of Lebesgue and counting measures, so they are of no help in practical cases that require tricky reasoning about other base measures. We present the first disintegrator that handles variable base measures, including discrete-continuous mixtures, dependent products, and disjoint sums. By analogy to type inference, our disintegrator can check a given base measure as well as infer an unknown one that is principal. We derive the disintegrator and prove it sound by equational reasoning from semantic specifications. It succeeds in a variety of applications where disintegration and density had not been previously mechanized.

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