Applying quantitative semantics to higher-order quantum computing

Finding a denotational semantics for higher order quantum computation is a long-standing problem in the semantics of quantum programming languages. Most past approaches to this problem fell short in one way or another, either limiting the language to an unusably small finitary fragment, or giving up important features of quantum physics such as entanglement. In this paper, we propose a denotational semantics for a quantum lambda calculus with recursion and an infinite data type, using constructions from quantitative semantics of linear logic

A Denotational Semantics for Communicating Unstructured Code

An important property of programming language semantics is that they should be compositional. However, unstructured low-level code contains goto-like commands making it hard to define a semantics that is compositional. In this paper, we follow the ideas of Saabas and Uustalu to structure low-level code. This gives us the possibility to define a compositional denotational semantics based on least fixed points to allow for the use of inductive verification methods. We capture the semantics of communication using finite traces similar to the denotations of CSP. In addition, we examine properties of this semantics and give an example that demonstrates reasoning about communication and jumps. With this semantics, we lay the foundations for a proof calculus that captures both, the semantics of unstructured low-level code and communication.Comment: In Proceedings FESCA 2015, arXiv:1503.0437

Metric Semantics and Full Abstractness for Action Refinement and Probabilistic Choice

This paper provides a case-study in the field of metric semantics for probabilistic programming. Both an operational and a denotational semantics are presented for an abstract process language L_pr, which features action refinement and probabilistic choice. The two models are constructed in the setting of complete ultrametric spaces, here based on probability measures of compact support over sequences of actions. It is shown that the standard toolkit for metric semantics works well in the probabilistic context of L_pr, e.g. in establishing the correctness of the denotational semantics with respect to the operational one. In addition, it is shown how the method of proving full abstraction --as proposed recently by the authors for a nondeterministic language with action refinement-- can be adapted to deal with the probabilistic language L_pr as well