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We present a formalisation in Agda of the theory of concurrent transitions, residuation and causal equivalence of traces for the π-calculus. Our formalisation employs de Bruijn indices and dependently typed syntax, and aligns the ‘proved transitions’ proposed by Boudol and Castellani in the context of CCS with the proof terms naturally present in Agda's representation of the labelled transition relation. Our main contributions are proofs of the ‘diamond lemma’ for the residuals of concurrent transitions and a formal definition of equivalence of traces up to permutation of transitions.In the π-calculus, transitions represent propagating binders whenever their actions involve bound names. To accommodate these cases, we require a more general diamond lemma where the target states of equivalent traces are no longer identical, but are related by abraidingthat rewires the bound and free names to reflect the particular interleaving of events involving binders. Our approach may be useful for modelling concurrency in other languages where transitions carry meta-data sensitive to particular interleavings, such as dynamically allocated memory addresses.

Program slicing provides explanations that illustrate how program outputs were produced from inputs. We build on an approach introduced in prior work by Perera et al., where dynamic slicing was defined for pure higher-order functional programs as a Galois connection between lattices of partial inputs and partial outputs. We extend this approach to imperative functional programs that combine higher-order programming with references and exceptions. We present proofs of correctness and optimality of our approach and a proof-of-concept implementation and experimental evaluation., Full version of ICFP 2017 paper, with appendices

Provenance is an increasing concern due to the ongoing revolution in sharing and processing scientific data on the Web and in other computer systems. It is proposed that many computer systems will need to become provenance-aware in order to provide satisfactory accountability, reproducibility, and trust for scientific or other high-value data. To date, there is not a consensus concerning appropriate formal models or security properties for provenance. In previous work, we introduced a formal framework for provenance security and proposed formal definitions of properties called disclosure and obfuscation.In this article, we study refined notions of positive and negative disclosure and obfuscation in a concrete setting, that of a general-purpose programing language. Previous models of provenance have focused on special-purpose languages such as workflows and database queries. We consider a higher-order, functional language with sums, products, and recursive types and functions, and equip it with a tracing semantics in which traces themselves can be replayed as computations. We present an annotation-propagation framework that supports many provenance views over traces, including standard forms of provenance studied previously. We investigate some relationships among provenance views and develop some partial solutions to the disclosure and obfuscation problems, including correct algorithms for disclosure and positive obfuscation based on trace slicing.