Simulations are widely-used notions of program refinement. This paper discusses and compares several of them, in particular notions of simulation that are both weak and sensitive to divergence. Complex simulation proofs performed in proof assistants, for instance in a verified compilation setting, often rely on variants of normed simulation, which is not complete with respect to divergence-sensitive weak simulation. We propose to bridge this gap with μdiv-simulation, a novel notion of simulation that is equivalent to classical divergence-sensitive weak simulation, and designed to be as comfortable to use as modern characterizations of normed simulation. We then define a parameterized notion of simulation that covers strong simulation, weak simulation, μdiv-simulation, and 9 more notions of simulation, and jointly establish various “up-to” reasoning techniques for these 12 notions. Our results are formalized in Rocq and instantiated on two case studies: Choice Trees and a CompCert pass. Verified compilation is a major motivation for our study, but because we work with an abstract LTS setting, our results are also relevant to other fields that make use of divergence-sensitive weak simulation, such as model checking.

Monadic interpreters have gained attention as a powerful tool for modeling and reasoning about first order languages. In particular in the Coq ecosystem, the Choice Tree (CTree) library provides generic tools to craft such interpreters in presence of divergence, stateful effects, failure, and non-determinism. This monadic approach allows the definition of semantics for programming languages that are modular in its effects, compositional w.r.t. its syntax, and executable. This paper demonstrates the use of CTrees to formalize a semantics for concurrency and weak memory models. We instantiate the approach over a minimal concurrent subset of LLVM IR. Our semantics is built in successive stages, interpreting each aspect of the semantics separately. In particular, a stage encodes multi-threading as an interleaving semantics, and another implements a weak memory model that supports various LLVM memory orderings. Furthermore, the modularity of the approach makes it possible to plug a different source language or memory model by changing a single interpretation phase. By leveraging the notions of (bi)similarity on CTrees, we establish the equational theory of our constructions, show how to transport equivalences through our layered construction, and prove simulation results between memory models. Finally, our model is executable, hence the semantics can be tested by extraction to OCaml.

Abstract This paper introduces Choice Trees (CTrees), a monad for modeling nondeterministic, recursive, and impure programs in Rocq . Inspired by Xia et al .’s ((2019) Proc. ACM Program. Lang. 4 (POPL)) ITrees, this novel data structure embeds computations into coinductive trees with three kinds of nodes: external events, internal steps, and delayed branching. This structure allows us to provide shallow embedding of denotational models with nondeterministic choice in the style of ccs , while recovering an inductive LTS view of the computation. CTrees leverage a vast collection of bisimulation and refinement tools well-studied on LTSs, with respect to which we establish a rich equational theory. We connect CTrees to the ITrees infrastructure by showing how a monad morphism embedding the former into the latter permits using CTrees to implement nondeterministic effects. We demonstrate the utility of CTrees by using them to model concurrency semantics in two case studies: ccs and cooperative multithreading.

In this paper we introduce FicWebBoard, a learning concept and accompanying online platform that allows teaching programming languages to highly heterogeneous groups of students. Students are given great freedom, in particular in their choice of programming languages, but not at the cost of the quality of supervision as they are still under a certain hidden control. Gamification and the opportunity to participate to a challenge (an optional competition), also help to make the concept attractive to students. This original approach targets students with basic knowledge about programming, and allows them to earn deeper or wider programming knowledge. To validate the approach, we designed a survey to collect feedback from past students after using this approach for seven years.

This paper introduces ctrees, a monad for modeling nondeterministic, recursive, and impure programs in Coq. Inspired by Xia et al.'s itrees, this novel data structure embeds computations into coinductive trees with three kind of nodes: external events, and two variants of nondeterministic branching. This apparent redundancy allows us to provide shallow embedding of denotational models with internal choice in the style of CCS, while recovering an inductive LTS view of the computation. ctrees inherit a vast collection of bisimulation and refinement tools, with respect to which we establish a rich equational theory. We connect ctrees to the itree infrastructure by showing how a monad morphism embedding the former into the latter permits to use ctrees to implement nondeterministic effects. We demonstrate the utility of ctrees by using them to model concurrency semantics in two case studies: CCS and cooperative multithreading.