This tutorial aims to introduce Hierarchical Linear Modeling (HLM). A simple explanation of HLM is provided that describes when to use this statistical technique and identifies key factors to consider before conducting this analysis. The first section of the tutorial defines HLM, clarifies its purpose, and states its advantages. The second section explains the mathematical theory, equations, and conditions underlying HLM. HLM hypothesis testing is performed in the third section. Finally, the fourth section provides a practical example of running HLM, with which readers can follow along. Throughout this tutorial, emphasis is placed on providing a straightforward overview of the basic principles of HLM.

We develop a mechanized proof of Featherweight Java with Assignment and Immutability in the Coq proof assistant. This is a step towards more machine-checked proofs of a non-trivial type system. We used object immutability close to that of IGJ [8] . We describe the challenges of the mechanization and the encoding we used inside of Coq.

Functional specifications describe what program components can do: the sufficient conditions to invoke a component's operations. They allow us to reason about the use of components in the closed world setting, where the component interacts with known client code, and where the client code must establish the appropriate pre-conditions before calling into the component. Sufficient conditions are not enough to reason about the use of components in the open world setting, where the component interacts with external code, possibly of unknown provenance, and where the component itself may evolve over time.In this open world setting, we must also consider the necessary conditions, i.e. what are the conditions without which an effect will not happen. In this paper we propose a language Chainmail for writing holistic specifications that focus on necessary conditions (as well as sufficient conditions). We give a formal semantics for Chainmail, and the core of Chainmail has been mechanised in the Coq proof assistant.

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Path dependent types have long served as an expressive component of the Scala programming language. They allow for the modelling of both bounded polymorphism and a degree of nominal subtyping. Nominality in turn provides the ability to capture first class modules. Thus a single language feature gives rise to a rich array of expressiveness. Recent work has proven path dependent types sound in the presence of both intersection and recursive types, but unfortunately typing remains undecidable, posing problems for programmers who rely on the results of type checkers. The Wyvern programming language is an object oriented language with path dependent types, recursive types and first class modules. In this paper we define two variants of Wyvern that feature decidable typing, along with machine checked proofs of decidability. Despite the restrictions, our approaches retain the ability to encode the parameteric polymorphism of Java generics along with many idioms of the Scala module system. CCS Concepts: • Software and its engineering → Formal language definitions; • Theory of computation → Program semantics.