Monads as an organizing principle for programming and semantics are notoriously difficult to grasp, yet they are a central and powerful abstraction in Haskell. This paper introduces a domain-specific language, MonadLab, that simplifies the construction of monads, and describes its implementation in Template Haskell. MonadLab makes monad construction truly first class, meaning that arcane theoretical issues with respect to monad transformers are completely hidden from the programmer. The motivation behind the design of MonadLab is to make monadic programming in Haskell simpler while providing a tool for non-Haskell experts that will assist them in understanding this powerful abstraction.

Recently there has been a great deal of interest in higherorder syntax which seeks to extend standard initial algebra semantics to cover languages with variable binding by using functor categories. The canonical example studied in the literature is that of the untyped λ-calculus which is handled as an instance of the general theory of binding algebras, cf. Fiore, Plotkin, Turi [8]. Another important syntactic construction is that of explicit substitutions. The syntax of a language with explicit substitutions does not form a binding algebra as an explicit substitution may bind an arbitrary number of variables. Nevertheless we show that the language given by a standard signature Σ and explicit substitutions is naturally modelled as the initial algebra of the endofunctor Id + FΣ ◦ + ◦ on a functor category. We also comment on the apparent lack of modularity in syntax with variable binding as compared to first-order languages. Categories and Subject Descriptors

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Effects are a powerful and convenient component of programming. They enable programmers to interact with the user, take advantage of efficient stateful memory, throw exceptions, and nondeterministically execute programs in parallel. However, they also complicate every aspect of reasoning about a program or language, and as a result it is crucially important to have a good understanding of what effects are and how they work. In this paper we present a new framework for formalizing the semantics of effects that is more general and thorough than previous techniques while clarifying many of the important concepts. By returning to the categorytheoretic roots of monads, our framework is rich enough to describe the semantics of effects for a large class of languages including common imperative and functional languages. It is also capable of capturing more expressive, precise, and practical effect systems than previous approaches. Finally, our framework enables one to reason about effects in a language-independent manner, and so can be applied to many stages of language design and implementation in order to create more broadly applicable tools for programming languages. 1.