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\chapter{A ML-flavoured programming language}
\label{ch:base-language}
In this chapter we introduce a core calculus, $\BCalc$, which we shall
In this chapter we introduce a core calculus, \BCalc{}, which we shall
later use as the basis for exploration of design considerations for
effect handlers. This calculus distils the `functional' essence of the
ML-flavoured multi-tier web-programming language
\Links~\cite{CooperLWY06}. As such $\BCalc$ may be regarded as a
faithful model of a prototypical and practical functional programming
language.
effect handlers. This calculus is based on \CoreLinks{} by
\citet{LindleyC12}, which distils the essence of the functional
multi-tier web-programming language
\Links{}~\cite{CooperLWY06}. \Links{} belongs to the
ML-family~\cite{MilnerTHM97} of programming languages as it features
typical characteristics of ML languages such as a static type system
supporting parametric polymorphism and type inference, and its
evaluation semantics is strict. However, \Links{} differentiates
itself from the rest of the ML-family by making crucial use of
\emph{row polymorphism} to support extensible records, variants, and
tracking of computational effects. Thus \Links{} has a rather strong
emphasis on structural types rather than nominal types.
\CoreLinks{} captures all of these properties of \Links{}. Our
calculus \BCalc{} differs in several aspects from \CoreLinks{}. For
example, the underlying formalism of \CoreLinks{} is call-by-value,
whilst the formalism of \BCalc{} is \emph{fine-grain
call-by-value}~\cite{LevyPT03}, which shares similarities with
A-normal form (ANF)~\cite{FlanaganSDF93} as it syntactically
distinguishes between value and computation terms by mandating every
intermediate computation being named. However unlike ANF, fine-grain
call-by-value remains closed under $\beta$-reduction. The reason for
choosing fine-grain call-by-value as our formalism is entirely due to
convenience. As we shall see in Chapter~\ref{ch:unary-handlers}
fine-grain call-by-value is a convenient formalism for working with
continuations. Another point of difference between \CoreLinks{} and
\BCalc{} is that the former models the integrated database query
sublanguage of \Links{}. We discard the query sublanguage altogether,
and instead focus entirely on the interaction with computational
effects.
\section{Syntax and static semantics}
\section{Type inference}
\label{sec:syntax-base-language}
\section{Type and effect inference}
\dhil{While I would like to detail the type and effect inference, it
may not be worth the effort. The reason I would like to do this goes
back to 2016 when Richard Eisenberg asked me about how we do effect
inference in Links.}
\section{Dynamic semantics}
\chapter{Unary handlers}
\label{ch:deep-handlers}
\label{ch:unary-handlers}
\section{Deep handlers}
\subsection{Syntax and static semantics}