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In this chapter, we provide an overview of the problem of container selection, and its effect on program correctness and performance.
We then provide an overview of how modern programming languages approach this problem, and how existing literature contributes.
Finally, we examine the gaps in the existing literature, and explain how this paper aims to contribute.
\section{Container Selection}
The vast majority of programs will use make extensive use of collection data types - types intended to hold many different instances of other data types.
This can refer to anything from fixed-size arrays, to growable linked lists, to associative key-value mappings or dictionaries.
In many languages, the standard library provides a variety of collections, forcing us to choose which one is best.
Consider the Rust types \code{Vec<T>} (a dynamic array) and \code{HashSet<T>} (a hash-based set).
If we care about the ordering, or about preserving duplicates, then we must use \code{Vec<T>}.
But if we don't, then \code{HashSet<T>} might be more performant, if we use \code{contains} a lot.
We refer to this problem as container selection, and say that we must satisfy both functional requirements, and non-functional requirements.
\subsection{Functional requirements}
The functional requirements tell us how the container will be used, and how it must behave.
Continuing with our previous example, we can see that \code{Vec} and \code{HashSet} implement different methods.
\code{Vec} implements \code{.get(index)} while \code{HashSet} doesn't - it wouldn't make sense for an unordered collection.
If we try to swap \code{Vec} for \code{HashSet}, the resulting program will likely not compile.
We will call the operations a container implements the ``syntactic properties'' of the container.
In object-oriented programming, we might say they must implement an interface, while in Rust, we would say that they implement a trait.
However, syntactic properties alone are not always enough to select an appropriate container.
Suppose our program only requires a container to have \code{.insert(value)}, and \code{.len()}.
Both \code{Vec} and \code{HashSet} will satisfy these requirements, but we might rely on \code{.len()} including duplicates.
In this case, \code{HashSet} would give us different behaviour, causing our program to behave incorrectly.
Therefore we also say that a container implementation has ``semantic properties''.
Intuitively we can think of this as what conditions the container upholds.
For a \code{HashSet}, this would include that there are never any duplicates, whereas for a Vec it would include that ordering is preserved.
\subsection{Non-functional requirements}
While meeting the functional requirements should ensure our program runs correctly, we also want to choose the 'best' type that we can.
Here we will consider 'best' as striking a balance between runtime and memory usage.
Prior work has shown that properly considering container selection selection can give substantial performance improvements, even in large applications.
For instance, tuning performed in \cite{chung_towards_2004} achieved an up to 70\% increase in the throughput of a complex web application, and a 15-40\% decrease in the runtime of several scientific applications.
\cite{l_liu_perflint_2009} found and suggested fixes for ``hundreds of suboptimal patterns in a set of large C++ benchmarks,'' with one such case improving performance by 17\%.
Similarly, \cite{jung_brainy_2011} achieves an average speedup of 27-33\% on real-world applications and libraries.
If we can find a selection of types that satisfy our functional requirements, then one obvious solution is to benchmark the program with each of these implementations in place, and see which works best.
This will obviously work, so long as our benchmarks are roughly representative of 'real world' inputs.
Unfortunately, this technique scales poorly for bigger applications.
As the number of container types we must select increases, the number of combinations we must try increases exponentially (assuming they all have roughly the same number of candidates).
This quickly becomes unfeasible, and so we must find other selection methods.
\section{Prior Literature}
In this section, we outline methods for container selection available in current programming languages, and their limitations.
We then examine some of the existing solutions for container selection, and their limitations.
\subsection{Approaches in common programming languages}
Modern programming languages broadly take one of two approaches to container selection.
Some languages, usually higher-level ones, recommend built-in structures as the default, using implementations that perform fine for the vast majority of use-cases.
One popular examples is Python, which uses dynamic arrays as its built-in list implementation.
This approach prioritises developer ergonomics: Programmers do not need to think about how these are implemented.
Usually, other implementations are possible, but are used only when needed and come at the cost of code readability.
In other languages, collections are given as part of a standard library, or must be written by the user.
Java comes with growable lists as part of its standard library, as does Rust (with some macros to make use easier).
In both cases, the ``blessed'' implementation of collections is not special - users can implement their own.
Often interfaces, or their closest equivalent, are used to distinguish 'similar' collections.
In Java, ordered collections implement the interface \code{List<E>}, while similar interfaces exist for \code{Set<E>}, \code{Queue<E>}, etc.
This means that when the developer chooses a type, the compiler enforces the syntactic requirements of the collection, and the writer of the implementaiton ``promises'' they have met the semantic requirements.
Whilst the approach Java takes is the most expressive, both of these approaches either put the choice on the developer, or remove the choice entirely.
This means that developers are forced to guess based on their knowledge of the underlying implementations, or to just pick the most common implementation.
\subsection{Chameleon}
Chameleon\parencite{shacham_chameleon_2009} is a tool for Java codebases, which uses a rules engine to identify sub-optimal choices.
It first collects statistics from program benchmarks using a ``semantic profiler''.
This includes the space used by collections over time, and the counts of each operation performed.
These statistics are tracked per individual collection allocated, and then aggregated by 'allocation context' - the call stack at the point where the allocation occured.
These aggregated statistics are then passed to a rules engine, which uses a set of rules to suggest places a different container type might improve performance.
This results in a flexible engine for providing suggestions, which can be extended with new rules and types as necessary.
To satisfy functional requirements, Chameleon only suggests new types that behave identically to the existing type.
This results in selection rules needing to be more restricted than they otherwise could be.
For instance, a rule cannot suggest a \code{HashSet} instead of a \code{LinkedList}, as the two are not semantically identical.
Chameleon has no way of knowing if doing so will break the program's functionality, and so it does not make a suggestion.
A similar rules-based approach was also used in \cite{l_liu_perflint_2009}, while \cite{jung_brainy_2011} uses a machine learning approach with similar statistics collection.
\subsection{CollectionSwitch}
CollectionSwitch\parencite{costa_collectionswitch_2018} is an online solution, which adapts as the program runs and new information becomes available.
First, a performance model is built for each container implementation.
This is done by performing each operation many times in succession, varying the length of the collection.
This data is used to fit a polynomial, which gives an estimate of cost of a specific operation at a given n.
This is then combined with the frequency of each operation counts to give cost estimates for each collection type, operation, and 'cost dimension' (time and space).
Rules then decide when switching to a new implementation is worth it based on these cost estimates and defined thresholds.
By generating a cost model based on benchmarks, CollectionSwitch manages to be more flexible than other rules-based approaches such as Chameleon.
It expects applications to use Java's \code{List}, \code{Set}, or \code{Map} interfaces, which express enough functional requirements for most problems.
\cite{hutchison_coco_2013} and \cite{osterlund_dynamically_2013} both also attempt online selection, however do so with a rules-based approach more similar to Chameleon \cite{shacham_chameleon_2009}.
\subsection{Primrose}
Primrose \parencite{qin_primrose_2023} focuses on the functional requirements of container selection.
It allows the application developer to specify both syntactic and semantic requirements using a Lisp DSL.
The available implementations are then checked against these requirements using an SMT solver, to obtain a set of usable implementations.
Developers must then choose which of these implementations will work best for their non-functional requirements.
This allows developers to express any combination of semantic requirements, rather than limiting them to common ones like Java's approach.
It can also be extended with new implementations as needed, although this does require modelling the semantics of the new implementation.
\section{Contributions}
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