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 approaches taken by modern programming languages and existing literature.
Finally, we explain how our system is novel, and the weaknesses in existing literature it addresses.

\section{Container Selection}

A container data structure is simply a structure which holds a collection of related values.
This could include a list (growable or otherwise), a set (with no duplicate elements), or something more complex (like a min heap).

In many languages, the standard library provides implementations of various container types, with users able to choose which is best for their program.
This saves users a lot of time, however selecting the best type is not always straightforward.

Consider a program which needs to store and query a set of numbers, and doesn't care about ordering or duplicates.
If the number of items ($n$) is small enough, it might be fastest to use a dynamically-sized array (known as a vector in many languages), and scan through each time we want to check if a number is inside.
On the other hand, if the set we deal with is much larger, we might need to use a more complex method to keep things fast.
A common example would be a hash set, which provides roughly the same lookup speed regardless of size, at the cost of being slower overall.

In this case, there are two factors driving our decision.
Our \emph{functional requirements} -- that we don't care about ordering or duplicates -- and our \emph{non-functional requirements} -- that we want our program to use resources efficiently.

\subsection{Functional requirements}

Functional requirements tell us how the container must behave in order for the program it's used in to function correctly.
Continuing with our previous example, we'll compare Rust's \code{Vec} implementation (a dynamic array), with its \code{HashSet} implementation (a hash table).

To start with, we can see that the two types have different methods.
\code{Vec} has a \code{.get(index)} method, while \code{HashSet} does not; \code{HashSet}s aren't ordered so this wouldn't make sense.
If we were building a program that needed an ordered collection, replacing \code{Vec} with \code{HashSet} would likely cause the compiler to raise an error.

We will call the operations that a container implementation provides the \emph{syntactic  properties} of the implementation.
In object-oriented programming, we might say they must implement an interface, while in Rust, we would say that they implement a trait.\footnote{Rust's traits are most similar to typeclasses from Haskell and other FP languages. Interfaces and typeclasses have important differences, but they are irrelevant in this case.}

However, syntactic properties alone are not always enough to select an appropriate container implementation.
Suppose our program only requires a type with the \code{.contains(value)} and \code{.len()} methods.
Both \code{Vec} and \code{HashSet} satisfy these requirements, but our program might also rely on the count returned from \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 \code{semantic properties}.
Intuitively we can think of this as what conditions are upheld.
For a \code{HashSet}, this would include that there are never any duplicates.
A \code{Vec} would not have this property, but would have the property that insertion order is preserved.

To select a correct container implementation, we then need to ensure we meet some syntactic and semantic requirements specific to our program.
So long as we specify our requiremets correctly, and use an implementation which provides all of the properties we're looking for, our program shouldn't be able to tell the difference.

\subsection{Non-functional requirements}

While meeting our program's functional requirements should ensure that it runs correctly, this doesn't say anything about our program's efficiency.
We likely also want to choose the most efficient implementation available, striking a balance between runtime and memory usage.

Prior work has demonstrated that the right container implementation can give substantial performance improvements.
\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} demonstrates an average increase in speed of 27-33\% on real-world applications and libraries using a similar approach.

If we can find a set of implementations that satisfy our functional requirements, then an obvious solution is to benchmark the program with each of these implementations in place.
This will obviously work, as long as our benchmarks are roughly representative of the real world.

Unfortunately, this technique scales poorly for larger applications.
As the number of types we must select increases, the number of combinations we have to try increases exponentially.
This quickly becomes unfeasible, so we must explore other selection methods.

\section{Prior literature}

In this section we outline methods for container selection available within and outside of current programming languages 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 well enough 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.
Often 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.
In both cases, the standard library implementation is not special --- users can implement their own and use them in the same ways.

Often interfaces, or their closest equivalent, are used to abstract over 'similar' collections.
In Java, ordered collections implement the interface \code{List<E>}, with similar interfaces for \code{Set<E>}, \code{Queue<E>}, etc.

This allows most code to be implementation-agnostic, however the developer must still choose a concrete implementation at some point.
This means that developers are forced to guess based on their knowledge of the underlying implementations, or simply choose the most common implementation.

\subsection{Rules-based approaches}

One approach to the container selection problem is to allow the developer to make the choice initially, but use some tool to detect poor choices.
Chameleon\citep{shacham_chameleon_2009} uses this approach.

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 passed to a rules engine, which uses a set of rules to suggest container types which might improve performance.
This results in a flexible engine for providing suggestions which can be extended with new rules and types as necessary.

However, adding new implementations requires the developer to write new suggestion rules.
This can be difficult as it requires the developer to understand all of the existing implementations' performance characteristics.

To satisfy functional requirements, Chameleon only suggests new types that behave identically to the existing type.
This results in selection rules being 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 the suggestion.

CoCo \citep{hutchison_coco_2013} and work by \"{O}sterlund \citep{osterlund_dynamically_2013} use similar techniques, but work as the program runs.
This works well for programs with different phases of execution, such as loading and then working on data.
However, the overhead from profiling and from checking rules may not be worth the improvements in other programs, where access patterns are roughly the same throughout.

\subsection{ML-based approaches}

Brainy\citep{jung_brainy_2011} gathers statistics similarly, however it uses machine learning (ML) for selection instead of programmed rules.

ML has the advantage of being able to detect patterns a human may not be aware of.
For example, Brainy takes into account statistics from hardware counters, which are difficult for a human to reason about.
This also makes it easier to add new collection implementations, as rules do not need to be written by hand.

\subsection{Estimate-based approaches}

CollectionSwitch\citep{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 gives an estimate of some cost for each operation at a given collection size.
We call the measure of cost the ``cost dimension''.
Examples of cost dimensions include memory usage and execution time.

This is combined with profiling information to give cost estimates for each collection type and cost dimension.
Switching between container types is then done based on the potential change in each cost dimension.
For instance, we may choose to switch if we reduce the estimated space cost by more than 20\%, so long as the estimated time cost doesn't increase by more than 20\%.

By generating a cost model based on benchmarks, CollectionSwitch manages to be more flexible than rule-based approaches.
Like ML approaches, adding new implementations requires little extra work, but has the advantage of being possible without having to re-train a model.

A similar approach is used by \cite{l_liu_perflint_2009} for the C++ standard library.
It focuses on measuring the cost and frequency of more fine-grained operations, such as list resizing.
However, it does not take the collection size into account.

\subsection{Functional requirements}

Most of the approaches we have highlighted focus on non-functional requirements, and use programming language features to enforce functional requirements.
We will now examine tools which focus on container selection based on functional requirements.

Primrose \citep{qin_primrose_2023} is one such tool, which uses a model-based approach.
It allows the application developer to specify semantic requirements using a Domain-Specific Language (DSL), and syntactic requirements using Rust's traits.

The semantic requirements are expressed as a list of predicates, each representing a semantic property.
Predicates act on an abstract model of the container type.
Each implementation also specifies the conditions it upholds using an abstract model.
A constraint solver then checks if a given implementation will always meet the conditions required by the predicate(s).

This allows developers to express any combination of semantic requirements, rather than limiting them to common ones (as in Java's approach).
It can also be extended with new implementations as needed, though this does require modelling the semantics of the new implementation.

\cite{franke_collection_2022} uses a similar idea, but is limited to properties defined by the library authors and implemented on the container implementations.

To select the final container implementation, both tools rely on benchmarking each candidate.
As we note above, this scales poorly.

\section{Contribution}

We aim to create a container selection method that addresses both functional and non-functional requirements.

Users should be able to specify their functional requirements in a way that is expressive enough for most usecases, and easy to integrate with existing projects.
It should also be easy to add new container implementations, and we should be able to use it on large projects without selection time becoming an issue.

We focus on offline container selection (done before the program is compiled), however we also attempt to detect when changing implementation at runtime is desirable.