---
title: "Reasons to Love the Field of Programming Languages"
date: 2025-12-06T18:08:24-08:00
draft: true
tags: ["Programming Languages", "Compilers", "Type Systems"]
---

I work at HPE on the
[Chapel Programming Language](https://chapel-lang.org). Recently, another HPE
person asked me:

> So, you work on the programming language. What's next for you?

This caught me off-guard because I hadn't even conceived of moving on.
I don't want to move on, because __I love the field of programming languages__.
In addition, I have come to think there is something in PL for everyone, from
theorists to developers to laypeople.
So, in that spirit, I am writing this list as a non-exhaustive survey that holds
the dual purpose of explaining my personal infatuation with PL, and providing
others with ways to engage with PL that align with their existing interests.

My general thesis goes something like this: programming languages are a unique
mix of the __inherently human and social__ and the __deeply mathematical__,
a mix that often remains deeply grounded in the practical, __low-level realities of
our hardware__.

Personally, I find all of these properties equally important, but we have to
start somewhere. Let's begin with the human aspect of programming languages.

### Human Aspects of PL

> Programs must be written for people to read, and only incidentally for machines
> to execute.
>
> --- Abelson & Sussman, _Structure and Interpretation of Computer Programs_.

As we learn more about the other creatures that inhabit our world, we discover
that they are similar to us in ways that we didn't expect. However, our
language is unique to us. It gives us the ability to go far beyond
the simple sharing of information: we communicate abstract concepts,
social dynamics, stories. In my view, storytelling is our birthright more
so than anything else.

I think this has always been reflected in the broader discipline of programming.
_Code should always tell a story_, I've heard throughout my education and career.
_It should explain itself_. In paradigms such as
[literate programming](https://en.wikipedia.org/wiki/Literate_programming),
we explicitly mix prose and code. Notebook technologies
like [Jupyter](https://jupyter.org/) intersperse computation with explanations
thereof.

* __Reason 1__: programming languages provide the foundation of expressing
  human thought and stories through code.

From flowery prose to clinical report, human expression takes a wide variety
of forms. The need to vary our descriptions is also well-served by the diversity
of PL paradigms. From stateful transformations in languages like Python and C++,
through pure and immutable functions in Haskell and Lean, to fully declarative
statements-of-fact in Nix, various languages have evolved to
support the many ways in which we wish to describe our world and our needs.

* __Reason 2__: diverse programming languages enable different perspectives
  and ways of storytelling, allowing us choice in how to express our thoughts
  and solve our problems.

Those human thoughts of ours are not fundamentally grounded in logic,
mathematics, or anything else. They are a product of millennia of evolution
through natural selection, of adaptation to ever-changing conditions.
Our cognition is limited, rife with blind spots, and partial to the subject
matter at hand. We lean on objects, actors, contracts, and more as helpful,
mammal-compatible analogies. I find this to be beautiful; here is something
we can really call ours.

* __Reason 3__: programming languages imbue the universe's fundamental rules of
  computation with humanity's identity and idiosyncrasies. They carve out
  a home for us within impersonal reality.

Storytelling (and, more generally, writing) is not just about communicating
with others. Writing helps clarify one's own thoughts, and to think deeper.
In his 1979 Turing Award lecture,
[Notation as a Tool of Thought](https://www.eecg.utoronto.ca/~jzhu/csc326/readings/iverson.pdf),
Kenneth Iverson, the creator of [APL](https://tryapl.org/), highlighted ways
in which programming languages, with their notation, can help express patterns
and facilitate thinking.

Throughout computing history, programming languages built abstractions that ---
together with advances in hardware --- made it possible to create ever more
complex software. Dijkstra's
[structured programming](https://en.wikipedia.org/wiki/Structured_programming)
crystallized the familiar patterns of `if`/`else` and `while` out of
a sea of control flow. Structures and objects partitioned data and state
into bundles that could be reasoned about, or put out of mind when irrelevant.
Recently, I dare say that notions of ownership and lifetimes popularized
by Rust have clarified how we think about memory.

* __Reason 4__: programming languages combat complexity, and give us tools to
  think and reason about unwieldy and difficult problems.

The fight against complexity occurs on more battlegrounds than PL design alone.
Besides its syntax and semantics, a programming language is comprised of its
surrounding tooling: its interpreter or compiler, perhaps its package manager
or even its editor. Language designers and developers take great care to
[improve the quality of error messages](https://elm-lang.org/news/compiler-errors-for-humans),
to provide [convenient editor tooling](https://chapel-lang.org/blog/posts/chapel-lsp/),
and build powerful package managers
like [Yarn](https://yarnpkg.com/). Thus, in each language project, there is
room for folks who, even if they are not particularly interested in grammars or
semantics, care about the user experience.

* __Reason 5__: programming languages provide numerous opportunities for
  thoughtful forays into the realms of User Experience and Human-Computer
  Interaction.

I hope you agree, by this point, that programming languages are fundamentally
tethered to the human. Like any human endeavor, then, they don't exist in
isolation. To speak a language, one usually wants a partner who understands
and speaks that same language. Likely, one wants a whole community, topics
to talk about, or even a set of shared beliefs or mythologies. This desire
maps onto the realm of programming languages. When using a particular PL,
you want to talk to others about your code, implement established design patterns,
use existing libraries.

I mentioned mythologies earlier. In some ways, language
communities do more than share know-how about writing code. In many
cases, I think language communities rally around ideals embodied by their
language. The most obvious example seems to be Rust. From what I've seen,
the Rust community believes in language design that protects its users
from the pitfalls of low-level programming. The Go community
believes in radical simplicity. Julia actively incorporates contributions from
diverse research projects into an interoperable set of scientific packages.

* __Reason 6__: programming languages are complex collaborative social projects
  that have the power to champion innovative ideas within the field of
  computer science.

So far, I've presented interpretations of the field of PL as tools for expression and thought,
human harbor to the universe's ocean, and collaborative social projects.
These interpretations coexist and superimpose, but they are only a fraction of
the whole. What has kept me enamored with PL is that it blends these human
aspects with a mathematical ground truth, through fundamental connections to
computation and mathematics.

### The Mathematics of PL

> Like buses: you wait two thousand years for a definition of “effectively
> calculable”, and then three come along at once.
>
> --- Philip Wadler, _Propositions as Types_

There are two foundations,
[lambda calculus](https://en.wikipedia.org/wiki/Lambda_calculus) and
[Turing machines](https://en.wikipedia.org/wiki/Turing_machine), that underpin
most modern PLs. The abstract notion of Turing machines
is closely related to, and most similar among the "famous" computational models,
to the
[von Neumann Architecture](https://en.wikipedia.org/wiki/Von_Neumann_architecture).
Through bottom-up organization of "control unit instructions" into
"structured programs" into the imperative high-level languages today, we can
trace the influence of Turing machines in C++, Python, Java, and many others.
At the same time, and running on the same hardware functional programming
languages like Haskell represent a chain of succession from the lambda calculus,
embellished today with types and numerous other niceties. These two lineages
are inseparably linked: they have been mathematically proven to be equivalent.
They are two worlds coexisting.

The two foundations have a crucial property in common: they are descriptions
of what can be computed. Both were developed initially as mathematical formalisms.
They are rooted not only in pragmatic concerns of "what can I do with
these transistors?", but in the deeper questions of "what can be done
with a computer?".

* __Reason 7__: programming languages are built on foundations of computation,
  and wield the power to compute anything we consider "effectively computable at all".

Because of these mathematical beginnings, we have long had precise and powerful
ways to talk about what code written in a particular language _means_.
This is the domain of _semantics_. Instead of reference implementations
of languages (CPython for Python, `rustc` for Rust), and instead of textual
specifications, we can explicitly map constructs in languages either to
mathematical objects ([denotational semantics](https://en.wikipedia.org/wiki/Denotational_semantics))
or to (abstractly) execute them ([operational semantics](https://en.wikipedia.org/wiki/Operational_semantics)).

To be honest, the precise and mathematical nature of these tools is, for me,
justification enough to love them. However, precise semantics for languages
have real advantages. For one, they allow us to compare programs' real
behavior with what we _expect_, giving us a "ground truth" when trying to
fix bugs or evolve the language. For another, they allow us to confidently
make optimizations: if you can _prove_ that a transformation won't affect
a program's behavior, but make it faster, you can safely use it. Finally,
the discipline of formalizing programming language semantics usually entails
boiling them down to their most essential components. Stripping the
[syntax sugar](https://en.wikipedia.org/wiki/Syntactic_sugar) helps clarify
how complex combinations of features should behave together.

Some of these techniques bear a noticeable resemblance to the study of
semantics in linguistics. Given our preceding discussion on the humanity
of programming languages, perhaps that's not too surprising.

* __Reason 8__: programming languages can be precisely formalized, giving
  exact, mathematical descriptions of how they should work.

In talking about how programs behave, we run into an important limitation
of reasoning about Turing machines and lambda calculus, stated precisely in
[Rice's theorem](https://en.wikipedia.org/wiki/Rice%27s_theorem):
all non-trivial semantic properties of programs (termination, throwing errors)
are undecidable. There will always be programs that elude not only human analysis,
but algorithmic understanding.

It is in the context of this constraint that I like to think about type systems.
The beauty of type systems, to me, is in how they tame the impossible.
Depending on the design of a type system, a well-typed program may well be
guaranteed not to produce any errors, or produce only the "expected" sort of
errors. By constructing reasonable _approximations_ of program
behavior, type systems allow us to verify that programs are well-behaved in
spite of Rice's theorem. Much of the time, too, we can do so in a way that is
straightforward for humans to understand and machines to execute.

* __Reason 9__: in the face of the fundamentally impossible, type systems
  grant us confidence in our programs for surprisingly little conceptual cost.

At first, type systems look like engineering formalisms. That
may well be the original intention, but in our invention of type systems,
we have actually completed a quadrant of a deeper connection: the
[Curry-Howard isomorphism](https://en.wikipedia.org/wiki/Curry%E2%80%93Howard_correspondence).
[Propositions](https://en.wikipedia.org/wiki/Proposition), in the logical sense,
correspond one-to-one with types of programs, and proofs of these propositions
correspond to programs that have the matching type.

This is an incredibly deep connection. In adding parametric polymorphism
to a type system (think Java generics, or C++ templates without specialization),
we augment the corresponding logic with the "for all x" (\(\forall x\)) quantifier.
Restrict the copying of values in a way similar to Rust, and you get an
[affine logic](https://en.wikipedia.org/wiki/Affine_logic), capable of reasoning about resources and their use.
In languages like Agda with [dependent types](https://en.wikipedia.org/wiki/Dependent_type),
you get a system powerful enough [to serve as a foundation for mathematics](https://en.wikipedia.org/wiki/Intuitionistic_type_theory).
Suddenly, you can write code and mathematically prove properties about that
code in the same language. I've done this in my work with
[formally-verified static program analysis]({{< relref "series/static-program-analysis-in-agda" >}}).

This connection proves appealing even from the perspective of "regular"
mathematics. We have developed established engineering practices
for writing code: review, deployment, documentation. What if we could use
the same techniques for doing mathematics? What if, through the deep
connection of programming languages to logic, we could turn mathematics
into a computer-verified, collaborative endeavor?
I therefore present:

* __Reason 10__: type systems for programming languages deeply correspond
  to logic, allowing us to mathematically prove properties about code,
  using code, and to advance mathematics through the practices of software engineering.

{{< details summary="Bonus meta-reason to love the mathy side of PL!" >}}
In addition to the theoretical depth, I also find great enjoyment in the way that PL is practiced.
Here more than elsewhere, the creativity and artfulness I've mentioned before come into
play. In PL, [inference rules](https://en.wikipedia.org/wiki/Rule_of_inference) are a
lingua franca through which the formalisms I've mentioned above are expressed
and shared. They are such a central tool in the field that I've
developed [a system for exploring them interactively]({{< relref "blog/bergamot" >}})
on this blog.

In me personally, inference rules spark joy. They are a concise and elegant
way to do much of the formal heavy-lifting I described in this section;
we use them for operational semantics, type systems, and sometimes more.
When navigating the variety and complexity of the many languages and type
systems out there, we can count on inference rules to take us directly to
what we need to know. This same variety naturally demands flexibility in
how rules are constructed, and what notation is used. Though this can sometimes
be troublesome (one [paper](https://labs.oracle.com/pls/apex/f?p=LABS%3A0%3A%3AAPPLICATION_PROCESS%3DGETDOC_INLINE%3A%3A%3ADOC_ID%3A959")
I've seen describes __27__ different ways of writing the simple operation of substitution in literature!),
it also creates opportunities for novel and elegant ways of formalizing
PL.

* __Bonus Reason__: the field of programming languages has a standard technique
  for expressing its formalisms, which precisely highlights core concepts
  and leaves room for creative expression and elegance.
{{< /details >}}