15-150: Principles of Functional Programming

376 points14
jstrieb8 hours ago

I loved 150 when I took it, and program in SML from time to time to this day.

Bob Harper (a CMU professor with a focus on PL theory) also has a really good SML reference that is closer to a textbook than lecture notes.

aroman12 hours ago

150 was one of my favorite courses at CMU; each homework really made me feel like I unlocked a new level of reasoning with code.

louthy11 hours ago

That's how I felt when I discovered FP after more than two decades writing procedural and OO code. It felt like I'd found a secret room where all the reasoning was kept.

adamddev13 hours ago

Yes! I love this description!

3abiton10 hours ago

Do you if any of the course material is available online or as a MOOC?

rashkov6 hours ago

Have a look at this similar course: I enjoyed it quite a bit and the lecturer is fantastic. It also uses SML and teaches similar material, though maybe not as in depth since this is just the first section of a three-part semester long course.

vermilingua11 hours ago

Content aside, what gorgeous slides. I wish any of my lecturers had the same eye for presentation.

frankbreetz13 hours ago

Does this include exercises? I didn't see any and I always find that the most useful part of learning.

brandonspark12 hours ago

Unfortunately, it does not. These lectures are "mine", in the sense that I developed all of them myself, but the homeworks and lab exercises are the combined efforts of generations of TAs and instructors from the past. It wouldn't be right for me to give them away. (they are also reused from time to time, so there are academic integrity concerns with that also)

brandonspark12 hours ago

(but I have thought of developing my own exercises independently to go with the lectures, to post on my website. This is generally a lot of work, though, so this might take some time, depending on how much people would benefit from it.)

bombcar5 hours ago

Could be a classic kickstarter campaign style thing.

brandonspark5 hours ago

Haha, maybe. I'm not looking to earn any money from this, though. Time is the bigger constraint in my life at the moment.

_a_a_a_10 hours ago


epgui9 hours ago

“Here is the fruit of my labour and love, which I give to you at no cost.”

“How dare you do it this way!”

Sirizarry9 hours ago

Being a cranky shithead and scrolling through HN. Name a more iconic duo. Seriously though, if your first reaction to a neat source of information is to shit on it with snark and thinly veiled assholerry, please leave the internet for a week. There are better ways to give constructive feedback

Ringz9 hours ago

Its not “How dare you do it this way!”. Its "Why do you fail in the end with the simplest and most obvious tasks?"

_a_a_a_9 hours ago
brandonspark11 hours ago

If you get to around lecture 9, a classic example I always tell people to start with is a calculator!

For instance, here's the SML code for it:

``` datatype exp =

    Num of int

  | Plus of exp * exp

  | Minus of exp * exp

  | Times of exp * exp

  | Div of exp * exp


Implement the function `eval : exp -> int`, which evaluates the expression as best as it can. Assume no division by zero.

Extra credit: Can you implement `eval' : exp -> int option`, that returns `SOME n` if the expression evaluates, and `NONE` if it divides by zero?

PennRobotics12 hours ago

Not exactly exercises, but there's which supports the course and explains each of the concepts as well as library documentation at the official class site,

It looks like their current workflow keeps exams and homeworks off the internet effectively, but there's a 6-year-old codebase at with 10-year-old homeworks and such.

mbivert11 hours ago

Rewriting standard list functions (map, fold, sum, etc.) is a good entry-level exercise.

A λ-calculus interpreter can be used as an intermediate level exercise. It is in particularly valuable in the context of solidifying one's understanding of functional programming.

You can also use "standard" textbooks, such as the SICP [0], and perform the exercises using the language of your choice, instead of Scheme/LISP.


fredgrott12 hours ago

making up your exercises is part of that fun journey of creating your own toolbox of functional programming in your language of choice!

ajbt20012813 hours ago

Of note, CMU produces a bunch of functional programming research, including a whole homotopy type theory department, so this is a quality source.

low_tech_punk12 hours ago

God send!! The FP learning resource is quite sparse on the internet. I’ve been looking for structured material like this for a while.

adamddev13 hours ago

If you're fairly new to FP I really recommend working through

hohohmm6 hours ago

Use to be called 15-212. TA-ed it for 1 semester. That's when I really understood programming.

andrewl13 hours ago

This looks valuable. And it is from the summer of 2023, so quite current.

esafak8 hours ago

Pretty good for a new grad!

agomez31412 hours ago

Great resource! Forgive my ignorance but why do so many modern functional programming courses use Standard ML instead of a Lisp dialect? Is it because of its built-in type-checking, or is it just how it's always been taught?

johnday12 hours ago

The value of purely functional programming languages, as opposed to functional programming languages like lisps, is that you get referential transparency, which means that when you define `a = b`, you know that you can always replace any instance of `a` with `b` and get the same answer. This is a very natural property in mathematics (algebraic rewritings are basically just this property writ large) and so it helps to draw nice parallels between the familiar notation of functions from mathematics and the "new" and "confusing" notion of functions in functional programming and other declarative languages.

As other posters have said, strong typing is also a nice property for lots of reasons, most notably it gives a platform to talk about ad-hoc and parametric polymorphism.

(I lecture on Functional Programming at the University of Warwick, where we use Haskell.)

tmvphil11 hours ago

I think SML isn't purely functional (although it naturally encourages a purely functional style).

albedoa12 hours ago

For those of us who are unfamiliar with Lisps, can you expand on how they break referential transparency (and how Standard ML contrasts in that regard)?

epgui9 hours ago

They don’t.

Or at least not inherently, if by “lisp” one is primarily referring to s-expressions.

medo-bear11 hours ago

He is probably talking about namespaces. In common lisp, for example,

   (a a)
calls a function 'a' on a variable 'a'. Lisp knows this because the first thing that comes after the left paren is a function
convolvatron10 hours ago
chriswarbo10 hours ago

"Lisp" is pretty broad. Whilst it was inspired by Lambda Calculus (the core of most FP languages), a lot of Lisp code is quite imperative (loops, mutable variables, control flow separate from data flow (e.g. exceptions/errors), etc.).

Scheme (and its dialects/descendants) tend to stick to a more functional style (although they also like to do stack-gymnastics with continuations, etc.). Many courses are based around Lisp.

One of the main features of the ML family is static typing, with algebraic datatypes, pattern-matching, etc. (i.e. the stuff that new languages like to call "modern", because they first saw it in Swift or something). That gives a useful mathematical perspective on code ("denotational semantics", i.e. giving meaning to what's written; as opposed to the common "operational semantics" of what it made my laptop do), and having type checking and inference makes it easier to do generic and higher-order programming (dynamic languages make that trivial in-the-small, but can make large systems painful to implement/debug/maintain/understand). This course seems to take such abstraction seriously, since it covers modules and functors too (which are another big feature of the ML family).

NOTE: In ML, the words "functor" and "applicative functor" tend to mean something very different (generic, interface-based programming) to their use in similar languages like Haskell (mapping functions over data, and sequencing actions together)

vmchale12 hours ago

It is statically typed, there's a lot of depth to that side of things (Curry-Howard isomorphism)

f1shy12 hours ago

My opinion: marketing. In my experience, if I tell someone „look here is Lisp“ they turn off and roll the eyes with a „ohh that DEAD origramming language“. If I instead say „look this new state of the art language called ML“ I get full attention and respect.

ajbt20012812 hours ago

No, it's definitely not because of marketing. SML is more of a dead language than most lisps. SML is used because it has a strong type checker, which is much more conducive to learning, and just having resilient programs in general.

bmacho11 hours ago

Why would they use a Lisp dialect instead of Standard ML? It looks ugly, it looks different from math, and different concepts have the same syntax. Standard ML looks nice, it looks like math, and different concepts have different syntax.

SomeRndName1111 hours ago

No, SML is actually quite verbose ang generally ugly, compared to say OCaml or F#, or even Scheme or Closure. This is why it is dead.

gsuuon9 hours ago

This looks cool! Just a note, it looks like the youtube playlist is in reverse order:

PennRobotics13 hours ago

Standard ML (sml / smlnj)

The instructor is clear, energetic, has a decent flow in the first lecture e.g. emphasizes the important points with vigor and repetition, switches media every 10 or 15 minutes, has a conversation with students. Slides are relatively noise-free and are informative; terms to know are highlighted.

I haven't watched a full functional programming lecture series yet, but I'd gladly audit this one.

As a "new" instructor (as in, not a TA anymore) he's got a bit of teaching talent. I hope he keeps a tight feedback loop and improves every year and continues publishing material.

imslavko12 hours ago

Slightly off-topic but what's a good forum to seek help on FP practices outside of the courses like this online?

Every winter break I get back into trying to learn more FP (in Haskell) and in the past several years I have been practicing algo problems (codeforces, advent of code, leetcode).

I always get stuck on more advanced graph algorithms where you traverse a and modify a graph, not a tree structure - it gets particularly tricky to work on circular data structures (I learned about "tying the knot" but it's incredibly challenging for me) and usually the runtime perf is sub-par both asymptotically and empirically.

kccqzy11 hours ago

Many graph algorithms are designed for imperative programming. It's safe to say that functional graph programming is still in its infancy. Alga[0], a system for algebraic graphs only came out in 2017. And efficient algorithms for graphs may yet to be discovered (even something as simple as reversing a list that's both efficient and elegant only came out in 1986!)

That said, as a beginner in functional programming, it would probably be good enough if you just focus on directly translating imperative graph algorithms to functional programming. You simply solve the problem by programming at a slightly lower level of abstraction.

[0]: or preprint at

philsnow10 hours ago

I don't know if [0] would be any help, it doesn't talk about graphs in particular but does talk about functional-focused approaches to data structures. This note[1] on the wikipedia page for the book says it better than I could:

> [...] consider a function that accepts a mutable list, removes the first element from the list, and returns that element. In a purely functional setting, removing an element from the list produces a new and shorter list, but does not update the original one. In order to be useful, therefore, a purely functional version of this function is likely to have to return the new list along with the removed element. In the most general case, a program converted in this way must return the "state" or "store" of the program as an additional result from every function call. Such a program is said to be written in store-passing style.



imslavko9 hours ago

Oh yeah, a pure function that accepts previous state, and returns the new state is the pattern I use a lot.

The issue is that it is hard to do on complex graph structures in an algorithm where incremental changes happen to the graph O(n) times - it ends up creating complex code and complex execution that might be slow to pass the time limit on Codeforces, let's say.

In the OCaml world maybe this is the place where you say "screw it, this abstracted function does some stateful temporary business, but it looks pure from the outside" but in Haskell it's a lot harder to pull off without going deep into monads (and I forget how those work every time).

kccqzy7 hours ago
low_tech_punk11 hours ago

My Scala friends heavily rely on discord, e.g. the one mentioned here:

It is language based community but they do have vibrant discussion on learning and theories.

systems12 hours ago

on the choice of language to teach the course why sml

i think there are a lot of nicer choice

   OCaml , its basically sml only more popular and used more in real life
   Haskell , again more popular , and used more in real life 
   Idris , newer and said to be more progressive 
   F# , a more practical choice and similar to sml 
   a lisp , well if you want to focus on the functional part and less on the types part
brandonspark12 hours ago

There's a few things which go into this (hi, I'm the instructor!).

One such reason is historical. Standard ML is a research language, and a significant amount of work on it was done by professors at Carnegie Mellon, who developed the curriculum for this course.

Even setting that aside though, I fully agree with the choice to teach it in SML. For transparency, I work professionally in OCaml, so I am not unfamiliar with it, and I enjoy it quite a bit. That being said, I think that the approach taken by CMU is best summarized as the fact that languages are ephemeral, and the concepts are what matters. We don't teach programming languages, we teach concepts -- so even if SML is not widely used, the tradeoff for having students have a simpler, less distracting, and better learning experience is well worth it.

OCaml has its own intricacies that make things difficult. For instance, you can go down a lot of rabbit holes with `dune` and `utop` and `ocamlc` and `ocamlopt` and all of these things, versus SML/NJ's simple interactive REPL. Another thing is that the language is just generally more "bloated" -- you can teach modules, but then what if a student starts running into first-class modules, recursive modules, or even beyond that, GADTs and classes and objects?

(as an aside, this is my primary reason for why I would not want to teach an introductory course in Haskell. To do anything, you suddenly need to understand the concept of type classes and lazy evaluation, and that's simply too much. I don't know much about the other languages.)

I think teaching is as much enabling students to succeed as it is to prevent them from shooting themselves in the foot. For an anecdote, there is an `Option.valOf` function (of type `'a option -> 'a`), which essentially is just a bad function that should be avoided where possible. Every semester, without fail, even though we never tell students that function exists, students are smart enough to use Google, and will use it anyways, ultimately harming themselves.

I think that same mentality applies to programming language choice, here. Keep it simple, keep it neat, and make sure that the students see what is necessary for their education, and not have to spend mental energy thinking about much more.

munchler12 hours ago

As a professional who uses F# every day, I appreciate this answer, even though it concerns me. Separating concepts from practical details is worthwhile, but can be taken too far. I think the FP community probably focuses a bit too much on theory. I would encourage you to consider teaching a more practical language, like F#, in the future.

bfors11 hours ago

I feel like F#'s commercial viability over other more computer sciencey FP languages is actually kind of a downside, from a "vibe" perspective. It seems like CS folks are not generally very interested in moving more towards the software engineering end of the discipline. Which is fair, because they are different things.

zem11 hours ago

i think someone with a good grounding in sml could get proficient ocaml or f# in under a month. sml is absolutely the right language to teach a course like this in.

munchler6 hours ago
agumonkey7 hours ago

having done the proglang course by dan grossman long ago, they use sml too, i knew lisps, ocaml, and others, but sml smallness was really really appealing

weatherlight11 hours ago

because SML is awesome, isn't going to change and is simple. you can learn the syntax in an afternoon, and really focus on learning FP semantics.

__rito__2 hours ago

Albeit little, installing SML still requires some anount of gymnastics, google searching, and copying stuff from SO, GH Gists, etc.

Yes, I agree broadly with the line of thinking that says- if you are learning FP, you must be willing to do these, but a beginner might be disheartened and turned away- especially as someone learning alone.

SomeRndName1111 hours ago

The problem that is extremely verbose though. OCaml is much more concise.

weatherlight10 hours ago

Both languages encourage a concise, functional programming style but with different flavors and toolsets. They are comparable, in terms of verbosity.

I think these are correct implementations of the tower of Hanoi.


    let rec hanoi n source target auxiliary =
      if n > 0 then begin
        hanoi (n - 1) source auxiliary target;
        Printf.printf "Move disk from %s to %s\n" source target;
        hanoi (n - 1) auxiliary target source


    fun hanoi n source target auxiliary =
      if n > 0 then (
        hanoi (n - 1) source auxiliary target;
        print ("Move disk from " ^ source ^ " to " ^ target ^ "\n");
        hanoi (n - 1) auxiliary target source
function definition, if expressions, recursion are more concise in SML, string interpolation is nicer in OCaml
c-c-c-c-c13 hours ago

Wow, he went from taking his bachelor to lecturing.

I always dreamt of that when going through my degree and encountering courses that needed a thorough rework.

shortrounddev212 hours ago

tbh if I were in a class taught by someone who had JUST finished their bachelor's degree, I'd take a lot of it with a grain of salt

medstrom12 hours ago

If you expect perfect factual accuracy from your teachers, yeah. On the flip side, they don't have the curse of knowledge yet i.e. it's still fresh in their mind what was difficult in the beginning, so they can probably explain very well. Just keep in mind who's teaching you, and it's just like if a co-student teaches you.

And if you feel you have to take what you hear with a grain of salt, that's probably good for your learning too.

shortrounddev212 hours ago

I just mean in terms of experience. If you deviate from textbook accuracy and go into providing practical advice for real-life scenarios, someone with only a bachelor's and no work history is someone who can only give you canned anecdotes from others. Looking at his resume, it looks like he's had some internships so he has a bit of experience, and that's probably worth something

gtchuang10 hours ago
elchananHaas12 hours ago

I went to CMU and was in AEPI fraternity with Brandon Wu. Brandon Wu is exceptional when it comes to functional programming. He was head TA of 15150 for a year, I have 100% confidence in him.

He took a break from TAing for some time, and when he returned he decided to have some fun with his application. He wrote a transpiler from a C like syntax to SML the day before his interview, and used it to joke that they should transition to teaching functional programming in C.

shortrounddev212 hours ago

Yeah idk anything about him in particular. I just mean that, on paper, someone who goes straight from bachelor's to teaching is someone who doesn't really have any experience. I notice that a lot of the people who extol the virtues of FP to me are a lot of people straight out of college and have little real-world reference for why FP is useful in a prod environment

frozenlettuce12 hours ago

My complaint with FP: Sometimes I just want to do something silly, like adding a log somewhere. If I choose to add said side effect, now all my functions are marked with an io signature (so there might be _other_, nastier side effects hiding there as well - mainly an issue if you have multiple people contributing to the same project). If I don't add the side effect, and choose to refactor multiple layers of code, I will need to make all my functions return multiple values and later fold over all the accumulated strings and... life is too short for that. The principles really resonate with me, but maybe we are limited by the current tooling, because the development experience is quite clunky in its current stage.

poorlyknit10 hours ago

In Haskell you have a lot of options to type your functions in a more granular way. Consider the type class MonadIO, which lets you specify that your function works on any monad that can do side effects, not just IO specifically:

    -- Before
    captureAudioDuration :: DeviceID -> DiffTime -> IO WaveData
    -- After
    captureAudioDuration' :: MonadIO m => DeviceID -> DiffTime -> m WaveData
You can build the same thing, but for logging!

    class Monad m => MonadLog m where
        log :: String -> m ()
    -- In IO, just log to stdout.
    -- Other implementations might be a state/writer monad
    -- or a library/application-specific monad for business logic.
    instance MonadLog IO where
        log msg = putStrLn ("log: " ++ msg)
    -- Before: Bad, doesn't actually do any IO but logging
    findShortestPath :: Node -> Node -> Graph -> IO [Node]
    -- After: Better, type signature gives us more details on what's happening.
    -- We can still use this in an IO context because IO has a MonadLog instance.
    -- However, trying to capture audio in this function using either
    -- of the functions above will lead to a type error.
    findShortestPath' :: MonadLog m => Node -> Node -> Graph -> m [Node]
As you can imagine this can get quite verbose and there's other patterns one can use. Feel free to ask any follow-up questions :)
brandonspark12 hours ago

This is Haskell-specific, it sounds like. I agree, the IO monad is really quite inconvenient sometimes.

I work in OCaml, which is also a functional language, but prints can be added in single lines. I address this point in Lecture 19 (Imperative Programming), actually, but my perspective is -- we invented immutability and purity to serve us, but we need not be fanatically beholden to it. In my opinion, I think Haskell goes in that direction, when every usage of IO now needs the IO monad to get involved.

A little mutability is OK. Functional programming is about the avoidance of side effects, more than simply forbidding it.

frozenlettuce12 hours ago

yeah, I've been trying to get this mindset as well - even though sometimes I feel that I'm "cheating" :)

mrkeen12 hours ago

Just let all your functions live in IO then. You'll still come out ahead.

Or do an unsafePerformIO.

Or use trace (where someone else has done the unsafePerformIO for you).

Or use a Writer.

Or introduce some logging capability (Logger m =>) onto your code.

Or take a look at all the man-hours that have been spent on trying to perfect logging:

frozenlettuce11 hours ago

yeah, biting the bullet seems to be the way to go. As you mention the lots of "man-hours that have been spent on trying to perfect logging", when doing research the usage of that time might be ok, but when building a product you might need to make concessions.

tromp12 hours ago

> Sometimes I just want to do something silly, like adding a log somewhere.

In Haskell, you can use Debug.Trace for just that purpose, when you don't want to change the type of your function.

frozenlettuce11 hours ago

I've been playing with purescript and found out that they have a similar library, thanks!

toast012 hours ago

You might benefit from a more pragmatic functional language. Erlang is broadly functional, but you can output from anywhere if you want to. It's probably one of the least pure functional languages out there, but it's super handy.

corethree2 hours ago

> If I choose to add said side effect, now all my functions are marked with an io signature

You got the wrong idea. You're supposed to write FP in a way where the side effect is highly layered and segregated away from pure code. IO are singularities within your chains of pure function compositions. As soon as you hit a singularity you have to break out of it as soon as possible.

The main idea is the meat. Keep your bread tiny and keep it very very separate from the meat.

The pattern is called Imperative Shell, functional core. Think of your IO as two pieces of bread in a sandwich and your pure code is the meat that connects the read to the write.

The game you're playing with haskell is to avoid letting the IO monad pollute any of your logic as much as possible.

Anyway that being said in applications where IO is all over the place... this pattern becomes largely ineffective. You basically have more bread than meat.

ElectricalUnion12 hours ago

From my limited knowledge of FP languages it is expected that pure code in fact doesn't evaluate anything until a monad forces it to evaluate.

You would then need a monad to evaluate the things you're attempting to log. And at that point you have a monad, so you can log as usual?

squillion10 hours ago

It's not about monads, it's about effectful code, which is represented by special types (e.g. IO in Haskell, Eff in PureScript). Effectful code can call pure code, but not vice-versa. Since a program will have to do something, the main function is always effectful, i.e. it returns an effectful special type. So you're right that pure code isn't evaluated until some effectful code is ultimately returned by the main function and executed (by a runtime or equivalent). However, in purely functional languages most code is pure, even though it's ultimately called by effectful code.

Monads and side-effects aren't intrinsically related. Simplifying, a monad is something with flatMap() - in JavaScript, Array and Promise are monads (kinda). What flatMap() gives you is the ability to chain things, which is useful to sequence side-effects so that they can be performed by a machine in a given order. That's why IO and Eff are monads.

freedomben13 hours ago

I do wish functional programming were more taught. we're getting to a point where I almost think OOP should be taught briefly and the rest of the focus on C/C++ for low level stuff (OS, data structures, some algorithms), and something functional or pseudo-functional for high level stuff. Most of the newer codebases in startups now require functional concepts to understand what's happening. For example, try writing modern JS without understanding .map, .reduce, et al, and function passing, etc.

Regardless I think it's important that students get exposed to more than just Python, which seems to increasingly be the only thing students come out knowing.

Mandelmus13 hours ago

> I do wish functional programming were more taught

My first CS bachelor's semester in Germany in 2017 taught functional programming using Haskell (as well as C and NASM assembly in another course on computer architecture).

OOP using Java and Python was only introduced in the second semester.

> Regardless I think it's important that students get exposed to more than just Python, which seems to increasingly be the only thing students come out knowing.

In my B.Sc. studies I used C, C++, Haskel, Assembly, Java, Python, and Swift.

randmeerkat12 hours ago

> My first CS bachelor's semester in Germany in 2017 taught functional programming using Haskell (as well as C and NASM assembly in another course on computer architecture).

Also worth mentioning that since this was in Germany not only was it a great education, but there’s no crippling student debt either.

RamblingCTO12 hours ago

Same here. Had Scala in my first year. Clojure and Racket later. On top of that I had C, ASM, Java, Python and R (had a focus on machine learning). So I got plenty of education in that department.

freedomben12 hours ago

There are definitely some good schools out there that expose students to a broad field. For anybody who is a student and looking, this is somethign I would strongly recommend considering.

airstrike11 hours ago

Hey Brandon, thanks for posting this. Off-topic but maybe consider serving up thumbnails on that page instead of the full-size pngs

Koshkin11 hours ago

It seems that the fundamental problem with the functional paradigm (in its pure form) is that the real world - including the architecture of the computer that is used to run the programs on - is full of side effects, i.e. is essentially "imperative," and with this impedance between them the idea creates more problems than it solves.

epgui9 hours ago

That’s like saying the problem with rulers is that the real world doesn’t have straight lines.

Or the problem with cleaning your room is that in the real world entropy only ever increases.

kccqzy8 hours ago

Any time an HN comment uses the phrase "fundamental problem" chances are the problem is not only not fundamental, but also rather fun to solve for the right kind of people.

whateveracct11 hours ago

on the contrary, i think FP (Haskell at least) gives you more & better tools to represent and wrangle side effects

kccqzy11 hours ago

Exactly. These languages come up with more and more strategies and abstractions (from monads to modern effect systems) to help you manage your side effects well. It then raises the level of abstraction in your programs to become simpler and more concise.

zubairq12 hours ago

Watching it now

narinxas13 hours ago

just in time for nobody to really care about programming because LLMs are so good at translation and all computer code and programing are a subfield of linguistics...

Verdex12 hours ago

Programming runs along the back of mathematics. A field famous for spending centuries wasting time on silly games until those same silly games end up being the foundation on which modern society functions.

Even if LLMs completely remove the need for programming (a rather big IF), this is not time wasted.

shepherdjerred12 hours ago

Functional programming is a perfect pairing with AI-generated code because the type systems are generally more expressive than non-functional languages, which means the compilers can catch all sorts of errors.

interiorchurch12 hours ago

As my mother used to say, we'll see...