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15-150: Principles of Functional Programming

448 points| brandonspark | 2 years ago |brandonspark.github.io

126 comments

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jstrieb|2 years 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.

http://www.cs.cmu.edu/~rwh/isml/book.pdf

zelphirkalt|2 years ago

I found the regular expression package as a first thing to make in SML waaay too complex. You already need to have a good understanding of the elements of SML syntax to understand how it works. This is definitely not for SML beginners. I recommend "Elements of ML Programming" by Jeffrey D. Ullman for people starting to learn SML. It too has some corners, that are less great for not so mathematically inclined people, but you will definitely learn the language and have exercises.

aroman|2 years 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.

louthy|2 years 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.

3abiton|2 years ago

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

frankbreetz|2 years ago

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

brandonspark|2 years 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)

brandonspark|2 years 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?

mbivert|2 years 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.

[0]: https://mitp-content-server.mit.edu/books/content/sectbyfn/b...

fredgrott|2 years ago

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

ajbt200128|2 years 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_punk|2 years 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.

valenterry|2 years ago

No word on where the concept originally comes from? (in the text/description)

Should have at least differentiated between "functional programming" and "pure functional programming" IMHO.

andrewl|2 years ago

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

agomez314|2 years 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?

johnday|2 years 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.)

chriswarbo|2 years 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)

vmchale|2 years ago

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

f1shy|2 years 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.

bmacho|2 years 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.

endgame|2 years ago

The lecture on CPS made things "click" for me in a way that they hadn't before. Thank you.

hohohmm|2 years ago

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

esafak|2 years ago

Pretty good for a new grad!

PennRobotics|2 years 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.

systems|2 years 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

brandonspark|2 years 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.

weatherlight|2 years 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.

imslavko|2 years 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.

kccqzy|2 years 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]: https://dl.acm.org/authorize?N46678 or preprint at https://github.com/snowleopard/alga-paper/releases/download/...

c-c-c-c-c|2 years 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.

shortrounddev2|2 years 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

freedomben|2 years 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.

Mandelmus|2 years 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.

unknown|2 years ago

[deleted]

frozenlettuce|2 years 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.

brandonspark|2 years 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.

poorlyknit|2 years 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 :)

mrkeen|2 years 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: https://hackage.haskell.org/packages/tag/logging

tromp|2 years 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.

toast0|2 years 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.

corethree|2 years 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.

zogrodea|2 years ago

Others have mentioned having the same problem with this issue. One post I particularly like about the subject is this one on function colouring (how lagnuages with async/await syntax have a similar "infection"; this is a response to the original post on function colouring and not the original post). https://www.tedinski.com/2018/11/13/function-coloring.html

ElectricalUnion|2 years 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?

Koshkin|2 years 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.

epgui|2 years 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.

whateveracct|2 years ago

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

zubairq|2 years ago

Watching it now

narinxas|2 years 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...

Verdex|2 years 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.

shepherdjerred|2 years 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.