The Science of Functional Programming [pdf]

https://github.com/winitzki/sofp/blob/master/sofp-src/sofp.pdf

by adamnemecek • 7 years ago

180 61 7 years ago

Tade05• 7 years ago

It requires a certain amount of mathematical experience and is not suitable for people who are unfamiliar with school-level algebra, or unwilling to learn difficult concepts through prolonged mental concentration and effort.

Why do materials on functional programming always have to be at least somewhat condescending towards the reader?

Or maybe: why such sentences seems to appear only in them?

ssivark2• 7 years ago

Maybe they’re defensive because readers keep complaining about not understanding the math they use?

Tade05• 7 years ago

So the retort is to imply that they didn't understand the math they had in school?

To me it comes off as somewhat douchy.

happytoexplain• 7 years ago

I don't really agree that the sentence is condescending. It's mostly accurate and the problem is described fairly neutrally.

jayd16• 7 years ago

This is saying "btw this subject isn't for lazy illiterates", presumably unlike other literature the reader is familiar with. What value does that add exactly?

BucketSort• 7 years ago

It's a good warning. I would only consider that condescending if I had some insecurity about my abilities.

AnimalMuppet• 7 years ago

To me, it seems that the "is not suitable" phrase was a bit condescending. Re-word that, and the warning may be fine.

Tade05• 7 years ago

Who is it targeted at though?

Because I find it hard to imagine somebody "unfamiliar with school-level math" picking it up in the first place.

classified3• 7 years ago

To understand how and why a C compiler works you don't need all that much algebra. If you thoroughly understand assembly, you're basically good to go.

To understand how and why an FP language compiler works you need to grok the lambda calculus (as a bare minimum). I'd call that algebra. To even understand what problems are being solved by closures, I really had to “learn difficult concepts through prolonged mental concentration and effort”. Giving newbies a heads-up that competent use of such a tool requires nontrivial knowledge is only fair.

iamaelephant• 7 years ago

Why do I need to understand how the compiler works, at that level of detail?

I don't see why understanding closures requires so much mental effort. Just using them a few times should give you a practical understanding of how they work. Closures are not a complicated concept - a bunch data your function has access to outside of its own scope.

jfoutz2• 7 years ago

eh, i dunno. i think anybody with a decent grip on any language can whip up a scheme compiler way faster than a C compiler. [1] is a very readable guide to scheme and its implementation. Will it be the fastest gun in the west? no. Is it a simple workable foundation that, like, anybody who can put together 100 lines of working code, in any language, can build? for sure. Compilation isn't magic.

Lambda calculus won't hurt. Implementing scheme (which imho is pretty darn close to the lambda calculus) really just requires understanding some operational semantics and you're good to go.

[1] (http://agl.cs.unm.edu/~williams/cs491/three-imp.pdf)

toast0• 7 years ago

Is it really that complicated?

A closure is essentially a function pointer with some additional data about what some of the symbols refer to. It happens that you're able to write the function nested inside another function.

Jonathanks• 7 years ago

When I gave this book an attempt, I appreciated the author's honesty about the difficulty of the material. I went with Real World Ocaml instead, intending to reattempt SoFP in the future. Today I suggested an addition to a section in Real World OCaml, and the author pointed out that the section was already so dense that adding the extra content would require more explanation. I now appreciate the difficulty in making such a technical material approachable by a less technical audience, and a heads up is appropriate.

Edit: (in light of another reply that mentioned the lambda calculus). The addition to Real World OCaml that I suggested was to call out the implementation of the Y combinator in the section on Memoization. The explanation used the Y combinator to work up to an implementation of memoization, and it was so intuitive that I felt it should be noted, but that won't easily fit into an already dense chapter.

traderjane• 7 years ago

Would it be less condescending if it didn't discuss requirements or difficulty?

Tade05• 7 years ago

How many people "unfamiliar with school-level math" do you know?

Seems like an odd group to target in such a warning.

jlarocco• 7 years ago

It would be less condescending if the author just stated what type of math was used and left out the passive aggressive nonsense about people "unwilling to learn difficult concepts through prolonged mental concentration and effort."

And I think that's what the OP is questioning. Most technical writing will spell out what's expected from the reader, but articles about FP also tend to have a "... if you're smart enough" sentiment added in.

DonaldPShimoda• 7 years ago

Functional programming is programming from a mathematical perspective — that's the essence of all of FP. Giving the unfamiliar a warning that "hey, this material is very math-y, and if you don't like math then this isn't for you" is a reasonable disclaimer.

Iwan-Zotow• 7 years ago

FP is basically algebra in some unusual form, therefore ...

coldtea• 7 years ago

Why do materials on functional programming always have to be at least somewhat condescending towards the reader? Or maybe: why such sentences seems to appear only in them?

Because who else will get to put in such a sentence? A PHP tutorial, or some Javascript one? On what intellectual grounds would they even be able to justify it?

Besides, the accusation is not even true. You can find many C tutorials that are equally "somewhat condescending towards the reader" -- eg. for not understanding pointers, not knowing how the metal works, etc...

nn3• 7 years ago

At least part of the reason d'etre for FP is to make people who took a lot of math courses at university feel like they didn't waste their education.

austincheney• 7 years ago

Yeah, this is completely unnecessary. All programming is algebra as algebra is the math logic and instructions.

I tell people who do analysis and planning for work they are doing calculus all day without realizing it as calculus is the math of continuous change. As a result an analyst who has never programmed before may find the concept of lambda calculus far easier to understand in practice without being a math scholar.

blondin• 7 years ago

haha, i was going to count and report the number of analogies to beauty, nature, painting, etc. but Chrome gave up on me. (come now Chrome, a PDF inside an HTML page making you crawl like a baby turtle!)

glad to find this comment though. it's the other thing that's a little bothersome with the FP community -- at least for me. to be honest, i don't think they realize they are doing any of this. they just seem like the PHD level mathematicians, so to speak, of the programming community!

agumonkey2• 7 years ago

Because people do struggle on the topic. It's a fair warning.

qwerty456127• 7 years ago

It hang my PC and I had to use the reset button. The CPU load went 100% and never fallen back (I waited for about 15 minutes). The PC became so extremely slow I couldn't even log-in to another Linux console.

I retried on Windows an it (the download button) worked just fine however.

shmageggy• 7 years ago

This page completely hung my Android phone too

boznz• 7 years ago

The web page kills a chromebook.. wtf

blunte• 7 years ago

It choked my Mac too. Apparently there's an embedded PDF viewer or PDF->HTML viewer in the Github page, and clearly it is not designed for a 450+ page PDF file.

lewisjoe• 7 years ago

I put together a list of links that helped me get a hang of things on my journey understanding the theories behind languages and their design - https://docs.google.com/document/d/1hFch8y9RVab9A7U6ocUzfmPQ...

The list isn't ordered or complete yet. I just started the doc today. I'll be adding stuff as I move along.

mlevental• 7 years ago

i haven't read this book but in undergrad I skimmed his linear algebra and it was great. it's still the clearest introduction to wedge and exterior products I've ever seen.

baby• 7 years ago

Here's the direct download link:

https://github.com/winitzki/sofp/raw/master/sofp-src/sofp.pd...

amelius• 7 years ago

Perhaps pedantic, but mathematics is not science, and neither is functional programming.

See: https://undsci.berkeley.edu/article/mathematics

Mathematics is such a useful tool that science could make few advances without it. However, math and standard sciences, like biology, physics, and chemistry, are distinct in at least one way: how ideas are tested and accepted based on evidence. Math doesn't rely on testing ideas against evidence from the natural world in the same way that other sciences do. Mathematical ideas are often accepted based on deductive proofs, while ideas in other sciences are generally accepted based on the accumulation of many different observations supporting the idea.

BlueGh0st• 7 years ago

Extremely pedantic. In fact, contradicted by your own reference.

The answer depends on one's philosophical views on the nature of mathematics — and in this area, philosophers and mathematicians have not reached a consensus
...
Now it's up to you. How is math similar to and different from science?

seanmcdirmid2• 7 years ago

From Wikipedia:

Science (from the Latin word scientia, meaning "knowledge") is a systematic enterprise that builds and organizes knowledge in the form of testable explanations and predictions about the universe.
Mathematics (from Greek μάθημα máthēma, "knowledge, study, learning") includes the study of such topics as quantity (number theory), structure (algebra), space (geometry), and change (mathematical analysis). It has no generally accepted definition.

One of those words is a bit more defined than the other. I’m not sure how the above qualifies as science.

goatlover• 7 years ago

Science is an investigation of the empirical, and as such relies on induction, whereas math is deductive and non-empirical. Even if Platonism is true, we don't gain knowledge of math via the senses (mathematical truths are not out there in the world but rather some non-material realm).

edflsafoiewq• 7 years ago

I assume it means "science" in the older sense of systematized knowledge, like in "the art and science of painting" or Gries's "The Science of Programming". Not in the sense of the scientific method.

oldandtired2• 7 years ago

This is why I don't use the word "science" when discussing "science" subjects. When I see the word "science" being bandied about, I take it that the person is NOT understanding what they are trying to discuss or do NOT have any ability to discuss the subject in a clear and precise manner.

The word carries too much baggage and for many discussions there are better, more precisely defined terminology to use.

My opinion only and may not at all work for you.

seanmcdirmid2• 7 years ago

I took it that they meant science in the very general sense. Of course, the right word should have been math or even “art”, but that word today is often just used to mean “fine art” rather than its more general traditional meaning. My guess is that “the art of functional programming” would make the less pedantic types more annoyed.

joker3• 7 years ago

Math is a formal science (https://en.wikipedia.org/wiki/Formal_science). That term seems to be a little bit obscure, but it's a useful idea.

russellbeattie2• 7 years ago

This is a real question for anyone who might know: Have mathematicians as a whole ever thought about moving from the age-old formulas using various Greek symbols to something more akin to a programming language? What I mean is, instead of writing π to instead use "pi", or "summation()" rather than using the capital sigma? Functions like sin(), cos(), etc. already look like that, I wonder why the derivative sign and others haven't been changed. Superscript and subscript as well, and prime marks. It all seems superfluous.

I guess what I'm asking is there an alternative to traditional mathematical notation that's commonly used?

dodobirdlord• 7 years ago

None that are widely used. What you're suggesting has no advantage over the existing approach and would significantly reduce the speed at which practitioners can read and write mathematical expressions. This is somewhat evident in your example of sin() and cos(). Even in situations like the trig functions where concepts aren't represented with special sigils (because there are too many of them and it would be silly), they are abbreviated in standard ways.

sine -> sin()

cosine -> cos()

tangent -> tan()

cotangent -> cot()

secant -> sec()

hyperbolic sine -> sinh()

hyperbolic cotangent -> coth()

etc.

BeetleB2• 7 years ago

What I mean is, instead of writing π to instead use "pi", or "summation()" rather than using the capital sigma?

Mathematicians would like to use one symbol for one entity. Is pi the same as π or just p multiplied by i?

As for summation vs Sigma? It'd take much longer to write, and probably a bigger pain to read. Having double summations is extremely common, and triple summations are fairly common as well. If you're doing mathematical manipulations/derivations with these, you'll have them on each line.

The terse syntax exists for a reason - it's efficient. If you read fairly old math books (e.g. from the Arabs, or even more resent), you'll see that they were very expressive. The use of symbols for algebra was a significant advancement in math.

agumonkey2• 7 years ago

MIT SICM book does try this.

Iirc sussman (and maybe Steele), weren't happy about the syntax. Thus re-expressing Lagrangian mechanics in a scheme.

russellbeattie2• 7 years ago

Nice, thanks.

antonvs2• 7 years ago

"summation()" rather than using the capital sigma?

Why do you think that would be an improvement?

nafizh• 7 years ago

Can anyone please comment on the book as a learning material for practical functional programming? All of the comments here are going on tangents (which is ok, but please also comment on the source material).

The Science of Functional Programming [pdf]

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