5 ms·
I feel like this is a lot less impressive nowadays that first-class functions are common. It might as well be Python: dx = .0001 def deriv(f):
by etaioinshrdlu 6y ago
I feel like this is a lot less impressive nowadays that first-class functions are common. It might as well be Python:
dx = .0001
def deriv(f):
def f_prime(x):
return (f(x+dx) - f(x)) / dx
return f_prime
- vitus 6y agoPython does not do tail recursion, though! def f(n): if n <= 0: return n return f(n-1) f(1000) will blow out your stack. Meanwhile, scheme@(guile-user)> (define (f n) (if (<= n 0) n (f (- n 1)))) scheme@(guile-user)> (f 1000000) $1 = 0 Also bear in mind that this was lesson 1 of an intro programming course that culminates in writing a Scheme interpreter in Scheme. There's something to be said about the simplicity / consistency of a language's syntax such that a first-year undergrad can implement it.
- taeric 6y agoThe truly mind blowing one, to me, is it is one of the first handful of lessons that they go over symbolic derivatives.
- spekcular 6y agoBut this is not symbolic differentiation, it's numerical differentiation. A true symbolic integrator would not give 48.00120000993502 when asked for the value of 3x^2 at 4. This kind of approximation exercise is given to calculus students all the time ("Use the definition of derivative to approximate the derivative of f(x) at 3 by taking dx=.001," etc.). edit: I misread! See reply below.
- taeric 6y agoRight, I was referencing later lessons. Section 2.3 of the book. Surprisingly early. Granted Knuth's work also did symbolic rather early. A bit harder to work with in his. Edit: To be fair, I could have worded that first post more clearly! :D
- etaioinshrdlu 6y agoIt seems like a lot of Lisps don't do tail call optimization either though, such as Emacs lisp, common lisp, and Clojure.
- taeric 6y agoThat was the point of the lecture talking about how their system /could/ do this. I get the impression that scheme was one of the first languages that mandated that, though I suspect someone with a better view of history can correct that. For common lisp, I thought it was just not required, but that it was common to do so?
- fishmaster 6y agoNot true, SBCL definitely has TCO.
- mrtranscendence 6y agoClojure is so close. I never understood why it went for a special form rather than proper TCO.
- pimeys 6y agoIf I remember correctly it is a restriction of JVM. That's why Scala also needs a special annotation for TCO.
- patrickthebold 6y agoThat's not quite right. In Scala, the annotation is there so you get a complier error if it does not do the optimization. It doesn't affect when the compiler actually does the annotation. As you can imagine, there are cases where the developer is counting on the optimization but the code isn't such that it can be made.
- waynesonfire 6y agoYour post got me curious and I did some googling. I think this explains it, https://softwareengineering.stackexchange.com/questions/157684/what-limitations-does-the-jvm-impose-on-tail-call-optimization https://softwareengineering.stackexchange.com/questions/1576... Looks like it's a scalac optimization that doesn't always work hence the need for the annotation to give the developer feedback. There is also a link to a Closure discussion board exploring why Clojure doesn't have the annotation, by design. I didn't read it as I'm not that interested.
- zitterbewegung 6y agoYann LeCun created a lisp called Lush which allowed for the intermixing of C code with lisp and also allowed for interaction with Python. Eventually he would later make Torch which used Lua which was inspired by Scheme. Then Tensorflow and Pytorch basically are the two large players in deep learning. Now Google has JAX which allows for symbolic differentiation of Python code.
- madhadron 6y agoOh, I forgot that Lush was LeCun's work. It was such an odd beast...
- gumby 6y ago> Also bear in mind that this was lesson 1 of an intro programming course Back in '83 when the author took 6.001 only a minority of students had previously used a computer (note that Hal is quoted as having said, “If you already know how to program..." (emphasis mine). For the majority of students back then this wasn't just "introduction to programming" but "introduction to computers". Lots of non-EECS students took the class.
- taeric 6y agoThis is certainly one of the earlier motivations on why you should make procedures "first-class" in the language. And, indeed, it should be equally impressive in any language that supports things as a first class member. I have come to feel that "first class" will eventually be expanded to "can operate against definitions as easily as with them." (That is, can your language let you modify code with the same style code that can be used to execute it?)
- dehrmann 6y agoIt's also pretty rare to write a derivative function. CRUD and ETL--that's what a language needs to be good at.
- danaliv 6y agoNot all of us write web apps. :)
- mattgreenrocks 6y agoMy life is so much better since I got out of that domain :)
- gugagore 6y agoIf there's already a language that's good at CRUD and ETL (or aims to be), and most programs are that, then it's not a problem to have other languages that are good at other things at the expense of being good at CRUD and ETL. Even if it's true, as you say, that it's rare to write a derivative function, it still does come up. And there should be a good way to express it in at least some languages.
- deleted 6y ago[deleted]