Thank you for the video, Alex! Good stuff, as always! I just wanted to add that one may use this mnemonic to help them understand a Church numeral in a real-life scenario - a Church numeral is basically the number of times you would apply a function f to value x! x - Church's zero f(x) - Church's one f(f(x)) - Church's two f(f(f(x))) - Church's three
ITS VERY USEFUL IN KNOWING BECAUSE WHEN YOU FELL LIKE THINGS ARE GOING COMPLEX YOU WILL KNOW THAT NOTHING IS COMPLEX ITS JUST THAT WE DONT KNOW THE ABSTRACTION BEHIND IT.
Awesome video Alex, thanks! :) I have one question though, where could I find a bunch of Lambda Expression examples to practice? Best regards, Lazar Grbovic
2 min 51 sec into the video and pause it to say... you should really kill the background music 🎶... still having trouble understanding and now I'm doing extra work trying to filter out the music
It can be useful when you're coming up with a programming language, to sort of outline what you're planning to implement and have a solid set of rules that you can build on
The lambda calculus is important as it represents a model of computation. This is known as the Church-Turing thesis(Everything that can be calculated can be shown to be calculated by either a turing machine or the lambda calculus, as both definitions are equivalent.) If you want to prove that something can or cannot be calculated, then you can make an appeal to the lambda calculus or turing machines.
I disagree with you. In the expression about nested function, i.e. lambaX.lambdaY.X it is f(X, f(Y)), wherr f(Y)=X, not f(X,Y). This is a huge difference.
It's actually very useful in making things clear in mathematics. It happens all the time that people define a function by writing down an expression that has a variable in it. For example, somebody might say something like: Consider the function x+1, or sin(2x). Those are not actually functions. They are instead incomplete expressions. But what's meant is the function that takes a value (or input) for x and returns a value that is computed from that. That would be expressed in the lambda calculus as: lambda x . x+1 Or lambda x . sin(2 x) That might sound like a triviality. Of course, that's what it means. But if you've ever taken a mathematics class that uses functions and variables, there's always some ambiguity. Does sin(2 x) mean a function, or does it mean the value of a function at some point x? It becomes more ambiguous if you are talking about functions of multiple variables. Suppose I write the expression sin(x) + a. What is "a" here? Is it a constant that I just haven't told you the value of, or is it a variable? You can view sin(x) + a in two different ways: (1) For every choice of a, there is a corresponding function sin(x) + a. This is a family of related functions. (2) It's a function of two variables: x and a. Lambda calculus makes it clear which one you are talking about: lambda x. sin(x) + a is a function of one variable, and a is a "parameter". lambda x . lambda a. sin(x) + a is a function of two variables, x and a.
"So you can increment the zero value and get one, which is pretty crazy!"... ookay wow, so next you're gonna tell us that you can draw a line on a sheet of paper and call it "revolutionary"?
Cmon, define a simple set of rules, which is so powerful and in essence simple as lamda calculus. With only 3 so incredibly simple rules, to be able to calculate any given computable function is huge.
@@paulus.schmaulus I was just joking. Of course the people that came up with this had some mad mathematic skills. I just don't share your passion for calculation models, but still have to learn this at uni :D
Your video finally made me understand something I couldn't wrap my head around When you drew out what went where and how things interacted it became so clear Thank you!! Chaining lambda functions is complicated but fun to learn about My first project was to reverse three arguments given to the function (λx.λy.λz.z y x) A B C ⇒ (λy.λz.z y A) B C ⇒ (λz.z B A) C ⇒ C B A
thank you, i have a scala exam in 10 days and you explain way better than my phd teacher who invented Scala
Scala is a great Language, much better than Java
I watched a few videos about lambda calculus but now it finally clicked for me. Thank you!
THANK YOU, you just explained in a sooo simple way something that I couldn't understand on any website or in my class.
Thank you for the video, Alex! Good stuff, as always!
I just wanted to add that one may use this mnemonic to help them understand a Church numeral in a real-life scenario - a Church numeral is basically the number of times you would apply a function f to value x!
x - Church's zero
f(x) - Church's one
f(f(x)) - Church's two
f(f(f(x))) - Church's three
\f.\x.f(f(x))
Anyone else find the music distracting?
It didn't distract me , I Fucking pissed me OFF!!!
It did not distract me, until I saw this comment.
I find it stupid
Argh that music
a bit too loud
You did it so well! What would I have done if it was not for your video, lol. Love you, man!
Thanks for starting at the bottom and building your way up, instead of starting from the top and using things you haven't explained yet.
This is a beautifully created video! love how you explained thankyouuu
This was exactly the video I wanted. Way to see a gap in the market and fill it! Do addition next, plz.
Gordon doesn't need to hear all this, he's a highly trained professional.
Finally, good ol' Alonzo gets his recognition!
Hello sir! You are awesome, and I can see you really like what you're teaching. Thank you so much for this video!
Thank you. I watched a few videos and got confused. This video cleared up all my confusion.
maybe without music so loud would be better this video, thanks anyway for the info
did anyone ever told you that you're a life savior
Nice calm blue background. Thankyou
Very clear description
The lambda calculus also had a big impact on imperative languages before it had an impact on declarative/functional ones
Best video on lambda calculus
This was so good!!!
Good explanation. But the background music is a bit distracting for me.
thanks from italy!!!! you are great
Every time I come back to lambda calculus, all I want is for my life to end...
ITS VERY USEFUL IN KNOWING BECAUSE WHEN YOU FELL LIKE THINGS ARE GOING COMPLEX YOU WILL KNOW THAT NOTHING IS COMPLEX ITS JUST THAT WE DONT KNOW THE ABSTRACTION BEHIND IT.
Awesome video Alex, thanks! :)
I have one question though, where could I find a bunch of Lambda Expression examples to practice?
Best regards,
Lazar Grbovic
Finally I understood the concept ☺️
thank you sooo much, that helps a lot.
λ, great video
2 min 51 sec into the video and pause it to say... you should really kill the background music 🎶... still having trouble understanding and now I'm doing extra work trying to filter out the music
Maybe it's because I'm not a comp sci student, but I still don't get the purpose of lambda calculus - how does it make life better?
It can be useful when you're coming up with a programming language, to sort of outline what you're planning to implement and have a solid set of rules that you can build on
The lambda calculus is important as it represents a model of computation. This is known as the Church-Turing thesis(Everything that can be calculated can be shown to be calculated by either a turing machine or the lambda calculus, as both definitions are equivalent.)
If you want to prove that something can or cannot be calculated, then you can make an appeal to the lambda calculus or turing machines.
I disagree with you. In the expression about nested function, i.e. lambaX.lambdaY.X it is f(X, f(Y)), wherr f(Y)=X, not f(X,Y). This is a huge difference.
Nice content 👍
Please next time decreases the volume of music 😭
I don’t get it? What is it used for? Seems a pretty long winded way to write 0 and 1
It's actually very useful in making things clear in mathematics.
It happens all the time that people define a function by writing down an expression that has a variable in it. For example, somebody might say something like: Consider the function x+1, or sin(2x). Those are not actually functions. They are instead incomplete expressions. But what's meant is the function that takes a value (or input) for x and returns a value that is computed from that. That would be expressed in the lambda calculus as:
lambda x . x+1
Or lambda x . sin(2 x)
That might sound like a triviality. Of course, that's what it means. But if you've ever taken a mathematics class that uses functions and variables, there's always some ambiguity. Does sin(2 x) mean a function, or does it mean the value of a function at some point x?
It becomes more ambiguous if you are talking about functions of multiple variables. Suppose I write the expression sin(x) + a. What is "a" here? Is it a constant that I just haven't told you the value of, or is it a variable? You can view sin(x) + a in two different ways:
(1) For every choice of a, there is a corresponding function sin(x) + a. This is a family of related functions.
(2) It's a function of two variables: x and a.
Lambda calculus makes it clear which one you are talking about:
lambda x. sin(x) + a
is a function of one variable, and a is a "parameter".
lambda x . lambda a. sin(x) + a
is a function of two variables, x and a.
After watching it for 5 munites while waiting on traffic, made me think that yeah it's hard 🙂
I think you have mistake in explaining : lambdaX.lambdaY.X. you convert it to f(x,y)=x which I think is incorrect shouldn't be f(x)=f(y)=x ?
KILL that music !!!!!!!!!!!!!!!!!!
Why?Its like porn! :D
🤯
Even more confused. Thanks.
Turn off music plz
Music is too loud
Next time please increase the music volume, I can still hear your voice.
thanks, but the music was a bit much
Personally loved the music!
me too!!
You literally made something great, and just ruined it with that music !
The video would have been better without the music.
gave up, the music...
lose the music
"So you can increment the zero value and get one, which is pretty crazy!"... ookay wow, so next you're gonna tell us that you can draw a line on a sheet of paper and call it "revolutionary"?
Cmon, define a simple set of rules, which is so powerful and in essence simple as lamda calculus. With only 3 so incredibly simple rules, to be able to calculate any given computable function is huge.
@@paulus.schmaulus I was just joking. Of course the people that came up with this had some mad mathematic skills. I just don't share your passion for calculation models, but still have to learn this at uni :D
this music is REALLY bad and distracting
Your video finally made me understand something I couldn't wrap my head around
When you drew out what went where and how things interacted it became so clear
Thank you!!
Chaining lambda functions is complicated but fun to learn about
My first project was to reverse three arguments given to the function
(λx.λy.λz.z y x) A B C
⇒ (λy.λz.z y A) B C
⇒ (λz.z B A) C
⇒ C B A
Interesting