/prog/ - the lambda

Name: Anonymous 2013-02-21 1:16

We can define a successor function, which takes a number n and returns n + 1 by adding an additional application of f:

    SUCC := λn.λf.λx.f (n f x)

Because the m-th composition of f composed with the n-th composition of f gives the m+n-th composition of f, addition can be defined as follows:

    PLUS := λm.λn.λf.λx.m f (n f x)

PLUS can be thought of as a function taking two natural numbers as arguments and returning a natural number; it can be verified that

    PLUS 2 3

and

    5

are equivalent lambda expressions. Since adding m to a number n can be accomplished by adding 1 m times, an equivalent definition is:

    PLUS := λm.λn.m SUCC n

Name: Anonymous 2013-02-21 1:42

sounds rather complicated for 2 + 3 = 5

Name: Anonymous 2013-02-21 5:15

Yup, well done. The lambda calculus is indeed Turing-complete. What's your point though?

Name: Anonymous 2013-02-21 5:44

Now try to do this in the simply typed lambda calculus.

Name: Anonymous 2013-02-21 9:18

shouldn't you only need one lambda (-anonymous function) ?
plus = @(x,y) x+y;
plus(2,3)
ans = 5

Name: Anonymous 2013-02-21 11:25

>>5
Uh, are you fucking retarded? You forgot your ^^, by the way.

Name: Anonymous 2013-02-21 13:45

>>5
Define 2, define 3, define 5.

Name: Anonymous 2013-02-21 14:00

>>5
MATLAB-fag detected. Die in a fire, come back when you'll use a true programming langage.

Name: Anonymous 2013-02-21 15:11

>>8
Retard-kun likes MATLAB and Octave. Don't blame him, he doesn't even know about Church numerals.

Name: Anonymous 2013-02-21 15:15

>>5
Please don't open that cocksucking mouth of yours if you aren't going to contribute.

Name: Anonymous 2013-02-21 15:23

Finding λ is much like solving for an integer that should never exist in the first place. Its forced mathematical theory creating numbers from thin air. Solving for λ in statistics can be very funny at times. We have all heard from trolls, however much statistical analysis is trolling at its very best.

Name: Anonymous 2013-02-21 15:24

>>11
Another retard pretending to be a troll?

Name: Anonymous 2013-02-21 15:39

>>10
I was just about to suck your cock, faggot.

Name: Anonymous 2013-02-21 16:41

Wow, Presburger arithmetic. Why do I care?

Name: Anonymous 2013-02-21 16:42

>>14
Maybe Peano was a kike? I don't know.

Name: Anonymous 2013-02-21 17:59

XDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDD

Name: >>5 2013-02-21 18:29

What a bunch of whingers..
I'm sure next you'll tell me doing 1000000 ^ 2 by adding +1 at a time is optimal due to tail-call optimisations..

Name: Anonymous 2013-02-21 18:38

...I'm beginning to think Lisp probably isn't that slow at all..
Just that retards are using recursion for the sake of using recursion..

Name: Anonymous 2013-02-21 18:40

>>17
Who the fuck said this was about optimal implementations? This is purely a theoretical exercise. But no, you have to try to look smart, and then you make look yourself like a fucking idiot.

Fuck off back to /b/, gigantic dumbfuck.

Name: Anonymous 2013-02-21 18:46

>>19 o-kay.. So what theory should i have gleaned from this?

Name: Anonymous 2013-02-21 18:52

forgive me if i don't understand SUCC := λn.λf.λx.f (n f x)

Name: Anonymous 2013-02-21 18:54

where is the +1, and why are there three(?) variables for an increment function?

Name: Anonymous 2013-02-21 19:03

>>21
Church notation.
Zero: λf.λz.z = zero applications of f to z = z
One = succ(zero) = (λn.λf.λx.f (n f x))(λf.λz.z) = ... = f(z)
Two = succ(one) = f(f(z)) and so on.
I'm sure you can do the derivation, it's just substitution.

Name: Anonymous 2013-02-21 19:07

...you're using a succ function to implement a plus function.. if succ does anything other than just +1, it is a plus function. therefore plus is a recursive function.

why is plus a recursive function?

Name: Anonymous 2013-02-21 19:13

>>24
Your reasoning does not follow, does "recursive function" mean what you think it means?

Name: Anonymous 2013-02-21 19:17

>>26 perhaps not..
still 10 +10 seems to get broken into 10 +1 +1 +1 +1 +1 +1 +1 +1 +1 +1 ?

Name: Anonymous 2013-02-21 19:20

>>26
Yes, but also the first 10 gets broken down to 0 +1 +1 +1 +1 +1 +1 +1 +1 +1 +1.

Name: Anonymous 2013-02-21 19:22

>>27 it's worse than i thought?

Name: Anonymous 2013-02-21 19:28

why are you pulling numbers to pieces?

Name: Anonymous 2013-02-21 19:35

...so 1000000 + 1000000 results in 2000000 inlined succ calls?

Name: Anonymous 2013-02-21 19:46

>>30
What's interesting is that if you have another implementation that agrees with this one, you can prove things with either or and they apply to both.

Name: Anonymous 2013-02-21 19:53

>>20
Read SICP.

Name: Anonymous 2013-02-21 19:57

>>32 nigga please

Name: Anonymous 2013-02-21 20:00

>>5,17,20-22
What the fuck are you doing on my /prog/?

Name: Anonymous 2013-02-21 20:04

>>34 http://dis.4chan.org/read/music/1360783549/9

Name: Anonymous 2013-02-21 20:12

>>31 like optimality?

Name: Anonymous 2013-02-21 20:13

>>35
What? What does that have to do with my question? Why the fuck did you post that? Are you a spammer?

Name: Anonymous 2013-02-21 20:22

>>37 is your name elmo by any chance?

Name: Anonymous 2013-02-21 20:33

>>1
how do define substract?

Name: Anonymous 2013-02-21 20:34

>>38
No, you shithead.

Why do you try so hard to act ``funny''? Are you underage? And it's about time you answer my questions.

Name: Anonymous 2013-02-21 20:34

>>34
http://www.google.com/search?q=how+to+geet+to+sesame+street

Name: Anonymous 2013-02-21 20:52

>>40 are you a phed or something?

Name: Anonymous 2013-02-21 20:55

>>42
No.

Look, faggot, is it that hard to answer the questions? I'm answering yours.

Name: Anonymous 2013-02-21 21:00

coined. phed. noun.
An old man pretending to be a child, and hanging around children, in the hopes of catching other old men pretending to be a child, and hanging around children..

No, im 26.

Why are you concerned with me, this is a thread discussing lambda calculus..?

Name: Anonymous 2013-02-21 21:03

>>44
Good fucking god, you finally answered. But you should act more mature, you're not 13 anymore.

I'm concerned about you because you abuse ellipsis and emoticons, and shitpost to the point of making some threads unbearable.

Name: Anonymous 2013-02-21 21:15

>>45 i'd be rather lonely.. ^^

Name: Anonymous 2013-02-22 2:19

hmm.. that syntax is pretty awful though, i still don't even know where to look to find the things it's supposed to be doing..

Name: Anonymous 2013-02-22 2:39

'mercury-rising' grade code obfuscation theory?
something worse than cargo-cult recursion?
'and maybe one day we'll go to rehab, or back to argentina...'

Name: Anonymous 2013-02-22 2:58

SICP may refer to:

Structure and Interpretation of Computer Programs, pronounced “sick-pea”

not even pronounced "cisp"

Name: Anonymous 2013-02-22 3:13

mfw first published 1984
thousands of uni students, all with good english skills
still pronounced "sick-pea"
Sertified Genius

Name: Anonymous 2013-02-22 3:36

I guess that's what you get for not teaching yourselves..
YHBT so hard i almost feel bad for pointing it out..

the lambda

1 Name: Anonymous 2013-02-21 1:16

2 Name: Anonymous 2013-02-21 1:42

3 Name: Anonymous 2013-02-21 5:15

4 Name: Anonymous 2013-02-21 5:44

5 Name: Anonymous 2013-02-21 9:18

6 Name: Anonymous 2013-02-21 11:25

7 Name: Anonymous 2013-02-21 13:45

8 Name: Anonymous 2013-02-21 14:00

9 Name: Anonymous 2013-02-21 15:11

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16 Name: Anonymous 2013-02-21 17:59

17 Name: >>5 2013-02-21 18:29

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Name: Anonymous 2013-02-21 1:16

Name: Anonymous 2013-02-21 1:42

Name: Anonymous 2013-02-21 5:15

Name: Anonymous 2013-02-21 5:44

Name: Anonymous 2013-02-21 9:18

Name: Anonymous 2013-02-21 11:25

Name: Anonymous 2013-02-21 13:45

Name: Anonymous 2013-02-21 14:00

Name: Anonymous 2013-02-21 15:11

Name: Anonymous 2013-02-21 15:15

Name: Anonymous 2013-02-21 15:23

Name: Anonymous 2013-02-21 15:24

Name: Anonymous 2013-02-21 15:39

Name: Anonymous 2013-02-21 16:41

Name: Anonymous 2013-02-21 16:42

Name: Anonymous 2013-02-21 17:59

Name: >>5 2013-02-21 18:29

Name: Anonymous 2013-02-21 18:38

Name: Anonymous 2013-02-21 18:40

Name: Anonymous 2013-02-21 18:46

Name: Anonymous 2013-02-21 18:52

Name: Anonymous 2013-02-21 18:54

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Name: Anonymous 2013-02-22 3:36