| Q. | Does someone know how to find the fixed point of a function in lambda calculus? | Related Search:
Programming & Design | | | Please explain giving an example!!
Take the case of the successor function, that calculates the successor of a number in lambda calculus.
Successor function in lambda calculus is
lam(n).lam(f).lam(x).f (n f x)
where n is a natural number written in form of a church numeral.
| | A. | what is lambda calculus? can you write down the equation | | | |
| Q. | Lambda Calculus, category theory, and discrete math? | Related Search:
Mathematics | | | I'm a computer science major and I'm trying to learn functional programming with haskell. I figured that a solid background in category theory, discrete math, and an understanding of Lambda Calculus would help a lot. I've even downloaded books on the subjects. However, they all assume that I understand the plethora of mathematical symbols used. Big O notation and certain symbols used in set theory. Can anyone recommend a good guide/reference for mathematical symbols?
| | A. | What's your math background? What's your goal? Plenty of people code in haskell and lisp without knowing a lot of the math. If your goals are more pure and theoretical, then you should want to know the math, so read on.
Just knowing notation won't help you that much. You should read some basic math material to really get comfortable with the stuff. Most books have an index of symbols, so you should get them for the reference if nothing else.
If you haven't taken an intro math logic course you need to start there. Buy a nice intro math logic book (Enderton is my favorite undergrad text, but if you're into CS there is a relatively nice book by Peter Andrews which also goes into some type theory. His notation is a little archaic and the book doesn't read too well, so be warned). You should know some basic math logic before doing set theory. For set theory, it's real crap in the way of texts. Levy's "Basic Set Theory" is the best intro text (and it's cheap) but it's very terse for an undergrad book. I suggest you browse the internet and find some course notes from someone.
If you haven't taken any algebra, buy a nice abstract algebra book. For the undergrad level, I like Fraleigh. This will help you if you're really interested in category theory, whose orgins are in algebraic topology.
As for lambda calculus, after you know some math logic, picking up the basics isn't hard. Church's book is still print (It's called "The Calculi of Lambda Conversion" I believe) and it's really short and to the point (albeit a little outdated, terse and containing archaic notation). Barendregt has probably the best book. Hindley has some books on Lambda Calculus and Combinatory Logic that might be of interest and are easier to read than Barendregt's (albeit less complete) and much easier to use as a reference.
Hope that helps. Goodluck. | | | |
| Q. | Can someone help me answering this Lambda Calculus Expression ? | Related Search:
Mathematics | | |
(\x.xxx)(\x.xxx) ?? To its normal form??
| | A. | [Link]  >
see if this helps---the informal description section | | | |
| Q. | I'm attempting to ratify article 36a of Vasum: A Methodology for the Synthesis of Lambda Calculus? | Related Search:
Sociology | | | According to Vasum: A Methodology for the Synthesis of Lambda Calculus, "In recent years, much research has been devoted to the improvement of IPv6; nevertheless, few have studied the visualization of write-back caches [6]. A technical challenge in networking is the study of optimal information. In fact, few researchers would disagree with the construction of robots, which embodies the confirmed principles of complexity theory. The development of 64 bit architectures would minimally degrade permutable modalities."
In light of this information, we see contrary information displayed in the construction of Mayan Pyramids using UFO's, the inscription of various Egyptian Hieroglyphics from the reign of Akhenaton, and the aesthetic tastes of the Jewish Cabal in Babylon. According to Professor Wilson, "we postulate that systems can investigate the location-identity split without needing to allow the improvement of rasterization. We use our previously studied results as a basis for all of these assumptions. This seems to hold in most cases."
How can I synthesize this information without having to seek emotional closure in the Parthenon in Athens, Greece? Will I need to consult several Christadelphians?
| | A. | As to the Parthenon, and this all that you speak, yours rests within. Go inside. You are never anywhere outside yourself but inside. The Parthenon does hold many secrets as Phidias warranted. So, if emotional closure is somewhat you seek, then go there, and you will find it there, for it is no more nor less than what the inner technologies express. | | | |
| Q. | lambda calculus reduction? | Related Search:
Mathematics | | | hello i need to reduse this lambda expression to its normal form:
((( \ f. \ x. \ y.x f y)p)q)r
\ denotes lambda
can someone tell me if i should start substituting r in place of f or p in place of f in this lambda expression...
thanks
| | A. | p. You should start by reducing
( \ f. \ x. \ y.x f y)p
to
\ x. \ y.x p y
and then go on to perform the other two reductions. | | | |
| Q. | Is question lambda a question that returns a question when it is given a question? | Related Search:
Philosophy | | | My friend told me about lambda calculus but i'm confused ):
| | A. | The code basically loops around the dinners returning the first Dinner or the default if none is found.
This is a case where the naming conventions used in a sample aren't always appropriate in production. Using a "d" as a local variable is usually fround upon and choosing a variable name of "dinner" would probably be more appropriate, although in this case the scope of d is so small it is clear either way, as long as you know how lambda expressions work. | | | |
| Q. | Calculus and Application? | Related Search:
Mathematics | | | A linear fourth-order ODE with constant coefficients is given by
y'''' + 2y''' + 6y'' + 8y' + 8y = 0. (3)
(a) Explain why non-trivial solutions must be of the form y = e^(lambda*x) and hence that the possible
values of satisfy the characteristic quartic equation
(lambda^2 + 4)(lambda^2 + 2*lambda + 2) = 0.
[5 marks]
(b) Hence, write down the general solution to the equation (3) as a linear combination of four
linearly-independent functions.
[4 marks]
(c) Show that there can be an infinite number of solutions to equation (3) for the boundary
conditions
y(0) = y(pi/2) = y(pi) = y(3pi/2) = 0.
| | A. | (a) Maybe the most straightforward proof would be to say "just try the expression A e^{λx} and see." The equation that you get is:
(λ⁴ + 2 λ³ + 6 λ² + 8 λ + 8) A e^{λx} = 0
Which has 4 solutions and therefore spans the solution space, if and only if the characteristic polynomial that you see there does not have repeated roots. This "only if" problem is a good example of exactly what could go wrong; you could have something like:
y'' − 2 y' + y = 0
Which only gives you one linearly independent solution λ = 1. You now have to try y = A x e^x to find the second solution.
Anyway, the remainder is factoring (λ⁴ + 2 λ³ + 6 λ² + 8 λ + 8) into
λ⁴ + 2 λ³ + 6 λ² + 8 λ + 8 = (λ² + 4) (λ² + 2λ + 2)
λ = ± 2i, or -1 ± i.
(b) You should know that e^{i θ} = cos θ + i sin θ, so that you understand that the above imaginary solutions represent sinusoidal functions. Our solutions family is therefore:
y(x) = A sin(2x) + B cos(2x) + C e^-x sin(x) + D e^-x cos(x).
(c) y(x) = A sin(2x). There are uncountably infinitely many A's to choose among. | | | |
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