It's always been my understanding that calculi were systems that defined
particular symbols and the legal methods of their manipulation in the context
of a particular calculus. The point, generally (har har), seems to be
abstraction. The lambda calculus describes computation without actually
im
On Wed, 2011-08-24 at 14:01 +0100, Tony Finch wrote:
> Ezra Cooper wrote:
> >
> > I believe this to be a general trait of things described as
> > "calculi"--that they have some form of name-binders, but I have never
> > seen that observation written down.
>
> Combinator calculi are a counter-exam
Ezra Cooper wrote:
>
> I believe this to be a general trait of things described as
> "calculi"--that they have some form of name-binders, but I have never
> seen that observation written down.
Combinator calculi are a counter-example.
Tony.
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On Tue, Aug 23, 2011 at 10:58 AM, Ezra Cooper wrote:
> An algebra is a specific kind of structure which is itself formalized
> mathematically. I've never seen a formalization of the notion of "a
> calculus" and I believe it to be a looser term, as KC defined it.
>
> Specifically, an algebra consi
An algebra is a specific kind of structure which is itself formalized
mathematically. I've never seen a formalization of the notion of "a calculus"
and I believe it to be a looser term, as KC defined it.
Specifically, an algebra consists of a set (or several "sorts" of sets) and
operations that
See Serge Lang's "Algebra".
2011/8/23 Rajesh S R :
> Slight digression. Why not Lambda "Algebra"?
> In particular, what is the criteria for a system to be calculus and how's it
> different from algebra?
>
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Regards,
KC
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Slight digression. Why not Lambda "Algebra"?
In particular, what is the criteria for a system to be calculus and how's it
different from algebra?
On Mon, Aug 22, 2011 at 12:41 AM, Jack Henahan wrote:
> The short answer is "because Church said so". But yes, it is basically
> because λ is the abst
I had thyroid cancer a few years ago; now I've lost my sense of tumour. :)
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KC
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KC wrote:
>
> Lambda abstraction was probably chosen in case someone found better
> abstractions; e.g. epsilon, delta, gamma, beta, alpha, ... :)
http://www-maths.swan.ac.uk/staff/jrh/papers/JRHHislamWeb.pdf
Page 7:
By the way, why did Church choose the notation "λ"? In [an unpublished
letter t
Definition of "calculus"
a : a method of computation or calculation in a special notation (as
of logic or symbolic logic)
b : the mathematical methods comprising differential and integral
calculus —often used with the
So a "calculus" means more than differentiation and integration it can
also me
From Cardone, Hindley "History of Lambda-calculus and
Combinatory Logic"[1]:
"(By the way, why did Church choose the notation “λ”? In [Church,
1964, §2] he stated clearly that it came from the notation “ˆ x” used
for class-abstraction by Whitehead and Russell, by first modifying “ˆ
x” to “∧x” to d
IIRC Church found it easy to write on paper.
On 21 August 2011 21:11, Jack Henahan wrote:
> The short answer is "because Church said so". But yes, it is basically
> because λ is the abstraction operator in the calculus.
>
> Why not alpha or beta calculus? What would we call alpha and beta conver
The short answer is "because Church said so". But yes, it is basically because
λ is the abstraction operator in the calculus.
Why not alpha or beta calculus? What would we call alpha and beta conversion,
then? :D
On Aug 21, 2011, at 12:37 PM, C K Kashyap wrote:
> Hi,
> Can someone please tell
Hi,
Can someone please tell me what is the root of the name lambda calculus? Is
it just because of the symbol lambda that is used?
Why not alpha or beta calculus?
Regards,
Kashyap
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