Combinator
In mathematics, a combinator is a function with no free variables.In computer science, combinators have been used as a basis for the semantics of functional programming languages.
A term of a combinator is either a constant, a variable, or an application of the form (A B), denoting the application of term A (a function of one argument) to term B. Application associates to the left in the absence of parentheses. All combinators can be defined as a composition of two basic combinators - S and K. These two and a third, I, are defined thus:
(S f g x) = (f x (g x)) (K x y) = x (I x) = x = (S K K x)
There is a simple translation between combinatory logic and the lambda-calculus. However, combinatorial expressions are much larger than their lambda-calculus equivalents.
A combinator of particular interest is the Y combinator, which is a fixed point combinator and can be used to implement recursion.
Other combinators were added by David Turner[?] in 1979 when he used combinators to implement SASL[?]:
(B f g x) = (f (g x)) (C f g x) = (f x g) (S' c f g x) = (c (f x) (g x)) (B* c f g x) = (c (f (g x))) (C' c f g x) = (c (f x) g)
Some special-purpose computers have been built to perform combinator calculations by graph reduction[?]. Examples include the SKIM[?] ("S-K-I machine") computer, built at Cambridge University, and the multiprocessor GRIP[?] ("Graph Reduction In Parallel") computer, built at UCL.
See also:
The original version of article was based on materical from FOLDOC, used with permission.
in Russia in the set of count Tolstoi's works. The omission is
guild tax.
{9} Omitted in authorized.html">authorized.html">authorized.html">authorized.html">authorized.html">authorized.html">authorized.html">authorized.html">authorized.html">authorized.html">authorized.html">authorized.html">authorized edition.
{10} Omitted by the censor in the authorized edition.
{11} Omitted by the Censor in the authorized edition.
{12} Omitted by the Censor in the authorized edition.
{13} Omitted by the Censor in the authorized edition.
{14} Omitted by the Censor from the authorized edition.
{15} Omitted by the Censor in the authorized edition.
{16} Omitted by the Censor in the authorized edition
{17} Omitted by the Censor in the authorized edition.
{18} Omitted by the Censor in the authorized edition.
{19} A very complicated sort of whist.
{20} The whole of this chapter is omitted by the Censor in the
sentence: "And I felt that in money.html">money.html">money, in money itself, in the
What is money?"
{21} Omitted by the Censor in the authorized edition.
{22} Omitted by the Censor in the authorized edition.
{23} The above passage is omitted in the authorized edition, and the
that, if I pity the tortured horse upon which I am riding, the first
concluding paragraph is replaced by the following: --"They say: The
the sea.html">sea.html">sea.html">sea.html">sea, and in order to recover it he took a bucket, and began to
intermission, and on the seventh day the spirit of the sea grew
his pearl. If our social evil.html">evil.html">evil of persecuting man were the sea, then
bailing out the sea of that evil. The prince of this world will take
but this social evil is not the sea, but a foul cesspool, which we
for us to come to our senses, and to comprehend what we are doing; to
.
On
wordlookup.net
All is still licensed under the GNU FDL.
It uses material from the wikipedia.
|
|