Search results
Results from the WOW.Com Content Network
The Y combinator is an implementation of a fixed-point combinator in lambda calculus. Fixed-point combinators may also be easily defined in other functional and imperative languages. The implementation in lambda calculus is more difficult due to limitations in lambda calculus. The fixed-point combinator may be used in a number of different areas:
In the lambda calculus, Y g is a fixed-point of g, ... SK and BCKW form complete combinator calculus systems that can express any lambda term - see the next section.
A Calculus of Mobile Processes, Part I (PostScript) (by Milner, Parrow, and Walker) shows a scheme for combinator graph reduction for the SKI calculus in pages 25–28. the Nock programming language may be seen as an assembly language based on SK combinator calculus in the same way that traditional assembly language is based on Turing machines.
Combinatory logic is a model of computation equivalent to lambda calculus, but without abstraction. The advantage of this is that evaluating expressions in lambda calculus is quite complicated because the semantics of substitution must be specified with great care to avoid variable capture problems.
The Y combinator may be used to implement the recursion. ... Using a lambda calculus calculator, the above expression reduces to 3, using normal order.
Also of note, Y combinator has a short expression in this system, as Y = BU(CBU) = BU(BWB) = B(W(WK))(BWB), where U = WI = SII is the self-application combinator. Using just two combinators, B and W , an infinite number of fixpoint combinators can be constructed, [ 2 ] one example being B ( WW )( BW ( BBB )), discovered by R ...
A version of the Y combinator, called the Y* poly-variadic fix-point combinator [5] is then used to calculate fixed point of all the functions at the same time. The result is a mutually recursive implementation of the let expression.
The Knights of the Lambda Calculus' recursive emblem celebrates LISP's theoretical foundation, the lambda calculus. Y in the emblem refers to the fixed-point combinator and the reappearance of the picture in itself refers to recursion. The Knights of the Lambda Calculus is a semi-fictional organization of expert Lisp and Scheme hackers.