Search results
Results From The WOW.Com Content Network
In computer science, a "let" expression associates a function definition with a restricted scope. The "let" expression may also be defined in mathematics, where it associates a Boolean condition with a restricted scope. The "let" expression may be considered as a lambda abstraction applied to a value.
The Carmichael lambda function of a prime power can be expressed in terms of the Euler totient. Any number that is not 1 or a prime power can be written uniquely as the product of distinct prime powers, in which case λ of the product is the least common multiple of the λ of the prime power factors. Specifically, λ(n) is given by the recurrence
Lambda calculus has a simple syntax and semantics, and is good for describing Lambda lifting. It is convenient to describe lambda lifting as a translations from lambda to a let expression, and lambda dropping as the reverse. This is because let expressions allow mutual recursion, which is, in a sense, more lifted than is supported in lambda ...
The lambda calculus, developed in the 1930s by Alonzo Church, is a formal system of computation built from function application. In 1937 Alan Turing proved that the lambda calculus and Turing machines are equivalent models of computation, [37] showing that the lambda calculus is Turing complete. Lambda calculus forms the basis of all functional ...
For each partition of n, let () denote the conjugacy class in corresponding to it (cf. the example below), and let denote the number of times j appears in (so =). Then the Frobenius formula states that the constant value of χ λ {\displaystyle \chi _{\lambda }} on C ( μ ) , {\displaystyle C(\mu ),}
In this case particular lambda terms (which define functions) are considered as values. "Running" (beta reducing) the fixed-point combinator on the encoding gives a lambda term for the result which may then be interpreted as fixed-point value. Alternately, a function may be considered as a lambda term defined purely in lambda calculus.
In probability theory and statistics, the exponential distribution or negative exponential distribution is the probability distribution of the distance between events in a Poisson point process, i.e., a process in which events occur continuously and independently at a constant average rate; the distance parameter could be any meaningful mono-dimensional measure of the process, such as time ...
Authors often introduce syntactic sugar, such as let, [k] to permit writing the above in the more intuitive order let f = N in M. By chaining such definitions, one can write a lambda calculus "program" as zero or more function definitions, followed by one lambda-term using those functions that constitutes the main body of the program.