what the value to lamda?
Answers
Lambda isn’t a “value” in the sense that π is a value, or e^3 is a value. It’s not even a value in the sense that x is a value in f(x)=x^2, where a numerical definition is unknown and so we would say that x is any value in the domain of our function, perhaps any real number, perhaps even a square matrix or a complex number, or maybe even something more constrained.
Lambdas are more of a type of value than a value in and of themselves. Lambdas are the objects in play and the principle actors of The Lambda Calculus (especially in the untyped LC). Lambdas are, as Adam Sroka succinctly put it in his now collapsed, but quite possibly sufficient answer “a function”.
Traditionally a lambda is a function that takes a lambda as an input, and gives you a lambda as an output, but in some types of lambda calculus, other types of arguments and outputs my be used such as numerical values.
Lambdas are usually written:
(λ parameter . output )( argument )
For example:
(λx.xx)(λy.y)
And then the argument replaces the parameter inside the output in a process known as reduction. (For a low down on the rules of LC, consider checking out my answer to on Stack Overflow for some mad fun times)
(λx.xx)(λy.y)
(=) xx [x := (λy.y)]
(=) (λy.y)(λy.y)
(=) (λy.y)(λz.z) - it’s important to distinguish names
(=) y [ y:=(λz.z)]
(=) λz.z
And of course in this notation, the purpose of the λ is syntactical, not semantic. It’s a constraint, and a promise that the following expression will be a lambda and will follow the rules of whichever games your lambdas might be playing at.
Answer:
Lambda = (E1 – E2) / E1.
Lambda may range in value from 0.0 to 1.0.
Explanation:
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