What is the lambda calculus?

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What is the lambda calculus?​

The Lambda calculus is an abstract mathematical theory of computation, involving λ\\lambdaλ functions. The lambda calculus can be thought of as the theoretical foundation of functional programming.

Is \\ lambda calculus a Turing complete language?​

It is a Turing complete language; that is to say, any machine which can compute the lambda calculus can compute everything a Turing machine can (and vice versa). \\lambda λ notation is based on function abstraction and application based on variable binding and substitution.
What is\\ lambda λ notation?
\\lambda λ notation is based on function abstraction and application based on variable binding and substitution. If you have done the same basic programming already, you might be familiar with lambda functions or anonymous functions.

How do you compute a lambda expression?​

\\big (\\lambda x.x^2\\big) 7, (λx.x2)7, which actually refers to 49. To compute a lambda expression is to transform it into a canonical form using a set of transformation rules/reductions, as we will see. We will see that the . \\bf {.}. (along with a few predefined variables) themselves are powerful enough to express any computable function.

The λ calculus is developed as a theory of functions for manipulating functions in a purely syntactic manner. All functional programming languages can be viewed as syntactic variations of the lambda calculus, so that both their semantics and implementation can be analysed in the context of the lambda calculus.

What is λ calculus?​

What is λ Calculus? λ Calculus is considered as the smallest universal programming language. The λ calculus is developed as a theory of functions for manipulating functions in a purely syntactic manner.
How do you construct all valid lambda expressions?
If x and y are lambda terms, then (x y) is a lambda term, and (λx.y) is a lambda term. From these three rules, we can construct all valid expressions. If we also agree to read all lambda expressions from left to right, we can omit a few of the parenthesis: (λy.xy) ab is the simplified version of ( ((λy. (x y)) a) b).

What is the difference between lambda and Lambda prefix?​

Lambda abstractions associate to the right, are prefixed with a lowercase lambda, and their child nodes are separated by periods. The lambda prefix is superfluous but improves clarity. With consecutive bindings (e.g. “λx.λy.λz.”), we omit all lambdas but the first, and omit all periods but the last (e.g. “λx y z.”).

How do you write FST in lambda calculus?​

The lambda term: fst = λx.λy.x takes two arguments and returns the first argument as the result (ignoring the second argument). Notice that (λx.λy.x)M N ≡ (λy.M)N ≡ M by β-equivalence. However, the manner in which the two arguments are provided to fst is typical of the lambda calculus higher-order character.