Search results
Results from the WOW.Com Content Network
Lambda calculus is Turing complete, that is, it is a universal model of computation that can be used to simulate any Turing machine. [3] Its namesake, the Greek letter lambda (λ), is used in lambda expressions and lambda terms to denote binding a variable in a function.
Alpha-conversion, sometimes known as alpha-renaming, [7] allows bound variable names to be changed. For example, alpha-conversion of . might yield .. Terms that differ only by alpha-conversion are called α-equivalent. Frequently in uses of lambda calculus, α-equivalent terms are considered to be equivalent.
The latter is guaranteed by the strong confluence property of reduction in this model of computation. Thus interaction nets provide a natural language for massive parallelism. Interaction nets are at the heart of many implementations of the lambda calculus, such as efficient closed reduction [2] and optimal, in Lévy's sense, Lambdascope. [3]
In programming language semantics, normalisation by evaluation (NBE) is a method of obtaining the normal form of terms in the λ-calculus by appealing to their denotational semantics. A term is first interpreted into a denotational model of the λ-term structure, and then a canonical (β-normal and η-long) representative is extracted by ...
3 : Number add 3 4 : Number add : Number -> Number -> Number Contrary to this, the untyped lambda calculus is neutral to typing at all, and many of its functions can be meaningfully applied to all type of arguments. The trivial example is the identity function id ≡ λ x . x. which simply returns whatever value it is applied to.
In computer science, lambda calculi are said to have explicit substitutions if they pay special attention to the formalization of the process of substitution.This is in contrast to the standard lambda calculus where substitutions are performed by beta reductions in an implicit manner which is not expressed within the calculus; the "freshness" conditions in such implicit calculi are a notorious ...
His invention of the lambda calculus. His use of the lambda calculus to prove that Peano arithmetic is undecidable. [11] His articulation of what has come to be known as the Church–Turing thesis. Being a founding editor of the Journal of Symbolic Logic, editing its reviews section for 43 years from 1936 until 1979.
In 1936, Alonzo Church created a method for defining functions called the λ-calculus. Within λ-calculus, he defined an encoding of the natural numbers called the Church numerals. A function on the natural numbers is called λ-computable if the corresponding function on the Church numerals can be represented by a term of the λ-calculus.