Examples of using Lambda calculus in English and their translations into Chinese
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What is Lambda Calculus?
Lambda calculus can be used to define what is a computable function.
So what exactly is lambda calculus?
The lambda calculus can be called the smallest universal programming language.
Haskell is a purely-functional programming language based on lambda calculus.
In the lambda calculus, Y g is a fixed-point of g, as it expands to g(Y g).
The purely functional programming language Haskell, based on lambda calculus.
Lambda calculus can be called the smallest universal programming language of the world.
Fortunately, Alonzo Church, the genius who invented the lambda calculus worked out how to do that.
Lambda calculus has greatly influenced functional programming languages, especially LISP.
These combinators are extremelyuseful when translating predicate logic or lambda calculus into combinator expressions.
A lambda calculus expression is completely valid only when all of its variables are bound.
It was introduced by Alonzo Church and Stephen Kleene in the 1930s;Church used the lambda calculus in 1936 to solve the Entscheidungsproblem.
Being based on lambda calculus ISWIM has higher order functions and lexically scoped variables.
In the latter 1930s, Alonzo Church and his students at Princetoninvented a rival formalism for functional abstraction, the lambda calculus, which proved more popular than combinatory logic.
The lambda calculus has greatly influenced the functional programming languages, especially LISP.
To formulate such a denotational semantics,one might first try to construct a model for the lambda calculus, in which a genuine(total) function is associated with each lambda term.
Church invents"lambda calculus" which today is an invaluable tool for computer scientists.
The lambda calculus may be seen as an idealised functional programming language, like Haskell or Standard ML.
This property is inherited from lambda calculus, where multi-argument functions are usually represented in curried form.
The lambda calculus is a formal system designed to investigate function definition, function application, and recursion.
For example the dependently typed lambda calculus with a type of all types(Type: Type) is not normalizing due to Girard's paradox.
Not all lambda calculus ideas transform to practice because lambda calculus was not designed to work under physical limitations.
The Knights of the Lambda Calculus is a semi-fictional organization of expert Lisp and Scheme hackers.
In lambda calculus, functions are'first-class' citizens, i. e functions can be used as inputs or be returned as outputs from other functions.
The important step to find a model for the lambda calculus is to consider only those functions(on such a partially ordered set) which are guaranteed to have least fixed points.
Not all lambda calculus ideas transform to practice because lambda calculus was not designed to work under physical limitations.
Such a model would formalize a link between the lambda calculus as a purely syntactic system and the lambda calculus as a notational system for manipulating concrete mathematical functions.
Moreover, in lambda calculus, notions such as'3' and'∗{\displaystyle*}' can be represented without any need for externally defined primitive operators or constants.
Various systems of typed lambda calculus including the simply typed lambda calculus, Jean-Yves Girard's System F, and Thierry Coquand's calculus of constructions are strongly normalizing.