Examples of using Lambda calculus in English and their translations into Croatian
{-}
-
Colloquial
-
Ecclesiastic
-
Computer
Main article: lambda calculus.
Lambda calculus and programming languages[edit].
Okay, I will just say one more thing Lambda calculus.
Okay. lambda calculus. Well, let me just say one more thing.
And if that wets your whistle, you know where to find me. Okay,I will just say one more thing: lambda calculus.
Lambda calculus. Well, let me just say one more thing, Okay.
I will just say one more thing: lambda calculus. And if that wets your whistle, you know where to find me.
Lambda Calculus. And if that wets your whistle, you know where to find me.
A classic paper highlighting the importance of lambda calculus as a basis for programming languages.
The lambda calculus emerged in his 1936 paper showing the unsolvability of the Entscheidungsproblem.
The availability of predicates and the above definition of TRUE andFALSE make it convenient to write"if-then-else" expressions in lambda calculus.
Contains the lambda calculus definitions of several familiar functions.
Typed lambda calculi with subtyping are the simply typed lambda calculus with conjunctive types and System F.
The lambda calculus influenced the design of the LISP programming language and functional programming languages in general.
In the latter 1930s, Alonzo Church andhis students at Princeton invented a rival formalism for functional abstraction, the lambda calculus, which proved more popular than combinatory logic.
Lambda calculus is Turing complete, that is, it is a universal model of computation that can be used to simulate any Turing machine.
For a more modern parallel treatment of combinatory logic and the lambda calculus, see Barendregt(1984), who also reviews the models Dana Scott devised for combinatory logic in the 1960s and 1970s.
Based on work by Berardi on pure type systems,Henk Barendregt proposed the Lambda cube to systematize the relations of pure typed lambda calculi including simply typed lambda calculus, System F, LF and the calculus of constructions.
Moreover, in the lambda calculus, notions such as'3' and'*' can be represented without any need for externally defined primitive operators or constants.
A more mathematically oriented definition with a similar"universal" nature was introduced by Alonzo Church,whose work on lambda calculus intertwined with Turing's in a formal theory of computation known as the Church-Turing thesis.
Whereas simply typed lambda calculus has variables ranging over functions, and binders for them, System F additionally has variables ranging over types, and binders for them.
Historically, ML was conceived to develop proof tactics in the LCF theorem prover whose language, pplambda, a combination of thefirst-order predicate calculus and the simply-typed polymorphic lambda calculus, had ML as its metalanguage.
It is possible to identify terms in lambda calculus, which, when suitably interpreted, behave like the number 3 and like the multiplication operator, q.v.
Lambda calculus is known to be computationally equivalent in power to many other plausible models for computation(including Turing machines); that is, any calculation that can be accomplished in any of these other models can be expressed in lambda calculus, and vice versa.
In mathematical logic and computer science, lambda calculus, also written as λ-calculus, is a formal system designed to investigate function definition, function application and recursion.
Lambda calculus and programming languages[edit] As pointed out by Peter Landin's 1965 paper A Correspondence between ALGOL 60 and Church's Lambda-notation, sequential procedural programming languages can be understood in terms of the lambda calculus, which provides the basic mechanisms for procedural abstraction and procedure(subprogram) application.
For a more modern treatment of combinatory logic and the lambda calculus together, see the book by Barendregt, which reviews the models Dana Scott devised for combinatory logic in the 1960s and 1970s.
System T extends the simply typed lambda calculus with a type of natural numbers and higher order primitive recursion; in this system all functions provably recursive in Peano arithmetic are definable.
Church and Turing then showed that the lambda calculus and the Turing machine used in Turing's halting problem were equivalent in capabilities, and subsequently demonstrated a variety of alternative"mechanical processes for computation.".