Examples of using Lambda calculus in English and their translations into Greek
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FALSE make it convenient to write"if-then-else" expressions in lambda calculus.
notation for computer programs, based on Alonzo Church's lambda calculus.
Formal calculi  such as the lambda calculus and combinatory logic are now studied as idealized programming languages.
especially higher-order predicate logic and lambda calculus, and makes use of the notions of intensional logic, via Kripke models.
As Peter Landin noted, the language Algol was the first language to combine seamlessly imperative effects with the(call-by-name) lambda calculus.
Instituting a simply typed lambda calculus over the type operators results in more than just a formalization of type constructors though.
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.
In 1940 Alonzo Church(re)formulated it as simply typed lambda calculus. and examined by Gödel in 1944.
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.
The important step to find a model for the lambda calculus is to consider only those functions(on such a partially ordered set)
We see that in typed lambda calculus every function(abstraction) must specify the type of its argument.
such as Markov algorithms, Lambda calculus, Post systems,
most scripting languages) or effectively for practical implementation( e. g., formal languages like lambda calculus); these are said to be garbage collected languages.
such as Markov algorithms, Lambda calculus, Post systems
of classes of categories, e.g. the simply typed lambda calculus is the language of Cartesian closed categories(CCCs).
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.
Church's type theory is a variant of the lambda calculus in which expressions(also called formulas
(In Church's original lambda calculus, the formal parameter of a lambda  expression was required to occur at least once in the function body,
in subsequent papers they proceeded to demonstrate the raw power of this practical use of lambda calculus.