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polymorphic lambda calculus or second-order lambda calculus) is a typed lambda calculus that introduces, to simply typed lambda calculus, a mechanism...

A typed lambda calculus is a typed formalism that uses the lambda-symbol ( λ {\displaystyle \lambda } ) to denote anonymous function abstraction. In this...

Lambda calculus (also written as λ-calculus) is a formal system in mathematical logic for expressing computation based on function abstraction and application...

simply typed lambda calculus ( λ → {\displaystyle \lambda ^{\to }} ), a form of type theory, is a typed interpretation of the lambda calculus with only one...

Functor (disambiguation). In the untyped lambda calculus, all functions are higher-order; in a typed lambda calculus, from which most functional programming...

inference and type checking for the second-order lambda calculus (or equivalent). Determining whether a first-order sentence in the logic of graphs can...

(also written lambda cube) is a framework introduced by Henk Barendregt to investigate the different dimensions in which the calculus of constructions...

mathematics, second-order logic is an extension of first-order logic, which itself is an extension of propositional logic. Second-order logic is in turn...

context of the lambda calculus, normal-order reduction refers to leftmost-outermost reduction in the sense given above. Normal-order reduction is normalizing...

a higher-order typed lambda calculus, initially developed by Thierry Coquand. It is well known for being at the top of Barendregt's lambda cube. It is...

representing data and operators in the lambda calculus. The Church numerals are a representation of the natural numbers using lambda notation. The method is named...

to arguments. It is central to programming languages derived from lambda calculus, such as LISP and Scheme, and also in functional languages. It has...

In calculus, the second derivative, or the second-order derivative, of a function f is the derivative of the derivative of f. Informally, the second derivative...

the lambda calculus and Turing machines are equivalent models of computation, showing that the lambda calculus is Turing complete. Lambda calculus forms...

of the simply typed lambda calculus to the dependent product type. The system λ Π 2 {\displaystyle \lambda \Pi 2} of second order dependent types is obtained...

version of the untyped lambda calculus. It was introduced by Moses Schönfinkel and Haskell Curry. All operations in lambda calculus can be encoded via abstraction...

and simply typed lambda calculus. Here is a non-exhaustive list: Girard-Reynolds System F as a common language for both second-order propositional logic...

f ′(x) up to a term of order h2. This can be proven by expanding the above expression in Taylor series, or by using the calculus of finite differences...

{\displaystyle Y=\lambda f.\ (\lambda x.f\ (x\ x))\ (\lambda x.f\ (x\ x))} (Here we use the standard notations and conventions of lambda calculus: Y is a function...

First-order logic—also called predicate logic, predicate calculus, quantificational logic—is a collection of formal systems used in mathematics, philosophy...