Second-Order lambda-calculus - definition. What is Second-Order lambda-calculus
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EXTENSION OF FIRST-ORDER LOGIC ALLOWING QUANTIFICATION OVER FUNCTIONS AND RELATIONS
Second order logic; Second Order Logical Language; Second Order Logic; Second-order predicate calculus; Second order predicate calculus; Henkin model; Existential second-order logic; Henkin semantics; Monadic second order; History of second-order logic; Semantics of second-order logic
  • [[Graffiti]] in [[Neukölln]] (Berlin) showing the simplest second-order sentence admitting nontrivial models, "∃φ φ".

Second-Order Lambda-calculus      
<language> (SOL) A typed lambda-calculus. ["Abstract Types have Existential Type", J. Mitchell et al, 12th POPL, ACM 1985, pp. 37-51]. (1995-07-29)
beta conversion         
FORMAL SYSTEM IN MATHEMATICAL LOGIC
Lamda calculus; Lambda-calculus; Lambda abstraction; Lambda-definable function; Lambda-definable functions; Lambda calculas; Beta reduction; Alpha conversion; Lambda-recursive function; Lambda programming; Eta reduction; Lambda Calculus; Untyped lambda calculus; Λ-calculus; Alpha equivalence; Eta expansion; Abstraction operator; Alpha reduction; Beta substitution; Beta conversion; Α conversion; Λ calculus; Β-reduction; B-reduction; L-calculus; L calculus; A conversion; Beta-reduction; Λa-calculus; Lanbda-calculus; Lambda kalkül; Alpha renaming; Lambda calculi; Λ-abstraction; AlphaRenaming; Α-conversion; Capture-avoiding substitution; Lambda term; Lamda expression; Alpha-renaming; Alpha-conversion; Eta conversion; Eta-conversion; Η-conversion; Η conversion; Lambda language; Type-free lambda calculus; Typefree lambda calculus; Type free lambda calculus; Eta-reduction; Functional abstraction; Λx; Λy; Λz; Anonymous function abstraction; Lambda-calculi; Lambda-term bound variables; Lambda terms; Alpha equivalent
<theory> A term from lambda-calculus for beta reduction or beta abstraction. (1999-01-15)
Lambda calculus         
FORMAL SYSTEM IN MATHEMATICAL LOGIC
Lamda calculus; Lambda-calculus; Lambda abstraction; Lambda-definable function; Lambda-definable functions; Lambda calculas; Beta reduction; Alpha conversion; Lambda-recursive function; Lambda programming; Eta reduction; Lambda Calculus; Untyped lambda calculus; Λ-calculus; Alpha equivalence; Eta expansion; Abstraction operator; Alpha reduction; Beta substitution; Beta conversion; Α conversion; Λ calculus; Β-reduction; B-reduction; L-calculus; L calculus; A conversion; Beta-reduction; Λa-calculus; Lanbda-calculus; Lambda kalkül; Alpha renaming; Lambda calculi; Λ-abstraction; AlphaRenaming; Α-conversion; Capture-avoiding substitution; Lambda term; Lamda expression; Alpha-renaming; Alpha-conversion; Eta conversion; Eta-conversion; Η-conversion; Η conversion; Lambda language; Type-free lambda calculus; Typefree lambda calculus; Type free lambda calculus; Eta-reduction; Functional abstraction; Λx; Λy; Λz; Anonymous function abstraction; Lambda-calculi; Lambda-term bound variables; Lambda terms; Alpha equivalent
Lambda calculus (also written as λ-calculus) is a formal system in mathematical logic for expressing computation based on function abstraction and application using variable binding and substitution. It is a universal model of computation that can be used to simulate any Turing machine.

ويكيبيديا

Second-order logic

In logic and 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 extended by higher-order logic and type theory.

First-order logic quantifies only variables that range over individuals (elements of the domain of discourse); second-order logic, in addition, also quantifies over relations. For example, the second-order sentence P x ( P x ¬ P x ) {\displaystyle \forall P\,\forall x(Px\lor \neg Px)} says that for every formula P, and every individual x, either Px is true or not(Px) is true (this is the law of excluded middle). Second-order logic also includes quantification over sets, functions, and other variables (see section below). Both first-order and second-order logic use the idea of a domain of discourse (often called simply the "domain" or the "universe"). The domain is a set over which individual elements may be quantified.