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- De_Bruijn_index abstract "In mathematical logic, the De Bruijn index is a notation invented by the Dutch mathematician Nicolaas Govert de Bruijn for representing terms in the λ calculus with the purpose of eliminating the names of the variable from the notation. Terms written using these indices are invariant with respect to α conversion, so the check for α-equivalence is the same as that for syntactic equality. Each De Bruijn index is a natural number that represents an occurrence of a variable in a λ-term, and denotes the number of binders that are in scope between that occurrence and its corresponding binder. The following are some examples: The term λx. λy. x, sometimes called the K combinator, is written as λ λ 2 with De Bruijn indices. The binder for the occurrence x is the second λ in scope. The term λx. λy. λz. x z (y z) (the S combinator), with De Bruijn indices, is λ λ λ 3 1 (2 1). The term λz. (λy. y (λx. x)) (λx. z x) is λ (λ 1 (λ 1)) (λ 2 1). See the following illustration, where the binders are coloured and the references are shown with arrows.Pictorial depiction of exampleDe Bruijn indices are commonly used in higher-order reasoning systems such as automated theorem provers and logic programming systems.".
- De_Bruijn_index thumbnail De_Bruijn_index_illustration_1.svg?width=300.
- De_Bruijn_index wikiPageID "10314482".
- De_Bruijn_index wikiPageLength "9022".
- De_Bruijn_index wikiPageOutDegree "32".
- De_Bruijn_index wikiPageRevisionID "665899067".
- De_Bruijn_index wikiPageWikiLink Automated_theorem_proving.
- De_Bruijn_index wikiPageWikiLink Bound_variable.
- De_Bruijn_index wikiPageWikiLink Category:Lambda_calculus.
- De_Bruijn_index wikiPageWikiLink Combinatory_logic.
- De_Bruijn_index wikiPageWikiLink De_Bruijn_notation.
- De_Bruijn_index wikiPageWikiLink Free_variable.
- De_Bruijn_index wikiPageWikiLink Free_variables_and_bound_variables.
- De_Bruijn_index wikiPageWikiLink Henk_Barendregt.
- De_Bruijn_index wikiPageWikiLink Higher-order_abstract_syntax.
- De_Bruijn_index wikiPageWikiLink Higher-order_logic.
- De_Bruijn_index wikiPageWikiLink Isabelle_(proof_assistant).
- De_Bruijn_index wikiPageWikiLink Isabelle_theorem_prover.
- De_Bruijn_index wikiPageWikiLink K_combinator.
- De_Bruijn_index wikiPageWikiLink Lambda_calculus.
- De_Bruijn_index wikiPageWikiLink Logic_programming.
- De_Bruijn_index wikiPageWikiLink Mathematical_logic.
- De_Bruijn_index wikiPageWikiLink Mathematician.
- De_Bruijn_index wikiPageWikiLink Meta-logic.
- De_Bruijn_index wikiPageWikiLink Metalogic.
- De_Bruijn_index wikiPageWikiLink Natural_number.
- De_Bruijn_index wikiPageWikiLink Netherlands.
- De_Bruijn_index wikiPageWikiLink Nicolaas_Govert_de_Bruijn.
- De_Bruijn_index wikiPageWikiLink Nominal_techniques.
- De_Bruijn_index wikiPageWikiLink Proof_assistant.
- De_Bruijn_index wikiPageWikiLink Rewriting.
- De_Bruijn_index wikiPageWikiLink S_combinator.
- De_Bruijn_index wikiPageWikiLink Scope_(computer_science).
- De_Bruijn_index wikiPageWikiLink Scope_(programming).
- De_Bruijn_index wikiPageWikiLink Variable_(mathematics).
- De_Bruijn_index wikiPageWikiLink Α_conversion.
- De_Bruijn_index wikiPageWikiLink Β-reduction.
- De_Bruijn_index wikiPageWikiLink Λ_calculus.
- De_Bruijn_index wikiPageWikiLink File:De_Bruijn_index_illustration_1.svg.
- De_Bruijn_index wikiPageWikiLinkText "De Bruijn index".
- De_Bruijn_index wikiPageWikiLinkText "De Bruijn index#Alternatives to De Bruijn indexes".
- De_Bruijn_index wikiPageWikiLinkText "De Bruijn indices".
- De_Bruijn_index wikiPageWikiLinkText "de Bruijn encodings".
- De_Bruijn_index wikiPageWikiLinkText "de Bruijn index".
- De_Bruijn_index wikiPageWikiLinkText "de Bruijn indices".
- De_Bruijn_index hasPhotoCollection De_Bruijn_index.
- De_Bruijn_index wikiPageUsesTemplate Template:Reflist.
- De_Bruijn_index subject Category:Lambda_calculus.
- De_Bruijn_index hypernym Notation.
- De_Bruijn_index type Model.
- De_Bruijn_index type Software.
- De_Bruijn_index type Model.
- De_Bruijn_index comment "In mathematical logic, the De Bruijn index is a notation invented by the Dutch mathematician Nicolaas Govert de Bruijn for representing terms in the λ calculus with the purpose of eliminating the names of the variable from the notation. Terms written using these indices are invariant with respect to α conversion, so the check for α-equivalence is the same as that for syntactic equality.".
- De_Bruijn_index label "De Bruijn index".
- De_Bruijn_index sameAs ド・ブラン・インデックス.
- De_Bruijn_index sameAs m.02q86f1.
- De_Bruijn_index sameAs Q5244288.
- De_Bruijn_index sameAs Q5244288.
- De_Bruijn_index wasDerivedFrom De_Bruijn_index?oldid=665899067.
- De_Bruijn_index depiction De_Bruijn_index_illustration_1.svg.
- De_Bruijn_index isPrimaryTopicOf De_Bruijn_index.