"beta reduction" meaning in All languages combined

See beta reduction on Wiktionary

Noun [English]

Forms: beta reductions [plural]
Head templates: {{en-noun|~}} beta reduction (countable and uncountable, plural beta reductions)
  1. The act of beta reducing, an instance of replacing a function call by the result of calling a function. Tags: countable, uncountable Coordinate_terms: alpha conversion, eta conversion
    Sense id: en-beta_reduction-en-noun-H5ZEKj1F Categories (other): English entries with incorrect language header, Pages with 1 entry, Pages with entries Disambiguation of English entries with incorrect language header: 53 47 Disambiguation of Pages with 1 entry: 52 48 Disambiguation of Pages with entries: 53 47
  2. (computing theory) One of the three rewrite rules of the lambda calculus, which states that the application of a lambda abstraction (λx.t) to a term s yields an expression t[s/x], "t with s instead of x", where all free instances of x in t have been replaced by s. Tags: countable, uncountable Categories (topical): Theory of computing
    Sense id: en-beta_reduction-en-noun-OpYVytSb Categories (other): English entries with incorrect language header, Pages with 1 entry, Pages with entries Disambiguation of English entries with incorrect language header: 53 47 Disambiguation of Pages with 1 entry: 52 48 Disambiguation of Pages with entries: 53 47 Topics: computing, computing-theory, engineering, mathematics, natural-sciences, physical-sciences, sciences

Inflected forms

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  "lang": "English",
  "lang_code": "en",
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  "senses": [
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      "coordinate_terms": [
        {
          "_dis1": "100 0",
          "word": "alpha conversion"
        },
        {
          "_dis1": "100 0",
          "word": "eta conversion"
        }
      ],
      "glosses": [
        "The act of beta reducing, an instance of replacing a function call by the result of calling a function."
      ],
      "id": "en-beta_reduction-en-noun-H5ZEKj1F",
      "links": [
        [
          "act",
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          "beta reducing",
          "beta reduce"
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        {
          "ref": "1996, Roberto DiCosmo with Vincent Danos, The Linear Logic Primer, Université de Paris VII, retrieved 2016-04-18, page 43:",
          "text": "A natural deduction tree can be put in exact correspondence with typed λ-calculus (that can be considered as just a notation for such deductions), and the cut-elimination in Natural Deduction corresponds exactly to β-reduction in λ-calculus.",
          "type": "quote"
        }
      ],
      "glosses": [
        "One of the three rewrite rules of the lambda calculus, which states that the application of a lambda abstraction (λx.t) to a term s yields an expression t[s/x], \"t with s instead of x\", where all free instances of x in t have been replaced by s."
      ],
      "id": "en-beta_reduction-en-noun-OpYVytSb",
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        "(computing theory) One of the three rewrite rules of the lambda calculus, which states that the application of a lambda abstraction (λx.t) to a term s yields an expression t[s/x], \"t with s instead of x\", where all free instances of x in t have been replaced by s."
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  "word": "beta reduction"
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    "Pages with entries"
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  "coordinate_terms": [
    {
      "word": "alpha conversion"
    },
    {
      "word": "eta conversion"
    }
  ],
  "forms": [
    {
      "form": "beta reductions",
      "tags": [
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  "head_templates": [
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  "lang": "English",
  "lang_code": "en",
  "pos": "noun",
  "senses": [
    {
      "glosses": [
        "The act of beta reducing, an instance of replacing a function call by the result of calling a function."
      ],
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        [
          "act",
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        [
          "beta reducing",
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        {
          "ref": "1996, Roberto DiCosmo with Vincent Danos, The Linear Logic Primer, Université de Paris VII, retrieved 2016-04-18, page 43:",
          "text": "A natural deduction tree can be put in exact correspondence with typed λ-calculus (that can be considered as just a notation for such deductions), and the cut-elimination in Natural Deduction corresponds exactly to β-reduction in λ-calculus.",
          "type": "quote"
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      ],
      "glosses": [
        "One of the three rewrite rules of the lambda calculus, which states that the application of a lambda abstraction (λx.t) to a term s yields an expression t[s/x], \"t with s instead of x\", where all free instances of x in t have been replaced by s."
      ],
      "links": [
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        "(computing theory) One of the three rewrite rules of the lambda calculus, which states that the application of a lambda abstraction (λx.t) to a term s yields an expression t[s/x], \"t with s instead of x\", where all free instances of x in t have been replaced by s."
      ],
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  ],
  "word": "beta reduction"
}

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This page is a part of the kaikki.org machine-readable All languages combined dictionary. This dictionary is based on structured data extracted on 2024-12-08 from the enwiktionary dump dated 2024-12-04 using wiktextract (bb46d54 and 0c3c9f6). The data shown on this site has been post-processed and various details (e.g., extra categories) removed, some information disambiguated, and additional data merged from other sources. See the raw data download page for the unprocessed wiktextract data.

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