{
  "aliases": null,
  "backlinks": null,
  "body": "\n## Definition\n\nLet $\\sigma$ be a [[signature|WDVVEYD6AT]] and let $V$ be a set of variables, disjoint from the symbols of $\\sigma$.\nThe set of *terms* over $\\sigma$ and $V$ is the smallest set of finite strings of symbols such that:\n\n1. every variable $x \\in V$ is a term;\n2. every constant symbol $c$ of $\\sigma$ is a term;\n3. if $f$ is a function symbol of $\\sigma$ of arity $n \\ge 1$ and $t_1, \\dots, t_n$ are terms, then $f(t_1, \\dots, t_n)$ is a term.\n\nA term with no variables is a *closed term*, or a *ground term*.\n\n## Remarks\n\nIn the signature of rings, $\\cdot(x, +(y, 1))$ is a term, usually written $x \\cdot (y + 1)$.\nIt is a term by clause 1 for $x$ and $y$, clause 2 for $1$, and clause 3 twice.\nIn the signature of ordered sets, $x \u003c y$ is not a term: $\u003c$ is a relation symbol, not a function symbol, so clause 3 does not apply.\nEvery term has a unique reading, so one can define functions on terms by recursion on this construction.\nIn Mathlib terms are `FirstOrder.Language.Term`.\n",
  "commit": "547b6eddb8f2feb8d579f2d633d22a27b7e132fc",
  "front": {
    "defines": "6D3WA7N2W4",
    "kind": "definition",
    "msc": [
      "03B10",
      "03C07"
    ],
    "name": "Term",
    "sources": [
      {
        "url": "https://en.wikipedia.org/wiki/Term_(logic)"
      }
    ],
    "tag": "BQQ0FPFZ67",
    "uses": [
      "WDVVEYD6AT"
    ]
  },
  "kind": "definition",
  "link": "https://math2.tamnd.com/node/BQQ0FPFZ67/",
  "links": [
    {
      "field": "defines",
      "target": "6D3WA7N2W4"
    },
    {
      "field": "uses",
      "target": "WDVVEYD6AT"
    }
  ],
  "markdown": "https://math2.tamnd.com/node/BQQ0FPFZ67.md",
  "msc": [
    "03B10",
    "03C07"
  ],
  "name": "Term",
  "prov": null,
  "role": "",
  "source": "https://github.com/tamnd/math2/blob/main/nodes/BQQ/BQQ0FPFZ67.md",
  "status": null,
  "tag": "BQQ0FPFZ67",
  "uri": "m2://BQQ0FPFZ67",
  "url": "https://math2.tamnd.com/wiki/term-definition/",
  "writing": {
    "tag": "BQQ0FPFZ67",
    "kind": "definition",
    "level": "W0",
    "next": [
      {
        "what": "an inventory row",
        "note": "the row of the inventory that the node accounts for",
        "have": 0,
        "want": 1
      },
      {
        "what": "a source with a locator",
        "have": 0,
        "want": 1
      }
    ]
  }
}