{
  "id": "type-theory",
  "domain": "foundations-logic",
  "type": "Concept",
  "title": "Type Theory",
  "slug": "type-theory",
  "url": "/mathematics/foundations-logic/type-theory/",
  "summary": "Organises mathematical objects by type to avoid paradoxes. Russell 1908; Church simply-typed lambda calculus 1940; Martin-Löf dependent type theory 1970s; Curry-Howard correspondence; HoTT and Voevodsky's Univalent Foundations.",
  "added_to_codex": "2026-07-09",
  "last_verified": "2026-07-09",
  "sources": [
    {
      "tier": 1,
      "citation": "Univalent Foundations Program (2013). Homotopy Type Theory. IAS."
    },
    {
      "tier": 1,
      "citation": "Martin-Löf, P. (1984). Intuitionistic Type Theory. Bibliopolis."
    },
    {
      "tier": 2,
      "citation": "Pierce, B.C. (2002). Types and Programming Languages. MIT Press."
    },
    {
      "tier": 3,
      "citation": "Wadler, P. (2015). Propositions as types. Communications of the ACM, 58(12), 75-84."
    }
  ],
  "entry_status": "live",
  "reading_levels_available": [
    "curious",
    "exploring",
    "deep_dive"
  ],
  "completeness": 1.0,
  "codex_version": "2.5"
}