# Type Theory

**Type:** Concept  
**Domain:** foundations-logic  
**Codex URL:** /mathematics/foundations-logic/type-theory/  
**Entry status:** Live — v1.0 (2026-07-09)

## 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.

## Sources
- [Tier 1] Univalent Foundations Program (2013). Homotopy Type Theory. IAS.
- [Tier 1] Martin-Löf, P. (1984). Intuitionistic Type Theory. Bibliopolis.
- [Tier 2] Pierce, B.C. (2002). Types and Programming Languages. MIT Press.
- [Tier 3] Wadler, P. (2015). Propositions as types. Communications of the ACM, 58(12), 75-84.

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*Mathematics Codex entry v1.0 — added 2026-07-09 — thecodex.expert/mathematics/*