Type Theory

Simply typed, dependent, and homotopy type theories.

foundation tier

Type Theory. Simply typed, dependent, and homotopy type theories.

Foundations and canonical references

The standard treatments of type theory approach the subject from complementary angles. Pierce, Types and Programming Languages (2002) is the anchor reference for the subject and lays out the core definitions, theorems, and worked examples that practitioners return to. Nederpelt, Type Theory and Formal Proof (2014) gives a parallel, more proof-oriented exposition of the same material and is widely used as a graduate text.

Open methodological questions for type theory include sharpening the bridges between foundational theory and computational practice, extending classical results to broader or more structured settings, and integrating the techniques surveyed above with adjacent mathematical disciplines. The references listed in this page are the entry points that current work builds on.

Prerequisites

Sources

  • textbook · primary · 2002
    Types and Programming Languages
    pierce-2002
  • textbook · primary · 2014
    Type Theory and Formal Proof
    nederpelt-2014, geuvers-2014

In context

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Explore

  1. 01

    Dependent Type Theory

    Martin-Löf type theory and Calculus of Inductive Constructions.
  2. 02

    Homotopy Type Theory

    Univalence, higher inductive types, and synthetic homotopy theory.
  3. 03

    Cubical Type Theory

    Computational interpretations of univalence.

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