Introduction to Dependent Type Theory

This sequence of posts is an introduction to Martin-Löf dependent type theory, based on the book Homotopy Type Theory (usually called HoTT), but without the homotopy part. These posts describe how to set up type theory as an alternative foundation of mathematics, in place of set theory.

Prior knowledge of set theory is required.

Ba­sic build­ing blocks of de­pen­dent type theory

Re­cre­at­ing logic in type theory

Clas­si­cal logic based on propo­si­tions-as-sub­s­in­gle­ton-types

Set-like math­e­mat­ics in type theory

Ex­ten­sion­al­ity and the uni­valence ax­iom of type theory