But type theory does not require a prior definition of the naturals.

A system of type theory requires some basic terms and types to operate on.

This is not surprising, given the close connection between type theory and programming languages.

Intuitionistic type theory uses types in the place of truth values.

This field of research is usually referred to as modern type theory.

The system developed and added features over time as type theory developed.

In type theory a typing environment represents the association between variables names and data types.

His most notable research is in the field of type theory.

The formal design and study of type systems is known as type theory.

Towards a practical programming language based on dependent type theory.